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      Dynamics of strongly interacting unstable two-solitons for generalized Korteweg-de Vries equations

      February 17, 2018

      Mathematics
      Analysis of PDEs
      We consider the generalized Korteweg-de Vries equation ∂tu=−∂x(∂x2u+f(u))\partial_t u = -\partial_x(\partial_x^2 u + f(u))∂t​u=−∂x​(∂x2​u+f(u)), where f(u)f(u)f(u) is an odd function of class C3C^3C3. Under some assumptions on fff, this equation admits \emph{solitary waves}, that is s...

      Optimizing generalized kernels of polygons

      February 16, 2018

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      Computer Science
      Computational Geometry
      Computational Geometry
      Let O\mathcal{O}O be a set of kkk orientations in the plane, and let PPP be a simple polygon in the plane. Given two points p,qp,qp,q inside PPP, we say that ppp O\mathcal{O}O-\emph{sees} qqq if there is an O\mathcal{O}O-\emph{staircase} contai...

      Minimal Algorithmic Information Loss Methods for Dimension Reduction, Feature Selection and Network Sparsification

      February 16, 2018

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      Computer Science
      Mathematics
      Physics
      Data Structures and Algorithms
      Information Theory
      Information Theory
      Physics and Society
      We present a novel, domain-agnostic, model-independent, unsupervised, and universally applicable approach for data summarization. Specifically, we focus on addressing the challenge of reducing certain dimensionality aspects, such as the num...

      Chromatic symmetric functions via the group algebra of SnS_nSn​

      February 15, 2018

      Mathematics
      Combinatorics
      Representation Theory
      We prove some Schur positivity results for the chromatic symmetric function XGX_GXG​ of a (hyper)graph GGG, using connections to the group algebra of the symmetric group. The first such connection works for (hyper)forests FFF: we describe the ...

      HiGrad: Uncertainty Quantification for Online Learning and Stochastic Approximation

      February 13, 2018

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      Statistics
      Computer Science
      Mathematics
      Machine Learning
      Distributed, Parallel, and Cluster Computing
      Optimization and Control
      Methodology
      Machine Learning
      Distributed, Parallel, and Cluster Computing
      Optimization and Control
      Methodology
      Stochastic gradient descent (SGD) is an immensely popular approach for online learning in settings where data arrives in a stream or data sizes are very large. However, despite an ever-increasing volume of work on SGD, much less is known ab...

      Pseudo-Gaussian Orthogonal Ensemble of Real Random Matrices

      February 13, 2018

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      Physics
      Mathematics
      Quantum Physics
      Statistical Mechanics
      Mathematical Physics
      Mathematical Physics
      Here, using two real non-zero parameters λ\lambdaλ and μ\muμ, we construct pseudo-Gaussian orthogonal ensembles of a large number NNN of n×nn \times nn×n (nnn even and large) real pseudo-symmetric matrices under the metric η\etaη using $ \mathc...

      Embedding Complexity In the Data Representation Instead of In the Model: A Case Study Using Heterogeneous Medical Data

      February 12, 2018

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      Statistics
      Applications
      Applications
      Electronic Health Records have become popular sources of data for secondary research, but their use is hampered by the amount of effort it takes to overcome the sparsity, irregularity, and noise that they contain. Modern learning architectu...

      Some arithmetic aspects of polynomial maps

      February 12, 2018

      Mathematics
      Algebraic Geometry
      The Jacobian conjecture is a well-known open problem in affine algebraic geometry that asks if any polynomial endomorphism of the affine space ACn\mathbb{A}_{\mathbb{C}}^{n}ACn​ (n≥2n\geq2n≥2) with jacobian 111 is an automorphism. We present a surve...

      The Third Evolution Equation for Optimal Control Computation

      February 11, 2018

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      Computer Science
      Mathematics
      Systems and Control
      Optimization and Control
      Systems and Control
      Optimization and Control
      The Variation Evolving Method (VEM) that originates from the continuous-time dynamics stability theory seeks the optimal solutions with variation evolution principle. After establishing the first and the second evolution equations within it...

      The Strange Attractor Model of Bipedal Locomotion and its Consequences on Motor Control

      February 9, 2018

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      Computer Science
      Robotics
      Despite decades of study, many unknowns exist about the mechanisms governing human locomotion. Current models and motor control theories can only partially capture the phenomenon. This may be a major cause of the reduced efficacy of lower l...
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