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Massless ground state for a compact SU2 matrix model in 4D ; We show the existence and uniqueness of a massless supersymmetric ground state wavefunction of a SU2 matrix model in a bounded smooth domain with Dirichlet boundary conditions. This is a gauge system and we provide a new framework to analyze the quantum spectral properties of this class of supersymmetric matrix models subject to constraints which can be generalized for arbitrary number of colors.

Realistic threegeneration models from SO32 heterotic string theory ; We search for realistic supersymmetric standardlike models from SO32 heterotic string theory on factorizable tori with multiple magnetic fluxes. Three chiral ganerations of quarks and leptons are derived from the adjoint and vector representations of SO12 gauge groups embedded in SO32 adjoint representation. Massless spectra of our models also include Higgs fields, which have desired Yukawa couplings to quarks and leptons at the treelevel.

A DempsterSchafer approach to Bell's inequalities ; We present an alternative approach to modeling EinsteinPodolskyRosenBohm EPRBtype experiments. The basis for our approach will be to replace the conventional Kolmogorov theory of probability, with the more general DempsterSchafer theory of evidence. This leads to the identification of a distinct type of epistemic uncertainty, which is not present in Kolmogorov theory, but which is relevant in modeling experiments with operationally incompatible observables. Our treatment naturally yields conditional relative frequencies, which are perfectly compatible with classical determinism and locality, but which do not satisfy Belltype inequalities.

Correlation functions in loop models ; In this paper we provide a step towards the understanding of the On bulk operator algebra. By using a mixture of analytical and numerical methods, we compute ratios of structure constants, and analyse the logarithmic structure of the transfer matrix. We believe that the On model for a generic value of n q q1 i.e. for q not a root of unity provides a toy model of a bulk logarithmic CFT that is considerably simpler than its counterparts at q a root of unity.

The simplest extension of Starobinsky inflation ; We consider the simplest extension to the Starobinsky model, by allowing an extra scalar field to help drive inflation. We perform our analysis in the Einstein frame and calculate the power spectra at the end of inflation to second order in the slowroll parameters. We find that the model gives predictions in great agreement with the current Planck data without the need for finetuning. Our results encourage current efforts to embed the model in a supergravity setting.

Radiative Neutrino Mass Models ; In this short review, we see some typical models in which light neutrino masses are generated at the loop level. These models involve new Higgs bosons whose Yukawa interactions with leptons are constrained by the neutrino oscillation data. Predictions about flavor structures of ell to overlineell1 ell2 ell3 and leptonic decays of new Higgs bosons via the constrained Yukawa interactions are briefly summarized in order to utilize such Higgs as a probe of nu physics.

Aftershocks and Omori's law in a modified CarlsonLanger model with nonlinear viscoelasticity ; A modified CarlsonLanger model for earthquakes is proposed, which includes nonlinear viscoelasticity. Several aftershocks are generated after the main shock owing to the damping of the additional viscoelastic force. Both the GutenbergRichter law and Omori's law are reproduced in a numerical simulation of the modified CarlsonLanger model on a critical percolation cluster of a square lattice.

Approaches for modeling magnetic nanoparticle dynamics ; Magnetic nanoparticles are useful biological probes as well as therapeutic agents. There have been several approaches used to model nanoparticle magnetization dynamics for both Brownian as well as N'eel rotation. The magnetizations are often of interest and can be compared with experimental results. Here we summarize these approaches including the StonerWohlfarth approach, and stochastic approaches including thermal fluctuations. Nonequilibrium related temperature effects can be described by a distribution function approach FokkerPlanck equation or a stochastic differential equation Langevin equation. Approximate models in several regimes can be derived from these general approaches to simplify implementation.

Optimal twotreatment crossover designs for binary response models ; Optimal twotreatment, p period crossover designs for binary responses are determined. The optimal designs are obtained by minimizing the variance of the treatment contrast estimator over all possible allocations of n subjects to 2p possible treatment sequences. An appropriate logistic regression model is postulated and the within subject covariances are modeled through a working correlation matrix. The marginal mean of the binary responses are fitted using generalized estimating equations. The efficiencies of some crossover designs for p2,3,4 periods are calculated. The effect of misspecified working correlation matrix on design efficiency is also studied.

Anisotropic stars with nonstatic conformal symmetry ; We have proposed a model for relativistic compact star with anisotropy and analytically obtained exact spherically symmetric solutions describing the interior of the dense star admitting nonstatic conformal symmetry. Several features of the solutions including drawbacks of the model have been explored and discussed. For this purpose we have provided the energy conditions, TOVequations and other physical requirements and thus thoroughly investigated stability, massradius relation and surface redshift of the model. It is observed that most of the features are well matched with the compact stars, like quarkstrange stars.

The symmetric sixvertex model and the Segre cubic threefold ; In this paper we investigate the mathematical properties of the integrability of the symmetric sixvertex model towards the view of Algebraic Geometry. We show that the algebraic variety originated from Baxter's commuting transfer method is birationally isomorphic to a ubiquitous threefold known as Segre cubic primal. This relation makes it possible to present the most generic solution for the YangBaxter triple associated to this lattice model. The respective mathrmRmatrix and Lax operators are parametrized by three independent affine spectral variables.

SEPIA Search for Proofs Using Inferred Automata ; This paper describes SEPIA, a tool for automated proof generation in Coq. SEPIA combines model inference with interactive theorem proving. Existing proof corpora are modelled using statebased models inferred from tactic sequences. These can then be traversed automatically to identify proofs. The SEPIA system is described and its performance evaluated on three Coq datasets. Our results show that SEPIA provides a useful complement to existing automated tactics in Coq.

MatrixFree Convex Optimization Modeling ; We introduce a convex optimization modeling framework that transforms a convex optimization problem expressed in a form natural and convenient for the user into an equivalent cone program in a way that preserves fast linear transforms in the original problem. By representing linear functions in the transformation process not as matrices, but as graphs that encode composition of linear operators, we arrive at a matrixfree cone program, i.e., one whose data matrix is represented by a linear operator and its adjoint. This cone program can then be solved by a matrixfree cone solver. By combining the matrixfree modeling framework and cone solver, we obtain a general method for efficiently solving convex optimization problems involving fast linear transforms.

