Datasets:

sswt

/

arxiv_sample_50K

like 0

The Generative Programs Framework ; Recently there has been significant interest in using causal modelling techniques to understand the structure of physical theories. However, the notion of causation' is limiting insisting that a physical theory must involve causal structure already places significant constraints on the form that theory may take. Thus in this paper, we aim to set out a more general structural framework. We argue that any quantitative physical theory can be represented in the form of a generative program, i.e. a list of instructions showing how to generate the empirical data; the informationprocessing structure associated with this program can be represented by a directed acyclic graph DAG. We suggest that these graphs can be interpreted as encoding relations of ontological priority,' and that ontological priority is a suitable generalisation of causation which applies even to theories that don't have a natural causal structure. We discuss some applications of our framework to philosophical questions about realism, operationalism, free will, locality and finetuning.

PIVEGAN Physics Informed Variational Embedding Generative Adversarial Networks for Stochastic Differential Equations ; We present a new category of physicsinformed neural networks called physics informed variational embedding generative adversarial network PIVEGAN, that effectively tackles the forward, inverse, and mixed problems of stochastic differential equations. In these scenarios, the governing equations are known, but only a limited number of sensor measurements of the system parameters are available. We integrate the governing physical laws into PIVEGAN with automatic differentiation, while introducing a variational encoder for approximating the latent variables of the actual distribution of the measurements. These latent variables are integrated into the generator to facilitate accurate learning of the characteristics of the stochastic partial equations. Our model consists of three components, namely the encoder, generator, and discriminator, each of which is updated alternatively employing the stochastic gradient descent algorithm. We evaluate the effectiveness of PIVEGAN in addressing forward, inverse, and mixed problems that require the concurrent calculation of system parameters and solutions. Numerical results demonstrate that the proposed method achieves satisfactory stability and accuracy in comparison with the previous physicsinformed generative adversarial network PIWGAN.

ExeDec Execution Decomposition for Compositional Generalization in Neural Program Synthesis ; When writing programs, people have the ability to tackle a new complex task by decomposing it into smaller and more familiar subtasks. While it is difficult to measure whether neural program synthesis methods have similar capabilities, we can measure whether they compositionally generalize, that is, whether a model that has been trained on the simpler subtasks is subsequently able to solve more complex tasks. In this paper, we characterize several different forms of compositional generalization that are desirable in program synthesis, forming a metabenchmark which we use to create generalization tasks for two popular datasets, RobustFill and DeepCoder. We then propose ExeDec, a novel decompositionbased synthesis strategy that predicts execution subgoals to solve problems stepbystep informed by program execution at each step. ExeDec has better synthesis performance and greatly improved compositional generalization ability compared to baselines.

An Asynchronous and LowPower True Random Number Generator using STTMTJ ; The emerging Spin Transfer Torque Magnetic Tunnel Junction STTMTJ technology exhibits interesting stochastic behavior combined with small area and low operation energy. It is, therefore, a promising technology for security applications, specifically the generation of random numbers. In this paper, STTMTJ is used to construct an asynchronous true random number generator TRNG with low power and a high entropy rate. The asynchronous design enables decoupling of the random number generation from the system clock, allowing it to be embedded in lowpower devices. The proposed TRNG is evaluated by a numerical simulation, using the LandauLifshitzGilbert LLG equation as the model of the STTMTJ devices. Design considerations, attack analysis, and process variation are discussed and evaluated. We show that our design is robust to process variation, achieving an entropy generating rate between 99.7Mbps and 127.8Mbps with 67.7 pJ per bit for 90 of the instances.

MobileVidFactory Automatic DiffusionBased Social Media Video Generation for Mobile Devices from Text ; Videos for mobile devices become the most popular access to share and acquire information recently. For the convenience of users' creation, in this paper, we present a system, namely MobileVidFactory, to automatically generate vertical mobile videos where users only need to give simple texts mainly. Our system consists of two parts basic and customized generation. In the basic generation, we take advantage of the pretrained image diffusion model, and adapt it to a highquality opendomain vertical video generator for mobile devices. As for the audio, by retrieving from our big database, our system matches a suitable background sound for the video. Additionally to produce customized content, our system allows users to add specified screen texts to the video for enriching visual expression, and specify texts for automatic reading with optional voices as they like.

Generation and characterization of polarizationentangled states using quantum dot singlephoton sources ; Singlephoton sources based on semiconductor quantum dots find several applications in quantum information processing due to their high singlephoton indistinguishability, ondemand generation, and low multiphoton emission. In this context, the generation of entangled photons represents a challenging task with a possible solution relying on the interference in probabilistic gates of identical photons emitted at different pulses from the same source. In this work, we implement this approach via a simple and compact design that generates entangled photon pairs in the polarization degree of freedom. We operate the proposed platform with single photons produced through two different pumping schemes, the resonant excited one and the longitudinalacoustic phononassisted configuration. We then characterize the produced entangled twophoton states by developing a complete model taking into account relevant experimental parameters, such as the secondorder correlation function and the HongOuMandel visibility. Our source shows longterm stability and high quality of the generated entangled states, thus constituting a reliable building block for optical quantum technologies.

Generative AI trial for nonviolent communication mediation ; Aiming for a mixbiotic society that combines freedom and solidarity among people with diverse values, I focused on nonviolent communication NVC that enables compassionate giving in various situations of social division and conflict, and tried a generative AI for it. Specifically, ChatGPT was used in place of the traditional certified trainer to test the possibility of mediating modifying input sentences in four processes observation, feelings, needs, and requests. The results indicate that there is potential for the application of generative AI, although not yet at a practical level. Suggested improvement guidelines included adding model responses, relearning revised responses, specifying appropriate terminology for each process, and reasking for required information. The use of generative AI will be useful initially to assist certified trainers, to prepare for and review events and workshops, and in the future to support consensus building and cooperative behavior in digital democracy, platform cooperatives, and cyberhuman social cooperating systems. It is hoped that the widespread use of NVC mediation using generative AI will lead to the early realization of a mixbiotic society.

TextPainter Multimodal Text Image Generation with Visualharmony and Textcomprehension for Poster Design ; Text design is one of the most critical procedures in poster design, as it relies heavily on the creativity and expertise of humans to design text images considering the visual harmony and textsemantic. This study introduces TextPainter, a novel multimodal approach that leverages contextual visual information and corresponding text semantics to generate text images. Specifically, TextPainter takes the globallocal background image as a hint of style and guides the text image generation with visual harmony. Furthermore, we leverage the language model and introduce a text comprehension module to achieve both sentencelevel and wordlevel style variations. Besides, we construct the PosterT80K dataset, consisting of about 80K posters annotated with sentencelevel bounding boxes and text contents. We hope this dataset will pave the way for further research on multimodal text image generation. Extensive quantitative and qualitative experiments demonstrate that TextPainter can generate visuallyandsemanticallyharmonious text images for posters.

Semantic Communications for Artificial Intelligence Generated Content AIGC Toward Effective Content Creation ; Artificial Intelligence Generated Content AIGC Services have significant potential in digital content creation. The distinctive abilities of AIGC, such as content generation based on minimal input, hold huge potential, especially when integrating with semantic communication SemCom. In this paper, a novel comprehensive conceptual model for the integration of AIGC and SemCom is developed. Particularly, a content generation level is introduced on top of the semantic level that provides a clear outline of how AIGC and SemCom interact with each other to produce meaningful and effective content. Moreover, a novel framework that employs AIGC technology is proposed as an encoder and decoder for semantic information, considering the joint optimization of semantic extraction and evaluation metrics tailored to AIGC services. The framework can adapt to different types of content generated, the required quality, and the semantic information utilized. By employing a Deep Q Network DQN, a case study is presented that provides useful insights into the feasibility of the optimization problem and its convergence characteristics.

BATINet BackgroundAware Text to Image Synthesis and Manipulation Network ; BackgroundInduced Text2Image BIT2I aims to generate foreground content according to the text on the given background image. Most studies focus on generating highquality foreground content, although they ignore the relationship between the two contents. In this study, we analyzed a novel BackgroundAware Text2Image BAT2I task in which the generated content matches the input background. We proposed a BackgroundAware Text to Image synthesis and manipulation Network BATINet, which contains two key components Position Detect Network PDN and Harmonize Network HN. The PDN detects the most plausible position of the textrelevant object in the background image. The HN harmonizes the generated content referring to background style information. Finally, we reconstructed the generation network, which consists of the multiGAN and attention module to match more user preferences. Moreover, we can apply BATINet to textguided image manipulation. It solves the most challenging task of manipulating the shape of an object. We demonstrated through qualitative and quantitative evaluations on the CUB dataset that the proposed model outperforms other stateoftheart methods.

DualStream Diffusion Net for TexttoVideo Generation ; With the emerging diffusion models, recently, texttovideo generation has aroused increasing attention. But an important bottleneck therein is that generative videos often tend to carry some flickers and artifacts. In this work, we propose a dualstream diffusion net DSDN to improve the consistency of content variations in generating videos. In particular, the designed two diffusion streams, video content and motion branches, could not only run separately in their private spaces for producing personalized video variations as well as content, but also be wellaligned between the content and motion domains through leveraging our designed crosstransformer interaction module, which would benefit the smoothness of generated videos. Besides, we also introduce motion decomposer and combiner to faciliate the operation on video motion. Qualitative and quantitative experiments demonstrate that our method could produce amazing continuous videos with fewer flickers.

Neural oscillators for generalization of physicsinformed machine learning ; A primary challenge of physicsinformed machine learning PIML is its generalization beyond the training domain, especially when dealing with complex physical problems represented by partial differential equations PDEs. This paper aims to enhance the generalization capabilities of PIML, facilitating practical, realworld applications where accurate predictions in unexplored regions are crucial. We leverage the inherent causality and temporal sequential characteristics of PDE solutions to fuse PIML models with recurrent neural architectures based on systems of ordinary differential equations, referred to as neural oscillators. Through effectively capturing longtime dependencies and mitigating the exploding and vanishing gradient problem, neural oscillators foster improved generalization in PIML tasks. Extensive experimentation involving timedependent nonlinear PDEs and biharmonic beam equations demonstrates the efficacy of the proposed approach. Incorporating neural oscillators outperforms existing stateoftheart methods on benchmark problems across various metrics. Consequently, the proposed method improves the generalization capabilities of PIML, providing accurate solutions for extrapolation and prediction beyond the training data.

Dissipative quantum Fisher information for a general Liouvillian parameterized process ; The dissipative quantum Fisher information DQFI for a dynamic map with a general parameter in an open quantum system is investigated, which can be regarded as an analog of the quantum Fisher information QFI in the Liouville space. We first derive a general dissipative generator in the Liouville space, and based on its decomposition form, find the DQFI stems from two parts. One is the dependence of eigenvalues of the Liouvillian supermatrix on the estimated parameter, which shows a linear dependence on time. The other is the variation of the eigenvectors with the estimated parameter. The relationship between this part and time presents rich characteristics, including harmonic oscillation, pure exponential gain and attenuation, as well as exponential gain and attenuation of oscillatory type, which depend specifically on the properties of the Liouville spectrum. This is in contrast to that of the conventional generator, where only oscillatory dependencies are seen. Further, we illustrate the theory through a toy model a twolevel system with spinflip noise. Especially, by using the DQFI, we demonstrated that the exceptional estimation precision cannot be obtained at the Liouvillian exceptional point.

Dynamic Strategy Chain Dynamic ZeroShot CoT for Long Mental Health Support Generation ; Long counseling Text Generation for Mental health support LTGM, an innovative and challenging task, aims to provide helpseekers with mental health support through a comprehensive and more acceptable response. The combination of chainofthought CoT prompting and Large Language Models LLMs is employed and get the SOTA performance on various NLP tasks, especially on text generation tasks. Zeroshot CoT prompting is one of the most common methods in CoT prompting. However, in the LTGM task, Zeroshot CoT prompting can not simulate a counselor or provide personalized strategies without effective mental health counseling strategy prompts. To tackle this challenge, we propose a zeroshot Dynamic Strategy Chain DSC prompting method. Firstly, we utilize GPT2 to learn the responses written by mental health counselors and dynamically generate mental health counseling strategies tailored to the helpseekers' needs. Secondly, the Zeroshot DSC prompting is constructed according to mental health counseling strategies and the helpseekers' post. Finally, the Zeroshot DSC prompting is employed to guide LLMs in generating more humanlike responses for the helpseekers. Both automatic and manual evaluations demonstrate that Zeroshot DSC prompting can deliver more humanlike responses than CoT prompting methods on LTGM tasks.

