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Title: A binomial random multigraph
Abstract: Fix a positive integer $n$, a real number $p\in (0,1]$, and a (perhaps random) hypergraph $\mathcal{H}$ on $[n]$. We introduce and investigate the following random multigraph model, which we denote $\mathbb{G}(n,p\, ; \,\mathcal{H})$: begin with an empty graph on $n$ vertices, which are labelled by the set $[n]$. For every $H\in \mathcal{H}$ choose, independently from previous choices, a doubleton from $H$, say $D = \{i,j\} \subset H$, uniformly at random and then introduce an edge between the vertices $i$ and $j$ in the graph with probability $p$, where each edge is introduced independently of all other edges. | math | 0 |
Title: Survey of 3D Human Body Pose and Shape Estimation Methods for Contemporary Dance Applications
Abstract: 3D human body shape and pose estimation from RGB images is a challenging problem with potential applications in augmented/virtual reality, healthcare and fitness technology and virtual retail. Recent solutions have focused on three types of inputs: i) single images, ii) multi-view images and iii) videos. In this study, we surveyed and compared 3D body shape and pose estimation methods for contemporary dance and performing arts, with a special focus on human body pose and dressing, camera viewpoint, illumination conditions and background conditions. We demonstrated that multi-frame methods, such as PHALP, provide better results than single-frame method for pose estimation when dancers are performing contemporary dances. | cs | 0 |
Title: Einstein Lorentzian solvable unimodular Lie groups
Abstract: The goal of this paper is to show that many key results found in the study of Einstein Lorentzian nilpotent Lie algebras can still hold in the more general settings of unimodular Lie algebras and (completely) solvable Lie algebras. | math | 1 |
Title: An Adjusted Nearest Neighbor Algorithm Maximizing the F-Measure from Imbalanced Data
Abstract: In this paper, we address the challenging problem of learning from imbalanced data using a Nearest-Neighbor (NN) algorithm. In this setting, the minority examples typically belong to the class of interest requiring the optimization of specific criteria, like the F-Measure. Based on simple geometrical ideas, we introduce an algorithm that reweights the distance between a query sample and any positive training example. This leads to a modification of the Voronoi regions and thus of the decision boundaries of the NN algorithm. We provide a theoretical justification about the weighting scheme needed to reduce the False Negative rate while controlling the number of False Positives. We perform an extensive experimental study on many public imbalanced datasets, but also on large scale non public data from the French Ministry of Economy and Finance on a tax fraud detection task, showing that our method is very effective and, interestingly, yields the best performance when combined with state of the art sampling methods. | cs | 1 |
Title: Calabi-Yau structures on Drinfeld quotients and Amiot's conjecture
Abstract: In 2009, Claire Amiot gave a construction of Calabi-Yau structures on Verdier quotients. We sketch how to lift it to the dg setting. We use this construction as an important step in an outline of the proof of her conjecture on the structure of 2-Calabi-Yau triangulated categories with a cluster-tilting object. | math | 0 |
Title: Bounds on the number of squares in recurrence sequences
Abstract: We investigate the number of squares in a very broad family of binary recurrence sequences with $u_{0}=1$. We show that there are at most two distinct squares in such sequences (the best possible result), except under such very special conditions where we prove there are at most three such squares. | math | 0 |
Title: The Effects of Generative AI on Computing Students' Help-Seeking Preferences
Abstract: Help-seeking is a critical way for students to learn new concepts, acquire new skills, and get unstuck when problem-solving in their computing courses. The recent proliferation of generative AI tools, such as ChatGPT, offers students a new source of help that is always available on-demand. However, it is unclear how this new resource compares to existing help-seeking resources along dimensions of perceived quality, latency, and trustworthiness. In this paper, we investigate the help-seeking preferences and experiences of computing students now that generative AI tools are available to them. We collected survey data (n=47) and conducted interviews (n=8) with computing students. Our results suggest that although these models are being rapidly adopted, they have not yet fully eclipsed traditional help resources. The help-seeking resources that students rely on continue to vary depending on the task and other factors. Finally, we observed preliminary evidence about how help-seeking with generative AI is a skill that needs to be developed, with disproportionate benefits for those who are better able to harness the capabilities of LLMs. We discuss potential implications for integrating generative AI into computing classrooms and the future of help-seeking in the era of generative AI. | cs | 0 |
Title: Stable minimal hypersurfaces in $\mathbf{R}^5$
Abstract: We show that a complete, two-sided, stable minimal hypersurface in $\mathbf{R}^5$ is flat. | math | 0 |
Title: Disentangle Estimation of Causal Effects from Cross-Silo Data
Abstract: Estimating causal effects among different events is of great importance to critical fields such as drug development. Nevertheless, the data features associated with events may be distributed across various silos and remain private within respective parties, impeding direct information exchange between them. This, in turn, can result in biased estimations of local causal effects, which rely on the characteristics of only a subset of the covariates. To tackle this challenge, we introduce an innovative disentangle architecture designed to facilitate the seamless cross-silo transmission of model parameters, enriched with causal mechanisms, through a combination of shared and private branches. Besides, we introduce global constraints into the equation to effectively mitigate bias within the various missing domains, thereby elevating the accuracy of our causal effect estimation. Extensive experiments conducted on new semi-synthetic datasets show that our method outperforms state-of-the-art baselines. | cs | 0 |
Title: Hypergraph reconstruction from noisy pairwise observations
Abstract: The network reconstruction task aims to estimate a complex system's structure from various data sources such as time series, snapshots, or interaction counts. Recent work has examined this problem in networks whose relationships involve precisely two entities-the pairwise case. Here we investigate the general problem of reconstructing a network in which higher-order interactions are also present. We study a minimal example of this problem, focusing on the case of hypergraphs with interactions between pairs and triplets of vertices, measured imperfectly and indirectly. We derive a Metropolis-Hastings-within-Gibbs algorithm for this model and use the algorithms to highlight the unique challenges that come with estimating higher-order models. We show that this approach tends to reconstruct empirical and synthetic networks more accurately than an equivalent graph model without higher-order interactions. | cs | 1 |
Title: Asymptotic stability and sharp decay rates to the linearly stratified Boussinesq equations in horizontally periodic strip domain
Abstract: We consider an initial boundary value problem of the multi-dimensional Boussinesq equations in the absence of thermal diffusion with velocity damping or velocity diffusion under the stress free boundary condition in horizontally periodic strip domain. We prove the global-in-time existence of classical solutions in high order Sobolev spaces satisfying high order compatibility conditions around the linearly stratified equilibrium, the convergence of the temperature to the asymptotic profile, and sharp decay rates of the velocity field and temperature fluctuation in all intermediate norms based on spectral analysis combined with energy estimates. To the best of our knowledge, our results provide first sharp decay rates for the temperature fluctuation and the vertical velocity to the linearly stratified Boussinesq equations in all intermediate norms. | math | 1 |
Title: Splines and Wavelets on Circulant Graphs
Abstract: We present novel families of wavelets and associated filterbanks for the analysis and representation of functions defined on circulant graphs. In this work, we leverage the inherent vanishing moment property of the circulant graph Laplacian operator, and by extension, the e-graph Laplacian, which is established as a parameterization of the former with respect to the degree per node, for the design of vertex-localized and critically-sampled higher-order graph (e-)spline wavelet filterbanks, which can reproduce and annihilate classes of (exponential) polynomial signals on circulant graphs. In addition, we discuss similarities and analogies of the detected properties and resulting constructions with splines and spline wavelets in the Euclidean domain. Ultimately, we consider generalizations to arbitrary graphs in the form of graph approximations, with focus on graph product decompositions. In particular, we proceed to show how the use of graph products facilitates a multi-dimensional extension of the proposed constructions and properties. | cs | 1 |
Title: Construction of Jacobi forms using adjoint of Jacobi-Serre derivative
Abstract: In the article, we study the Oberdieck derivative defined on the space of weak Jacobi forms. We prove that the Oberdieck derivative maps a Jacobi form to a Jacobi form. Moreover, we study the adjoint of Oberdieck derivative of a Jacobi cusp form with respect to Petersson scalar product defined on the space of Jacobi forms. As a consequence, we also obtain the adjoint of Jacobi-Serre derivative (defined in an unpublished work of Oberdieck). As an application, we obtain certain relations among the Fourier coefficients of Jacobi forms. | math | 0 |
Title: Submodular Mutual Information for Targeted Data Subset Selection
Abstract: With the rapid growth of data, it is becoming increasingly difficult to train or improve deep learning models with the right subset of data. We show that this problem can be effectively solved at an additional labeling cost by targeted data subset selection(TSS) where a subset of unlabeled data points similar to an auxiliary set are added to the training data. We do so by using a rich class of Submodular Mutual Information (SMI) functions and demonstrate its effectiveness for image classification on CIFAR-10 and MNIST datasets. Lastly, we compare the performance of SMI functions for TSS with other state-of-the-art methods for closely related problems like active learning. Using SMI functions, we observe ~20-30% gain over the model's performance before re-training with added targeted subset; ~12% more than other methods. | cs | 1 |
Title: Decentralized Multi-Task Online Convex Optimization Under Random Link Failures
Abstract: Decentralized optimization methods often entail information exchange between neighbors. Transmission failures can happen due to network congestion, hardware/software issues, communication outage, and other factors. In this paper, we investigate the random link failure problem in decentralized multi-task online convex optimization, where agents have individual decisions that are coupled with each other via pairwise constraints. Although widely used in constrained optimization, conventional saddle-point algorithms are not directly applicable here because of random packet dropping. To address this issue, we develop a robust decentralized saddle-point algorithm against random link failures with heterogeneous probabilities by replacing the missing decisions of neighbors with their latest received values. Then, by judiciously bounding the accumulated deviation stemming from this replacement, we first establish that our algorithm achieves $\mathcal{O}(\sqrt{T})$ regret and $\mathcal{O}(T^\frac{3}{4})$ constraint violations for the full information scenario, where the complete information on the local cost function is revealed to each agent at the end of each time slot. These two bounds match, in order sense, the performance bounds of algorithms with perfect communications. Further, we extend our algorithm and analysis to the two-point bandit feedback scenario, where only the values of the local cost function at two random points are disclosed to each agent sequentially. Performance bounds of the same orders as the full information case are derived. Finally, we corroborate the efficacy of the proposed algorithms and the analytical results through numerical simulations. | cs | 0 |
