System Identification Through Lipschitz Regularized Deep Neural Networks,
2021
Worcester Polytechnic Institute
System Identification Through Lipschitz Regularized Deep Neural Networks, Elisa Negrini, Giovanna Citti, Luca Capogna
Mathematics Sciences: Faculty Publications
In this paper we use neural networks to learn governing equations from data. Specifically we reconstruct the right-hand side of a system of ODEs x˙(t)=f(t,x(t)) directly from observed uniformly time-sampled data using a neural network. In contrast with other neural network-based approaches to this problem, we add a Lipschitz regularization term to our loss function. In the synthetic examples we observed empirically that this regularization results in a smoother approximating function and better generalization properties when compared with non-regularized models, both on trajectory and non-trajectory data, especially in presence of noise. In contrast with sparse regression approaches, since neural networks …
Fundamental Solutions For The Dirac Equation In Curved Spacetime And Generalized Euler-Poisson-Darboux Equation,
2021
The University of Texas Rio Grande Valley
Fundamental Solutions For The Dirac Equation In Curved Spacetime And Generalized Euler-Poisson-Darboux Equation, Karen Yagdjian, Anahit Galstian
School of Mathematical & Statistical Sciences Faculty Publications
We present the fundamental solutions for the spin-1/2 fields propagating in spacetimes with power type expansion/contraction and the fundamental solution of the Cauchy problem for the Dirac equation. The derivation of these fundamental solutions is based on formulas for the solutions to the generalized Euler-Poisson-Darboux equation, which are obtained by the integral transform approach.
Formal Oscillatory Distributions,
2021
Abilene Christian University
Formal Oscillatory Distributions, Alexander Karabegov
Mathematics
The formal asymptotic expansion of an oscillatory in- tegral whose phase function has one nondegenerate critical point is a formal distribution supported at the critical point which is applied to the amplitude. This formal distribution is called a formal oscillatory integral (FOI). We introduce the notion of a formal oscillatory distribution supported at a point. We prove that a formal distribution is given by some FOI if and only if it is an oscillatory distribution that has a certain nondegeneracy property. We also prove that a star product ? on a Poisson manifold M is natural in the sense of …
Effects Of Refuge Prey On Stability Of The Prey-Predator Model Subject To Immigrants: A Mathematical Modelling Approach,
2021
Mkwawa University College of Education, P. O. Box 2513, Iringa Tanzania
Effects Of Refuge Prey On Stability Of The Prey-Predator Model Subject To Immigrants: A Mathematical Modelling Approach, Mussa Amos Stephano, Il Hyo Jung
Tanzania Journal of Science
Prey-predator system is enormously complex and nonlinear interaction between species. Such complexity regularly requires development of new approaches which involves more factors in analysis of its population dynamics. In this paper, we formulate a modified Lotka-Volterra model that incorporates factors such as refuge prey and immigrants. We investigate the effects of refuge prey and immigrants by varying the refuge factor, with and without immigrants. The results show that with Holling’s type I functional response, the proposed model is asymptotically convergent when a refuge prey factor is introduced. Moreover, with Holling’s type II functional response, the proposed mathematical model is unstable …
Inversion–Free Iterative Method For Finding Symmetric Solution Of The Nonlinear Matrix Equation X-A^* X^Q A=I (Q≥2),
2021
Department of Mathematics, Physics and Informatics, Mkwawa University College of Education, University of Dar es Salaam, P. O. Box 2513, Iringa, Tanzania
Inversion–Free Iterative Method For Finding Symmetric Solution Of The Nonlinear Matrix Equation X-A^* X^Q A=I (Q≥2), Chacha Stephen Chacha
Tanzania Journal of Science
In this paper, we propose the inversion free iterative method to find symmetric solution of the nonlinear matrix equation where is an unknown symmetric solution, is a given Hermitian matrix and is a positive integer. The convergence of the proposed method is derived. Numerical examples demonstrate that the proposed iterative method is quite efficient and converges well when the initial guess is sufficiently close to the approximate solution. Keywords: Symmetric solution, nonlinear matrix equation, inversion free, iterative method.
A Mathematical Analysis Of An In-Vivo Ebola Virus Transmission Dynamics Model,
2021
Department of Physical Sciences, The Open University of Tanzania, Dar es Salaam, Tanzania
A Mathematical Analysis Of An In-Vivo Ebola Virus Transmission Dynamics Model, Seleman Ismail, Adeline Peter Mtunya
Tanzania Journal of Science
Ebola virus (EBOV) infection is a hemorrhagic and hazardous disease, which is among the most shocking threats to human health causing a large number of deaths. Currently, there are no approved curative therapies for the disease. In this study, a mathematical model for in-vivo Ebola virus transmission dynamics was analyzed. The analysis of the model mainly focused on the sensitivity of basic reproductive number, pertaining to the model parameters. Particularly, the sensitivity indices of all parameters of were computed by using the forward normalized sensitivity index method. The results showed that a slight change in the infection rate immensely influences …
Participatory Action Research: Undergraduate Researchers Engaging Secondary Students In Social Justice Mathematics,
2021
Purdue University
Participatory Action Research: Undergraduate Researchers Engaging Secondary Students In Social Justice Mathematics, Isabelle Miller, Alexis Grimes, Camryn Adkison
The Journal of Purdue Undergraduate Research
No abstract provided.