Standard Model Effective Field Theory Integrating out VectorLike Fermions ; We apply the covariant derivative expansion of the ColemanWeinberg potential to vectorlike fermion models, matching the UV theory to the relevant dimension6 operators in the standard model effective field theory. The gamma matrix induced complication in the fermionic covariant derivative expansion is studied in detail, and all the contributing combinations are enumerated. From this analytical result we also provide numerical constraints for a generation of vectorlike quarks and vectorlike leptons.

The bandcentre anomaly in the 1D Anderson model with correlated disorder ; We study the bandcentre anomaly in the onedimensional Anderson model with weak correlated disorder. Our analysis is based on the Hamiltonian map approach; the correspondence between the discrete model and its continuous counterpart is discussed in detail. We obtain analytical expressions of the localisation length and of the invariant measure of the phase variable, valid for energies in a neighbourhood of the band centre. By applying these general results to specific forms of correlated disorder, we show how correlations can enhance or suppress the anomaly at the band centre.

Nonstandard supersymmetry breaking and Dirac gaugino masses without supersoftness ; I consider models in which nonstandard supersymmetry breaking terms, including Dirac gaugino masses, arise from Fterm breaking mediated by operators with a 1M3 suppression. In these models, the supersoft properties found in the case of Dterm breaking are absent in general, but can be obtained as a special case that is a fixed point of the renormalization group equations. The mu term is replaced by three distinct supersymmetrybreaking parameters, decoupling the Higgs scalar potential from the Higgsino masses. Both holomorphic and nonholomorphic scalar cubic interactions with minimal flavor violation are induced in the supersymmetric Standard Model Lagrangian.

The KantowskiSachs quantum model with stiff matter fluid ; In this paper we study the quantum cosmological KantowskiSachs model and solve the WheelerDeWitt equation in minisuperspace to obtain the wave function of the corresponding universe. The perfect fluid is described by the Schutz's canonical formalism, which allows to attribute dynamical degrees of freedom to matter. The time is introduced phenomenologically using the fluid's degrees of freedom. In particular, we adopt a stiff matter fluid. The viability of this model is analyzed and discussed.

Diffusive dynamics and stochastic models of turbulent axisymmetric wakes ; A modelling methodology to reproduce the experimental measurements of a turbulent flow under the presence of symmetry is presented. The flow is a threedimensional wake generated by an axisymmetric body. We show that the dynamics of the turbulent wake flow can be assimilated by a nonlinear twodimensional Langevin equation, the deterministic part of which accounts for the broken symmetries which occur at the laminar and transitional regimes at low Reynolds numbers and the stochastic part of which accounts for the turbulent fluctuations. Comparison between theoretical and experimental results allows the extraction of the model parameters.

Combining Grassmann algebra with entanglement renormalization method ; By combining the Grassmann algebra with multiscale entanglement renormalization ansatz MERA, we introduce a new unbiased and effective numerical method for simulating 2D strongly correlated electronic systems. The new GMERA method inherits all the advantages of MERA, which constructs the variational wave function based on complicated tensor network. Besides it can deal with fermionic properties of the system due to Grassmann algebra through local tensor contractions. This general method can treat different tensor network structures in a universal way. We show several benchmark calculations of the GMERA method, including the free fermion model, tight binding model, as well as the tJ model with hole doping.

Mixtures of Multivariate Power Exponential Distributions ; An expanded family of mixtures of multivariate power exponential distributions is introduced. While fitting heavytails and skewness has received much attention in the modelbased clustering literature recently, we investigate the use of a distribution that can deal with both varying tailweight and peakedness of data. A family of parsimonious models is proposed using an eigendecomposition of the scale matrix. A generalized expectationmaximization algorithm is presented that combines convex optimization via a minorizationmaximization approach and optimization based on accelerated line search algorithms on the Stiefel manifold. Lastly, the utility of this family of models is illustrated using both toy and benchmark data.

Tridiagonal random matrix Gaussian fluctuations and deviations ; This paper is devoted to the Gaussian fluctuations and deviations of the traces of tridiagonal random matrix. Under quite general assumptions, we prove that the traces are approximately normal distributed. Multidimensional central limit theorem is also obtained here. These results have several applications to various physical models and random matrix models, such as the Anderson model, the random birthdeath Markov kernel, the random birthdeath Q matrix and the betaHermite ensemble. Furthermore, under some independent and identically distributed condition, we also prove the large deviation principle as well as the moderate deviation principle for the traces.

Hints of the jet composition in gammaray bursts from dissipative photosphere models ; We present a model for gammaray bursts where a dissipative photosphere provides the usual spectral peak around MeV energies accompanied by a subdominant thermal component. We treat the initial acceleration of the jet in a general way, allowing for magnetic field and baryon dominated outflows. In this model, the GeV emission associated with GRBs observed by Fermi LAT, arises as the interaction of photospheric radiation and the shocked electrons at the deceleration radius. Through recently discovered correlations between the thermal and nonthermal peaks within individual bursts, we are able to infer whether the jet was Poynting flux or baryon dominated.

Emergence of synchrony in an Adaptive Interaction Model ; In a HumanComputer Interaction context, we aim to elaborate an adaptive and generic interaction model in two different use cases Embodied Conversational Agents and Creative Musical Agents for musical improvisation. To reach this goal, we'll try to use the concepts of adaptation and synchronization to enhance the interactive abilities of our agents and guide the development of our interaction model, and will try to make synchrony emerge from nonverbal dimensions of interaction.

Large NonGaussianity in SlowRoll Inflation ; Canonical models of singlefield, slowroll inflation do not lead to appreciable nonGaussianity, unless derivative interactions of the inflaton become uncontrollably large. We propose a novel slowroll scenario where scalar perturbations propagate at a subluminal speed, leading to sizeable equilateral nonGaussianity, frm equilrm NLpropto 1cs4, largely insensitive to the ultraviolet physics. The model is based on a lowenergy effective theory characterized by weakly broken invariance under internal galileon transformations, phitophibmu xmu, which protects the properties of perturbations from large quantum corrections. This provides the unique alternative to models such as DBI inflation in generating strongly subluminalnonGaussian scalar perturbations.

Global small solutions to a tropical climate model without thermal diffusion ; We obtain the global wellposedness of classical solutions to a tropical climate model derived by FeireislMajdaPauluis in citeFMP with only the dissipation of the first baroclinic model of the velocity eta Delta v under small initial data. The main difficulty is the absence of thermal diffusion as the work by LiTiti in citeLT. To overcome it, we exploit the structure of the equations coming from the coupled terms, dissipation term and damp term. Then we find the hidden thermal diffusion. In addition, based on the LittlewoodPalay theory, we establish a generalized commutator estimate, which may be applied to other partial differential equations.

