Functional Bayesian Filter. (arXiv:1911.10606v1 [eess.SP])

We present a general nonlinear Bayesian filter for high-dimensional state estimation using the theory of reproducing kernel Hilbert space (RKHS). Applying kernel method and the representer theorem to perform linear quadratic estimation in a functional space, we derive a Bayesian recursive state estimator for a general nonlinear dynamical system in the original input space. Unlike…

Multi-Agent Reinforcement Learning: A Selective Overview of Theories and Algorithms. (arXiv:1911.10635v1 [cs.LG])

Recent years have witnessed significant advances in reinforcement learning (RL), which has registered great success in solving various sequential decision-making problems in machine learning. Most of the successful RL applications, e.g., the games of Go and Poker, robotics, and autonomous driving, involve the participation of more than one single agent, which naturally fall into the…

A Unified Deep Learning Approach for Prediction of Parkinson’s Disease. (arXiv:1911.10653v1 [cs.LG])

The paper presents a novel approach, based on deep learning, for diagnosis of Parkinson’s disease through medical imaging. The approach includes analysis and use of the knowledge extracted by Deep Convolutional and Recurrent Neural Networks (DNNs) when trained with medical images, such as Magnetic Resonance Images and DaTscans. Internal representations of the trained DNNs constitute…

Predator-Prey Interaction Model with Hunting Cooperation among Predators and Allee Effect in Prey. (arXiv:1911.10299v1 [math.DS])

This paper investigates a dynamical predator-prey interaction model that incorporates: (a) hunting cooperation among predators; (b) Allee effect in prey. We show all possible boundary and interior solutions. In order to analyze the stability of the solution, we make use of the Jacobian matrix and the resultant characteristic polynomial. Particularly, the sign of the eigenvalue…

Metastability as a coexistence mechanism in a model for dryland vegetation patterns. (arXiv:1911.11022v1 [q-bio.PE])

Vegetation patterns are a ubiquitous feature of water-deprived ecosystems. Despite the competition for the same limiting resource, coexistence of several plant species is commonly observed. We propose a two-species reaction-diffusion model based on the single-species Klausmeier model, to analytically investigate the existence of states in which both species coexist. Ecologically, the study finds that coexistence…

Architectural configurations, atlas granularity and functional connectivity with diagnostic value in Autism Spectrum Disorder. (arXiv:1911.11024v1 [cs.LG])

Currently, the diagnosis of Autism Spectrum Disorder (ASD) is dependent upon a subjective, time-consuming evaluation of behavioral tests by an expert clinician. Non-invasive functional MRI (fMRI) characterizes brain connectivity and may be used to inform diagnoses and democratize medicine. However, successful construction of deep learning models from fMRI requires addressing key choices about the model’s…

Convexification for a 3D inverse scattering problem with the moving point source. (arXiv:1911.10289v1 [math.NA])

For the first time, we develop in this paper the globally convergent convexification numerical method for a Coefficient Inverse Problem for the 3D Helmholtz equation for the case when the backscattering data are generated by a point source running along an interval of a straight line and the wavenumber is fixed. Thus, by varying the…

Topologically Mapping the Macroeconomy. (arXiv:1911.10476v1 [econ.EM])

An understanding of the economic landscape in a world of ever increasing data necessitates representations of data that can inform policy, deepen understanding and guide future research. Topological Data Analysis offers a set of tools which deliver on all three calls. Abstract two-dimensional snapshots of multi-dimensional space readily capture non-monotonic relationships, inform of similarity between…

Comparison between the linear and nonlinear homogenization of graphene and silicon. (arXiv:1911.10370v1 [physics.optics])

In this paper, we use a versatile homogenization approach to model the linear and nonlinear optical response of two metasurfaces: a plasmonic metasurface consisting of a square array of graphene cruciform patches and a dielectric metasurface consisting of a rectangular array of photonic crystal (PhC) cavities in a silicon PhC slab waveguide. The former metasurface…

Bayesian nonparametric estimation in the current status continuous mark model. (arXiv:1911.10387v1 [math.ST])

In this paper we consider the current status continuous mark model where, if the event takes place before an inspection time $T$ a “continuous mark” variable is observed as well. A Bayesian nonparametric method is introduced for estimating the distribution function of the joint distribution of the event time ($X$) and mark ($Y$). We consider…