Title: Aggregation over Metric Spaces: Proposing and Voting in Elections, Budgeting, and Legislation
Abstract: We present a unifying framework encompassing many social choice settings. Viewing each social choice setting as voting in a suitable metric space, we consider a general model of social choice over metric spaces, in which---similarly to the spatial model of elections---each voter specifies an ideal element of the metric space. The ideal element functions as a vote, where each voter prefers elements that are closer to her ideal element. But it also functions as a proposal, thus making all participants equal not only as voters but also as proposers. We consider Condorcet aggregation and a continuum of solution concepts, ranging from minimizing the sum of distances to minimizing the maximum distance. We study applications of the abstract model to various social choice settings, including single-winner elections, committee elections, participatory budgeting, and participatory legislation. For each setting, we compare each solution concept to known voting rules and study various properties of the resulting voting rules. Our framework provides expressive aggregation for a broad range of social choice settings while remaining simple for voters, and may enable a unified and integrated implementation for all these settings, as well as unified extensions such as sybil-resiliency, proxy voting, and deliberative decision making. | cs | 1 |
Title: Aerial Manipulator Force Control Using Control Barrier Functions
Abstract: This article studies the problem of applying normal forces on a surface, using an underactuated aerial vehicle equipped with a dexterous robotic arm. A force-motion high-level controller is designed based on a Lyapunov function encompassing alignment and exerted force errors. This controller is coupled with a Control Barrier Function constraint under an optimization scheme using Quadratic Programming. This aims to enforce a prescribed relationship between the approaching motion for the end-effector and its alignment with the surface, thus ensuring safe operation. An adaptive low-level controller is devised for the aerial vehicle, capable of tracking velocity commands generated by the high-level controller. Simulations and experiments are presented to demonstrate the force exertion stability and safety of the controller in cases of large disturbances. | cs | 0 |
Title: Inequity aversion improves cooperation in intertemporal social dilemmas
Abstract: Groups of humans are often able to find ways to cooperate with one another in complex, temporally extended social dilemmas. Models based on behavioral economics are only able to explain this phenomenon for unrealistic stateless matrix games. Recently, multi-agent reinforcement learning has been applied to generalize social dilemma problems to temporally and spatially extended Markov games. However, this has not yet generated an agent that learns to cooperate in social dilemmas as humans do. A key insight is that many, but not all, human individuals have inequity averse social preferences. This promotes a particular resolution of the matrix game social dilemma wherein inequity-averse individuals are personally pro-social and punish defectors. Here we extend this idea to Markov games and show that it promotes cooperation in several types of sequential social dilemma, via a profitable interaction with policy learnability. In particular, we find that inequity aversion improves temporal credit assignment for the important class of intertemporal social dilemmas. These results help explain how large-scale cooperation may emerge and persist. | cs | 1 |
Title: Investigation of the Sense of Agency in Social Cognition, based on frameworks of Predictive Coding and Active Inference: A simulation study on multimodal imitative interaction
Abstract: When agents interact socially with different intentions, conflicts are difficult to avoid. Although how agents can resolve such problems autonomously has not been determined, dynamic characteristics of agency may shed light on underlying mechanisms. The current study focused on the sense of agency (SoA), a specific aspect of agency referring to congruence between the agent's intention in acting and the outcome. Employing predictive coding and active inference as theoretical frameworks of perception and action generation, we hypothesize that regulation of complexity in the evidence lower bound of an agent's model should affect the strength of the agent's SoA and should have a critical impact on social interactions. We built a computational model of imitative interaction between a robot and a human via visuo-proprioceptive sensation with a variational Bayes recurrent neural network, and simulated the model in the form of pseudo-imitative interaction using recorded human body movement data. A key feature of the model is that each modality's complexity can be regulated differently with a hyperparameter assigned to each module. We first searched for an optimal setting that endows the model with appropriate coordination of multimodal sensation. This revealed that the vision module's complexity should be more tightly regulated than that of the proprioception module. Using the optimally trained model, we examined how changing the tightness of complexity regulation after training affects the strength of the SoA during interactions. The results showed that with looser regulation, an agent tends to act more egocentrically, without adapting to the other. In contrast, with tighter regulation, the agent tends to follow the other by adjusting its intention. We conclude that the tightness of complexity regulation crucially affects the strength of the SoA and the dynamics of interactions between agents. | cs | 1 |
Title: Collective Choice Theory in Collaborative Computing
Abstract: This paper presents some fundamental collective choice theory for information system designers, particularly those working in the field of computer-supported cooperative work. This paper is focused on a presentation of Arrow's Possibility and Impossibility theorems which form the fundamental boundary on the efficacy of collective choice: voting and selection procedures. It restates the conditions that Arrow placed on collective choice functions in more rigorous second-order logic, which could be used as a set of test conditions for implementations, and a useful probabilistic result for analyzing votes on issue pairs. It also describes some simple collective choice functions. There is also some discussion of how enterprises should approach putting their resources under collective control: giving an outline of a superstructure of performative agents to carry out this function and what distributing processing technology would be needed. | cs | 1 |
Title: DeepOnet Based Preconditioning Strategies For Solving Parametric Linear Systems of Equations
Abstract: We introduce a new class of hybrid preconditioners for solving parametric linear systems of equations. The proposed preconditioners are constructed by hybridizing the deep operator network, namely DeepONet, with standard iterative methods. Exploiting the spectral bias, DeepONet-based components are harnessed to address low-frequency error components, while conventional iterative methods are employed to mitigate high-frequency error components. Our preconditioning framework comprises two distinct hybridization approaches: direct preconditioning (DP) and trunk basis (TB) approaches. In the DP approach, DeepONet is used to approximate an action of an inverse operator to a vector during each preconditioning step. In contrast, the TB approach extracts basis functions from the trained DeepONet to construct a map to a smaller subspace, in which the low-frequency component of the error can be effectively eliminated. Our numerical results demonstrate that utilizing the TB approach enhances the convergence of Krylov methods by a large margin compared to standard non-hybrid preconditioning strategies. Moreover, the proposed hybrid preconditioners exhibit robustness across a wide range of model parameters and problem resolutions. | math | 0 |
Title: Optimal cross-learning for contextual bandits with unknown context distributions
Abstract: We consider the problem of designing contextual bandit algorithms in the ``cross-learning'' setting of Balseiro et al., where the learner observes the loss for the action they play in all possible contexts, not just the context of the current round. We specifically consider the setting where losses are chosen adversarially and contexts are sampled i.i.d. from an unknown distribution. In this setting, we resolve an open problem of Balseiro et al. by providing an efficient algorithm with a nearly tight (up to logarithmic factors) regret bound of $\widetilde{O}(\sqrt{TK})$, independent of the number of contexts. As a consequence, we obtain the first nearly tight regret bounds for the problems of learning to bid in first-price auctions (under unknown value distributions) and sleeping bandits with a stochastic action set. At the core of our algorithm is a novel technique for coordinating the execution of a learning algorithm over multiple epochs in such a way to remove correlations between estimation of the unknown distribution and the actions played by the algorithm. This technique may be of independent interest for other learning problems involving estimation of an unknown context distribution. | cs | 0 |
Title: Evaluating Language-Model Agents on Realistic Autonomous Tasks
Abstract: In this report, we explore the ability of language model agents to acquire resources, create copies of themselves, and adapt to novel challenges they encounter in the wild. We refer to this cluster of capabilities as "autonomous replication and adaptation" or ARA. We believe that systems capable of ARA could have wide-reaching and hard-to-anticipate consequences, and that measuring and forecasting ARA may be useful for informing measures around security, monitoring, and alignment. Additionally, once a system is capable of ARA, placing bounds on a system's capabilities may become significantly more difficult. We construct four simple example agents that combine language models with tools that allow them to take actions in the world. We then evaluate these agents on 12 tasks relevant to ARA. We find that these language model agents can only complete the easiest tasks from this list, although they make some progress on the more challenging tasks. Unfortunately, these evaluations are not adequate to rule out the possibility that near-future agents will be capable of ARA. In particular, we do not think that these evaluations provide good assurance that the ``next generation'' of language models (e.g. 100x effective compute scaleup on existing models) will not yield agents capable of ARA, unless intermediate evaluations are performed during pretraining. Relatedly, we expect that fine-tuning of the existing models could produce substantially more competent agents, even if the fine-tuning is not directly targeted at ARA. | cs | 0 |
Title: New Perspective on Progressive GANs Distillation for One-class Novelty Detection