A mechanical model for guided motion of mammalian cells ; We introduce a generic, purely mechanical model for environment sensitive motion of mammalian cells that is applicable to chemotaxis, haptotaxis, and durotaxis as modes of motility. It is able to theoretically explain all relevant experimental observations, in particular, the high efficiency of motion, the behavior on inhomogeneous substrates, and the fixation of the lagging pole during motion. Furthermore, our model predicts that efficiency of motion in following a gradient depends on cell geometry with more elongated cells being more efficient.

Emergence of classical gravity and the objective reduction of the quantum state in deterministic models of quantum mechanics ; Models for deterministic quantum mechanics of CartanRanders type are introduced, together with the fundamental notions of the concentration of measure theory. We explain how the application of the concentration of measure to CartanRanders models provides a framework from which it emerge 1. The invariance under infinitesimal diffeomorphisms of the macroscopic dynamics 2. A mechanism for reduction of the quantum state and 3. The Weak Equivalence Principle.

Martingale property of exponential semimartingales a note on explicit conditions and applications to financial models ; We give a collection of explicit sufficient conditions for the true martingale property of a wide class of exponentials of semimartingales. We express the conditions in terms of semimartingale characteristics. This turns out to be very convenient in financial modeling in general. Especially it allows us to carefully discuss the question of welldefinedness of semimartingale Libor models, whose construction crucially relies on a sequence of measure changes.

Continuous opinions and discrete actions in social networks a multiagent system approach ; This paper proposes and analyzes a novel multiagent opinion dynamics model in which agents have access to actions which are quantized version of the opinions of their neighbors. The model produces different behaviors observed in social networks such as disensus, clustering, oscillations, opinion propagation, even when the communication network is connected. The main results of the paper provides the characterization of preservation and diffusion of actions under general communication topologies. A complete analysis allowing the opinion forecasting is given in the particular cases of complete and ring communication graphs. Numerical examples illustrate the main features of this model.

An InformationTheoretic Foundation for the Weighted Updating Model ; Weighted Updating generalizes Bayesian updating, allowing for biased beliefs by weighting the likelihood function and prior distribution with positive real exponents. I provide a rigorous foundation for the model by showing that transforming a distribution by exponential weighting and normalizing systematically affects the information entropy of the resulting distribution. For weights greater than one the resulting distribution has less information entropy than the original distribution, and vice versa. The entropy of a distribution measures how informative a decision maker is treating the underlying observations, so this result suggests a useful interpretation of the weights. For example, a weight greater than one on a likelihood function models an individual who is treating the associated observations as being more informative than a perfect Bayesian would.

Tutte polynomials and randomcluster models in Bernoulli cell complexes ; This paper studies Bernoulli cell complexes from the perspective of persistent homology, Tutte polynomials, and randomcluster models. Following the previous work 9, we first show the asymptotic order of the expected lifetime sum of the persistent homology for the Bernoulli cell complex process on the ellcubical lattice. Then, an explicit formula of the expected lifetime sum using the Tutte polynomial is derived. Furthermore, we study a higher dimensional generalization of the randomcluster model derived from the EdwardsSokal type coupling, and show some basic results such as the positive association and the relation to the Tutte polynomial.

Modeling and optimization of the antenna system with focal plane array for the new generation radio telescopes with wide field of view ; The model of the reflector antenna system with focal plane array, lownoise amplifier and beamformer is developed in the work. The beamformer strategy is suggested to reduce the receiving sensitivity ripple inside field of view of the telescope, while the sensitivity itself drops slightly less than 10. The system APERTIF which is currently under development in Netherlands Institute For Radioastronomy, ASTRON has been analyzed using developed model, and numerical results are presented. The obtained numerical results have been verified experimentally in anechoic chamber as well as on one of the dishes of the Westerbork Synthesis Radio Telescope all measurements have been done in ASTRON.

A multiscale approach for spatially inhomogeneous disease dynamics ; In this paper we introduce an agentbased epidemiological model that generalizes the classical SIR model by Kermack and McKendrick. We further provide a multiscale approach to the derivation of a macroscopic counterpart via the meanfield limit. The chain of equations acquired via the multiscale approach are investigated, analytically as well as numerically. The outcome of these results provide strong evidence of the models' robustness and justifies their applicability in describing disease dynamics, in particularly when mobility is involved.

Nonsymbolic Text Representation ; We introduce the first generic text representation model that is completely nonsymbolic, i.e., it does not require the availability of a segmentation or tokenization method that attempts to identify words or other symbolic units in text. This applies to training the parameters of the model on a training corpus as well as to applying it when computing the representation of a new text. We show that our model performs better than prior work on an information extraction and a text denoising task.

Nuclear Numerical Range and Quantum Error Correction Codes for nonunitary noise models ; We introduce a notion of nuclear numerical range defined as the set of expectation values of a given operator A among normalized pure states, which belong to the nucleus of an auxiliary operator Z. This notion proves to be applicable to investigate models of quantum noise with blockdiagonal structure of the corresponding Kraus operators. The problem of constructing a suitable quantum error correction code for this model can be restated as a geometric problem of finding intersection points of certain sets in the complex plane. This technique, worked out in the case of twoqubit systems, can be generalized for larger dimensions.

Cosmological Attractors and Anisotropies in Two Measure Theories, Effective EYMH systems, and OffDiagonal Inflation Models ; Applying the anholonomic frame deformation method, we construct various classes of cosmological solutions for effective Einstein YangMills Higgs, and two measure theories. The types of models considered are FreedmanLemaitreRobertsonWalker, Bianchi, Kasner and models with attractor configurations. The various regimes pertaining to plateautype inflation, quadratic inflation, Starobinsky type and Higgs type inflation are presented.

Active Fault Tolerant Flight Control System Design ; In this paper we investigate the design of an active fault tolerant control system applicable to autonomous flight. The system comprises a nonlinear model predictive based controller integrated with an unscented Kalman filter for fault detection and identification. We apply the fault tolerant control system design to a generic aircraft model, and simulate a failed engine scenario. The results show that the system correctly identifies the fault within seconds of occurrence and updates the nonlinear model predictive controller which is then able to reallocate control authority to the healthy actuators based upon up to date fault information.