ZeroLeak Using LLMs for Scalable and Cost Effective SideChannel Patching ; Security critical software, e.g., OpenSSL, comes with numerous sidechannel leakages left unpatched due to a lack of resources or experts. The situation will only worsen as the pace of code development accelerates, with developers relying on Large Language Models LLMs to automatically generate code. In this work, we explore the use of LLMs in generating patches for vulnerable code with microarchitectural sidechannel leakages. For this, we investigate the generative abilities of powerful LLMs by carefully crafting prompts following a zeroshot learning approach. All generated code is dynamically analyzed by leakage detection tools, which are capable of pinpointing information leakage at the instruction level leaked either from secret dependent accesses or branches or vulnerable Spectre gadgets, respectively. Carefully crafted prompts are used to generate candidate replacements for vulnerable code, which are then analyzed for correctness and for leakage resilience. From a costperformance perspective, the GPT4based configuration costs in API calls a mere few cents per vulnerability fixed. Our results show that LLMbased patching is far more costeffective and thus provides a scalable solution. Finally, the framework we propose will improve in time, especially as vulnerability detection tools and LLMs mature.

ARTIST ARTificial Intelligence for Simplified Text ; Complex text is a major barrier for many citizens when accessing public information and knowledge. While often done manually, Text Simplification is a key Natural Language Processing task that aims for reducing the linguistic complexity of a text while preserving the original meaning. Recent advances in Generative Artificial Intelligence AI have enabled automatic text simplification both on the lexical and syntactical levels. However, as applications often focus on English, little is understood about the effectiveness of Generative AI techniques on lowresource languages such as Dutch. For this reason, we carry out empirical studies to understand the benefits and limitations of applying generative technologies for text simplification and provide the following outcomes 1 the design and implementation for a configurable text simplification pipeline that orchestrates stateoftheart generative text simplification models, domain and reader adaptation, and visualisation modules; 2 insights and lessons learned, showing the strengths of automatic text simplification while exposing the challenges in handling cultural and commonsense knowledge. These outcomes represent a first step in the exploration of Dutch text simplification and shed light on future endeavours both for research and practice.

Situated Natural Language Explanations ; Natural language is among the most accessible tools for explaining decisions to humans, and large pretrained language models PLMs have demonstrated impressive abilities to generate coherent natural language explanations NLE. The existing NLE research perspectives do not take the audience into account. An NLE can have high textual quality, but it might not accommodate audiences' needs and preference. To address this limitation, we propose an alternative perspective, situated NLE, including a situated generation framework and a situated evaluation framework. On the generation side, we propose simple prompt engineering methods that adapt the NLEs to situations. In human studies, the annotators preferred the situated NLEs. On the evaluation side, we set up automated evaluation scores in lexical, semantic, and pragmatic categories. The scores can be used to select the most suitable prompts to generate NLEs. Situated NLE provides a perspective to conduct further research on automatic NLE generations.

Edge Generation Scheduling for DAG Tasks using Deep Reinforcement Learning ; Directed acyclic graph DAG tasks are currently adopted in the realtime domain to model complex applications from the automotive, avionics, and industrial domain that implement their functionalities through chains of intercommunicating tasks. This paper studies the problem of scheduling realtime DAG tasks by presenting a novel schedulability test based on the concept of trivial schedulability. Using this schedulability test, we propose a new DAG scheduling framework edge generation scheduling EGS that attempts to minimize the DAG width by iteratively generating edges while guaranteeing the deadline constraint. We study how to efficiently solve the problem of generating edges by developing a deep reinforcement learning algorithm combined with a graph representation neural network to learn an efficient edge generation policy for EGS. We evaluate the effectiveness of the proposed algorithm by comparing it with stateoftheart DAG scheduling heuristics and an optimal mixedinteger linear programming baseline. Experimental results show that the proposed algorithm outperforms the stateoftheart by requiring fewer processors to schedule the same DAG tasks.

Delocalisation enables efficient charge generation in organic photovoltaics, even with little to no energetic offset ; Organic photovoltaics OPVs are promising candidates for solarenergy conversion, with device efficiencies continuing to increase. However, the precise mechanism of how charges separate in OPVs is not well understood because low dielectric constants produce a strong attraction between the charges, which they must overcome to separate. Separation has been thought to require energetic offsets at donoracceptor interfaces, but recent materials have enabled efficient charge generation with small offsets, or with none at all in neat materials. Here, we extend delocalised kinetic Monte Carlo dKMC to develop a threedimensional model of charge generation that includes disorder, delocalisation, and polaron formation in every step from photoexcitation to charge separation. Our simulations show that delocalisation dramatically increases chargegeneration efficiency, partly by enabling excitons to dissociate in the bulk. Therefore, charge generation can be efficient even in devices with little to no energetic offset, including neat materials. Our findings demonstrate that the underlying quantummechanical effect that improves the chargeseparation kinetics is faster and longerdistance hops between delocalised states, mediated by hybridised states of exciton and chargetransfer character.

Fully Embedded TimeSeries Generative Adversarial Networks ; Generative Adversarial Networks GANs should produce synthetic data that fits the underlying distribution of the data being modeled. For real valued timeseries data, this implies the need to simultaneously capture the static distribution of the data, but also the full temporal distribution of the data for any potential time horizon. This temporal element produces a more complex problem that can potentially leave current solutions underconstrained, unstable during training, or prone to varying degrees of mode collapse. In FETSGAN, entire sequences are translated directly to the generator's sampling space using a seq2seq style adversarial auto encoder AAE, where adversarial training is used to match the training distribution in both the feature space and the lower dimensional sampling space. This additional constraint provides a loose assurance that the temporal distribution of the synthetic samples will not collapse. In addition, the First Above Threshold FAT operator is introduced to supplement the reconstruction of encoded sequences, which improves training stability and the overall quality of the synthetic data being generated. These novel contributions demonstrate a significant improvement to the current state of the art for adversarial learners in qualitative measures of temporal similarity and quantitative predictive ability of data generated through FETSGAN.

From Pixels to Portraits A Comprehensive Survey of Talking Head Generation Techniques and Applications ; Recent advancements in deep learning and computer vision have led to a surge of interest in generating realistic talking heads. This paper presents a comprehensive survey of stateoftheart methods for talking head generation. We systematically categorises them into four main approaches imagedriven, audiodriven, videodriven and others including neural radiance fields NeRF, and 3Dbased methods. We provide an indepth analysis of each method, highlighting their unique contributions, strengths, and limitations. Furthermore, we thoroughly compare publicly available models, evaluating them on key aspects such as inference time and humanrated quality of the generated outputs. Our aim is to provide a clear and concise overview of the current landscape in talking head generation, elucidating the relationships between different approaches and identifying promising directions for future research. This survey will serve as a valuable reference for researchers and practitioners interested in this rapidly evolving field.

Boundary multifractality in the spin quantum Hall symmetry class with interaction ; Generalized multifractality characterizes system size dependence of pure scaling local observables at Anderson transitions in all ten symmetry classes of disordered systems. Recently, the concept of generalized multifractality has been extended to boundaries of critical disordered noninteracting systems. Here we study the generalized boundary multifractality in the presence of electronelectron interaction, focusing on the spin quantum Hall symmetry class class C. Employing the twoloop renormalization group analysis within Finkel'stein nonlinear sigma model we compute the anomalous dimensions of the pure scaling operators located at the boundary of the system. We find that generalized boundary multifractal exponents are twice larger than their bulk counterparts. Exact symmetry relations between generalized boundary multifractal exponents in the case of noninteracting systems are explicitly broken by the interaction.

Mutual Information Maximizing Quantum Generative Adversarial Network and Its Applications in Finance ; One of the most promising applications in the era of NISQ Noisy IntermediateScale Quantum computing is quantum machine learning. Quantum machine learning offers significant quantum advantages over classical machine learning across various domains. Specifically, generative adversarial networks have been recognized for their potential utility in diverse fields such as image generation, finance, and probability distribution modeling. However, these networks necessitate solutions for inherent challenges like mode collapse. In this study, we capitalize on the concept that the estimation of mutual information between highdimensional continuous random variables can be achieved through gradient descent using neural networks. We introduce a novel approach named InfoQGAN, which employs the Mutual Information Neural Estimator MINE within the framework of quantum generative adversarial networks to tackle the mode collapse issue. Furthermore, we elaborate on how this approach can be applied to a financial scenario, specifically addressing the problem of generating portfolio return distributions through dynamic asset allocation. This illustrates the potential practical applicability of InfoQGAN in realworld contexts.

T2IW Joint Text to Image Watermark Generation ; Recent developments in textconditioned image generative models have revolutionized the production of realistic results. Unfortunately, this has also led to an increase in privacy violations and the spread of false information, which requires the need for traceability, privacy protection, and other security measures. However, existing texttoimage paradigms lack the technical capabilities to link traceable messages with image generation. In this study, we introduce a novel task for the joint generation of text to image and watermark T2IW. This T2IW scheme ensures minimal damage to image quality when generating a compound image by forcing the semantic feature and the watermark signal to be compatible in pixels. Additionally, by utilizing principles from Shannon information theory and noncooperative game theory, we are able to separate the revealed image and the revealed watermark from the compound image. Furthermore, we strengthen the watermark robustness of our approach by subjecting the compound image to various postprocessing attacks, with minimal pixel distortion observed in the revealed watermark. Extensive experiments have demonstrated remarkable achievements in image quality, watermark invisibility, and watermark robustness, supported by our proposed set of evaluation metrics.

Quantum Quenches of Conformal Field Theory with Open Boundary ; We develop a method to derive the exact formula of entanglement entropy for generic inhomogeneous conformal field theory CFT quantum quenches with open boundary condition OBC, which characterizes the generic boundary effect unresolved by analytical methods in the past. We identify the generic OBC quenches with Euclidean path integrals in complicated spacetime geometries, and we show that a special class of OBC quenches, including the Mobius and sinesquaredeformation quenches, have simple boundary effects calculable from Euclidean path integrals in a simple strip spacetime geometry. We verify that our generic CFT formula matches well with free fermion tightbinding model numerical calculations for various quench problems with OBC. Our method can be easily generalized to calculate any local quantities expressible as onepoint functions in such quantum quench problems.

Generalized Graphon Process Convergence of Graph Frequencies in Stretched Cut Distance ; Graphons have traditionally served as limit objects for dense graph sequences, with the cut distance serving as the metric for convergence. However, sparse graph sequences converge to the trivial graphon under the conventional definition of cut distance, which make this framework inadequate for many practical applications. In this paper, we utilize the concepts of generalized graphons and stretched cut distance to describe the convergence of sparse graph sequences. Specifically, we consider a random graph process generated from a generalized graphon. This random graph process converges to the generalized graphon in stretched cut distance. We use this random graph process to model the growing sparse graph, and prove the convergence of the adjacency matrices' eigenvalues. We supplement our findings with experimental validation. Our results indicate the possibility of transfer learning between sparse graphs.

ACT Empowering Decision Transformer with Dynamic Programming via Advantage Conditioning ; Decision Transformer DT, which employs expressive sequence modeling techniques to perform action generation, has emerged as a promising approach to offline policy optimization. However, DT generates actions conditioned on a desired future return, which is known to bear some weaknesses such as the susceptibility to environmental stochasticity. To overcome DT's weaknesses, we propose to empower DT with dynamic programming. Our method comprises three steps. First, we employ insample value iteration to obtain approximated value functions, which involves dynamic programming over the MDP structure. Second, we evaluate action quality in context with estimated advantages. We introduce two types of advantage estimators, IAE and GAE, which are suitable for different tasks. Third, we train an AdvantageConditioned Transformer ACT to generate actions conditioned on the estimated advantages. Finally, during testing, ACT generates actions conditioned on a desired advantage. Our evaluation results validate that, by leveraging the power of dynamic programming, ACT demonstrates effective trajectory stitching and robust action generation in spite of the environmental stochasticity, outperforming baseline methods across various benchmarks. Additionally, we conduct an indepth analysis of ACT's various design choices through ablation studies.

Towards Reliable Domain Generalization A New Dataset and Evaluations ; There are ubiquitous distribution shifts in the real world. However, deep neural networks DNNs are easily biased towards the training set, which causes severe performance degradation when they receive outofdistribution data. Many methods are studied to train models that generalize under various distribution shifts in the literature of domain generalization DG. However, the recent DomainBed and WILDS benchmarks challenged the effectiveness of these methods. Aiming at the problems in the existing research, we propose a new domain generalization task for handwritten Chinese character recognition HCCR to enrich the application scenarios of DG method research. We evaluate eighteen DG methods on the proposed PaHCC Printed and Handwritten Chinese Characters dataset and show that the performance of existing methods on this dataset is still unsatisfactory. Besides, under a designed dynamic DG setting, we reveal more properties of DG methods and argue that only the leaveonedomainout protocol is unreliable. We advocate that researchers in the DG community refer to dynamic performance of methods for more comprehensive and reliable evaluation. Our dataset and evaluations bring new perspectives to the community for more substantial progress. We will make our dataset public with the article published to facilitate the study of domain generalization.