Abstract: One-class novelty detection is conducted to identify anomalous instances, with different distributions from the expected normal instances. In this paper, the Generative Adversarial Network based on the Encoder-Decoder-Encoder scheme (EDE-GAN) achieves state-of-the-art performance. The two factors bellow serve the above purpose: 1) The EDE-GAN calculates the distance between two latent vectors as the anomaly score, which is unlike the previous methods by utilizing the reconstruction error between images. 2) The model obtains best results when the batch size is set to 1. To illustrate their superiority, we design a new GAN architecture, and compare performances according to different batch sizes. Moreover, with experimentation leads to discovery, our result implies there is also evidence of just how beneficial constraint on the latent space are when engaging in model training. In an attempt to learn compact and fast models, we present a new technology, Progressive Knowledge Distillation with GANs (P-KDGAN), which connects two standard GANs through the designed distillation loss. Two-step progressive learning continuously augments the performance of student GANs with improved results over single-step approach. Our experimental results on CIFAR-10, MNIST, and FMNIST datasets illustrate that P-KDGAN improves the performance of the student GAN by 2.44%, 1.77%, and 1.73% when compressing the computationat ratios of 24.45:1, 311.11:1, and 700:1, respectively. | cs | 1 |
Title: Factorial Moments of the Geometric Distribution of Order $k$
Abstract: We derive a simple expression for the $r^{th}$ factorial moment $\mu_{(r)}$ of the geometric distribution of order $k$ with success parameter $p\in(0,1)$ (and $q=1-p$) in terms of its probability mass function $f_k(n)$. Specifically, $\mu_{(r)} = r!f_k((r+1)k+r)/((qp^k)^{r+1})$. | math | 0 |
Title: Quantum Sets of Compact Quantum Groups
Abstract: Q-system completion can be thought of as a notion of higher idempotent completion of C*-2-categories. We introduce a notion of quantum bi-elements, and study Q-system completion in the context of compact quantum groups. We relate our notion of quantum bi-elements to already known notions of quantum sets and quantum functions, and provide a description of Q-system completion of the C*-2-category of compact quantum groups using quantum bi-elements | math | 0 |
Title: Representing General Stochastic Processes as Martingale Laws
Abstract: Random variables $X^i$, $i=1,2$ are 'probabilistically equivalent' if they have the same law. Moreover, in any class of equivalent random variables it is easy to select canonical representatives. The corresponding questions are more involved for processes $X^i$ on filtered stochastic bases $(\Omega^i, \mathcal F^i, \mathbb P^i, (\mathcal F^i_t)_{t\in [0,1]})$. Here equivalence in law does not capture relevant properties of processes such as the solutions to stochastic control or multistage decision problems. This motivates Aldous to introduce the stronger notion of synonymity based on prediction processes. Stronger still, Hoover--Keisler formalize what it means that $X^i$, $i=1,2$ have the same probabilistic properties. We establish that canonical representatives of the Hoover--Keisler equivalence classes are given precisely by the set of all Markov-martingale laws on a specific nested path space $\mathsf M_\infty$. As a consequence we obtain that, modulo Hoover--Keisler equivalence, the class of stochastic processes forms a Polish space. On this space, processes are topologically close iff they model similar probabilistic phenomena. In particular this means that their laws as well as the information encoded in the respective filtrations are similar. Importantly, compact sets of processes admit a Prohorov-type characterization. We also obtain that for every stochastic process, defined on some abstract basis, there exists a process with identical probabilistic properties which is defined on a standard Borel space. | math | 0 |
Title: The number of points from a random lattice that lie inside a ball
Abstract: We prove a sharp bound for the remainder term of the number of lattice points inside a ball, when averaging over a compact set of (not necessarily unimodular) lattices, in dimensions two and three. We also prove that such a bound cannot hold if one averages over the space of all lattices. | math | 1 |
Title: Generalizing Tanisaki's ideal via ideals of truncated symmetric functions
Abstract: We define a family of ideals $I_h$ in the polynomial ring $\mathbb{Z}[x_1,...,x_n]$ that are parametrized by Hessenberg functions $h$ (equivalently Dyck paths or ample partitions). The ideals $I_h$ generalize algebraically a family of ideals called the Tanisaki ideal, which is used in a geometric construction of permutation representations called Springer theory. To define $I_h$, we use polynomials in a proper subset of the variables ${x_1,...,x_n}$ that are symmetric under the corresponding permutation subgroup. We call these polynomials {\em truncated symmetric functions} and show combinatorial identities relating different kinds of truncated symmetric polynomials. We then prove several key properties of $I_h$, including that if $h>h'$ in the natural partial order on Dyck paths then $I_{h} \subset I_{h'}$, and explicitly construct a Gr\"{o}bner basis for $I_h$. We use a second family of ideals $J_h$ for which some of the claims are easier to see, and prove that $I_h = J_h$. The ideals $J_h$ arise in work of Ding, Develin-Martin-Reiner, and Gasharov-Reiner on a family of Schubert varieties called partition varieties. Using earlier work of the first author, the current manuscript proves that the ideals $I_h = J_h$ generalize the Tanisaki ideals both algebraically and geometrically, from Springer varieties to a family of nilpotent Hessenberg varieties. | math | 1 |
Title: Semi-Infinite Cycles in Floer Theory: Viterbo's Theorem
Abstract: This is the first of a series of papers on foundations of Floer theory. We give an axiomatic treatment of the geometric notion of a semi-infinite cycle. Using this notion, we introduce a bordism version of Floer theory for the cotangent bundle of a compact manifold M. Our construction is geometric and does not require the compactness and gluing results traditionally used to setup Floer theory. Finally, we prove a bordism version of Viterbo's theorem relating Floer bordism of the cotangent bundle to the ordinary bordism groups of the free loop space of M. | math | 1 |
Title: Carleman estimates for third order operators of KdV and non KdV-type and applications
Abstract: In this paper we study a class of variable coefficient third order partial differential operators on $\mathbb{R}^{n+1}$, containing, as a subclass, some variable coefficient operators of KdV-type in any space dimension. For such a class, as well as for the adjoint class, we obtain a Carleman estimate and the local solvability at any point of $\mathbb{R}^{n+1}$. A discussion of possible applications in the context of dispersive equations is provided. | math | 0 |
Title: Knowledge Enhanced Conditional Imputation for Healthcare Time-series
Abstract: This study presents a novel approach to addressing the challenge of missing data in multivariate time series, with a particular focus on the complexities of healthcare data. Our Conditional Self-Attention Imputation (CSAI) model, grounded in a transformer-based framework, introduces a conditional hidden state initialization tailored to the intricacies of medical time series data. This methodology diverges from traditional imputation techniques by specifically targeting the imbalance in missing data distribution, a crucial aspect often overlooked in healthcare datasets. By integrating advanced knowledge embedding and a non-uniform masking strategy, CSAI adeptly adjusts to the distinct patterns of missing data in Electronic Health Records (EHRs). | cs | 0 |
Title: Mutual-visibility problems on graphs of diameter two
Abstract: The mutual-visibility problem in a graph $G$ asks for the cardinality of a largest set of vertices $S\subseteq V(G)$ so that for any two vertices $x,y\in S$ there is a shortest $x,y$-path $P$ so that all internal vertices of $P$ are not in $S$. This is also said as $x,y$ are visible with respect to $S$, or $S$-visible for short. Variations of this problem are known, based on the extension of the visibility property of vertices that are in and/or outside $S$. Such variations are called total, outer and dual mutual-visibility problems. This work is focused on studying the corresponding four visibility parameters in graphs of diameter two, throughout showing bounds and/or closed formulae for these parameters. The mutual-visibility problem in the Cartesian product of two complete graphs is equivalent to (an instance of) the celebrated Zarankievicz's problem. Here we study the dual and outer mutual-visibility problem for the Cartesian product of two complete graphs and all the mutual-visibility problems for the direct product of such graphs as well. We also study all the mutual-visibility problems for the line graphs of complete and complete bipartite graphs. As a consequence of this study, we present several relationships between the mentioned problems and some instances of the classical Tur\'an problem. Moreover, we study the visibility problems for cographs and several non-trivial diameter-two graphs of minimum size. | math | 0 |
Title: Local semicircle law with imprimitive variance matrix
Abstract: We extend the proof of the local semicircle law for generalized Wigner matrices given in [4] to the case when the matrix of variances has an eigenvalue $ -1 $. In particular, this result provides a short proof of the optimal local Marchenko-Pastur law at the hard edge (i.e. around zero) for sample covariance matrices $ \boldsymbol{\mathrm{X}}^\ast \boldsymbol{\mathrm{X}} $, where the variances of the entries of $ \boldsymbol{\mathrm{X}} $ may vary. | math | 1 |
Title: Passivity-Preserving Safety-Critical Control using Control Barrier Functions
Abstract: In this letter we propose a holistic analysis merging the techniques of passivity-based control (PBC) and control barrier functions (CBF). We constructively find conditions under which passivity of the closed-loop system is preserved under CBF-based safety-critical control. The results provide an energetic interpretation of safety-critical control schemes, and induce novel passive designs which are less conservative than standard methods based on damping injection. The results are specialised to port-Hamiltonian systems and simulations are performed on a cart-pole system. | cs | 0 |
Title: Generalized integral type Hilbert operator acting on weighted Bloch space
Abstract: Let $\mu$ be a finite Borel measure on $[0,1)$. In this paper, we consider the generalized integral type Hilbert operator $$\mathcal{I}_{\mu_{\alpha+1}}(f)(z)=\int_{0}^{1}\frac{f(t)}{(1-tz)^{\alpha+1}}d\mu(t)\ \ \ (\alpha>-1).$$ The operator $\mathcal{I}_{\mu_{1}}$ has been extensively studied recently. The aim of this paper is to study the boundedness(resp. compactness) of $\mathcal{I}_{\mu_{\alpha+1}}$ acting from the normal weight Bloch space into another of the same kind. As consequences of our study, we get completely results for the boundedness of $ \mathcal{I}_{\mu_{\alpha+1}}$ acting between Bloch type spaces, logarithmic Bloch spaces among others. | math | 1 |
Title: A finite difference scheme for two-dimensional singularly perturbed convection-diffusion problem with discontinuous source term
Abstract: We propose a finite difference scheme for the numerical solution of a two-dimensional singularly perturbed convection-diffusion partial differential equation whose solution features interacting boundary and interior layers, the latter due to discontinuities in source term. The problem is posed on the unit square. The second derivative is multiplied by a singular perturbation parameter, $\epsilon$, while the nature of the first derivative term is such that flow is aligned with a boundary. These two facts mean that solutions tend to exhibit layers of both exponential and characteristic type. We solve the problem using a finite difference method, specially adapted to the discontinuities, and applied on a piecewise-uniform (Shishkin). We prove that that the computed solution converges to the true one at a rate that is independent of the perturbation parameter, and is nearly first-order. We present numerical results that verify that these results are sharp. | math | 0 |