Modelling Sentence Pairs with Treestructured Attentive Encoder ; We describe an attentive encoder that combines treestructured recursive neural networks and sequential recurrent neural networks for modelling sentence pairs. Since existing attentive models exert attention on the sequential structure, we propose a way to incorporate attention into the tree topology. Specially, given a pair of sentences, our attentive encoder uses the representation of one sentence, which generated via an RNN, to guide the structural encoding of the other sentence on the dependency parse tree. We evaluate the proposed attentive encoder on three tasks semantic similarity, paraphrase identification and truefalse question selection. Experimental results show that our encoder outperforms all baselines and achieves stateoftheart results on two tasks.

Blowup for a Three Dimensional KellerSegel Model with Consumption of Chemoattractant ; We investigate blowup properties for the initialboundary value problem of a KellerSegel model with consumption of chemoattractant when the spatial dimension is three. Through a kinetic reformulation of the KellerSegel model, we first derive some higherorder estimates and obtain certain blowup criteria for the local classical solutions. These blowup criteria generalize the results in 4,5 from the whole space mathbbR3 to the case of bounded smooth domain Omegasubset mathbbR3. Lower global blowup estimate on nLinftyOmega is also obtained based on our higherorder estimates. Moreover, we prove local nondegeneracy for blowup points.

Kinematic equivalence between models driven by DBI field with constant and exotic holographic quintessence cosmological models ; We show the kinematic equivalence between cosmological models driven by DiracBornInfeld fields phi with constant proper velocity of the brane and exponential potential VV0eBphi and interactive cosmological systems with Modified Holographic Ricci type fluids as dark energy in flat FriedmannRobertsonWalker cosmologies.

Unified description of dark energy and dark matter in mimetic matter model ; The existence of dark matter and dark energy in cosmology is implied by various observations, however, they are still unclear because they have not been directly detected. In this Letter, an unified model of dark energy and dark matter that can explain the evolution history of the Universe later than inflationary era, the time evolution of the growth rate function of the matter density contrast, the flat rotation curves of the spiral galaxies, and the gravitational experiments in the solar system is proposed in mimetic matter model.

Properties of JP 12 baryon octets at low energy ; The statistical model in combination with detailed balance principle is able to phenomenological calculate and analyze spin and flavor dependent properties like magnetic moments with effective masses, effective charge, with both effective mass and effective charge, quark spin polarization and distribution, strangeness suppression factor. The magnetic moments of the octet baryons are analyzed within the statistical model, by putting emphasis on the SU3 symmetry breaking effects generated by the mass difference between the strange and non strange quarks. The work presented here assume hadrons with a sea having admixture of quarkgluon Fock states. The results obtained have been compared with theoretical models and experimental data.

Estimating Derivatives of FunctionValued Parameters in a Class of Moment Condition Models ; We develop a general approach to estimating the derivative of a functionvalued parameter thetaou that is identified for every value of u as the solution to a moment condition. This setup in particular covers many interesting models for conditional distributions, such as quantile regression or distribution regression. Exploiting that thetaou solves a moment condition, we obtain an explicit expression for its derivative from the Implicit Function Theorem, and estimate the components of this expression by suitable sample analogues, which requires the use of local linear smoothing. Our estimator can then be used for a variety of purposes, including the estimation of conditional density functions, quantile partial effects, and structural auction models in economics.

Electroweak vacuum stability in the HiggsDilaton theory ; We study the stability of the Electroweak EW vacuum in a scaleinvariant extension of the Standard Model and General Relativity, known as a HiggsDilaton theory. The safety of the EW vacuum against possible transition towards another vacuum is a necessary condition for the model to be phenomenologically acceptable. We find that, within a wide range of parameters of the theory, the decay rate is significantly suppressed compared to that of the Standard Model. We also discuss properties of a tunneling solution that are specific to the HiggsDilaton theory.

Recurrence of the frog model on the 3,2alternating tree ; Consider a growing system of random walks on the 3,2alternating tree, where generations of nodes alternate between having two and three children. Any time a particle lands on a node which has not been visited previously, a new particle is activated at that node, and begins its own random walk. The model described belongs to a class of problems that are collectively referred to as the frog model. Building on a recent proof of recurrence meaning infinitely many frogs hit the root with probability one on the regular binary tree, this paper establishes recurrence for the 3,2alternating case.

Multiview Regularized Gaussian Processes ; Gaussian processes GPs have been proven to be powerful tools in various areas of machine learning. However, there are very few applications of GPs in the scenario of multiview learning. In this paper, we present a new GP model for multiview learning. Unlike existing methods, it combines multiple views by regularizing marginal likelihood with the consistency among the posterior distributions of latent functions from different views. Moreover, we give a general point selection scheme for multiview learning and improve the proposed model by this criterion. Experimental results on multiple real world data sets have verified the effectiveness of the proposed model and witnessed the performance improvement through employing this novel point selection scheme.

A model for Faraday pilot waves over variable topography ; Couder and Fort discovered that droplets walking on a vibrating bath possess certain features previously thought to be exclusive to quantum systems. These millimetric droplets synchronize with their Faraday wavefield, creating a macroscopic pilotwave system. In this paper we exploit the fact that the waves generated are nearly monochromatic and propose a hydrodynamic model capable of quantitatively capturing the interaction between bouncing drops and a variable topography. We show that our reduced model is able to reproduce some important experiments involving the droptopography interaction, such as nonspecular reflection and singleslit diffraction.

Influence of the number of predecessors in interaction within accelerationbased flow models ; In this paper, the stability of the uniform solutions is analysed for microscopic flow models in interaction with Kge1 predecessors. We calculate general conditions for the linear stability on the ring geometry and explore the results with particular pedestrian and carfollowing models based on relaxation processes. The uniform solutions are stable if the relaxation times are sufficiently small. The analysis is focused on the relevance of the number of predecessors in the dynamics. Unexpected nonmonotonic relations between K and the stability are presented.

A Quantum Kalman FilterBased PID Controller ; We give a concrete description of a controlled quantum stochastic dynamical model corresponding to a quantum system a cavity mode under going continual quadrature measurements, with a PID controller acting on the filtered estimate for the mode operator. Central use is made of the input and output pictures when constructing the model these unitarily equivalent pictures are presented in the paper, and used to transfer concepts relating to the controlled internal dynamics to those relating to measurement output, and vice versa. The approach shows the general principle for investigating mathematically and physically consistent models in which standard control theoretic methods are to be extended to the quantum setting.