FgT2M FineGrained TextDriven Human Motion Generation via Diffusion Model ; Textdriven human motion generation in computer vision is both significant and challenging. However, current methods are limited to producing either deterministic or imprecise motion sequences, failing to effectively control the temporal and spatial relationships required to conform to a given text description. In this work, we propose a finegrained method for generating highquality, conditional human motion sequences supporting precise text description. Our approach consists of two key components 1 a linguisticsstructure assisted module that constructs accurate and complete language feature to fully utilize text information; and 2 a contextaware progressive reasoning module that learns neighborhood and overall semantic linguistics features from shallow and deep graph neural networks to achieve a multistep inference. Experiments show that our approach outperforms textdriven motion generation methods on HumanML3D and KIT test sets and generates better visually confirmed motion to the text conditions.

Scaled PromptTuning for FewShot Natural Language Generation ; The increasingly Large Language Models LLMs demonstrate stronger language understanding and generation capabilities, while the memory demand and computation cost of finetuning LLMs on downstream tasks are nonnegligible. Besides, finetuning generally requires a certain amount of data from individual tasks whilst data collection cost is another issue to consider in realworld applications. In this work, we focus on ParameterEfficient FineTuning PEFT methods for fewshot Natural Language Generation NLG, which freeze most parameters in LLMs and tune a small subset of parameters in fewshot cases so that memory footprint, training cost, and labeling cost are reduced while maintaining or even improving the performance. We propose a Scaled PromptTuning SPT method which surpasses conventional PT with better performance and generalization ability but without an obvious increase in training cost. Further study on intermediate SPT suggests the superior transferability of SPT in fewshot scenarios, providing a recipe for datadeficient and computationlimited circumstances. Moreover, a comprehensive comparison of existing PEFT methods reveals that certain approaches exhibiting decent performance with modest training cost such as PrefixTuning in prior study could struggle in fewshot NLG tasks, especially on challenging datasets.

Robustness for Spectral Clustering of General Graphs under Local Differential Privacy ; Spectral clustering is a widely used algorithm to find clusters in networks. Several researchers have studied the stability of spectral clustering under local differential privacy with the additional assumption that the underlying networks are generated from the stochastic block model SBM. However, we argue that this assumption is too restrictive since social networks do not originate from the SBM. Thus, delve into an analysis for general graphs in this work. Our primary focus is the edge flipping method a common technique for protecting local differential privacy. On a positive side, our findings suggest that even when the edges of an nvertex graph satisfying some reasonable wellclustering assumptions are flipped with a probability of Olog nn, the clustering outcomes are largely consistent. Empirical tests further corroborate these theoretical findings. Conversely, although clustering outcomes have been stable for dense and wellclustered graphs produced from the SBM, we show that in general, spectral clustering may yield highly erratic results on certain dense and wellclustered graphs when the flipping probability is omegalog nn. This indicates that the best privacy budget obtainable for general graphs is Thetalog n.

Search and Learning for Unsupervised Text Generation ; With the advances of deep learning techniques, text generation is attracting increasing interest in the artificial intelligence AI community, because of its wide applications and because it is an essential component of AI. Traditional text generation systems are trained in a supervised way, requiring massive labeled parallel corpora. In this paper, I will introduce our recent work on search and learning approaches to unsupervised text generation, where a heuristic objective function estimates the quality of a candidate sentence, and discrete search algorithms generate a sentence by maximizing the search objective. A machine learning model further learns from the search results to smooth out noise and improve efficiency. Our approach is important to the industry for building minimal viable products for a new task; it also has high social impacts for saving human annotation labor and for processing lowresource languages.

Accelerating Large Batch Training via Gradient Signal to Noise Ratio GSNR ; As models for nature language processing NLP, computer vision CV and recommendation systems RS require surging computation, a large number of GPUsTPUs are paralleled as a large batch LB to improve training throughput. However, training such LB tasks often meets large generalization gap and downgrades final precision, which limits enlarging the batch size. In this work, we develop the variance reduced gradient descent technique VRGD based on the gradient signal to noise ratio GSNR and apply it onto popular optimizers such as SGDAdamLARSLAMB. We carry out a theoretical analysis of convergence rate to explain its fast training dynamics, and a generalization analysis to demonstrate its smaller generalization gap on LB training. Comprehensive experiments demonstrate that VRGD can accelerate training 1sim 2 times, narrow generalization gap and improve final accuracy. We push the batch size limit of BERT pretraining up to 128k64k and DLRM to 512k without noticeable accuracy loss. We improve ImageNet Top1 accuracy at 96k by 0.52pp than LARS. The generalization gap of BERT and ImageNet training is significantly reduce by over 65.

A general method to reconstruct strong gravitational lenses based on the singular perturbative approach ; The number of gravitational arcs systems detected is increasing quickly and should even increase at a faster rate in the near future. This wealth of new gravitational arcs requires the development of a purely automated method to reconstruct the lens and source. A general reconstruction method based on the singular perturbative approach is proposed in this paper. This method generates a lens and source reconstruction directly from the gravitational arc image. The method is fully automated and works in two steps. The first step is to generate a guess solution based on the circular solution in the singular perturbative approach. The second step is to break the sign degeneracy and to refine the solution by using a general source model. The refinement of the solution is conducted step by step to avoid the sourcelens degeneracy issue. One important asset of this automated method is that the lens solution is written in universal terms which allows the computation of statistics. Considering the large number of lenses which should be available in the near future this ability to compute unbiased statistics is an important asset.

Spider4SPARQL A Complex Benchmark for Evaluating Knowledge Graph Question Answering Systems ; With the recent spike in the number and availability of Large Language Models LLMs, it has become increasingly important to provide large and realistic benchmarks for evaluating Knowledge Graph Question Answering KBQA systems. So far the majority of benchmarks rely on patternbased SPARQL query generation approaches. The subsequent natural language NL question generation is conducted through crowdsourcing or other automated methods, such as rulebased paraphrasing or NL question templates. Although some of these datasets are of considerable size, their pitfall lies in their patternbased generation approaches, which do not always generalize well to the vague and linguistically diverse questions asked by humans in realworld contexts. In this paper, we introduce Spider4SPARQL a new SPARQL benchmark dataset featuring 9,693 previously existing manually generated NL questions and 4,721 unique, novel, and complex SPARQL queries of varying complexity. In addition to the NLSPARQL pairs, we also provide their corresponding 166 knowledge graphs and ontologies, which cover 138 different domains. Our complex benchmark enables novel ways of evaluating the strengths and weaknesses of modern KGQA systems. We evaluate the system with stateoftheart KGQA systems as well as LLMs, which achieve only up to 45 execution accuracy, demonstrating that Spider4SPARQL is a challenging benchmark for future research.

AutoAgents A Framework for Automatic Agent Generation ; Large language models LLMs have enabled remarkable advances in automated tasksolving with multiagent systems. However, most existing LLMbased multiagent approaches rely on predefined agents to handle simple tasks, limiting the adaptability of multiagent collaboration to different scenarios. Therefore, we introduce AutoAgents, an innovative framework that adaptively generates and coordinates multiple specialized agents to build an AI team according to different tasks. Specifically, AutoAgents couples the relationship between tasks and roles by dynamically generating multiple required agents based on task content and planning solutions for the current task based on the generated expert agents. Multiple specialized agents collaborate with each other to efficiently accomplish tasks. Concurrently, an observer role is incorporated into the framework to reflect on the designated plans and agents' responses and improve upon them. Our experiments on various benchmarks demonstrate that AutoAgents generates more coherent and accurate solutions than the existing multiagent methods. This underscores the significance of assigning different roles to different tasks and of team cooperation, offering new perspectives for tackling complex tasks. The repository of this project is available at httpsgithub.comLinkSoulAIAutoAgents.

Operatorfree Equilibrium on the Sphere ; We propose a generalized minimum discrepancy, which derives from Legendre's ODE and spherical harmonic theoretics to provide a new criterion of equidistributed pointsets on the sphere. A continuous and derivative kernel in terms of elementary functions is established to simplify the computation of the generalized minimum discrepancy. We consider the deterministic point generated from Pycke's statistics to integrate a Franke function for the sphere and investigate the discrepancies of points systems embedding with different kernels. Quantitive experiments are conducted and the results are analyzed. Our deduced model can explore latent point systems, that have the minimum discrepancy without the involvement of pseudodifferential operators and Beltrami operators, by the use of derivatives. Compared to the random point generated from the Monte Carlo method, only a few points generated by our method are required to approximate the target in arbitrary dimensions.

Enhancing Representation Generalization in Authorship Identification ; Authorship identification ascertains the authorship of texts whose origins remain undisclosed. That authorship identification techniques work as reliably as they do has been attributed to the fact that authorial style is properly captured and represented. Although modern authorship identification methods have evolved significantly over the years and have proven effective in distinguishing authorial styles, the generalization of stylistic features across domains has not been systematically reviewed. The presented work addresses the challenge of enhancing the generalization of stylistic representations in authorship identification, particularly when there are discrepancies between training and testing samples. A comprehensive review of empirical studies was conducted, focusing on various stylistic features and their effectiveness in representing an author's style. The influencing factors such as topic, genre, and register on writing style were also explored, along with strategies to mitigate their impact. While some stylistic features, like character ngrams and function words, have proven to be robust and discriminative, others, such as content words, can introduce biases and hinder crossdomain generalization. Representations learned using deep learning models, especially those incorporating character ngrams and syntactic information, show promise in enhancing representation generalization. The findings underscore the importance of selecting appropriate stylistic features for authorship identification, especially in crossdomain scenarios. The recognition of the strengths and weaknesses of various linguistic features paves the way for more accurate authorship identification in diverse contexts.

Quantum generative adversarial learning in photonics ; Quantum Generative Adversarial Networks QGANs, an intersection of quantum computing and machine learning, have attracted widespread attention due to their potential advantages over classical analogs. However, in the current era of Noisy IntermediateScale Quantum NISQ computing, it is essential to investigate whether QGANs can perform learning tasks on nearterm quantum devices usually affected by noise and even defects. In this Letter, using a programmable silicon quantum photonic chip, we experimentally demonstrate the QGAN model in photonics for the first time, and investigate the effects of noise and defects on its performance. Our results show that QGANs can generate highquality quantum data with a fidelity higher than 90, even under conditions where up to half of the generator's phase shifters are damaged, or all of the generator and discriminator's phase shifters are subjected to phase noise up to 0.04pi. Our work sheds light on the feasibility of implementing QGANs on NISQera quantum hardware.

LichtenbaumHartshorne vanishing theorem for generalized local cohomology modules ; Let R be a commutative Noetherian ring, and let mathfrak a be a proper ideal of R. Let M be a nonzero finitely generated Rmodule with the finite projective dimension p. Also, let N be a nonzero finitely generated Rmodule with Nneqmathfraka N, and assume that c is the greatest nonnegative integer with the property that operatornameHimathfrak aN, the ith local cohomology module of N with respect to mathfrak a, is nonzero. It is known that operatornameHimathfrak aM, N, the ith generalized local cohomology module of M and N with respect to mathfrak a, is zero for all ipc. In this paper, we obtain the coassociated prime ideals of operatornameHpcmathfrak aM, N. Using this, in the case when R is a local ring and c is equal to the dimension of N, we give a necessary and sufficient condition for the vanishing of operatornameHpcmathfrak aM, N which extends the LichtenbaumHartshorne vanishing theorem for generalized local cohomology modules.

Not all spacetime coordinates for generalrelativistic ray tracing are created equal ; Models for the observational appearance of astrophysical black holes rely critically on accurate generalrelativistic ray tracing and radiation transport to compute the intensity measured by a distant observer. In this paper, we illustrate how the choice of coordinates and initial conditions affect this process. In particular, we show that propagating rays from the camera to the source leads to different solutions if the spatial part of the momentum of the photon points towards the horizon or away from it. In doing this, we also show that coordinates that are well suited for numerical GeneralRelativistic MagnetoHydroDynamic GRMHD simulations are typically not optimal for generic ray tracing. We discuss the implications for blackhole images and show that radiation transport in optimal and nonoptimal spacetime coordinates lead to the same images up to numerical errors and algorithmic choices.

Advection Dominated Accretion Flows. A Toy Disk Model ; A toy model of a disk undergoing steady state accretion onto a black hole is presented. The disk is in a hydrostatic equilibrium for all radii r rin, with the inner disk radius located between the marginally stable and marginally bound orbits rms rin rmb. Matter flows from the disk through a narrow cusp at rms and falls freely into the black hole, carrying with it no thermal energy. At radii larger than rout the disk is assumed to radiate away all locally generated heat, and therefore the disk is geometrically thin for r rout. We assume that no heat generated in the inner disk, with rout r rin can be radiated away, i.e. the disk is 100 advective, and it becomes geometrically thick in this range of radii. All enthalpy of the thick disk is used up to press the inner disk radius towards the marginally bound orbit, and to lower the efficiency of conversion of accreted mass into radiation generated only for r rout, by assumption. Conservation laws of mass, angular momentum and energy make it possible to calculate the inner thick disk radius rin for any specified value of its outer radius rout. As the nature of disk viscosity is not known there is some freedom in choosing the shape of the thick disk, subject to several general conditions, which include the hydrostatic equilibrium everywhere for r rin. The main purpose of this toy model is to emphasize the effect the disk thickness has on lowering the energetic efficiency of a black hole accretion.