Title: On Spectral Approximations With Nonstandard Weight Functions and Their Implementations to Generalized Chaos Expansions
Abstract: In this manuscript, we analyze the expansions of functions in orthogonal polynomials associated with a general weight function in a multidimensional setting. Such orthogonal polynomials can be obtained by Gram-Schmidt orthogonalization. However, in most cases, they are not eigenfunctions of some singular Sturm-Liouville problem, as is the case for classical polynomials. Therefore, standard results regarding convergence cannot be applied. Furthermore, since in general, the weight functions are not a tensor product of one-dimensional functions, the orthogonal polynomials are not a tensor product of one-dimensional orthogonal polynomials, as well. In this work, we determine the convergence rate using a comparison Lemma. We also present a spectrally convergent, multidimensional, integration method. Numerical examples demonstrate the efficacy of the proposed method. We show that the use of nonstandard weight functions can allow for efficient integration of singular functions. We also apply this method to Generalized Polynomial Chaos Expansions in the case of dependent random variables. | math | 1 |
Title: Towards an Automatic System for Extracting Planar Orientations from Software Generated Point Clouds
Abstract: In geology, a key activity is the characterisation of geological structures (surface formation topology and rock units) using Planar Orientation measurements such as Strike, Dip and Dip Direction. In general these measurements are collected manually using basic equipment; usually a compass/clinometer and a backboard, recorded on a map by hand. Various computing techniques and technologies, such as Lidar, have been utilised in order to automate this process and update the collection paradigm for these types of measurements. Techniques such as Structure from Motion (SfM) reconstruct of scenes and objects by generating a point cloud from input images, with detailed reconstruction possible on the decimetre scale. SfM-type techniques provide advantages in areas of cost and usability in more varied environmental conditions, while sacrificing the extreme levels of data fidelity. Here is presented a methodology of data acquisition and a Machine Learning-based software system: GeoStructure, developed to automate the measurement of orientation measurements. Rather than deriving measurements using a method applied to the input images, such as the Hough Transform, this method takes measurements directly from the reconstructed point cloud surfaces. Point cloud noise is mitigated using a Mahalanobis distance implementation. Significant structure is characterised using a k-nearest neighbour region growing algorithm, and final surface orientations are quantified using the plane, and normal direction cosines. | cs | 1 |
Title: The cyclic open-closed map, u-connections and R-matrices
Abstract: This paper considers the (negative) cyclic open-closed map $\mathcal{OC}^{-}$, which maps the cyclic homology of the Fukaya category of a symplectic manifold to its $S^1$-equivariant quantum cohomology. We prove (under simplifying technical hypotheses) that this map respects the respective natural connections in the direction of the equivariant parameter. In the monotone setting this allows us to conclude that $\mathcal{OC}^{-}$ intertwines the decomposition of the Fukaya category by eigenvalues of quantum cup product with the first Chern class, with the Hukuhara-Levelt-Turrittin decomposition of the quantum cohomology. We also explain how our results relate to the Givental-Teleman classification of semisimple cohomological field theories: in particular, how the R-matrix is related to $\mathcal{OC}^{-}$ in the semisimple case; we also consider the non-semisimple case. | math | 1 |
Title: Near-optimal constructions of constant weight codes and constant composition codes asymptotically attaining the Johnson bound: the odd distances
Abstract: Constant weight codes (CWCs) and constant composition codes (CCCs) are two important classes of codes that have been studied extensively in both combinatorics and coding theory for nearly sixty years. In this paper we show that for {\it all} fixed odd distances, there exist near-optimal CWCs and CCCs asymptotically achieving the classic Johnson-type upper bounds. Let $A_q(n,w,d)$ denote the maximum size of $q$-ary CWCs of length $n$ with constant weight $w$ and minimum distance $d$. One of our main results shows that for {\it all} fixed $q,w$ and odd $d$, one has $\lim_{n\rightarrow\infty}\frac{A_q(n,d,w)}{\binom{n}{t}}=\frac{(q-1)^t}{\binom{w}{t}}$, where $t=\frac{2w-d+1}{2}$. This implies the existence of near-optimal generalized Steiner systems originally introduced by Etzion, and can be viewed as a counterpart of a celebrated result of R\"odl on the existence of near-optimal Steiner systems. Note that prior to our work, very little is known about $A_q(n,w,d)$ for $q\ge 3$. A similar result is proved for the maximum size of CCCs. We provide different proofs for our two main results, based on two strengthenings of the well-known Frankl-R\"odl-Pippenger theorem on the existence of near-optimal matchings in hypergraphs: the first proof follows by Kahn's linear programming variation of the above theorem, and the second follows by the recent independent work of Delcour-Postle, and Glock-Joos-Kim-K\"uhn-Lichev on the existence of near-optimal matchings avoiding certain forbidden configurations. We also present several intriguing open questions for future research. | math | 0 |
Title: Finite variations on the isoperimetric problem
Abstract: The isoperimetric problem asks for the maximum area of a region of given perimeter. It is natural to consider other measurements of a region, such as the diameter and width, and ask for the extreme value of one when another is fixed. The solution of these problems is known if the competing regions are general convex disks, however several of these problems are still open if the competing regions are polygons with at most a given number of sides. The present work surveys these problems. | math | 1 |
Title: Human activity recognition from mobile inertial sensors using recurrence plots
Abstract: Inertial sensors are present in most mobile devices nowadays and such devices are used by people during most of their daily activities. In this paper, we present an approach for human activity recognition based on inertial sensors by employing recurrence plots (RP) and visual descriptors. The pipeline of the proposed approach is the following: compute RPs from sensor data, compute visual features from RPs and use them in a machine learning protocol. As RPs generate texture visual patterns, we transform the problem of sensor data classification to a problem of texture classification. Experiments for classifying human activities based on accelerometer data showed that the proposed approach obtains the highest accuracies, outperforming time- and frequency-domain features directly extracted from sensor data. The best results are obtained when using RGB RPs, in which each RGB channel corresponds to the RP of an independent accelerometer axis. | cs | 1 |
Title: A conformal integral invariant on Riemannian foliations
Abstract: Let $M$ be a closed manifold which admits a foliation structure $\mathcal{F}$ of codimension $q\geq 2$ and a bundle-like metric $g_0$. Let $[g_0]_B$ be the space of bundle-like metrics which differ from $g_0$ only along the horizontal directions by a multiple of a positive basic function. Assume $Y$ is a transverse conformal vector field and the mean curvature of the leaves of $(M,\mathcal{F},g_0)$ vanishes. We show that the integral $\int_MY(R^T_{g^T})d\mu_g$ is independent of the choice of $g\in [g_0]_B$, where $g^T$ is the transverse metric induced by $g$ and $R^T$ is the transverse scalar curvature. Moreover if $q\geq 3$, we have $\int_MY(R^T_{g^T})d\mu_g=0$ for any $g\in [g_0]_B$. However there exist codimension 2 minimal Riemannian foliations $(M,\mathcal{F},g)$ and transverse conformal vector fields $Y$ such that $\int_MY(R^T_{g^T})d\mu_g\neq 0$. Therefore, it is a nontrivial obstruction for the transverse Yamabe problem on minimal Riemannian foliation of codimension 2. | math | 1 |
Title: A Moebius inversion formula to discard tangled hyperbolic surfaces
Abstract: Recent literature on Weil-Petersson random hyperbolic surfaces has met a consistent obstacle: the necessity to condition the model, prohibiting certain rare geometric patterns (which we call tangles), such as short closed geodesics or embedded surfaces of short boundary length. The main result of this article is a Moebius inversion formula, allowing to integrate the indicator function of the set of tangle-free surfaces in a systematic, tractable way. It is inspired by a key step of Friedman's celebrated proof of Alon's conjecture. We further prove that our tangle-free hypothesis significantly reduces the number of local topological types of short geodesics, replacing the exponential proliferation observed on tangled surfaces by a polynomial growth. | math | 0 |
Title: Distillation-based fabric anomaly detection
Abstract: Unsupervised texture anomaly detection has been a concerning topic in a vast amount of industrial processes. Patterned textures inspection, particularly in the context of fabric defect detection, is indeed a widely encountered use case. This task involves handling a diverse spectrum of colors and textile types, encompassing a wide range of fabrics. Given the extensive variability in colors, textures, and defect types, fabric defect detection poses a complex and challenging problem in the field of patterned textures inspection. In this article, we propose a knowledge distillation-based approach tailored specifically for addressing the challenge of unsupervised anomaly detection in textures resembling fabrics. Our method aims to redefine the recently introduced reverse distillation approach, which advocates for an encoder-decoder design to mitigate classifier bias and to prevent the student from reconstructing anomalies. In this study, we present a new reverse distillation technique for the specific task of fabric defect detection. Our approach involves a meticulous design selection that strategically highlights high-level features. To demonstrate the capabilities of our approach both in terms of performance and inference speed, we conducted a series of experiments on multiple texture datasets, including MVTEC AD, AITEX, and TILDA, alongside conducting experiments on a dataset acquired from a textile manufacturing facility. The main contributions of this paper are the following: a robust texture anomaly detector utilizing a reverse knowledge-distillation technique suitable for both anomaly detection and domain generalization and a novel dataset encompassing a diverse range of fabrics and defects. | cs | 0 |
Title: Twice $Q$-polynomial distance-regular graphs of diameter 4
Abstract: It is known that a distance-regular graph with valency $k$ at least three admits at most two Q-polynomial structures. % In this note we show that all distance-regular graphs with diameter four and valency at least three admitting two $Q$-polynomial structures are either dual bipartite or almost dual imprimitive. By the work of Dickie \cite{Dickie} this implies that any distance-regular graph with diameter $d$ at least four and valency at least three admitting two $Q$-polynomial structures is, provided it is not a Hadamard graph, either the cube $H(d,2)$ with $d$ even, the half cube ${1}/{2} H(2d+1,2)$, the folded cube $\tilde{H}(2d+1,2)$, or the dual polar graph on $[^2A_{2d-1}(q)]$ with $q\ge 2$ a prime power. | math | 1 |
Title: Sommets fortement critiques d'un tournoi indécomposable