Testing models of extragalactic ray propagation using observations of extreme blazars in GeV and TeV energy ranges ; We briefly review contemporary extragalactic gammaray propagation models. It is shown that the Extragalactic Magnetic Field EGMF strength and structure are poorly known. Strict lower limits on the EGMF strength in voids are of order 10171020 G, thus allowing a substantial contribution of a secondary component generated by electromagnetic cascades to the observable spectrum. We show that this electromagnetic cascade model is supported by data from imaging Cherenkov telescopes and the Fermi LAT detector.

Value of the Cosmological Constant in Emergent Quantum Gravity ; It is suggested that the exact value of the cosmological constant could be derived from first principles, based on entanglement of the Standard Model field vacuum with emergent holographic quantum geometry. For the observed value of the cosmological constant, geometrical information is shown to agree closely with the spatial information density of the QCD vacuum, estimated in a freefield approximation. The comparison is motivated by a model of exotic rotational fluctuations in the inertial frame that can be precisely tested in laboratory experiments. Cosmic acceleration in this model is always positive, but fluctuates with characteristic coherence length approx 100km and bandwidth approx 3000 Hz.

New recursive approximations for variableorder fractional operators with applications ; To broaden the range of applicability of variableorder fractional differential models, reliable numerical approaches are needed to solve the model equation. In this paper, we develop Laguerre spectral collocation methods for solving variableorder fractional initial value problems on the half line. Specifically, we derive threeterm recurrence relations to efficiently calculate the variableorder fractional integrals and derivatives of the modified generalized Laguerre polynomials, which lead to the corresponding fractional differentiation matrices that will be used to construct the collocation methods. Comparison with other existing methods shows the superior accuracy of the proposed spectral collocation methods.

FR cosmology via Noether symmetry and lambdaChaplygin Gas like model ; In this work, we consider FR alternative theories of gravity with an eye to Noether symmetry through the gauge theorem. For nonvacuum models, one finds Lambda like gravity with energy density of Chaplygin Gas. We also obtain the effective equation of state parameter for corresponding cosmology and scale factor behavior with respect to cosmic time which show that the model provides viable EoS and scale factor with respect to observational data.

cal Nextended supersymmetric Calogero models ; We propose a new cal Nextended supersymmetric sun spinCalogero model. Employing a generalized Hamiltonian reduction adopted to the supersymmetric case, we explicitly construct a novel rational nparticle Calogero model with an arbitrary even number of supersymmetries. It features cal Nn2 rather than cal Nn fermionic coordinates and increasingly high fermionic powers in the supercharges and the Hamiltonian.

Can recurrent neural networks warp time ; Successful recurrent models such as long shortterm memories LSTMs and gated recurrent units GRUs use ad hoc gating mechanisms. Empirically these models have been found to improve the learning of medium to long term temporal dependencies and to help with vanishing gradient issues. We prove that learnable gates in a recurrent model formally provide quasi invariance to general time transformations in the input data. We recover part of the LSTM architecture from a simple axiomatic approach. This result leads to a new way of initializing gate biases in LSTMs and GRUs. Ex perimentally, this new chrono initialization is shown to greatly improve learning of long term dependencies, with minimal implementation effort.

Stability of white holes revisited ; It is shown that the models of white hole interacting with external matter can be made stable by introduction of a negative central mass. Similar results are obtained for the models of white hole, interacting with null shells, with radial flows of matter and with photon gas. In realistic models, a naked timelike singularity corresponding to the negative mass is hidden under a coat of positive mass, providing an extremely strong redshift for photons born in the Planck neighborhood of the singularity and observed at infinity, thereby realizing the principle of cosmic censorship in a relaxed form.

The role of shortterm immigration on disease dynamics An SIR model with agestructure ; We formulate an agestructured nonlinear partial differential equation model that features shortterm immigration effects in a population. Individuals can immigrate into the population as any of the three stages in the model susceptible, infected or recovered. Global stability of the immigrationfree and infectionfree equilibria is discussed. A generalized numerical framework is established and specific shortterm immigration scenarios are explored.

Closed dendroidal sets and unital operads ; We discuss a variant of the category of dendroidal sets, the socalled closed dendroidal sets which are indexed by trees without leaves. This category carries a Quillen model structure which behaves better than the one on general dendroidal sets, mainly because it satisfies the pushoutproduct property, hence induces a symmetric monoidal structure on its homotopy category. We also study complete Segal style model structures on closed dendroidal spaces, and various Quillen adjunctions to model categories on all dendroidal sets or spaces. As a consequence, we deduce a Quillen equivalence from closed dendroidal sets to the category of unital simplicial operads, as well as to that of simplicial operads which are unital uptohomotopy. The proofs exhibit several new combinatorial features of categories of closed trees.

Irregular model sets and tame dynamics ; We study the dynamical properties of irregular model sets and show that the translation action on their hull always admits an infinite independence set. The dynamics can therefore not be tame and the topological sequence entropy is strictly positive. Extending the proof to a more general setting, we further obtain that tame implies regular for almost automorphic group actions on compact spaces. In the converse direction, we show that even in the restrictive case of Euclidean cut and project schemes irregular model sets may be uniquely ergodic and have zero topological entropy. This provides negative answers to questions by Schlottmann and Moody in the Euclidean setting.

Unsupervised PseudoLabeling for Extractive Summarization on Electronic Health Records ; Extractive summarization is very useful for physicians to better manage and digest Electronic Health Records EHRs. However, the training of a supervised model requires diseasespecific medical background and is thus very expensive. We studied how to utilize the intrinsic correlation between multiple EHRs to generate pseudolabels and train a supervised model with no external annotation. Experiments on realpatient data validate that our model is effective in summarizing crucial diseasespecific information for patients.

2 Higgs Doublet Model Evolver Manual ; TwoHiggsDoublet Model Evolver 2HDME is a C program that provides the functionality to perform fast renormalization group equation running of the general, potentially CPviolating, 2 Higgs Doublet Model at 2loop order. Simple treelevel calculations of masses; calculations of the oblique parameters S, T and U; different parameterizations of the scalar potential; tests of perturbativity, unitarity and treelevel stability of the scalar potential are also implemented. We briefly describe the 2HDME's structure, provide a demonstration of how to use it and list some of the most useful functions.

On the cumulative Parisian ruin of multidimensional Brownian motion models ; Consider a multidimensional Brownian motion which models the surplus processes of multiple lines of business of an insurance company. Our main result gives exact asymptotics for the cumulative Parisian ruin probability as the initial capital tends to infinity. An asymptotic distribution for the conditional cumulative Parisian ruin time is also derived. The obtained results on the cumulative Parisian ruin can be seen as generalizations of some of the results derived in Debicki et al 2018, Stochastic Processes and Their Applications. As a particular interesting case, the twodimensional Brownian motion risk model is discussed in detail.