Secondorder Perturbations of the Friedmann World Model ; We consider instability of the Friedmann world model to the secondorder in perturbations. We present the perturbed set of equations up to the secondorder in the Friedmann background world model with general spatial curvature and the cosmological constant. We consider systems with the completely general imperfect fluids, the minimally coupled scalar fields, the electromagnetic field, and the generalized gravity theories. We also present the case of null geodesic equations, and the one based on the relativistic Boltzmann equation. In due stage a decomposition is made for the scalar, vector and tensortype perturbations which couple each other to the secondorder. Gauge issue is resolved to each order. The basic equations are presented without imposing any gauge condition, thus in a gaugeready form so that we can use the full advantage of having the gauge freedom in analysing the problems. As an application we show that to the secondorder in perturbation the relativistic pressureless ideal fluid of the scalartype reproduces exactly the known Newtonian result. As another application we rederive the largescale conserved quantities of the pure scalar and tensorperturbations to the second order, first shown by Salopek and Bond, now from the exact equations. Several other applications are made as well.

An integral equation approach to timedependent kinematic dynamos in finite domains ; The homogeneous dynamo effect is at the root of cosmic magnetic field generation. With only a very few exceptions, the numerical treatment of homogeneous dynamos is carried out in the framework of the differential equation approach. The present paper tries to facilitate the use of integral equations in dynamo research. Apart from the pedagogical value to illustrate dynamo action within the wellknown picture of BiotSavart's law, the integral equation approach has a number of practical advantages. The first advantage is its proven numerical robustness and stability. The second and perhaps most important advantage is its applicability to dynamos in arbitrary geometries. The third advantage is its intimate connection to inverse problems relevant not only for dynamos but also for technical applications of magnetohydrodynamics. The paper provides the first general formulation and application of the integral equation approach to timedependent kinematic dynamos in finite domains. For the spherically symmetric alpha2 dynamo model it is shown how the general formulation is reduced to a coupled system of two radial integral equations for the defining scalars of the poloidal and the toroidal field components. The integral equation formulation for spherical dynamos with general velocity fields is also derived. Two numerical examples, the alpha2 dynamo model with radially varying alpha, and the BullardGellman model illustrate the equivalence of the approach with the usual differential equation method.

Generic twophase coexistence in nonequilibrium systems ; Gibbs' phase rule states that twophase coexistence of a singlecomponent system, characterized by an ndimensional parameterspace, may occur in an n1dimensional region. For example, the two equilibrium phases of the Ising model coexist on a line in the temperaturemagneticfield phase diagram. Nonequilibrium systems may violate this rule and several models, where phase coexistence occurs over a finite ndimensional region of the parameter space, have been reported. The first example of this behaviour was found in Toom's model Toom,Geoff,GG, that exhibits generic bistability, i.e. twophase coexistence over a finite region of its twodimensional parameter space see Section 1. In addition to its interest as a genuine nonequilibrium property, generic multistability, defined as a generalization of bistability, is both of practical and theoretical relevance. In particular, it has been used recently to argue that some complex structures appearing in nature could be truly stable rather than metastable with important applications in theoretical biology, and as the theoretical basis for an errorcorrection method in computer science see GG,Gacs for an illuminating and pedagogical discussion of these ideas.

NonCommutative Topology for Curved Quantum Causality ; A quantum causal topology is presented. This is modeled after a noncommutative scheme type of theory for the curved finitary spacetime sheaves of the nonabelian incidence Rota algebras that represent gravitational quantum causal sets'. The finitary spacetime primitive algebra scheme structures for quantum causal sets proposed here are interpreted as the kinematics of a curved and reticular local quantum causality. Dynamics for quantum causal sets is then represented by appropriate scheme morphisms, thus it has a purely categorical description that is manifestly gaugeindependent'. Hence, a schematic version of the Principle of General Covariance of General Relativity is formulated for the dynamically variable quantum causal sets. We compare our noncommutative schemetheoretic curved quantum causal topology with some recent Cquantale models for nonabelian generalizations of classical commutative topological spaces or locales, as well as with some relevant recent results obtained from applying sheaf and topostheoretic ideas to quantum logic proper. Motivated by the latter, we organize our finitary spacetime primitive algebra schemes of curved quantum causal sets into a toposlike structure, coined quantum topos', and argue that it is a sound model of a structure that Selesnick has anticipated to underlie Finkelstein's reticular and curved quantum causal net. At the end we conjecture that the fundamental quantum timeasymmetry that Penrose has expected to be the main characteristic of the elusive true quantum gravity' is possibly of a kinematical or structural rather than of a dynamical character, and we also discuss the possibility of a unified description of quantum logic and quantum gravity in quantum topostheoretic terms.

Thermodynamics with longrange interactions from Ising models to blackholes ; New methods are presented which enables one to analyze the thermodynamics of systems with longrange interactions. Generically, such systems have entropies which are nonextensive, do not scale with the size of the system. We show how to calculate the degree of nonextensivity for such a system. We find that a system interacting with a heat reservoir is in a probability distribution of canonical ensembles. The system still possesses a parameter akin to a global temperature, which is constant throughout the substance. There is also a useful quantity which acts like a it local temperatures and it varies throughout the substance. These quantities are closely related to counterparts found in general relativity. A lattice model with longrange spinspin coupling is studied. This is compared with systems such as those encountered in general relativity, and gravitating systems with Newtoniantype interactions. A longrange lattice model is presented which can be seen as a blackhole analog. One finds that the analog's temperature and entropy have many properties which are found in blackholes. Finally, the entropy scaling behavior of a gravitating perfect fluid of constant density is calculated. For weak interactions, the entropy scales like the volume of the system. As the interactions become stronger, the entropy becomes higher near the surface of the system, and becomes more areascaling.

Synthetic LISA Simulating Time Delay Interferometry in a Model LISA ; We report on three numerical experiments on the implementation of TimeDelay Interferometry TDI for LISA, performed with Synthetic LISA, a CPython package that we developed to simulate the LISA science process at the level of scientific and technical requirements. Specifically, we study the lasernoise residuals left by firstgeneration TDI when the LISA armlengths have a realistic time dependence; we characterize the armlengthmeasurements accuracies that are needed to have effective lasernoise cancellation in both first and secondgeneration TDI; and we estimate the quantization and telemetry bitdepth needed for the phase measurements. Synthetic LISA generates synthetic time series of the LISA fundamental noises, as filtered through all the TDI observables; it also provides a streamlined module to compute the TDI responses to gravitational waves according to a full model of TDI, including the motion of the LISA array and the temporal and directional dependence of the armlengths. We discuss the theoretical model that underlies the simulation, its implementation, and its use in future investigations on system characterization and dataanalysis prototyping for LISA.

On the Relation between Mass and Charge A Pure Geometric Approach ; A new solution of the field equations of the generalized field theory, constructed by Mikhail and Wanas in 1977, has been obtained. The geometric structure used, in the present application, is an absolute parallelism APspace with spherical symmetry type FIGI. The solution obtained represents a generalized field outside a charged massive central body. Two schemes have been used to get the physical meaning of the solution The first is related to the metric of the Riemannian space associated with the APstructure. The second is connected to a covariant scheme known as itType Analysis. It is shown that the dependence on both schemes for interpreting the results obtained, is more better than the dependence on the metric of the Riemannian space associated with the APstructure. In General, if we consider the solution obtained as representing a geometric model for an elementary charged particle, then the results of the present work can be summarized in the following points. i It is shown that the mass of the particle is made of two contributions The first is the gravitational contribution, and the second is the contribution due to the existence of charge. ii The model allows for the existence of a charged particle whose mass is completely electromagnetic in origin. iii The model prevents the existence of a charged massless particle. iv The electromagnetic contribution, to the mass, is independent of the sign of the electric charge. v It is shown that the mass of the electron or a positron is purely made of its charge.

The Dualized Standard Model and its Applicationsan Interim Report ; Based on a nonabelian generalization of electricmagnetic duality, the Dualized Standard Model DSM suggests a natural explanation for exactly 3 generations of fermions as the dual colour' widetildeSU3 symmetry broken in a particular manner. The resulting scheme then offers on the one hand a fermion mass hierarchy and a perturbative method for calculating the mass and mixing parameters of the Standard Model fermions, and on the other testable predictions for new phenomena ranging from rare meson decays to ultrahigh energy cosmic rays. Calculations to 1loop order gives, at the cost of adjusting only 3 real parameters, values for the following quantities all except one in very good agreement with experiment the quark CKM matrix elements Vrs, the lepton CKM matrix elements Urs, and the second generation masses mc, ms, mmu. This means, in particular, that it gives near maximal mixing Umu3 between numu and nutau as observed by SuperKamiokande, Kamiokande and Soudan, while keeping small the corresponding quark angles Vcb, Vts. In addition, the scheme gives i rough orderofmagnitude estimates for the masses of the lowest generation, ii predictions for low energy FCNC effects such as KL to e mu, iii a possible explanation for the longstanding puzzle of air showers beyond the GZK cutoff. All these together, however, still represent but a portion of the possible physical consequences derivable from the DSM scheme the majority of which are yet to be explored.

Bulk Scalar Stabilization of the Radion without Metric BackReaction in the RandallSundrum Model ; Generalizations of the RandallSundrum model containing a bulk scalar field Phi interacting with the curvature R through the general coupling R fPhi are considered. We derive the general form of the effective 4D potential for the spinzero fields and show that in the mass matrix the radion mixes with the KaluzaKlein modes of the bulk scalar fluctuations. We demonstrate that it is possible to choose a nontrivial background form Phi0y where y is the extra dimension coordinate for the bulk scalar field such that the exact RandallSundrum metric is preserved i.e. such that there is no backreaction. We compute the mass matrix for the radion and the KK modes of the excitations of the bulk scalar relative to the background configuration Phi0y and find that the resulting mass matrix implies a nonzero value for the mass of the radion identified as the state with the lowest eigenvalue of the scalar mass matrix. We find that this mass is suppressed relative to the Planck scale by the standard warp factor needed to explain the hierarchy puzzle, implying that a mass sim 1tev is a natural order of magnitude for the radion mass. The general considerations are illustrated in the case of a model containing an RPhi2 interaction term.

Baryon Inhomogeneity Generation in the QuarkGluon Plasma Phase ; We discuss the possibility of generation of baryon inhomogeneities in a quarkgluon plasma phase due to moving Z3 interfaces. By modeling the dependence of effective mass of the quarks on the Polyakov loop order parameter, we study the reflection of quarks from collapsing Z3 interfaces and estimate resulting baryon inhomogeneities in the context of the early universe. We argue that in the context of certain low energy scale inflationary models, it is possible that large Z3 walls arise at the end of the reheating stage. Collapse of such walls could lead to baryon inhomogeneities which may be separated by large distances near the QCD scale. Importantly, the generation of these inhomogeneities is insensitive to the order, or even the existence, of the quarkhadron phase transition. We also briefly discuss the possibility of formation of quark nuggets in this model, as well as baryon inhomogeneity generation in relativistic heavyion collisions.

Constrained KP Hierarchies Additional Symmetries, DarbouxBacklund Solutions and Relations to MultiMatrix Models ; This paper provides a systematic description of the interplay between a specific class of reductions denoted as cKPrm r,m geq 1 of the primary continuum integrable system the KadomtsevPetviashvili sf KP hierarchy and discrete multimatrix models. The relevant integrable cKPrm structure is a generalization of the familiar rreduction of the full sf KP hierarchy to the SLr generalized KdV hierarchy sf cKPr,0. The important feature of cKPrm hierarchies is the presence of a discrete symmetry structure generated by successive DarbouxBacklund DB transformations. This symmetry allows for expressing the relevant taufunctions as Wronskians within a formalism which realizes the taufunctions as DB orbits of simple initial solutions. In particular, it is shown that any DB orbit of a sf cKPr,1 defines a generalized 2dimensional Toda lattice structure. Furthermore, we consider the class of truncated sf KP hierarchies sl i.e., those defined via WilsonSato dressing operator with a finite truncated pseudodifferential series and establish explicitly their close relationship with DB orbits of cKPrm hierarchies. This construction is relevant for finding partition functions of the discrete multimatrix models. The next important step involves the reformulation of the familiar nonisospectral additional symmetries of the full sf KP hierarchy so that their action on cKPrm hierarchies becomes consistent with the constraints of the reduction. Moreover, we show that the correct modified additional symmetries are compatible with the discrete DB symmetry on the cKPrm DB orbits. The above technical arsenal is subsequently applied to obtain complete

Hidden Algebras of the super Calogero and Sutherland models ; We propose to parametrize the configuration space of onedimensional quantum systems of N identical particles by the elementary symmetric polynomials of bosonic and fermionic coordinates. It is shown that in this parametrization the Hamiltonians of the AN, BCN, BN, CN and DN Calogero and Sutherland models, as well as their supersymmetric generalizations, can be expressed for arbitrary values of the coupling constants as quadratic polynomials in the generators of a Borel subalgebra of the Lie algebra glN1 or the Lie superalgebra glN1N for the supersymmetric case. These algebras are realized by first order differential operators. This fact establishes the exact solvability of the models according to the general definition given by one of the authors in 1994, and implies that the Calogero and JackSutherland polynomials, as well as their supersymmetric generalizations, are related to finitedimensional irreducible representations of the Lie algebra glN1 and the Lie superalgebra glN1N.