Abstract: Let $T=(V,A)$ be a tournament. For $X\subseteq V$, the subtournament of $T$ induced by $X$ is denoted by $T[X]$. A subset $I$ of $V$ is an interval of $T$ provided that for every $a,b\in I$ and $x\in V\setminus I$, $(a,x)\in A$ if and only if $(b,x)\in A$. For example, $\varnothing $, ${x}$ ($x \in V$) and $V$ are intervals of $T$, called trivial intervals. The tournament $T$ is indecomposable if all its intervals are trivial, otherwise, it is decomposable. A critical tournament is an indecomposable tournament $T$ of cardinality $\geqslant 5$ such that every vertex $x$ of $T$ is critical, i.e., the subtournament $T[V(T)\setminus\{x\}]$ is decomposable. Given an indecomposable tournament $T$, a vertex $x$ of $T$ is strongly critical, if for every $X\subseteq V(T)$ such that $x\in X$, $\vert X\vert \geqslant 5$ and $T[X]$ is indecomposable, $x$ is a critical vertex of $T[X]$. Let $T$ be an indecomposable tournament and let $\mathscr{C}(T)$ be the set of the strongly critical vertices of $T$. We prove that, if $T$ is non-critical, then $f(T):=\vert \mathscr{C}(T)\vert \leqslant 4$, and that the correspondence $f(T)$ is decreasing from the class of indecomposable and non-critical tournaments (defined by means of embedding) to $\{0,1,2,3,4\}$. By giving examples, we also verify that the bounds 0 and 4 are optimal. This article is an extract from my master's thesis \cite{mon mast\`ere}. | math | 0 |
Title: Wide Neural Networks Forget Less Catastrophically
Abstract: A primary focus area in continual learning research is alleviating the "catastrophic forgetting" problem in neural networks by designing new algorithms that are more robust to the distribution shifts. While the recent progress in continual learning literature is encouraging, our understanding of what properties of neural networks contribute to catastrophic forgetting is still limited. To address this, instead of focusing on continual learning algorithms, in this work, we focus on the model itself and study the impact of "width" of the neural network architecture on catastrophic forgetting, and show that width has a surprisingly significant effect on forgetting. To explain this effect, we study the learning dynamics of the network from various perspectives such as gradient orthogonality, sparsity, and lazy training regime. We provide potential explanations that are consistent with the empirical results across different architectures and continual learning benchmarks. | cs | 1 |
Title: A Soft Recommender System for Social Networks
Abstract: Recent social recommender systems benefit from friendship graph to make an accurate recommendation, believing that friends in a social network have exactly the same interests and preferences. Some studies have benefited from hard clustering algorithms (such as K-means) to determine the similarity between users and consequently to define degree of friendships. In this paper, we went a step further to identify true friends for making even more realistic recommendations. we calculated the similarity between users, as well as the dependency between a user and an item. Our hypothesis is that due to the uncertainties in user preferences, the fuzzy clustering, instead of the classical hard clustering, is beneficial in accurate recommendations. We incorporated the C-means algorithm to get different membership degrees of soft users' clusters. Then, the users' similarity metric is defined according to the soft clusters. Later, in a training scheme we determined the latent representations of users and items, extracting from the huge and sparse user-item-tag matrix using matrix factorization. In the parameter tuning, we found the optimum coefficients for the influence of our soft social regularization and the user-item dependency terms. Our experimental results convinced that the proposed fuzzy similarity metric improves the recommendations in real data compared to the baseline social recommender system with the hard clustering. | cs | 1 |
Title: The Gossiping Insert-Eliminate Algorithm for Multi-Agent Bandits
Abstract: We consider a decentralized multi-agent Multi Armed Bandit (MAB) setup consisting of $N$ agents, solving the same MAB instance to minimize individual cumulative regret. In our model, agents collaborate by exchanging messages through pairwise gossip style communications on an arbitrary connected graph. We develop two novel algorithms, where each agent only plays from a subset of all the arms. Agents use the communication medium to recommend only arm-IDs (not samples), and thus update the set of arms from which they play. We establish that, if agents communicate $\Omega(\log(T))$ times through any connected pairwise gossip mechanism, then every agent's regret is a factor of order $N$ smaller compared to the case of no collaborations. Furthermore, we show that the communication constraints only have a second order effect on the regret of our algorithm. We then analyze this second order term of the regret to derive bounds on the regret-communication tradeoffs. Finally, we empirically evaluate our algorithm and conclude that the insights are fundamental and not artifacts of our bounds. We also show a lower bound which gives that the regret scaling obtained by our algorithm cannot be improved even in the absence of any communication constraints. Our results thus demonstrate that even a minimal level of collaboration among agents greatly reduces regret for all agents. | cs | 1 |
Title: Effective randomness, strong reductions and Demuth's theorem
Abstract: We study generalizations of Demuth's Theorem, which states that the image of a Martin-L\"of random real under a tt-reduction is either computable or Turing equivalent to a Martin-L\"of random real. We show that Demuth's Theorem holds for Schnorr randomness and computable randomness (answering a question of Franklin), but that it cannot be strengthened by replacing the Turing equivalence in the statement of the theorem with wtt-equivalence. We also provide some additional results about the Turing and tt-degrees of reals that are random with respect to some computable measure. | math | 1 |
Title: Almost periodic invariant tori for the NLS on the circle
Abstract: In this paper we study the existence and linear stability of almost periodic solutions for a NLS equation on the circle with external parameters. Starting from the seminal result of Bourgain (2005) on the quintic NLS, we propose a novel approach allowing to prove in a unified framework the persistence of finite and infinite dimensional invariant tori, which are the support of the desired solutions. The persistence result is given through a rather abstract "counter-term theorem" `a la Herman, directly in the original elliptic variables without passing to action-angle ones. Our framework allows us to find "many more" almost periodic solutions with respect to the existing literature and consider also non-translation invariant PDEs. | math | 1 |
Title: From microscopic theory to macroscopic theory: dynamics of the rod-like liquid crystal molecules
Abstract: Starting from Doi-Onsager equation for the liquid crystal, we first derive the Q-tensor equation by the Bingham closure. Then we derive the Ericksen-Leslie equation from the Q-tensor equation by taking the small Deborah number limit. | math | 1 |
Title: Presentations of configuration categories
Abstract: The configuration category of a manifold is a topological category which we view as a Segal space, via the nerve construction. Our main result is that the unordered configuration category, suitably truncated, admits a finite presentation as a complete Segal space if the manifold in question is the interior of a compact manifold. | math | 0 |
Title: Learning Multi-Step Manipulation Tasks from A Single Human Demonstration
Abstract: Learning from human demonstrations has exhibited remarkable achievements in robot manipulation. However, the challenge remains to develop a robot system that matches human capabilities and data efficiency in learning and generalizability, particularly in complex, unstructured real-world scenarios. We propose a system that processes RGBD videos to translate human actions to robot primitives and identifies task-relevant key poses of objects using Grounded Segment Anything. We then address challenges for robots in replicating human actions, considering the human-robot differences in kinematics and collision geometry. To test the effectiveness of our system, we conducted experiments focusing on manual dishwashing. With a single human demonstration recorded in a mockup kitchen, the system achieved 50-100% success for each step and up to a 40% success rate for the whole task with different objects in a home kitchen. Videos are available at https://robot-dishwashing.github.io | cs | 0 |
Title: Revisiting Norm Estimation in Data Streams
Abstract: The problem of estimating the pth moment F_p (p nonnegative and real) in data streams is as follows. There is a vector x which starts at 0, and many updates of the form x_i <-- x_i + v come sequentially in a stream. The algorithm also receives an error parameter 0 < eps < 1. The goal is then to output an approximation with relative error at most eps to F_p = ||x||_p^p. Previously, it was known that polylogarithmic space (in the vector length n) was achievable if and only if p <= 2. We make several new contributions in this regime, including: (*) An optimal space algorithm for 0 < p < 2, which, unlike previous algorithms which had optimal dependence on 1/eps but sub-optimal dependence on n, does not rely on a generic pseudorandom generator. (*) A near-optimal space algorithm for p = 0 with optimal update and query time. (*) A near-optimal space algorithm for the "distinct elements" problem (p = 0 and all updates have v = 1) with optimal update and query time. (*) Improved L_2 --> L_2 dimensionality reduction in a stream. (*) New 1-pass lower bounds to show optimality and near-optimality of our algorithms, as well as of some previous algorithms (the "AMS sketch" for p = 2, and the L_1-difference algorithm of Feigenbaum et al.). As corollaries of our work, we also obtain a few separations in the complexity of moment estimation problems: F_0 in 1 pass vs. 2 passes, p = 0 vs. p > 0, and F_0 with strictly positive updates vs. arbitrary updates. | cs | 1 |
Title: Provable Computational and Statistical Guarantees for Efficient Learning of Continuous-Action Graphical Games
Abstract: In this paper, we study the problem of learning the set of pure strategy Nash equilibria and the exact structure of a continuous-action graphical game with quadratic payoffs by observing a small set of perturbed equilibria. A continuous-action graphical game can possibly have an uncountable set of Nash euqilibria. We propose a $\ell_{12}-$ block regularized method which recovers a graphical game, whose Nash equilibria are the $\epsilon$-Nash equilibria of the game from which the data was generated (true game). Under a slightly stringent condition on the parameters of the true game, our method recovers the exact structure of the graphical game. Our method has a logarithmic sample complexity with respect to the number of players. It also runs in polynomial time. | cs | 1 |
Title: Knutson ideals and determinantal ideals of Hankel matrices
Abstract: Motivated by a work of Knutson, in a recent paper Conca and Varbaro have defined a new class of ideals, namely "Knutson ideals", starting from a polynomial $f$ with squarefree leading term. We will show that the main properties that this class has in polynomial rings over fields of characteristic $p$ are preserved when one introduces the definition of Knutson ideal also in polynomial rings over fields of characteristic zero. Then we will show that determinantal ideals of Hankel matrices are Knutson ideals for a suitable choice of the polynomial $f$. | math | 1 |
Title: Modeling Image Structure with Factorized Phase-Coupled Boltzmann Machines
Abstract: We describe a model for capturing the statistical structure of local amplitude and local spatial phase in natural images. The model is based on a recently developed, factorized third-order Boltzmann machine that was shown to be effective at capturing higher-order structure in images by modeling dependencies among squared filter outputs (Ranzato and Hinton, 2010). Here, we extend this model to $L_p$-spherically symmetric subspaces. In order to model local amplitude and phase structure in images, we focus on the case of two dimensional subspaces, and the $L_2$-norm. When trained on natural images the model learns subspaces resembling quadrature-pair Gabor filters. We then introduce an additional set of hidden units that model the dependencies among subspace phases. These hidden units form a combinatorial mixture of phase coupling distributions, concentrated in the sum and difference of phase pairs. When adapted to natural images, these distributions capture local spatial phase structure in natural images. | cs | 1 |