Quantum spins and random loops on the complete graph ; We present a systematic analysis of quantum Heisenberg, XY and interchange models on the complete graph. These models exhibit phase transitions accompanied by spontaneous symmetry breaking, which we study by calculating the generating function of expectations of powers of the averaged spin density. Various critical exponents are determined. Certain objects of the associated loop models are shown to have properties of PoissonDirichlet distributions.

Matrix model and Yukawa couplings on the noncommutative torus ; The IKKT model is proposed as a nonperturbative formulation of superstring theory. We propose a Dirac operator on the noncommutative torus,which is consistent with the IKKT model, based on noncommutative geometry. Next, we consider zeromode equations of the Dirac operator with magnetic fluxes. We find that zeromode solutions have the chirality and the generation structures similar to the commutative case. Moreover, we compute Yukawa couplings of chiral matter fields.

ABJM Matrix Model and 2D Toda Lattice Hierarchy ; It was known that onepoint functions in the ABJM matrix model obtained by applying the localization technique to onepoint functions of the halfBPS Wilson loop operator in the ABJM theory satisfy the JacobiTrudi formula, which strongly indicates the integrable structure of the system. In this paper, we identify the integrable structure of twopoint functions in the ABJM matrix model as the twodimensional Toda lattice hierarchy. The identification implies infinitely many nonlinear differential equations for the generating function of the twopoint functions.

Estimating the black hole mass of NGC1313 X1 based on the spectral and timing properties ; The discovery of 32 quasiperiodic oscillations QPOs in the ultraluminous Xray source NGC 1313 X1 suggests it harbors an intermediatemass black hole IMBH. We test this numerically by modelling the 32 QPOs and the associated Xray spectrum based on the epicyclic resonance model and a diskcorona model with largescale magnetic fields generated by the Cosmic Battery mechanism. The combined QPOfrequency and spectral fitting indicates that the BH mass ranges from 2524Msun to 6811Msun confirming its IMBH nature, and the BH spin is probably higher than 0.3.

Warm PseudoScalar Inflation ; In this note, we will introduce an action for warm inflation model with direct coupling between the pseudoscalar field and massless SU2 gauge fields. The potential of inflaton is protected against the thermal corrections in a thermal bath of gauge fields even with strong direct interaction between inflaton and light fields. The dissipation parameter of this model is approximately constant in the highdissipative regime. In this regime, the model is compatible with observational data and nonGaussianity is in order of Hubble slowroll parameter fracepsilonphi1Q even in fMp limit.

Modelling and simulation of multifractal starshaped particles ; The problem of constructing flexible stochastic models to describe the variability in shape of solid particles is challenging. Natural objects often exhibit mono or multifractal features, i.e. irregular shapes and selfsimilar patterns. This paper presents a general framework for modelling threedimensional starshaped particles with a locally variable Hausdorff or fractal dimension. In our approach, the radial function of the particle is represented by an anisotropic Gaussian random field on the sphere. We additionally derive a simulation algorithm being parenthetical to the spectral turning bands method proposed in Euclidean spaces. We illustrate the use of our proposal through numerical examples, including a multifractal simulated version of the Earth topography.

Sparse Least Squares Low Rank Kernel Machines ; A general framework of least squares support vector machine with low rank kernels, referred to as LRLSSVM, is introduced in this paper. The special structure of low rank kernels with a controlled model size brings sparsity as well as computational efficiency to the proposed model. Meanwhile, a twostep optimization algorithm with three different criteria is proposed and various experiments are carried out using the example of the socall robust RBF kernel to validate the model. The experiment results show that the performance of the proposed algorithm is comparable or superior to several existing kernel machines.

Possibilistic investment models with background risk ; In the study of investment problem, aside from the investment risk the background risk appears. Both the investment risk and the background risk are probabilistically described by random variables. This paper starts from the hypothesis that the two types of risk can be represented both probabilistically by random variables and possibilistically by fuzzy numbers. We will study three models in which the investment risk and the background risk can be fuzzy numbers, a random variabla fuzzy number and a fuzzy numbera random variable. A portfolio problem is formulated for each model and an approximate calculation formula of the optimal solution is proved.

Enhanced Variational Inference with Dyadic Transformation ; Variational autoencoder is a powerful deep generative model with variational inference. The practice of modeling latent variables in the VAE's original formulation as normal distributions with a diagonal covariance matrix limits the flexibility to match the true posterior distribution. We propose a new transformation, dyadic transformation DT, that can model a multivariate normal distribution. DT is a singlestage transformation with low computational requirements. We demonstrate empirically on MNIST dataset that DT enhances the posterior flexibility and attains competitive results compared to other VAE enhancements.

Derivation of NonLocal Macroscopic Traffic Equations and Consistent Traffic Pressures from Microscopic CarFollowing Models ; This contribution compares several different approaches allowing one to derive macroscopic traffic equation directly from microscopic carfollowing models. While it is shown that some conventional approaches lead to theoretical problems, it is proposed to use a smooth particle hydrodynamic approach and to avoid gradient expansions. The derivation circumvents approximations and, therefore, demonstrates the large range of validity of macroscopic traffic equations, without the need of averaging over many vehicles. It also gives an expression for the traffic pressure'', which generalizes previously used formulas. Furthermore, the method avoids theoretical inconsistencies of macroscopic traffic models, which have been criticized in the past by Daganzo and others.

An extension of the cosmological standard model with a bounded Hubble expansion rate ; The possibility of having an extension of the cosmological standard model with a Hubble expansion rate H constrained to a finite interval is considered. Two periods of accelerated expansion arise naturally when the Hubble expansion rate approaches to the two limiting values. The new description of the history of the universe is confronted with cosmological data and with several theoretical ideas going beyond the standard cosmological model.

Dynamics of thematic information flows ; The studies of the dynamics of topical dataflow of new information in the framework of a logistic model were suggested. The condition of topic balance, when the number of publications on all topics is proportional to the information space and time, was presented. General time dependence of the publication intensity in the Internet, devoted to particular topics, was observed; unlike an exponent model, it has a saturation area. Some limitations of a logistic model were identified opening the way for further research.