Trace and chiral anomalies in string and ordinary field theory from Feynman diagrams for nonlinear sigma models ; We write general oneloop anomalies of string field theory as path integrals on a torus for the corresponding nonlinear sigma model. This extends the work of AlvarezGaum'e and Witten from quantum mechanics to two dimensions. Higher worldvolume loops contribute in general to nontopological anomalies and a formalism to compute these is developed. We claim that i for general anomalies one should not use the propagator widely used in string theory but rather the one obtained by generalization from quantum mechanics, but ii for chiral anomalies both propagators give the same result. As a check of this claim in a simpler model we compute trace anomalies in quantum mechanics. The propagator with a centerofmass zero mode indeed does not give the correct result for the trace anomaly while the propagator for fluctuations qi tau satisfying qi tau 1 qi tau 0 0 yields in d2 and d4 dimensions the correct results from two and threeloop graphs. We then return to heterotic string theory and calculate the contributions to the anomaly from the different spin structures for d2. We obtain agreement with the work of Pilch, Schellekens and Warner and that of Li in the sector with spacetime fermions. In the other sectors, where no explicit computations have been performed in the past and for which one needs higher loops, we find a genuine divergence, whose interpretation is unclear to us. We discuss whether or not this leads to a new anomaly.

Stability of sixdimensional hyperstring braneworlds ; We study a sixdimensional braneworld model with infinite warped extra dimensions in the case where the fourdimensional brane is described by a topological vortex of a U1 symmetrybreaking Abelian Higgs model in presence of a negative cosmological constant. A detailed analysis of the microscopic parameters leading to a finite volume spacetime in the extra dimensions is numerically performed. As previously shown, we find that a finetuning is required to avoid any kind of singularity on the brane. We then discuss the stability of the vortex by investigating the scalar part of the gaugeinvariant perturbations around this finetuned configuration. It is found that the hyperstring forming Higgs and gauge fields, as well as the background metric warp factors, cannot be perturbed at all, whereas transverse modes can be considered stable. The warped spacetime structure that is imposed around the vortex thus appears severely constrained and cannot generically support nonempty universe models. The genericness of our conclusions is discussed; this will shed some light on the possibility of describing our spacetime as a general sixdimensional warped braneworld.

Topological strings on noncommutative manifolds ; We identify a deformation of the N2 supersymmetric sigma model on a CalabiYau manifold X which has the same effect on Bbranes as a noncommutative deformation of X. We show that for hyperkahler X such deformations allow one to interpolate continuously between the Amodel and the Bmodel. For generic values of the noncommutativity and the Bfield, properties of the topologically twisted sigmamodels can be described in terms of generalized complex structures introduced by N. Hitchin. For example, we show that the path integral for the deformed sigmamodel is localized on generalized holomorphic maps, whereas for the Amodel and the Bmodel it is localized on holomorphic and constant maps, respectively. The geometry of topological Dbranes is also best described using generalized complex structures. We also derive a constraint on the Chern character of topological Dbranes, which includes Abranes and Bbranes as special cases.

Spontaneous Lorentz Violation, NambuGoldstone Modes, and Gravity ; The fate of the NambuGoldstone modes arising from spontaneous Lorentz violation is investigated. Using the vierbein formalism, it is shown that up to 10 Lorentz and diffeomorphism NambuGoldstone modes can appear and that they are contained within the 10 modes of the vierbein associated with gauge degrees of freedom in a Lorentzinvariant theory. A general treatment of spontaneous local Lorentz and diffeomorphism violation is given for various spacetimes, and the fate of the NambuGoldstone modes is shown to depend on both the spacetime geometry and the dynamics of the tensor field triggering the spontaneous Lorentz violation. The results are illustrated within the general class of bumblebee models involving vacuum values for a vector field. In Minkowski and Riemann spacetimes, the bumblebee model provides a dynamical theory generating a photon as a NambuGoldstone boson for spontaneous Lorentz violation. The Maxwell and EinsteinMaxwell actions are automatically recovered in axial gauge. Associated effects of potential experimental relevance include Lorentzviolating couplings in the matter and gravitational sectors of the StandardModel Extension and unconventional Lorentzinvariant couplings. In RiemannCartan spacetime, the possibility also exists of a Higgs mechanism for the spin connection, leading to the absorption of the propagating NambuGoldstone modes into the torsion component of the gravitational field.

Gaudin's model and the generating function of the Wronski map ; We consider the Gaudin model associated to a point z in Cn with pairwise distinct coordinates and to the subspace of singular vectors of a given weight in the tensor product of irreducible finitedimensional sl2representations, G. The Bethe equations of this model provide the critical point system of a remarkable rational symmetric function. Any critical orbit determines a common eigenvector of the Gaudin hamiltonians called a Bethe vector. In ReV, it was shown that for generic z the Bethe vectors span the space of singular vectors, i.e. that the number of critical orbits is bounded from below by the dimension of the space of singular vectors. The upper bound by the same number is one of the main results of SV. In the present paper we get this upper bound in another, less technical'', way. The crucial observation is that the symmetric function defining the Bethe equations can be interpreted as the generating function of the map sending a pair of complex polynomials into their Wronski determinant the critical orbits determine the preimage of a given polynomial under this map. Within the framework of the Schubert calculus, the number of critical orbits can be estimated by the intersection number of special Schubert classes. Relations to the sl2 representation theory F imply that this number is the dimension of the space of singular vectors. We prove also that the spectrum of the Gaudin hamiltonians is simple for generic z.

Homogeneous spaces and FaddeevSkyrme models ; We study geometric variational problems for a class of effective models in quantum field theory known as FaddeevSkyrme models. Mathematically one considers minimizing an energy functional on homotopy classes of maps from closed 3manifolds into homogeneous spaces of compact Lie groups. The energy minimizers known as Hopfions describe stable configurations of subatomic particles such as protons and their strong interactions. In particular, we introduce novel Sobolev spaces suitable for our variational problem and develop the notion of homotopy type for maps in such spaces that generalizes homotopy for smooth and continuous maps. This notion is based on defining a generalized Hopf invariant for Sobolev maps into homogeneous spaces that was previously known only for maps into S2. Since the spaces in question are neither linear nor even convex we represent maps by gauge potentials that form a linear space and reformulate the problem in terms of these potentials. However, this representation of maps introduces some gauge ambiguity into the picture and we work out 'gauge calculus' for the principal bundles involved to apply the gaugefixing techniques that eliminate the ambiguity. These bundles arise as pullbacks of the structure bundles Hhra Gto GH of homogeneous spaces and we study their topology and geometry that are of independent interest. Our main results include proving existence of Hopfions as finite energy Sobolev maps in each generalized homotopy class when the target space is a symmetric space. For more general spaces we obtain a weaker result on existence of minimizers only in each 2homotopy class.

Quantum fluctations of coherent light in nonlinear media ; The interaction of coherent light with a nonlinear medium is modeled here by a general quantum anharmonic oscillator. The model is not exactly solvable in a closed analytical form. But we need operator solutions of the equations of motion corresponding to these models in order to study the quantum fluctuations of coherent light in nonlinear media. In the present work we derive approximate operator solutions. From these solutions we observe that there exists an apparent discrepancy between the solutions obtained by different techniques. We compare different solutions and conclude that all correct solutions are equivalent and the apparent discrepancy is due to the use of different ordering of the operators. We use these solutions to investigate the possibilities of observing different optical phenomena in a nonlinear dielectric medium. To be precise, we have studied quantum phase fluctuations of coherent light in a third order inversion symmetric nonlinear medium. Fluctuations in phase space quadrature for the same system are studied and the possibility of generating squeezed state is reported. Fluctuations in photon number are studied and the nonclassical phenomenon of antibunching is predicted. We have generalized the results obtained for third order nonlinear medium and have studied the interaction of an intense laser beam with a general m1th order nonlinear medium. Aharanov Anandan nonadiabatic geometric phase is also discussed in the context of m1th order nonlinear medium.

Quantum Analogical Modeling A General Quantum Computing Algorithm for Predicting Language Behavior ; This paper proposes a general quantum algorithm that can be applied to any classical computer program. Each computational step is written using reversible operators, but the operators remain classical in that the qubits take on values of only zero and one. This classical restriction on the quantum states allows the copying of qubits, a necessary requirement for doing general classical computation. Parallel processing of the quantum algorithm proceeds because of the superpositioning of qubits, the only aspect of the algorithm that is strictly quantum mechanical. Measurement of the system collapses the superposition, leaving only one state that can be observed. In most instances, the loss of information as a result of measurement would be unacceptable. But the linguistically motivated theory of Analogical Modeling AM proposes that the probabilistic nature of language behavior can be accurately modeled in terms of the simultaneous analysis of all possible contexts referred to as supracontexts providing one selects a single supracontext from those supracontexts that are homogeneous in behavior namely, supracontexts that allow no increase in uncertainty. The amplitude for each homogeneous supracontext is proportional to its frequency of occurrence, with the result that the probability of selecting one particular supracontext to predict the behavior of the system is proportional to the square of its frequency.

Dynamical nonaxisymmetric instabilities in rotating relativistic stars ; We present new results on dynamical instabilities in rapidly rotating neutronstars. In particular, using numerical simulations in full General Relativity, we analyse the effects that the stellar compactness has on the threshold for the onset of the dynamical barmode instability, as well as on the appearance of other dynamical instabilities. By using an extrapolation technique developed and tested in our previous study 1, we explicitly determine the threshold for a wide range of compactnesses using four sequences of models of constant baryonic mass comprising a total of 59 stellar models. Our calculation of the threshold is in good agreement with the Newtonian prediction and improves the previous postNewtonian estimates. In addition, we find that for stars with sufficiently large mass and compactness, the m3 deformation is the fastest growing one. For all of the models considered, the nonaxisymmetric instability is suppressed on a dynamical timescale with an m1 deformation dominating the final stages of the instability. These results, together with those presented in 1, suggest that an m1 deformation represents a general and latetime feature of nonaxisymmetric dynamical instabilities both in full General Relativity and in Newtonian gravity.

New multivariate central limit theorems in linear structural and functional errorinvariables models ; This paper deals simultaneously with linear structural and functional errorinvariables models SEIVM and FEIVM, revisiting in this context generalized and modified least squares estimators of the slope and intercept, and some methods of moments estimators of unknown variances of the measurement errors. New joint central limit theorems CLT's are established for these estimators in the SEIVM and FEIVM under some first time, so far the most general, respective conditions on the explanatory variables, and under the existence of four moments of the measurement errors. Moreover, due to them being in Studentized forms to begin with, the obtained CLT's are a priori nearly, or completely, databased, and free of unknown parameters of the distribution of the errors and any parameters associated with the explanatory variables. In contrast, in related CLT's in the literature so far, the covariance matrices of the limiting normal distributions are, in general, complicated and depend on various, typically unknown parameters that are hard to estimate. In addition, the very forms of the CLT's in the present paper are universal for the SEIVM and FEIVM. This extends a previously known interplay between a SEIVM and a FEIVM. Moreover, though the particular methods and details of the proofs of the CLT's in the SEIVM and FEIVM that are established in this paper are quite different, a unified general scheme of these proofs is constructed for the two models herewith.

Type I NonAbelian Superconductors in Supersymmetric Gauge Theories ; NonBPS nonAbelian vortices with CP1 internal moduli space are studied in an N2 supersymmetric U1 x SU2 gauge theory with softly breaking adjoint mass terms. For generic internal orientations the classical force between two vortices can be attractive or repulsive. On the other hand, the mass of the scalars in the theory is always less than that of the vector bosons; also, the force between two vortices with the same CP1 orientation is always attractive for these reasons we interpret our model as a nonAbelian generalization of type I superconductors. We compute the effective potential in the limit of two well separated vortices. It is a function of the distance and of the relative colourflavour orientation of the two vortices; in this limit we find an effective description in terms of two interacting CP1 sigma models. In the limit of two coincident vortices we find two different solutions with the same topological winding and, for generic values of the parameters, different tensions. One of the two solutions is described by a CP1 effective sigma model, while the other is just an Abelian vortex without internal degrees of freedom. For generic values of the parameters, one of the two solutions is metastable, while there are evidences that the other one is truly stable.