Title: Standing waves with prescribed $L^2$-norm to nonlinear Schrödinger equations with combined inhomogeneous nonlinearities
Abstract: In this paper, we are concerned with solutions to the following nonlinear Schr\"odinger equation with combined inhomogeneous nonlinearities, $$ -\Delta u + \lambda u= \mu |x|^{-b}|u|^{q-2} u + |x|^{-b}|u|^{p-2} u \quad \mbox{in} \,\, \R^N, $$ under the $L^2$-norm constraint $$ \int_{\R^N} |u|^2 \, dx=c>0, $$ where $N \geq 1$, $\mu =\pm 1$, $2<q<p<{2(N-b)}/{(N-2)^+}$, $0<b<\min\{2, N\}$ and the parameter $\lambda \in \R$ appearing as Lagrange multiplier is unknown. In the mass subcritical case, we establish the compactness of any minimizing sequence to the minimization problem given by the underlying energy functional restricted on the constraint. As a consequence of the compactness of any minimizing sequence, orbital stability of minimizers is derived. In the mass critical and supercritical cases, we investigate the existence, radial symmetry and orbital instability of solutions. Meanwhile, we consider the existence, radial symmetry and algebraical decay of ground states to the corresponding zero mass equation with defocusing perturbation. In addition, dynamical behaviors of solutions to the Cauchy problem for the associated dispersive equation are discussed. | math | 0 |
Title: Comparative Analysis of Engagement, Themes, and Causality of Ukraine-Related Debunks and Disinformation
Abstract: This paper compares quantitatively the spread of Ukraine-related disinformation and its corresponding debunks, first by considering re-tweets, replies, and favourites, which demonstrate that despite platform efforts Ukraine-related disinformation is still spreading wider than its debunks. Next, bidirectional post-hoc analysis is carried out using Granger causality tests, impulse response analysis and forecast error variance decomposition, which demonstrate that the spread of debunks has a positive impact on reducing Ukraine-related disinformation eventually, albeit not instantly. Lastly, the paper investigates the dominant themes in Ukraine-related disinformation and their spatiotemporal distribution. With respect to debunks, we also establish that around 18% of fact-checks are debunking claims which have already been fact-checked in another language. The latter finding highlights an opportunity for better collaboration between fact-checkers, so they can benefit from and amplify each other's debunks through translation, citation, and early publication online. | cs | 1 |
Title: Fourier neural operator based fluid-structure interaction for predicting the vesicle dynamics
Abstract: Solving complex fluid-structure interaction (FSI) problems, characterized by nonlinear partial differential equations, is crucial in various scientific and engineering applications. Traditional computational fluid dynamics (CFD) solvers are insufficient to meet the growing requirements for large-scale and long-period simulations. Fortunately, the rapid advancement in neural networks, especially neural operator learning mappings between function spaces, has introduced novel approaches to tackle these challenges via data-driven modeling. In this paper, we propose a Fourier neural operator-based fluid-structure interaction solver (FNO-based FSI solver) for efficient simulation of FSI problems, where the solid solver based on the finite difference method is seamlessly integrated with the Fourier neural operator to predict incompressible flow using the immersed boundary method. We analyze the performance of the FNO-based FSI solver in the following three situations: training data with or without the steady state, training method with one-step label or multi-step labels, and prediction in interpolation or extrapolation. We find that the best performance for interpolation is achieved by training the operator with multi-step labels using steady-state data. Finally, we train the FNO-based FSI solver using this optimal training method and apply it to vesicle dynamics. The results show that the FNO-based FSI solver is capable of capturing the variations in the fluid and the vesicle. | math | 0 |
Title: Universal sequences of composition operators
Abstract: Let $G$ and $\Omega$ be two planar domains. We give necessary and sufficient conditions on a sequence $(\phi_n)$ of eventually injective holomorphic mappings from $G$ to $\Omega$ for the existence of a function $f\in H(\Omega)$ whose orbit under the composition by $(\phi_n)$ is dense in $H(G)$. This extends a result of the same nature obtained by Grosse-Erdmann and Mortini when $G=\Omega$. An interconnexion between the topological properties of $G$ and $\Omega$ appears. Further, in order to exhibit in a natural way holomorphic functions with wild boundary behaviour on planar domains, we study a certain type of universality for sequences of continuous mappings from a union of Jordan curves to a domain. | math | 1 |
Title: On mild solutions to some dissipative SPDEs on $L^p$ spaces with additive noise
Abstract: We establish well-posedness in the mild sense for a class of stochastic semilinear evolution equations on $L^p$ spaces on bounded domains of $\mathbb{R}^n$ with a nonlinear drift term given by the superposition operator generated by a monotone function on the real line with power-like growth. The noise is of additive type with respect to a cylindrical Wiener process, with diffusion coefficient not necessarily of $\gamma$-Radonifying type. | math | 0 |
Title: $q$-deformation of Aomoto complex
Abstract: A degree one element of the Orlik-Solomon algebra of a hyperplane arrangement defines a cochain complex known as the Aomoto complex. The Aomoto complex can be considerd as the ``linear approximation'' of the twisted cochain complex with coefficients in a complex rank one local system. In this paper, we discuss $q$-deformations of the Aomoto complex. The $q$-deformation is defined by replacing the entries of representation matrices of the coboundary maps with their $q$-analogues. While the resulting maps do not generally define cochain complexes, for certain special basis derived from real structures, the $q$-deformation becomes again a cochain complex. Moreover, it exhibits universality in the sense that any specialization of $q$ to a complex number yields the cochain complex computing the corresponding local system cohomology group. | math | 0 |
Title: A Pragmatic Look at Deep Imitation Learning
Abstract: The introduction of the generative adversarial imitation learning (GAIL) algorithm has spurred the development of scalable imitation learning approaches using deep neural networks. Many of the algorithms that followed used a similar procedure, combining on-policy actor-critic algorithms with inverse reinforcement learning. More recently there have been an even larger breadth of approaches, most of which use off-policy algorithms. However, with the breadth of algorithms, everything from datasets to base reinforcement learning algorithms to evaluation settings can vary, making it difficult to fairly compare them. In this work we re-implement 6 different IL algorithms, updating 3 of them to be off-policy, base them on a common off-policy algorithm (SAC), and evaluate them on a widely-used expert trajectory dataset (D4RL) for the most common benchmark (MuJoCo). After giving all algorithms the same hyperparameter optimisation budget, we compare their results for a range of expert trajectories. In summary, GAIL, with all of its improvements, consistently performs well across a range of sample sizes, AdRIL is a simple contender that performs well with one important hyperparameter to tune, and behavioural cloning remains a strong baseline when data is more plentiful. | cs | 1 |
Title: Quotient polynomials with positive coefficients
Abstract: We give an optimal necessary and sufficient condition for the quotient polynomial and remainder in the division algorithm to have positive coefficients. | math | 1 |
Title: A Neural Lip-Sync Framework for Synthesizing Photorealistic Virtual News Anchors
Abstract: Lip sync has emerged as a promising technique for generating mouth movements from audio signals. However, synthesizing a high-resolution and photorealistic virtual news anchor is still challenging. Lack of natural appearance, visual consistency, and processing efficiency are the main problems with existing methods. This paper presents a novel lip-sync framework specially designed for producing high-fidelity virtual news anchors. A pair of Temporal Convolutional Networks are used to learn the cross-modal sequential mapping from audio signals to mouth movements, followed by a neural rendering network that translates the synthetic facial map into a high-resolution and photorealistic appearance. This fully trainable framework provides end-to-end processing that outperforms traditional graphics-based methods in many low-delay applications. Experiments also show the framework has advantages over modern neural-based methods in both visual appearance and efficiency. | cs | 1 |
Title: Large deviation principle for slow-fast rough differential equations via controlled rough paths
Abstract: We prove a large deviation principle for the slow-fast rough differential equations under the controlled rough path framework. The driver rough paths are lifted from the mixed fractional Brownian motion with Hurst parameter $H\in (1/3,1/2)$. Our approach is based on the continuity of the solution mapping and the variational framework for mixed fractional Brownian motion. By utilizing the variational representation, our problem is transformed into a qualitative property of the controlled system. In particular, the fast rough differential equation coincides with It\^o SDE almost surely, which possesses a unique invariant probability measure with frozen slow component. We then demonstrate the weak convergence of the controlled slow component by averaging with respect to the invariant measure of the fast equation and exploiting the continuity of the solution mapping. | math | 0 |
Title: Adversarial Machine Learning-Enabled Anonymization of OpenWiFi Data
Abstract: Data privacy and protection through anonymization is a critical issue for network operators or data owners before it is forwarded for other possible use of data. With the adoption of Artificial Intelligence (AI), data anonymization augments the likelihood of covering up necessary sensitive information; preventing data leakage and information loss. OpenWiFi networks are vulnerable to any adversary who is trying to gain access or knowledge on traffic regardless of the knowledge possessed by data owners. The odds for discovery of actual traffic information is addressed by applied conditional tabular generative adversarial network (CTGAN). CTGAN yields synthetic data; which disguises as actual data but fostering hidden acute information of actual data. In this paper, the similarity assessment of synthetic with actual data is showcased in terms of clustering algorithms followed by a comparison of performance for unsupervised cluster validation metrics. A well-known algorithm, K-means outperforms other algorithms in terms of similarity assessment of synthetic data over real data while achieving nearest scores 0.634, 23714.57, and 0.598 as Silhouette, Calinski and Harabasz and Davies Bouldin metric respectively. On exploiting a comparative analysis in validation scores among several algorithms, K-means forms the epitome of unsupervised clustering algorithms ensuring explicit usage of synthetic data at the same time a replacement for real data. Hence, the experimental results aim to show the viability of using CTGAN-generated synthetic data in lieu of publishing anonymized data to be utilized in various applications. | cs | 0 |