DrellYan production of Heavy Vectors in Higgsless models ; We study the DrellYan production of heavy vector and axialvector states of generic Higgsless models at hadron colliders. We analyse in particular the ll, WZ, and three SM gauge boson final states. In the ll case we show how present Tevatron data restricts the allowed parameter space of these models. The two and three gauge boson final states especially WZ, WWZ, and WZZ are particularly interesting in view of the LHC, especially for light axialvector masses, and could shed more light on the role of spin1 resonances in the electroweak precision tests.

Viscous Ricci Dark Energy ; We investigate the viscous Ricci dark energy RDE model by assuming that there is bulk viscosity in the linear barotropic fluid and the RDE. In the RDE model without bulk viscosity, the universe is younger than some old objects at some redshifts. Since the age of the universe should be longer than any objects in the universe, the RDE model suffers the age problem, especially when we consider the object APM 082795255 at z3.91, whose age is t 2.1 Gyr. In this letter, we find that once the viscosity is taken into account, this age problem is alleviated.

Halo abundances in the fnl model ; We show how the excursion set moving barrier model for halo abundances may be generalized to the local nonGaussian fnl model. Our estimate assumes that the distribution of step sizes depends on fnl, but that they are otherwise uncorrelated. Our analysis is consistent with previous results for the case of a constant barrier, and highlights some implicit assumptions. It also clarifies the basis of an approximate analytic solution to the moving barrier problem in the Gaussian case, and shows how it might be improved.

Conformal Supersymmetry Breaking in Vectorlike Gauge Theories ; A new class of models of dynamical supersymmetry breaking is proposed. The models are based on SUNC gauge theories with NFNC flavors of quarks and singlets. Dynamically generated superpotential exibits runaway behavior. By embedding the models into conformal field theories at high energies, the runaway potential is stabilized by strong quantum corrections to the Kahler potential. The quantum corrections are large but nevertheless can be controlled due to superconformal symmetry of the theories.

A TeV scale model for neutrino mass, dark matter and baryon asymmetry ; We discuss a TeV scale model which would explain neutrino oscillation, dark matter, and baryon asymmetry of the Universe simultaneously by the dynamics of the extended Higgs sector and TeVscale righthanded neutrinos with imposed an exact Z2 symmetry. Tiny neutrino masses are generated at the three loop level, a singlet scalar field is a candidate of dark matter, and a strong first order phase transition is realized for successful electroweak baryogenesis. The model provides various discriminative predictions, so that it is testable at the current and future experiments.

Charged Current Coherent Pion Production in Neutrino Scattering ; We summarise here the main differences of three models of neutrinoinduced coherent pion production, namely the ReinSehgal and BergerSehgal models based on the Partially Conserved Axial Current theorem and the AlvarezRuso textitet al. model which is using a microscopic approach. Their predictions in the event generators are compared against recent experimental measurements for a neutrino energy from 0.5 to 20 GeV.

LSTMbased MixtureofExperts for KnowledgeAware Dialogues ; We introduce an LSTMbased method for dynamically integrating several wordprediction experts to obtain a conditional language model which can be good simultaneously at several subtasks. We illustrate this general approach with an application to dialogue where we integrate a neural chat model, good at conversational aspects, with a neural questionanswering model, good at retrieving precise information from a knowledgebase, and show how the integration combines the strengths of the independent components. We hope that this focused contribution will attract attention on the benefits of using such mixtures of experts in NLP.

Small field inflation in cal N1 supergravity with a single chiral superfield ; We consider new inflation inflationary models at small fields, embedded in minimal cal N1 supergravity with a single chiral superfield. Imposing a period of inflation compatible with experiment severely restricts possible models, classified in perturbation theory. If moreover we impose that the field goes to large values and very small potential at the current time, like would be needed for instance for the inflaton being the volume modulus in large extra dimensional scenarios, the possible models are restricted to very contrived superpotentials.

On Radiative Fluids in Anisotropic Spacetimes ; We apply the secondorder IsraelStewart theory of relativistic fluid and thermodynamics to a physically realistic model of a radiative fluid in a simple anisotropic cosmological background. We investigate the asymptotic future of the resulting cosmological model and review the role of the dissipative phenomena in the early Universe. We demonstrate that the transport properties of the fluid alone, if described appropriately, do not explain the presently observed accelerated expansion of the Universe. Also, we show that, in constrast to the mathematical fluid models widely used before, the radiative fluid does approach local thermal equilibrium at late times, although very slowly, due to the cosmological expansion.

Classical dynamics of the Bianchi IX model with timelike singularity ; We study the dynamics of the vacuum Bianchi IX model with timelike singularity and compare it with the dynamics of the Bianchi IX model with cosmological singularity. We show that differences in the signs of some terms in the set of equations specifying the dynamics of both spacetimes lead to significant differences in their properties.

Finite Volume Method for the Relativistic Burgers Model on a 11Dimensional de Sitter Spacetime ; Several generalizations of the relativistic models of Burgers equations have recently been established and developed on different spacetime geometries. In this work, we take into account the de Sitter spacetime geometry, introduce our relativistic model by a technique based on the vanishing pressure Euler equations of relativistic compressible fluids on a 11dimensional background and construct a second order Godunov type finite volume scheme to examine numerical experiments within an analysis of the cosmological constant. Numerical results demonstrate the efficiency of the method for solutions containing shock and rarefaction waves.

Dynamic polaron response from variational imaginary time evolution ; An variational expression for the zero temperature polaron impedance is obtained by minimizing the free energy in a generalized quadratic Feynman model. The impedance function of the quadratic model serves as the variational parameter. It is shown that a very small change in the energy can be accompanied by a large change in the optical conductivity. This is related to the insensitivity of the JensenFeynman free energy to the UV properties of the model. Analytic and numeric results are derived for the Frohlich polaron in weak and strong coupling. Standard results are recovered at weak coupling but, more importantly, strong coupling inconsistencies are removed.

A model of global magnetic reconnection rate in relativistic collisionless plasmas ; A model of global magnetic reconnection rate in relativistic collisionless plasmas is developed and validated by the fully kinetic simulation. Through considering the force balance at the upstream and downstream of the diffusion region, we show that the global rate is bounded by a value sim 0.3 even when the local rate goes up to sim O1 and the local inflow speed approaches the speed of light in strongly magnetized plasmas. The derived model is general and can be applied to magnetic reconnection under widely different circumstances.