Transverse coherence properties of Xray beams in thirdgeneration synchrotron radiation sources ; This article describes a complete theory of spatial coherence for undulator radiation sources. Current estimations of coherence properties often assume that undulator sources are quasihomogeneous, like thermal sources, and rely on the application of the van CittertZernike theorem for calculating the degree of transverse coherence. Such assumption is not adequate when treating third generation light sources, because the verticalgeometrical emittance of the electron beam is comparable or even much smaller than the radiation wavelength in a very wide spectral interval that spans over four orders of magnitude from 0.1 Angstrom up to 103 Angstrom. Sometimes, the socalled GaussianSchell model, that is widely used in statistical optics in the description of partiallycoherent sources, is applied as an alternative to the quasihomogeneous model. However, as we will demonstrate, this model fails to properly describe coherent properties of Xray beams from nonhomogeneous undulator sources. As a result, a more rigorous analysis is required. We propose a technique, based on statistical optics and Fourier optics, to explicitly calculate the crossspectral density of an undulator source in the most general case, at any position after the undulator. Our theory, that makes consistent use of dimensionless analysis, allows relatively easy treatment and physical understanding of many asymptotes of the parameter space, together with their region of applicability. Particular emphasis is given to the asymptotic situation when the horizontal emittance is much larger than the radiation wavelength, and the vertical emittance is arbitrary. This case is practically relevant for third generation synchrotron radiation sources.

The adjusted Viterbi training for hidden Markov models ; The EM procedure is a principal tool for parameter estimation in the hidden Markov models. However, applications replace EM by Viterbi extraction, or training VT. VT is computationally less intensive, more stable and has more of an intuitive appeal, but VT estimation is biased and does not satisfy the following fixed point property. Hypothetically, given an infinitely large sample and initialized to the true parameters, VT will generally move away from the initial values. We propose adjusted Viterbi training VA, a new method to restore the fixed point property and thus alleviate the overall imprecision of the VT estimators, while preserving the computational advantages of the baseline VT algorithm. Simulations elsewhere have shown that VA appreciably improves the precision of estimation in both the special case of mixture models and more general HMMs. However, being entirely analytic, the VA correction relies on infinite Viterbi alignments and associated limiting probability distributions. While explicit in the mixture case, the existence of these limiting measures is not obvious for more general HMMs. This paper proves that under certain mild conditions, the required limiting distributions for general HMMs do exist.

Hotspot model for accretion disc variability as random process ; Theory of random processes provides an attractive mathematical tool to describe the fluctuating signal from accreting sources, such as active galactic nuclei and Galactic black holes observed in Xrays. These objects exhibit featureless variability on different timescales, probably originating from an accretion disc. We study the basic features of the power spectra in terms of a general framework, which permits semianalytical determination of the power spectral density PSD of the resulting light curve. We consider the expected signal generated by an ensemble of spots randomly created on the accretion disc surface. Spot generation is governed by Poisson or by Hawkes processes. We include general relativity effects shaping the signal on its propagation to a distant observer. We analyse the PSD of a spotted disc light curve and show the accuracy of our semianalytical approach by comparing the obtained PSD with the results of Monte Carlo simulations. The asymptotic slopes of PSD are 0 at low frequencies and they drop to 2 at high frequencies, usually with a single frequency break. More complex twopeak solutions also occur. The amplitude of the peaks and their frequency difference depend on the inherent timescales of the model. At intermediate frequencies, the intrinsic PSD is influenced by the individual light curve profile as well as by the type of the underlying process. However, even in cases when two Lorentzians seem to dominate the PSD, it does not necessarily imply that two single oscillation mechanisms operate simultaneously. Instead, it may well be the manifestation of the avalanche mechanism. The main advantage of our approach is an insight in the model functioning and the fast evaluation of the PSD.

Secular dynamics of coplanar, nonresonant planetary system under the general relativity and quadrupole moment perturbations ; We construct a secular theory of a coplanar system of Nplanets not involved in strong mean motion resonances, and which are far from collision zones. Besides the pointtopoint Newtonian mutual interactions, we consider the general relativity corrections to the gravitational potential of the star and the innermost planet, and also a modification of this potential by the quadrupole moment and tidal distortion of the star. We focus on hierarchical planetary systems. A survey regarding model parameters the masses, semimajor axes, spin rate of the star reveals a rich and nontrivial dynamics of the secular system. Our study is focused on its equilibria. Such solutions predicted by the classic secular theory, which correspond to aligned mode I or antialigned mode II apsides, may be strongly affected by the gravitational corrections. The so called true secular resonance, which is a new feature of the classic twoplanet problem discovered by Michtchenko Malhotra 2004, may appear in other, different regions of the phase space of the generalized model. We found bifurcations of mode II which emerge new, yet unknown in the literature, secularly unstable equilibria and a complex structure of the phase space. These equilibria may imply secularly unstable orbital configurations even for nitially moderate eccentricities. The point mass gravity corrections can affect the long termstability in the secular time scale, which may directly depend on the age of the host star through its spin rate. We also analyze the secular dynamics of the upsilon Andromede system in the realm of the generalized model. Also in this case of the threeplanet system, new secular equilibria may appear.

MultiField Inflation on the Landscape ; We examine a wide class of multifield inflationary models based on fields that decay or stabilize during inflation in a staggered fashion. The fields driving assisted inflation are on flat, short stretches, before they encounter a sharp drop; whenever a field encounters such a drop due to its slow roll evolution, its energy is transferred to other degrees of freedom, i.e. radiation. The rate at which fields decay is determined dynamically and it is not a free parameter in this class of models. To compute observables, we generalize the analytic framework of staggered inflation, allowing for more general initial conditions and varying potentials. By searching for generic situations arising on the landscape, we arrive at a setup involving linear or hilltop potentials and evenly spread out initial field values. This scenario is not more fine tuned than largefield models, despite the fact that many more degrees of freedom are involved. Further, the etaproblem can be alleviated. The additional decrease of the potential energy caused by the decay of fields provides leading order contribution to observables, such as the scalar and tensor spectral index or the tensor to scalar ratio, for which we derive general expressions. We compare the predictions with WMAP5 constraints and find that hilltop potentials are borderline ruled out at the 2sigmalevel, while linear potentials are in excellent agreement with observations. We further comment on additional sources of gravitational waves and nonGaussianities that could serve as a smoking gun for staggered inflation.

On the Non Perturbative Origin of Quark Masses in Dbrane GUT Models ; We examine the issue of generating the perturbatively absent bf 10 cdot bf 10 cdot bf 5H SU5flipped SU5Yukawa couplings in type II Dbrane orientifold compactifications of string theory both at the perturbative PER and the nonperturbative NP level. We find at the PER level, higher order terms like bf 10 cdot bf 10 cdot bfbar 5H cdotbfbar 5H cdot bfbar 5H cdot bfbar 5H cdot bf 1H cdot bf 1H in SU5 may be responsible for the relevant quark mass generation in models with general intersecting D6branes. Euclidean D2brane instantons on the other hand can also generate at the NP via the term bf 10 cdot bf 10 cdot bfbar 5H cdotbfbar 5H cdot bfbar 5H cdot bfbar 5H the relevant quark masses by the use of just the U1b brane, for SU5 and flipped SU5 GUTS classes of models. We provide local examples of rigid O1 instantons within the T6mathbb Z2 times mathbb Z2' toroidal orientifold with torsion, whose NP contribution to the masses gets minimal as it is induced by just a duplicated disk diagram.

Dynamics of the bacterial flagellar motor with multiple stators ; The bacterial flagellar motor drives the rotation of flagellar filaments and enables many species of bacteria to swim. Torque is generated by interaction of stator units, anchored to the peptidoglycan cell wall, with the rotor. Recent experiments Yuan, J. Berg, H. C. 2008 PNAS 105, 11821185 show that near zero load the speed of the motor is independent of the number of stators. Here, we introduce a mathematical model of the motor dynamics that explains this behavior based on a general assumption that the stepping rate of a stator depends on the torque exerted by the stator on the rotor. We find that the motor dynamics can be characterized by two time scales the movingtime interval for the mechanical rotation of the rotor and the waitingtime interval determined by the chemical transitions of the stators. We show that these two time scales depend differently on the load, and that their crossover provides the microscopic explanation for the existence of two regimes in the torquespeed curves observed experimentally. We also analyze the speed fluctuation for a single motor using our model. We show that the motion is smoothed by having more stator units. However, the mechanism for such fluctuation reduction is different depending on the load. We predict that the speed fluctuation is determined by the number of steps per revolution only at low load and is controlled by external noise for high load. Our model can be generalized to study other molecular motor systems with multiple powergenerating units.

Identifying MultiTop Events from Gluino Decay at the LHC ; We study the LHC signal of a light gluino whose cascade decay is dominated by channels involving top, and, sometimes, bottom quarks. This is a generic signature for a number of supersymmetry breaking scenarios considered recently, where the squarks are heavier than gauginos. Third generation final states generically dominate since third generation squarks are typically somewhat lighter in these models. At the LHC we demonstrate that early discovery is possible due to the existence of multilepton multibottom final states which have fairly low Standard Model background. We find that the best discovery channel is 'same sign dilepton'. The relative decay branching ratios into tt, tb and bb states carry important information about the underlying model. Although reconstruction will yield evidence for the existence of top quarks in the event, we demonstrate that identifying multiple top quarks suffers from low efficiency and large combinatorial background, due to the large number of final state particles. We propose a fitting method which takes advantage of excesses in a large number of channels. We demonstrate such a method will allow us to extract information about decay branching ratios with moderate integrated luminosities. In addition, the method also gives an upper bound on the gluino production cross section and an estimate of the gluino mass.

Fermion flavor mixing in models with dynamical mass generation ; We present a modelindependent method of dealing with fermion flavor mixing in the case when instead of constant, momentumindependent mass matrices one has rather momentumdependent selfenergies. This situation is typical for strongly coupled models of dynamical fermion mass generation. We demonstrate our approach on the example of quark mixing. We show that quark selfenergies with a generic momentum dependence lead to an effective CabibboKobayashiMaskawa CKM matrix, which turns out to be in general nonunitary, in accordance with previous claims of other authors, and to nontrivial flavor changing electromagnetic and neutral currents. We also discuss some conceptual consequences of the momentumdependent selfenergies and show that in such a case the interaction basis and the mass basis are not related by a unitary transformation. In fact, we argue that the latter is merely an effective concept, in a specified sense. While focusing mainly on the fermionic selfenergies, we also study the effects of momentumdependent radiative corrections to the gauge bosons and to the proper vertices. Our approach is based on an application of the LehmannSymanzikZimmermann LSZ reduction formula and for the special case of constant selfenergies it gives the same results as the standard approach based on the diagonalization of mass matrices.

Rotation and helicity as dynamo generators in idealized plasma cosmologies ; Recently Kleides et al IJMPA textbf11, 1697 2008 found a growing rate for magnetic fields in ideal plasma cosmologies by making use of general relativistic Friedmann model. This growth rate of fracdeltaBBsimfracttH14 indicates the presence of a slow dynamo in the universe. More recently Hasseein Phys Plasmas 2009 have also investigate Beltrami magnetic fields in plasma universe. Here general relativisticGR MHD dynamo equation, recently given by Clarkson and Marklund Monthly Not Roy Astr Soc 2005 is used to investigate the relation between collapsing of the isotropic universe and dynamo action in ideal and dissipative cosmologies. Dynamo action can be supported in these phases as long as the kinetic helicity overcomes universe diffusion effects. A cosmological Beltrami flow in 3D shows that helicities may act constructively on gravitational collapse and enhance dynamo action. A slow dynamo action is found in the static Einstein universe also filled with a Beltrami flow. A rotating, shearfree Bianchi typeIX universe, is obtained, by magnetically perturbing the Einstein static model inducing slow dynamos in the model. Magnetic field growth of Bapproxt, which is stronger than Harrison estimate of Bapproxt45 is obtained. CMB limits on the expansion, global rotation and slow dynamos are given and a less slower dynamo than the one obtained by Kleides et al, is found with fracdeltaBBsimThetat.

Optimal reinsuranceinvestment problems for general insurance models ; In this paper the utility optimization problem for a general insurance model is studied. The reserve process of the insurance company is described by a stochastic differential equation driven by a Brownian motion and a Poisson random measure, representing the randomness from the financial market and the insurance claims, respectively. The random safety loading and stochastic interest rates are allowed in the model so that the reserve process is nonMarkovian in general. The insurance company can manage the reserves through both portfolios of the investment and a reinsurance policy to optimize a certain utility function, defined in a generic way. The main feature of the problem lies in the intrinsic constraint on the part of reinsurance policy, which is only proportional to the claimsize instead of the current level of reserve, and hence it is quite different from the optimal investmentconsumption problem with constraints in finance. Necessary and sufficient conditions for both well posedness and solvability will be given by modifying the duality method'' in finance and with the help of the solvability of a special type of backward stochastic differential equations.