Title: A scalable computational platform for particulate Stokes suspensions
Abstract: We describe a computational framework for simulating suspensions of rigid particles in Newtonian Stokes flow. One central building block is a collision-resolution algorithm that overcomes the numerical constraints arising from particle collisions. This algorithm extends the well-known complementarity method for non-smooth multi-body dynamics to resolve collisions in dense rigid body suspensions. This approach formulates the collision resolution problem as a linear complementarity problem with geometric `non-overlapping' constraints imposed at each timestep. It is then reformulated as a constrained quadratic programming problem and the Barzilai-Borwein projected gradient descent method is applied for its solution. This framework is designed to be applicable for any convex particle shape, e.g., spheres and spherocylinders, and applicable to any Stokes mobility solver, including the Rotne-Prager-Yamakawa approximation, Stokesian Dynamics, and PDE solvers (e.g., boundary integral and immersed boundary methods). In particular, this method imposes Newton's Third Law and records the entire contact network. Further, we describe a fast, parallel, and spectrally-accurate boundary integral method tailored for spherical particles, capable of resolving lubrication effects. We show weak and strong parallel scalings up to $8\times 10^4$ particles with approximately $4\times 10^7$ degrees of freedom on $1792$ cores. We demonstrate the versatility of this framework with several examples, including sedimentation of particle clusters, and active matter systems composed of ensembles of particles driven to rotate. | cs | 1 |
Title: Kodaira-Saito vanishing for the irregular Hodge filtration
Abstract: After making correct, and then improving, our definition of the category of irregular mixed Hodge modules thanks to Mochizuki's recent results arXiv:2108.03843, we show how these results allow us to obtain Kodaira-Saito-type vanishing theorems for the irregular Hodge filtration of irregular mixed Hodge modules. | math | 0 |
Title: Kernel Theorems in Coorbit Theory
Abstract: We prove general kernel theorems for operators acting between coorbit spaces. These are Banach spaces associated to an integrable representation of a locally compact group and contain most of the usual function spaces (Besov spaces, modulation spaces, etc.). A kernel theorem describes the form of every bounded operator between a coorbit space of test functions and distributions by means of a kernel in a coorbit space associated to the tensor product representation. As special cases we recover Feichtinger's kernel theorem for modulation spaces and the recent generalizations by Cordero and Nicola. We also obtain a kernel theorem for operators between the Besov spaces $\dot{B}^0_{1,1}$ and $\dot{B}^{0}_{\infty, \infty }$. | math | 1 |
Title: Some asymptotic formulae involving Cohen-Ramanujan expansions
Abstract: Some necessary and sufficient conditions for the existence of Cohen-Ramanujan expansions for arithmetical functions were provided by these authors in [\textit{arXive preprint arXive:2205.08466}, 2022]. Given two arithmetical functions $f$ and $g$ with absolutely convergent Cohen-Ramanujan expansions, we derive an asymptotic formula for $\sum_{n\leq N}f(n)g(n+h)$ where $h$ is a fixed positive integer. We also provide Cohen-Ramanujan expansions for certain functions to illustrate some of the results we prove consequently. | math | 0 |
Title: Long time behavior for collisional strongly magnetized plasma in three space dimensions
Abstract: We consider the long time evolution of a population of charged particles, under strong magnetic fields and collision mechanisms. We derive a fluid model and justify the asymptotic behavior toward smooth solutions of this regime. In three space dimensions, a constraint ocurs along the parallel direction. For eliminating the corresponding Lagrange multiplier, we average along the magnetic lines. | math | 0 |
Title: On the Composability of Statistically Secure Random Oblivious Transfer
Abstract: We show that stand-alone statistically secure random oblivious transfer protocols based on two-party stateless primitives are statistically universally composable. I.e. they are simulatable secure with an unlimited adversary, an unlimited simulator and an unlimited environment machine. Our result implies that several previous oblivious transfer protocols in the literature which were proven secure under weaker, non-composable definitions of security can actually be used in arbitrary statistically secure applications without lowering the security. | cs | 1 |
Title: Igusa zeta functions and the non-archimedean SYZ fibration
Abstract: We explain the proof, obtained in collaboration with Chenyang Xu, of a 1999 conjecture of Veys about poles of maximal order of Igusa zeta functions. The proof technique is based on the Minimal Model Program in birational geometry, but the proof was heavily inspired by ideas coming from non-archimedean geometry and mirror symmetry; we will outline these relations at the end of the paper. This text is intended to be a low-tech introduction to these topics; we only assume that the reader has a basic knowledge of algebraic geometry. | math | 1 |
Title: WFTNet: Exploiting Global and Local Periodicity in Long-term Time Series Forecasting
Abstract: Recent CNN and Transformer-based models tried to utilize frequency and periodicity information for long-term time series forecasting. However, most existing work is based on Fourier transform, which cannot capture fine-grained and local frequency structure. In this paper, we propose a Wavelet-Fourier Transform Network (WFTNet) for long-term time series forecasting. WFTNet utilizes both Fourier and wavelet transforms to extract comprehensive temporal-frequency information from the signal, where Fourier transform captures the global periodic patterns and wavelet transform captures the local ones. Furthermore, we introduce a Periodicity-Weighted Coefficient (PWC) to adaptively balance the importance of global and local frequency patterns. Extensive experiments on various time series datasets show that WFTNet consistently outperforms other state-of-the-art baseline. Code is available at https://github.com/Hank0626/WFTNet. | cs | 0 |
Title: $L^p$ Maximal regularity for vector-valued Schrödinger operators
Abstract: In this paper we consider the vector-valued Schr\"{o}dinger operator $-\Delta + V$, where the potential term $V$ is a matrix-valued function whose entries belong to $L^1_{\rm loc}(\mathbb{R}^d)$ and, for every $x\in\mathbb{R}^d$, $V(x)$ is a symmetric and nonnegative definite matrix, with non positive off-diagonal terms and with eigenvalues comparable each other. For this class of potential terms we obtain maximal inequality in $L^1(\mathbb{R}^d,\mathbb{R}^m).$ Assuming further that the minimal eigenvalue of $V$ belongs to some reverse H\"older class of order $q\in(1,\infty)\cup\{\infty\}$, we obtain maximal inequality in $L^p(\mathbb{R}^d,\mathbb{R}^m)$, for $p$ in between $1$ and some $q$. | math | 0 |
Title: Probabilistic representation for mild solution of the Navier-Stokes equations
Abstract: This paper is based on a formulation of the Navier-Stokes equations developed by Iyer and Constantin \cite{Cont} , where the velocity field of a viscous incompressible fluid is written as the expected value of a stochastic process. Our contribution is to establish this probabilistic representation formula for mild solutions of the Navier-Stokes equations on $\mathbb{R}^{d} $. | math | 1 |
Title: Physics-informed graph neural Galerkin networks: A unified framework for solving PDE-governed forward and inverse problems
Abstract: Despite the great promise of the physics-informed neural networks (PINNs) in solving forward and inverse problems, several technical challenges are present as roadblocks for more complex and realistic applications. First, most existing PINNs are based on point-wise formulation with fully-connected networks to learn continuous functions, which suffer from poor scalability and hard boundary enforcement. Second, the infinite search space over-complicates the non-convex optimization for network training. Third, although the convolutional neural network (CNN)-based discrete learning can significantly improve training efficiency, CNNs struggle to handle irregular geometries with unstructured meshes. To properly address these challenges, we present a novel discrete PINN framework based on graph convolutional network (GCN) and variational structure of PDE to solve forward and inverse partial differential equations (PDEs) in a unified manner. The use of a piecewise polynomial basis can reduce the dimension of search space and facilitate training and convergence. Without the need of tuning penalty parameters in classic PINNs, the proposed method can strictly impose boundary conditions and assimilate sparse data in both forward and inverse settings. The flexibility of GCNs is leveraged for irregular geometries with unstructured meshes. The effectiveness and merit of the proposed method are demonstrated over a variety of forward and inverse computational mechanics problems governed by both linear and nonlinear PDEs. | cs | 1 |
Title: Asymptotic $l_p$ spaces and bounded distortions
Abstract: The new class of Banach spaces, so-called asymptotic $l_p$ spaces, is introduced and it is shown that every Banach space with bounded distortions contains a subspace from this class. The proof is based on an investigation of certain functions, called enveloping functions, which are intimately connected with stabilization properties of the norm. | math | 1 |
Title: On gamma factors for representations of finite general linear groups
Abstract: We use the Langlands--Shahidi method in order to define the Shahidi gamma factor for a pair of irreducible generic representations of $\operatorname{GL}_n\left(\mathbb{F}_q\right)$ and $\operatorname{GL}_m\left(\mathbb{F}_q\right)$. We prove that the Shahidi gamma factor is multiplicative and show that it is related to the Jacquet--Piatetski-Shapiro--Shalika gamma factor. As an application, we prove a converse theorem based on the absolute value of the Shahidi gamma factor, and improve the converse theorem of Nien. As another application, we give explicit formulas for special values of the Bessel function of an irreducible generic representation of $\operatorname{GL}_n\left(\mathbb{F}_q\right)$. | math | 0 |
Title: Locally anti de Sitter spaces and deformation quantization
Abstract: In the first part we define a "BTZ" black hole in anti de Sitter space in any dimension by defining as "singular" the closed orbits of the Iwasawa component of SO(2,n). In the second part, a strict quantization of the black hole by action of group is performed and its Dirac operator is computed. We introduce, in the appendix, most of the notions about homogeneous spaces and Iwasawa decompositions that are needed. Explicit matricial decompositions are given for every Lie algebra that will be used in the thesis: sl(2,R), so(1,n), so(2,n), sl(2,C) and sp(2,R). | math | 1 |
Title: Detection and Discovery of Misinformation Sources using Attributed Webgraphs
Abstract: Website reliability labels underpin almost all research in misinformation detection. However, misinformation sources often exhibit transient behavior, which makes many such labeled lists obsolete over time. We demonstrate that Search Engine Optimization (SEO) attributes provide strong signals for predicting news site reliability. We introduce a novel attributed webgraph dataset with labeled news domains and their connections to outlinking and backlinking domains. We demonstrate the success of graph neural networks in detecting news site reliability using these attributed webgraphs, and show that our baseline news site reliability classifier outperforms current SoTA methods on the PoliticalNews dataset, achieving an F1 score of 0.96. Finally, we introduce and evaluate a novel graph-based algorithm for discovering previously unknown misinformation news sources. | cs | 0 |
Title: How to Scale Up the Spectral Efficiency of Multi-way Massive MIMO Relaying?