Contourbased 3d tongue motion visualization using ultrasound image sequences ; This article describes a contourbased 3D tongue deformation visualization framework using Bmode ultrasound image sequences. A robust, automatic tracking algorithm characterizes tongue motion via a contour, which is then used to drive a generic 3D Finite Element Model FEM. A novel contourbased 3D dynamic modeling method is presented. Modal reduction and modal warping techniques are applied to model the deformation of the tongue physically and efficiently. This work can be helpful in a variety of fields, such as speech production, silent speech recognition, articulation training, speech disorder study, etc.

The Exponential Flexible Weibull Extension Distribution ; This paper is devoted to study a new three parameters model called the Exponential Flexible Weibull extension EFWE distribution which exhibits bathtubshaped hazard rate. Some of it's statistical properties are obtained including ordinary and incomplete moments, quantile and generating functions, reliability and order statistics. The method of maximum likelihood is used for estimating the model parameters and the observed Fisher's information matrix is derived. We illustrate the usefulness of the proposed model by applications to real data.

The theory of the Double Solution Dynamical issues in quantum systems in the semiclassical regime ; The dynamical mismatch observed in quantum systems in the semiclassical regime challenge the Pilot wave model. Indeed the dynamics and properties of such systems depend on the trajectories of the classically equivalent system, whereas the de BroglieBohm trajectories are generically nonclassical. In this work we examine the situation for the model favoured by de Broglie, the theory of the Double Solution DS. We will see that the original DS model applied to semiclassical systems is also prone to the dynamical mismatch. However we will argue that the DS theory can be modified in order to yield propagation of the singularity in accord with the underlying classical dynamics of semiclassical systems.

Finitedimensional collisionless kinetic theory ; A collisionless kinetic plasma model may often be cast as an infinitedimensional noncanonical Hamiltonian system. I show that, when this is the case, the model can be discretized in space and particles while preserving its Hamiltonian structure, thereby producing a finitedimensional Hamiltonian system that approximates the original kinetic model. I apply the general theory to two example systems the relativistic VlasovMaxwell system with spin, and a gyrokinetic VlasovMaxwell system.

A New Class of Cosmologically Viable' fR Models ; Instead of assuming a form of gravity and demand cosmology fit with Lambda CDM, a potentially viable' fR gravity model is derived assuming an alternative model of cosmology. Taking the designer' approach to fR, a new class of solutions are derived starting with linear coasting cosmology in which scale factor linearly increases with time during matter domination. The derived forms of fR are presented as result.

Approximate explicit model predictive control via piecewise nonlinear system identification ; This article presents an identification methodology to capture general relationships, with application to piecewise nonlinear approximations of model predictive control for constrained nonlinear systems. The mathematical formulation takes, at each iteration, the form of a constrained linear or quadratic optimization problem that is mathematically feasible as well as numerically tractable. The efficiency of the devised methodology is demonstrated via two industrial applications. Results suggest the possibility to achieve high approximate precision with limited number of regions, leading to a significant reduction in computation time when compared to the stateoftheart implicit model predictive control solvers.

Fitting MAq Models in the Closed Invertible Region ; The use of reparameterization in the maximization of the likelihood function of the MAq model is discussed. A general method for testing for the presence of a parameter estimate on the boundary of an MAq model is presented. This test is illustrated with a brief simulation experiment for the MAq for q1,2,3,4 in which it is shown that the probability of an estimate being on the boundary increases with q.

Phase Plane Analysis of MetricScalar Torsion Model for Interacting Dark Energy ; We study the phase space dynamics of the nonminimally coupled MetricScalarTorsion model in both Jordan and Einstein frames. We specifically check for the existence of critical points which yield stable solutions representing the current state of accelerated expansion of the universe fuelled by the Dark Energy. It is found that such solutions do indeed exist, subject to constraints on the free model parameter. In fact the evolution of the universe at these stable critical points exactly matches the evolution given by the cosmological solutions we found analytically in our previous work on the subject.

Equivalence of Einstein and Jordan frames in quantized cosmological models ; The present work shows that the mathematical equivalence of Jordan frame and its conformally transformed version, the Einstein frame, so far as BransDicke theory is concerned, survives a quantization of cosmological models in the theory. We work with the WheelerdeWitt quantization scheme and take up quite a few anisotropic cosmological models as examples. We effectively show that the transformation from Jordan to Einstein frame is a canonical one and hence two frames are equivalent description of same physical scenario.

Noether Symmetry Approach in fmathcalG,T Gravity ; We explore the recently introduced modified GaussBonnet gravity 1, fmathcalG,T pragmatic with mathcalG, the GaussBonnet term, and T, the trace of the energymomentum tensor. Noether symmetry approach has been used to develop some cosmologically viable fmathcalG,T gravity models. The Noether equations of modified gravity are reported for flat FRW universe. Two specific models have been studied to determine the conserved quantities and exact solutions. In particular, the well known deSitter solution is reconstructed for some specific choice of fmathcalG,T gravity model.

Static Analysis of Communicating Processes using Symbolic Transducers ; We present a general model allowing static analysis based on abstract interpretation for systems of communicating processes. Our technique, inspired by Regular Model Checking, represents set of program states as lattice automata and programs semantics as symbolic transducers. This model can express dynamic creationdestruction of processes and communications. Using the abstract interpretation framework, we are able to provide a sound overapproximation of the reachability set of the system thus allowing us to prove safety properties. We implemented this method in a prototype that targets the MPI library for C programs.

Widerangetunable Diraccone band structure in a chiraltimesymmetric nonHermitian system ; We establish a connection between an arbitrary Hermitian tightbinding model with chiral C symmetry and its nonHermitian counterpart with chiraltime CT symmetry.We show that such a nonHermitian Hamiltonian is pseudoHermitian. The eigenvalues and eigenvectors of the nonHermitian Hamiltonian can be easily obtained from those of its parent Hermitian Hamiltonian. It provides a way to generate a class of nonHermitian models with a tunable full real band structure by means of additional imaginary potentials.We also present an illustrative example that could achieve a cone structure from the energy band of a twolayer Hermitian square lattice model.

Best linear unbiased estimators in continuous time regression models ; In this paper the problem of best linear unbiased estimation is investigated for continuoustime regression models. We prove several general statements concerning the explicit form of the best linear unbiased estimator BLUE, in particular when the error process is a smooth process with one or several derivatives of the response process available for construction of the estimators. We derive the explicit form of the BLUE for many specific models including the cases of continuous autoregressive errors of order two and integrated error processes such as integrated Brownian motion. The results are illustrated by several examples.