Quench dynamics near a quantum critical point application to the sineGordon model ; We discuss the quench dynamics near a quantum critical point focusing on the sineGordon model as a primary example. We suggest a unified approach to sudden and slow quenches, where the tuning parameter lambdat changes in time as lambdatsim upsilon tr, based on the adiabatic expansion of the excitation probability in powers of upsilon. We show that the universal scaling of the excitation probability can be understood through the singularity of the generalized adiabatic susceptibility chi2r2lambda, which for sudden quenches r0 reduces to the fidelity susceptibility. In turn this class of susceptibilities is expressed through the moments of the connected correlation function of the quench operator. We analyze the excitations created after a sudden quench of the cosine potential using a combined approach of formfactors expansion and conformal perturbation theory for the lowenergy and highenergy sector respectively. We find the general scaling laws for the probability of exciting the system, the density of excited quasiparticles, the entropy and the heat generated after the quench. In the two limits where the sineGordon model maps to hard core bosons and free massive fermions we provide the exact solutions for the quench dynamics and discuss the finite temperature generalizations.

A ThreeGeneration CalabiYau Manifold with Small Hodge Numbers ; We present a complete intersection CalabiYau manifold Y that has Euler number 72 and which admits free actions by two groups of automorphisms of order 12. These are the cyclic group Z12 and the nonAbelian dicyclic group Dic3. The quotient manifolds have chi6 and Hodge numbers h11,h211,4. With the standard embedding of the spin connection in the gauge group, Y gives rise to an E6 gauge theory with 3 chiral generations of particles. The gauge group may be broken further by means of the Hosotani mechanism combined with continuous deformation of the background gauge field. For the nonAbelian quotient we obtain a model with 3 generations with the gauge group broken to that of the standard model. Moreover there is a limit in which the quotients develop 3 conifold points. These singularities may be resolved simultaneously to give another manifold with h11,h212,2 that lies right at the tip of the distribution of CalabiYau manifolds. This strongly suggests that there is a heterotic vacuum for this manifold that derives from the 3 generation model on the quotient of Y. The manifold Y may also be realised as a hypersurface in the toric variety. The symmetry group does not act torically, nevertheless we are able to identify the mirror of the quotient manifold by adapting the construction of Batyrev.

Merger of white dwarfneutron star binaries Prelude to hydrodynamic simulations in general relativity ; White dwarfneutron star binaries generate detectable gravitational radiation. We construct Newtonian equilibrium models of corotational white dwarfneutron star WDNS binaries in circular orbit and find that these models terminate at the Roche limit. At this point the binary will undergo either stable mass transfer SMT and evolve on a secular time scale, or unstable mass transfer UMT, which results in the tidal disruption of the WD. The path a given binary will follow depends primarily on its mass ratio. We analyze the fate of known WDNS binaries and use population synthesis results to estimate the number of LISAresolved galactic binaries that will undergo either SMT or UMT. We model the quasistationary SMT epoch by solving a set of simple ordinary differential equations and compute the corresponding gravitational waveforms. Finally, we discuss in general terms the possible fate of binaries that undergo UMT and construct approximate Newtonian equilibrium configurations of merged WDNS remnants. We use these configurations to assess plausible outcomes of our future, fully relativistic simulations of these systems. If sufficient WD debris lands on the NS, the remnant may collapse, whereby the gravitational waves from the inspiral, merger, and collapse phases will sweep from LISA through LIGO frequency bands. If the debris forms a disk about the NS, it may fragment and form planets.

Constraints on Perturbative fR Gravity via Neutron Stars ; We study the structure of neutron stars in perturbative fR gravity models with realistic equations of state. We obtain massradius relations in a gravity model of the form fRRalpha R2. We find that deviations from the results of general relativity, comparable to the variations due to using different equations of state EoS', are induced for alpha 109 cm2. Some of the soft EoS' that are excluded within the framework of general relativity can be reconciled with the 2 solar mass neutron star recently observed for certain values of alpha within this range. For some of the EoS' we find that a new solution branch, which allows highly massive neutron stars, exists for values of alpha greater than a few 109 cm2. We find constraints on alpha for a variety of EoS' using the recent observational constraints on the massradius relation. These are all 5 orders of magnitude smaller than the recent constraint obtained via Gravity Probe B for this gravity model. The associated length scale sqrtalpha 105 cm is only an order of magnitude smaller than the typical radius of a neutron star, the probe used in this test. This implies that real deviations from general relativity can be even smaller.

Effective Supersymmetry at the LHC ; We investigate the phenomenology of Effective Supersymmetry ESUSY models wherein electroweak gauginos and third generation scalars have masses up to about 1TeV while first and second generation scalars lie in the multiTeV range. Such models ameliorate the SUSY flavor and CP problems via a decoupling solution, while at the same time maintaining naturalness. In our analysis, we assume independent GUT scale mass parameters for third and firstsecond generation scalars and for the Higgs scalars, in addition to m12, tanbeta and A0, and require radiative electroweak symmetry breaking as usual. We analyse the parameter space which is consistent with current constraints, by means of a Markov Chain Monte Carlo scan. The lightest MSSM particle LMP is mostly, but not always the lightest neutralino, and moreover, the thermal relic density of the neutralino LMP is frequently very large. These models may phenomenologically be perfectly viable if the LMP before nucleosynthesis decays into the axino plus SM particles. Dark matter is then an axionaxino mixture. At the LHC, the most important production mechanisms are gluino production for m12 700GeV and third generation squark production, while SUSY events rich in bjets are the hallmark of the ESUSY scenario. We present a set of ESUSY benchmark points with characteristic features and discuss their LHC phenomenology.

Fermion masses and mixing in a 41dimensional SU5 domainwall brane model ; We study the fermion mass and mixing hierarchy problems within the context of the SU5 41d domainwall brane model of Davies, George and Volkas. In this model, the ordinary fermion mass relations of SU5 grand unified theories are avoided since the masses are proportional to overlap integrals of the profiles of the electroweak Higgs and the chiral components of each fermion, which are split into different 31d hyperplanes according to their hypercharges. We show that the fermion mass hierarchy without electroweak mixing can be generated naturally from these splittings, that generation of the CKM matrix looks promising, and that the Cabibbo angle along with the mass hierarchy can be generated for the case of Majorana neutrinos from a more modest hierarchy of parameters. We also show that under some assumptions made on the parameter space, the generation of realistic lepton mixing angles is not possible without finetuning, which argues for a flavour symmetry to enforce the required relations.

Affine generalizations of gravity in the light of modern cosmology ; We discuss new models of an affine' theory of gravity in multidimensional spacetimes with symmetric connections. We use and develop ideas of Weyl, Eddington, and Einstein, in particular, Einstein's proposal to specify the space time geometry by use of the Hamilton principle. More specifically, the connection coefficients are determined using a geometric' Lagrangian that is an arbitrary function of the generalized nonsymmetric Ricci curvature tensor and, possibly, of other fundamental tensors expressed in terms of the connection coefficients regarded as independent variables. Such a theory supplements the standard Einstein gravity with dark energy the cosmological constant, in the first approximation, a neutral massive or tachyonic vector field vecton, and massive or tachyonic scalar fields. These fields couple only to gravity and can generate dark matter andor inflation. The new field masses real or imaginary have a geometric origin and must appear in any concrete model. The concrete choice of the geometric Lagrangian determines further details of the theory, for example, the nature of the vector and scalar fields that can describe massive particles, tachyons, or even phantoms'. In natural' geometric theories, which are discussed here, dark energy must also arise. We mainly focus on intricate relations between geometry and dynamics while only very briefly considering approximate cosmological models inspired by the geometric approach.

Primordial nonGaussianities in general modified gravitational models of inflation ; We compute the threepoint correlation function of primordial scalar density perturbations in a general singlefield inflationary scenario, where a scalar field phi has a direct coupling with the Ricci scalar R and the GaussBonnet term GB. Our analysis also covers the models in which the Lagrangian includes a function nonlinear in the field kinetic energy Xnabla phi22, and a Galileontype field selfinteraction Gphi, XBox phi, where G is a function of phi and X. We provide a general analytic formula for the equilateral nonGaussianity parameter fNLequil associated with the bispectrum of curvature perturbations. A quasi de Sitter approximation in terms of slowvariation parameters allows us to derive a simplified form of fNLequil convenient to constrain various inflation models observationally. If the propagation speed of the scalar perturbations is much smaller than the speed of light, the GaussBonnet term as well as the Galileontype field selfinteraction can give rise to large nonGaussianities testable in future observations. We also show that, in BransDicke theory with a field potential including fR gravity, fNLequil is of the order of slowroll parameters as in standard inflation driven by a minimally coupled scalar field.

NonGaussianity of scalar perturbations generated by conformal mechanisms ; We consider theories which explain the flatness of the power spectrum of scalar perturbations in the Universe by conformal invariance, such as conformal rolling model and Galilean Genesis. We show that to the leading it nonlinear order, perturbations in all models from this class behave in one and the same way, at least if the energy density of the relevant fields is small compared to the total energy density spectator approximation. We then turn to the intrinsic nonGaussianities in these models as opposed to nonGaussianities that may be generated during subsequent evolution. The intrinsic bispectrum vanishes, so we perform the complete calculation of the trispectrum and compare it with the trispecta of local forms in various limits. The most peculiar feature of our trispectrum is a fairly mild singularity in the limit where two momenta are equal in absolute value and opposite in direction folded limit. Generically, the intrinsic nonGaussianity can be of detectable size.

The kSZ effect as a test of general radial inhomogeneity in LTB cosmology ; The apparent accelerating expansion of the Universe, determined from observations of distant supernovae, and often taken to imply the existence of dark energy, may alternatively be explained by the effects of a giant underdense void if we relax the assumption of homogeneity on large scales. Recent studies have made use of the sphericallysymmetric, radiallyinhomogeneous LemaitreTolmanBondi LTB models to derive strong constraints on this scenario, particularly from observations of the kinematic SunyaevZel'dovich kSZ effect which is sensitive to large scale inhomogeneity. However, most of these previous studies explicitly set the LTB 'bang time' function to be constant, neglecting an important freedom of the general solutions. Here we examine these models in full generality by relaxing this assumption. We find that although the extra freedom allowed by varying the bang time is sufficient to account for some observables individually, it is not enough to simultaneously explain the supernovae observations, the smallangle CMB, the local Hubble rate, and the kSZ effect. This set of observables is strongly constraining, and effectively rules out simple LTB models as an explanation of dark energy.

Relativistic collapse and explosion of rotating supermassive stars with thermonuclear effects ; We present results of general relativistic simulations of collapsing supermassive stars with and without rotation using the twodimensional general relativistic numerical code Nada, which solves the Einstein equations written in the BSSN formalism and the general relativistic hydrodynamics equations with high resolution shock capturing schemes. These numerical simulations use an equation of state which includes effects of gas pressure, and in a tabulated form those associated with radiation and the electronpositron pairs. We also take into account the effect of thermonuclear energy released by hydrogen and helium burning. We find that objects with a mass of 5x105 solar mass and an initial metallicity greater than ZCNO0.007 do explode if nonrotating, while the threshold metallicity for an explosion is reduced to ZCNO0.001 for objects uniformly rotating. The critical initial metallicity for a thermonuclear explosion increases for stars with mass 106 solar mass. For those stars that do not explode we follow the evolution beyond the phase of black hole formation. We compute the neutrino energy loss rates due to several processes that may be relevant during the gravitational collapse of these objects. The peak luminosities of neutrinos and antineutrinos of all flavors for models collapsing to a BH are 1055 ergs. The total radiated energy in neutrinos varies between 1056 ergs for models collapsing to a BH, and 10451046 ergs for models exploding.

Can quantum lattice be generated through several classical ones superimposed in spacetime continuum ; This paper has few different, but interrelated, goals. At first, we will propose a version of discretization of quantum field theory Chapter 3. We will write down Lagrangians for sample bosonic fields Section 3.1 and also attempt to generalize them to fermionic QFT Section 3.2. At the same time, we will insist that the elements of our discrete space are embedded into a continuum. This will allow us to embed several different lattices into the same continuum and view them as separate quantum field configurations. Classical parameters will be used in order to specify which lattice each given element belongs to. Furthermore, another set of classical parameters will be proposed in order to define socalled probability amplitude of each field configuration, embodied by a corresponding lattice, taking place Chapter 2. Apart from that, we will propose a set of classical signals that propagate throughout continuum, and define their dynamics in such a way that they produce the mathematical information consistent with the desired quantum effects within the lattices we are concerned about Chapter 4. Finally, we will take advantage of the lack of true quantum mechanics, and add gravity in such a way that avoids the issue of its quantization altogether Chapter 5. In the process of doing so, we will propose a gravitybased collapse model of a wave function. In particular, we will claim that the collapse of a wave function is merely a result of states that violate Einstein's equation being thrown away. The mathematical structure of this model in particular, the appeal to gambler's ruin will be similar to GRW collapse models.