Abstract: This paper considers a decode-and-forward (DF) multi-way massive multiple-input multiple-output (MIMO) relay system where many users exchange their data with the aid of a relay station equipped with a massive antenna array. We propose a new transmission protocol which leverages successive cancelation decoding and zero-forcing (ZF) at the users. By using properties of massive MIMO, a tight analytical approximation of the spectral efficiency is derived. We show that our proposed scheme uses only half of the time-slots required in the conventional scheme (in which the number of time-slots is equal to the number of users [1]), to exchange data across different users. As a result, the sum spectral efficiency of our proposed scheme is nearly double the one of the conventional scheme, thereby boosting the performance of multi-way massive MIMO to unprecedented levels. | cs | 1 |
Title: Smooth invariant foliations and Koopman eigenfunctions about stable equilibria of semiflows
Abstract: We consider a $C^r$ semiflow $\{ \varphi_t \}_{t \geq 0}$ on a Banach space $X$ admitting a stable fixed point $x$. We show, along the lines of the parameterization method (Cabr\'e et al., 2003), the existence of a $C^r$ invariant foliation tangent to $X_1$ at $x$, for an arbitrary $D \varphi_t(x)$-invariant subspace $X_1 \subset X$ satisfying some additional spectral conditions. Uniqueness ensues in a subclass of sufficiently smooth invariant foliations tangent to $X_1$ at $x$. We then draw relations to Koopman theory, and thereby establish the existence and uniqueness, in some appropriate sense, of $C^r$ Koopman eigenfunctions. We demonstrate that these results apply to the case of the Navier-Stokes system, the archetypal example considered by the modern upheaval of applied 'Koopmanism'. | math | 0 |
Title: DCR-Consistency: Divide-Conquer-Reasoning for Consistency Evaluation and Improvement of Large Language Models
Abstract: Evaluating the quality and variability of text generated by Large Language Models (LLMs) poses a significant, yet unresolved research challenge. Traditional evaluation methods, such as ROUGE and BERTScore, which measure token similarity, often fail to capture the holistic semantic equivalence. This results in a low correlation with human judgments and intuition, which is especially problematic in high-stakes applications like healthcare and finance where reliability, safety, and robust decision-making are highly critical. This work proposes DCR, an automated framework for evaluating and improving the consistency of LLM-generated texts using a divide-conquer-reasoning approach. Unlike existing LLM-based evaluators that operate at the paragraph level, our method employs a divide-and-conquer evaluator (DCE) that breaks down the paragraph-to-paragraph comparison between two generated responses into individual sentence-to-paragraph comparisons, each evaluated based on predefined criteria. To facilitate this approach, we introduce an automatic metric converter (AMC) that translates the output from DCE into an interpretable numeric score. Beyond the consistency evaluation, we further present a reason-assisted improver (RAI) that leverages the analytical reasons with explanations identified by DCE to generate new responses aimed at reducing these inconsistencies. Through comprehensive and systematic empirical analysis, we show that our approach outperforms state-of-the-art methods by a large margin (e.g., +19.3% and +24.3% on the SummEval dataset) in evaluating the consistency of LLM generation across multiple benchmarks in semantic, factual, and summarization consistency tasks. Our approach also substantially reduces nearly 90% of output inconsistencies, showing promise for effective hallucination mitigation. | cs | 0 |
Title: The Unreasonable Effectiveness of Deep Evidential Regression
Abstract: There is a significant need for principled uncertainty reasoning in machine learning systems as they are increasingly deployed in safety-critical domains. A new approach with uncertainty-aware regression-based neural networks (NNs), based on learning evidential distributions for aleatoric and epistemic uncertainties, shows promise over traditional deterministic methods and typical Bayesian NNs, notably with the capabilities to disentangle aleatoric and epistemic uncertainties. Despite some empirical success of Deep Evidential Regression (DER), there are important gaps in the mathematical foundation that raise the question of why the proposed technique seemingly works. We detail the theoretical shortcomings and analyze the performance on synthetic and real-world data sets, showing that Deep Evidential Regression is a heuristic rather than an exact uncertainty quantification. We go on to discuss corrections and redefinitions of how aleatoric and epistemic uncertainties should be extracted from NNs. | cs | 1 |
Title: An Improved Algorithm for Computing All the Best Swap Edges of a Tree Spanner
Abstract: A tree $\sigma$-spanner of a positively real-weighted $n$-vertex and $m$-edge undirected graph $G$ is a spanning tree $T$ of $G$ which approximately preserves (i.e., up to a multiplicative stretch factor $\sigma$) distances in $G$. Tree spanners with provably good stretch factors find applications in communication networks, distributed systems, and network design. However, finding an optimal or even a good tree spanner is a very hard computational task. Thus, if one has to face a transient edge failure in $T$, the overall effort that has to be afforded to rebuild a new tree spanner (i.e., computational costs, set-up of new links, updating of the routing tables, etc.) can be rather prohibitive. To circumvent this drawback, an effective alternative is that of associating with each tree edge a best possible (in terms of resulting stretch) swap edge -- a well-established approach in the literature for several other tree topologies. Correspondingly, the problem of computing all the best swap edges of a tree spanner is a challenging algorithmic problem, since solving it efficiently means to exploit the structure of shortest paths not only in $G$, but also in all the scenarios in which an edge of $T$ has failed. For this problem we provide a very efficient solution, running in $O(n^2 \log^4 n)$ time, which drastically improves (almost by a quadratic factor in $n$ in dense graphs!) on the previous known best result. | cs | 1 |
Title: Force-Based Atomistic/Continuum Blending for Multilattices
Abstract: We formulate the blended force-based quasicontinuum (BQCF) method for multilattices and develop rigorous error estimates in terms of the approximation parameters: atomistic region, blending region and continuum finite element mesh. Balancing the approximation parameters yields a convergent atomistic/continuum multiscale method for multilattices with point defects, including a rigorous convergence rate in terms of the computational cost. The analysis is illustrated with numerical results for a Stone--Wales defect in graphene. | math | 1 |
Title: Adaptive Population-based Simulated Annealing for Uncertain Resource Constrained Job Scheduling
Abstract: Transporting ore from mines to ports is of significant interest in mining supply chains. These operations are commonly associated with growing costs and a lack of resources. Large mining companies are interested in optimally allocating their resources to reduce operational costs. This problem has been previously investigated in the literature as resource constrained job scheduling (RCJS). While a number of optimisation methods have been proposed to tackle the deterministic problem, the uncertainty associated with resource availability, an inevitable challenge in mining operations, has received less attention. RCJS with uncertainty is a hard combinatorial optimisation problem that cannot be solved efficiently with existing optimisation methods. This study proposes an adaptive population-based simulated annealing algorithm that can overcome the limitations of existing methods for RCJS with uncertainty including the premature convergence, the excessive number of hyper-parameters, and the inefficiency in coping with different uncertainty levels. This new algorithm is designed to effectively balance exploration and exploitation, by using a population, modifying the cooling schedule in the Metropolis-Hastings algorithm, and using an adaptive mechanism to select perturbation operators. The results show that the proposed algorithm outperforms existing methods across a wide range of benchmark RCJS instances and uncertainty levels. Moreover, new best known solutions are discovered for all but one problem instance across all uncertainty levels. | cs | 1 |
Title: Improved estimators in Bell regression model with application
Abstract: In this paper, we propose the application of shrinkage strategies to estimate coefficients in the Bell regression models when prior information about the coefficients is available. The Bell regression models are well-suited for modeling count data with multiple covariates. Furthermore, we provide a detailed explanation of the asymptotic properties of the proposed estimators, including asymptotic biases and mean squared errors. To assess the performance of the estimators, we conduct numerical studies using Monte Carlo simulations and evaluate their simulated relative efficiency. The results demonstrate that the suggested estimators outperform the unrestricted estimator when prior information is taken into account. Additionally, we present an empirical application to demonstrate the practical utility of the suggested estimators. | math | 0 |
Title: An algorithm for estimating the crossing number of dense graphs, and continuous analogs of the crossing and rectilinear crossing numbers
Abstract: We present a deterministic $n^{2+o(1)}$-time algorithm that approximates the crossing number of any graph $G$ of order $n$ up to an additive error of $o(n^4)$. We also provide a randomized polynomial-time algorithm that constructs a drawing of $G$ with $\text{cr}(G)+o(n^4)$ crossings. These results are made interesting by the well known fact that every dense $n$-vertex graph has crossing number $\Theta(n^4)$. Our work builds on a technique developed by Fox, Pach and S\'uk, who obtained very similar results for the rectilinear crossing number. The results by the aforementioned authors and in this paper imply that the (normalized) crossing and rectilinear crossing numbers are estimable parameters. Motivated by this, we introduce two graphon parameters, the \textit{crossing density} and the \textit{rectilinear crossing density}, and then we prove that, in a precise sense, these are the correct continuous analogs of the crossing and rectilinear crossing numbers of graphs. | math | 0 |
Title: Nonlinear diffusion equations with nonlinear gradient noise
Abstract: We prove the existence and uniqueness of entropy solutions for nonlinear diffusion equations with nonlinear conservative gradient noise. As particular applications our results include stochastic porous media equations, as well as the one-dimensional stochastic mean curvature flow in graph form. | math | 1 |
Title: The Solvability of Interpretability Evaluation Metrics
Abstract: Feature attribution methods are popular for explaining neural network predictions, and they are often evaluated on metrics such as comprehensiveness and sufficiency. In this paper, we highlight an intriguing property of these metrics: their solvability. Concretely, we can define the problem of optimizing an explanation for a metric, which can be solved by beam search. This observation leads to the obvious yet unaddressed question: why do we use explainers (e.g., LIME) not based on solving the target metric, if the metric value represents explanation quality? We present a series of investigations showing strong performance of this beam search explainer and discuss its broader implication: a definition-evaluation duality of interpretability concepts. We implement the explainer and release the Python solvex package for models of text, image and tabular domains. | cs | 1 |
Title: Hadwiger's conjecture and topological bounds
Abstract: The Odd Hadwiger's conjecture, formulated by Gerards and Seymour in 1995, is a substantial strengthening of Hadwiger's famous coloring conjecture from 1943. We investigate whether the hierarchy of topological lower bounds on the chromatic number, introduced by Matou\v{s}ek and Ziegler (2003) and refined recently by Daneshpajouh and Meunier (2023), forms a potential avenue to a disproof of Hadwiger's conjecture or its odd-minor variant. In this direction, we prove that, in a very general sense, every graph $G$ that admits a topological lower bound of $t$ on its chromatic number, contains $K_{\lfloor t/2\rfloor +1}$ as an odd-minor. This solves a problem posed by Simonyi and Zsb\'{a}n [European Journal of Combinatorics, 31(8), 2110--2119 (2010)]. We also prove that if for a graph $G$ the Dol'nikov-K\v{r}\'{i}\v{z} lower bound on the chromatic number (one of the lower bounds in the aforementioned hierarchy) attains a value of at least $t$, then $G$ contains $K_t$ as a minor. Finally, extending results by Simonyi and Zsb\'{a}n, we show that the Odd Hadwiger's conjecture holds for Schrijver and Kneser graphs for any choice of the parameters. The latter are canonical examples of graphs for which topological lower bounds on the chromatic number are tight. | math | 0 |
Title: Joint distribution in residue classes of families of polynomially-defined multiplicative functions
Abstract: We study the distribution of families of multiplicative functions among the coprime residue classes to moduli varying uniformly in a wide range, when the multiplicative functions can be controlled by the values of polynomials at the first few prime powers. We obtain complete uniform extensions of a criterion of Narkiewicz for families of such multiplicative functions, thus also generalizing and improving upon previous work for a single such function and establishing results that are optimal in most parameters and hypotheses. As a special case of our results, for any fixed $\epsilon>0$, the Euler totient function $\phi(n)$ and sum of divisors function $\sigma(n)$ are jointly asymptotically equidistributed among the reduced residue classes to moduli $q$ coprime to $6$ varying uniformly up to $(\log x)^{(1-\epsilon)\alpha(q)}$, where $\alpha(q) = \prod_{\ell \mid q} (\ell-3)/(\ell-1)$; furthermore, the coprimality restriction is necessary and the range of $q$ is essentially optimal. | math | 0 |
Title: The extension problem in free harmonic analysis
Abstract: This paper studies certain aspects of harmonic analysis on nonabelian free groups. We focus on the concept of a positive definite function on the free group and our primary goal is to understand how such functions can be extended from balls of finite radius to the entire group. Previous work showed that such extensions always exist and we study the problem of simultaneous extension of multiple positive definite functions. More specifically, we define a concept of 'relative energy' which measures the proximity between a pair of positive definite functions, and show that a pair of positive definite functions on a finite ball can be extended to the entire group without increasing their relative energy. The proof is analytic, involving differentiation of noncommutative Szego parameters. | math | 1 |