A unified formulation of Gaussian vs. sparse stochastic processes Part II Discretedomain theory ; This paper is devoted to the characterization of an extended family of CARMA continuoustime autoregressive moving average processes that are solutions of stochastic differential equations driven by white Levy innovations. These are completely specified by 1 a set of poles and zeros that fixes their correlation structure, and 2 a canonical infinitelydivisible probability distribution that controls their degree of sparsity with the Gaussian model corresponding to the least sparse scenario. The generalized CARMA processes are either stationary or nonstationary, depending on the location of the poles in the complex plane. The most basic nonstationary representatives with a single pole at the origin are the Levy processes, which are the nonGaussian counterparts of Brownian motion. We focus on the general analogtodiscrete conversion problem and introduce a novel splinebased formalism that greatly simplifies the derivation of the correlation properties and joint probability distributions of the discrete versions of these processes. We also rely on the concept of generalized increment process, which suppresses all long range dependencies, to specify an equivalent discretedomain innovation model. A crucial ingredient is the existence of a minimallysupported function associated with the whitening operator L; this Bspline, which is fundamental to our formulation, appears in most of our formulas, both at the level of the correlation and the characteristic function. We make use of these discretedomain results to numerically generate illustrative examples of sparse signals that are consistent with the continuousdomain model.

Higgs search and flavorsafe fermion mass generation ; We study a scenario of electroweak symmetry breaking where the weak gauge boson masses arises significantly from a fermiophobic source. To minimize flavor violation, the fermion mass generation is still due to one light doublet scalar. One of the realizations is the Bosonic Technicolor model. In these scenarios, the Yukawa couplings between the light scalar and the standard model fermions are in general enhanced while the couplings between the light scalar and weak gauge bosons are reduced. Even though the flavor violation induced by the neutral scalar at the tree level can be avoided, the charged scalar state inevitably mediate flavor changing neutral current processes. With the enhancement in the Yukawa couplings, one expects serious constraints of such models from flavor violating effects. We find that the most severe bound comes from neutral meson mixing of B0dbarB0d. Large parameter space is excluded if the weak gauge boson mass generation is dominated by the fermophobic sector. However, the correlation between the Yukawa coupling and charged scalar mass show that a factor of two enhancement in top Yukawa coupling is still allowed for charged scalar heavier than 500 GeV. We use this as a benchmark point to study the phenomenology of the light scalar. It is interesting that the destructive interference between the top quark loop and the Wboson loop in the diphoton channel becomes significant and makes the channel negligible. In the light scalar region, the search becomes much more challenging than the conventional SM Higgs boson.

Anatomy of bispectra in general singlefield inflation modal expansions ; We discuss bispectra of singlefield inflationary models described by general Lorentz invariant Lagrangians that are at most first order in field derivatives, including the fastroll models investigated by Noller and Magueijo. Based on a factor analysis, we identify the least correlated basic contributions to the general shape and show quantitatively which templates provide a good approximation. We compute how relative contributions of basic shapes to the total bispectrum scale as slow roll is relaxed. To enable future comparison with CMB observations, we provide a modal expansion of these nonseparable bispectra in Fourier space, employing the formalism by Shellard et al. Convergence is rapid, usually better than ninetyfive percent with less than thirty modes, due to the smoothness of these primordial shapes. Truncated polynomial modal expansions have restrictions, which we highlight using an example with slow convergence. The particular shape originates from particle production during inflation common in trapped inflation and entails both localized and oscillatory features. We show that this shape can be recovered efficiently using a Fourier basis and outline the prospect of future model parameter extraction and Nbody simulations based on modal techniques.

The Status of GMSB After 1fb at the LHC ; We thoroughly investigate the current status of supersymmetry in light of the latest searches at the LHC, using General Gauge Mediation GGM as a wellmotivated signature generator that leads to many different simplified models. We consider all possible promptlydecaying NLSPs in GGM, and by carefully reinterpreting the existing LHC searches, we derive limits on both colored and electroweak SUSY production. Overall, the coverage of GGM parameter space is quite good, but much discovery potential still remains even at 7 TeV. We identify several regions of parameter space where the current searches are the weakest, typically in models with electroweak production, third generation sfermions or squeezed spectra, and we suggest how ATLAS and CMS might modify their search strategies given the understanding of GMSB at 1fb. In particular, we propose the use of leptonic MT2 to suppress tbar t backgrounds. Because we express our results in terms of simplified models, they have broader applicability beyond the GGM framework, and give a global view of the current LHC reach. Our results on 3rd generation squark NLSPs in particular can be viewed as setting direct limits on naturalness.

The precursory electric signals, observed before the Izmit Turkey EQ Mw 7.6, August 17th, 1999, analyzed in terms of a hypothetically preactivated, in the focal area, large scale piezoelectric mechanism ; The generated, prior to the Izmit Turkey large EQ, preseismic electric signals were recorded in Greece by the VOL Earth's electric field monitoring site. In order to explain their peculiar character and their generating mechanism, a large scale piezoelectric mechanism was assumed that was initiated in the Izmit seismogenic region long before the EQ occurrence time. The theoretical analysis of the adopted physical model justifies the generation of a number of specific electric signals that can be emitted from the focal area before the rock formation failure. The processing of the registered by the VOL monitoring site raw data revealed the presence of similar signals as the expected theoretical ones. Therefore, it is concluded that long before the Izmit EQ occurrence a large scale piezoelectric mechanism was initiated that was modulated too by the tidally triggered lithospheric oscillation and therefore generated the observed preseismic electric signals. The adopted piezoelectric model provides critical information about the time of occurrence of the seismogenic area rock formation failure and therefore the possibility for a real shortterm time prediction of a large EQ. The other two predictive EQ parameters, location and magnitude, are discussed in the frame of electric field triangulation and the Lithospheric Seismic Energy Flow Model LSEFM.

The New Flavor of Higgsed Gauge Mediation ; Recent LHC bounds on squark masses combined with naturalness and flavor considerations motivate nontrivial sfermion mass spectra in the supersymmetric Standard Model. These can arise if supersymmetry breaking is communicated to the visible sector via new extended gauge symmetries. Such extended symmetries must be spontaneously broken, or confined, complicating the calculation of soft masses. We develop a new formalism for calculating perturbative gaugemediated twoloop soft masses for gauge groups with arbitrary patterns of spontaneous symmetry breaking, simplifying the framework of Higgsed gauge mediation. The resulting expressions can be applied to Abelian and nonAbelian gauge groups, opening new avenues for supersymmetric model building. We present a number of examples using our method, ranging from grand unified threshold corrections in standard gauge mediation to soft masses in gauge extensions of the Higgs sector that can raise the Higgs mass through nondecoupling Dterms. We also outline a new mediation mechanism called flavor mediation, where supersymmetry breaking is communicated via a gauged subgroup of Standard Model flavor symmetries. Flavor mediation can automatically generate suppressed masses for thirdgeneration squarks and implies a nearly exact U2 symmetry in the first two generations, yielding a natural SUSY spectrum without imposing ad hoc global symmetries or giving preferential treatment to particular generations.

A possible fundamental theory of Cooper Pair formation in unconventional superconductivity ; The successful application of the electronphonon interaction EPI mechanism in formulating the BardeenCooperSchrieffer BCS theory of superconductivity is among the most outstanding intellectual achievements in theoretical physics because of the successful application of the theory to the conventional superconducting materials. Therefore, its unsuccessful application to the nonconventional superconducting materials has led to the search for new theories which generalized it, include an interplay with other mechanisms or are formulated from non EPI mechanisms. We observe in this current study that to achieve a generalized theory of superconductivity, there is need to first developed a quantitative structure model of the Cooper pair formation CPF in line with the formulation of the molecules in nature which has given birth to hadronic mechanics. This generalized formulation is the isosuperonductivity model which is based on the observation that the Cooper pair of the standard BCS model may have a nonlocalnonhamiltonian structure equivalent to the strong interaction hadronic mechanics HM structure of the neutral pion, as compressed positronium atom at short distances 1 F sim 1013 cm. The equivalent but approximate description at large distances 1 F is by the quantum mechanical superexchange interaction. This generalized CPF has been used to successfully explain the highTc superconductivity in the cuprates as well as to account for the transition temperatures of these materials. It is also used to account for the highTc iron based superconducting materials.

Finitetime future singularities models in fT gravity and the effects of viscosity ; We investigate models of future finitetime singularities in fT theory, where T is the torsion scalar. The algebraic function fT is put as the teleparallel term T plus an arbitrary function gT. A suitable expression of the Hubble parameter is assumed and constraints are imposed in order to provide an expanding universe. Two parameters beta and Hs that appear in the Hubble parameter are relevant in specifying the types of singularities. Differential equations of gT are established and solved, leading to the algebraic fT models for each type of future finite time singularity. Moreover, we take into account the viscosity in the fluid and discuss three interesting cases constant viscosity, viscosity proportional to sqrtT and the general one where the viscosity is proportional to Tn2, where n is a natural number. We see that for the first and second cases, in general, the singularities are robust against the viscous fluid, while for the general case, the Big Rip and the Big Freeze can be avoided from the effects of the viscosity for some values of n.

Elliptical galaxies kinematics within general relativity with renormalization group effects ; The renormalization group framework can be applied to Quantum Field Theory on curved spacetime, but there is no proof whether the betafunction of the gravitational coupling indeed goes to zero in the far infrared or not. In a recent paper we have shown that the amount of dark matter inside spiral galaxies may be negligible if a small running of the General Relativity coupling G is present. Here we extend the proposed model to elliptical galaxies and present a detailed analysis on the modeling of NGC 4494 an ordinary elliptical and NGC 4374 a giant elliptical. In order to compare our results to a well known alternative model to the standard dark matter picture, we also evaluate NGC 4374 with MOND. In this galaxy MOND leads to a significative discrepancy with the observed velocity dispersion curve and has a significative tendency towards tangential anisotropy. On the other hand, the approach based on the renormalization group and general relativity RGGR could be applied with good results to these elliptical galaxies and is compatible with lower masstolight ratios of about the Kroupa IMF type.

Large Deviations for Stochastic Partial Differential Equations Driven by a Poisson Random Measure ; Stochastic partial differential equations driven by Poisson random measures PRM have been proposed as models for many different physical systems, where they are viewed as a refinement of a corresponding noiseless partial differential equations PDE. A systematic framework for the study of probabilities of deviations of the stochastic PDE from the deterministic PDE is through the theory of large deviations. The goal of this work is to develop the large deviation theory for small Poisson noise perturbations of a general class of deterministic infinite dimensional models. Although the analogous questions for finite dimensional systems have been well studied, there are currently no general results in the infinite dimensional setting. This is in part due to the fact that in this setting solutions may have little spatial regularity, and thus classical approximation methods for large deviation analysis become intractable. The approach taken here, which is based on a variational representation for nonnegative functionals of general PRM, reduces the proof of the large deviation principle to establishing basic qualitative properties for controlled analogues of the underlying stochastic system. As an illustration of the general theory, we consider a particular system that models the spread of a pollutant in a waterway.

On a preferential attachment and generalized Polya's urn model ; We study a general preferential attachment and Polya's urn model. At each step a new vertex is introduced, which can be connected to at most one existing vertex. If it is disconnected, it becomes a pioneer vertex. Given that it is not disconnected, it joins an existing pioneer vertex with probability proportional to a function of the degree of that vertex. This function is allowed to be vertexdependent, and is called the reinforcement function. We prove that there can be at most three phases in this model, depending on the behavior of the reinforcement function. Consider the set whose elements are the vertices with cardinality tending a.s. to infinity. We prove that this set either is empty, or it has exactly one element, or it contains all the pioneer vertices. Moreover, we describe the phase transition in the case where the reinforcement function is the same for all vertices. Our results are general, and in particular we are not assuming monotonicity of the reinforcement function. Finally, consider the regime where exactly one vertex has a degree diverging to infinity. We give a lower bound for the probability that a given vertex ends up being the leading one, that is, its degree diverges to infinity. Our proofs rely on a generalization of the Rubin construction given for edgereinforced random walks, and on a Brownian motion embedding.

Observational Constraints on Gauge Field Production in Axion Inflation ; Models of axion inflation are particularly interesting since they provide a natural justification for the flatness of the potential over a superPlanckian distance, namely the approximate shiftsymmetry of the inflaton. In addition, most of the observational consequences are directly related to this symmetry and hence are correlated. Large tensor modes can be accompanied by the observable effects of a the shiftsymmetric coupling phi Ftilde F to a gauge field. During inflation this coupling leads to a copious production of gauge quanta and consequently a very distinct modification of the primordial curvature perturbations. In this work we compare these predictions with observations. We find that the leading constraint on the model comes from the CMB power spectrum when considering both WMAP 7year and ACT data. The bispectrum generated by the nonGaussian inversedecay of the gauge field leads to a comparable but slightly weaker constraint. There is also a constraint from mudistortion using TRIS plus COBEFIRAS data, but it is much weaker. Finally we comment on a generalization of the model to massive gauge fields. When the mass is generated by some light Higgs field, observably large local nonGaussianity can be produced.