A Clark-Ocone Type Formula Via Itô Calculus And Its Application To Finance,
2021
Keio University, 2-15-45 Mita, Minato-ku, Tokyo, 108-8345, Japan
A Clark-Ocone Type Formula Via Itô Calculus And Its Application To Finance, Takuji Arai, Ryoichi Suzuki
Journal of Stochastic Analysis
No abstract provided.
The Phase Transition Of Discrepancy In Random
Hypergraphs,
2021
University of Toronto,
The Phase Transition Of Discrepancy In Random Hypergraphs, Calum Macrury, Tomáš Masarík, Leilani Pai, Xavier Perez Gimenez
Department of Mathematics: Faculty Publications
Motivated by the Beck-Fiala conjecture, we study the discrepancy problem in two related models of random hypergraphs on n vertices and m edges. In the first (edge-independent) model, a random hypergraph H1 is constructed by fixing a parameter p and allowing each of the n vertices to join each of the m edges independently with probability p. In the parameter range in which pn ⟶ ∞ and pm ⟶ ∞, we show that with high probability (w.h.p.) H1 has discrepancy at least Ω(2-n/m √pn) when m = O(n …
Three Essays On The Political Economics Of Conflict.,
2021
Indian Statistical Institute
Three Essays On The Political Economics Of Conflict., Dripto Bakshi Dr.
Doctoral Theses
A standard practice in the sociological and comparative-politics literature is to interpret ethnicity broadly as identity cleavages deriving from non-class categories such as language, religion, race and caste. In recent decades, conflicts between ‘ethnic’ communities, i.e., groups divided along non-class identity dimensions such as race, language, and, in particular, religion, have attained increasing salience in many countries. In response to this, a large analytical and empirical literature has developed both in political science and in political economics that seeks to explicate various aspects of this phenomenon. This thesis aims to throw light on two major aspects of ethnic conflicts. (1) …
Some Contributions To Free Probability And Random Matrices.,
2021
Indian Statistical Institute
Some Contributions To Free Probability And Random Matrices., Sukrit Chakraborty Dr.
Doctoral Theses
No abstract provided.
Unary-Determined Distributive ℓ -Magmas And Bunched Implication Algebras,
2021
Chapman University
Unary-Determined Distributive ℓ -Magmas And Bunched Implication Algebras, Natanael Alpay, Peter Jipsen, Melissa Sugimoto
Mathematics, Physics, and Computer Science Faculty Articles and Research
A distributive lattice-ordered magma (dℓ-magma) (A,∧,∨,⋅) is a distributive lattice with a binary operation ⋅ that preserves joins in both arguments, and when ⋅ is associative then (A,∨,⋅) is an idempotent semiring. A dℓ-magma with a top ⊤ is unary-determined if x⋅y=(x⋅⊤∧y)∨(x∧⊤⋅y). These algebras are term-equivalent to a subvariety of distributive lattices with ⊤ and two join-preserving unary operations p, q. We obtain simple conditions on p, q such that x⋅y=(px∧y)∨(x∧qy) is associative, commutative, idempotent and/or has an identity element. This generalizes previous results on the structure of doubly idempotent semirings and, in the case when the …
Algorithmic Correspondence For Relevance Logics, Bunched Implication Logics, And Relation Algebras Via An Implementation Of The Algorithm Pearl,
2021
University of the Witwatersrand, Johannesburg
Algorithmic Correspondence For Relevance Logics, Bunched Implication Logics, And Relation Algebras Via An Implementation Of The Algorithm Pearl, Willem Conradie, Valentin Goranko, Peter Jipsen
Mathematics, Physics, and Computer Science Faculty Articles and Research
The non-deterministic algorithmic procedure PEARL (acronym for ‘Propositional variables Elimination Algorithm for Relevance Logic’) has been recently developed for computing first-order equivalents of formulas of the language of relevance logics LR in terms of the standard Routley-Meyer relational semantics. It succeeds on a large class of axioms of relevance logics, including all so called inductive formulas. In the present work we re-interpret PEARL from an algebraic perspective, with its rewrite rules seen as manipulating quasi-inequalities interpreted over Urquhart’s relevant algebras, and report on its recent Python implementation. We also show that all formulae on which PEARL succeeds are canonical, i.e., …
Calculating Infinitesimal Generators,
2021
Hofstra University, Hempstead, NY 11549, USA
Calculating Infinitesimal Generators, Majnu John, Yihren Wu
Journal of Stochastic Analysis
No abstract provided.
Isometric Flows Of G 2-Structures,
2021
The University of Texas Rio Grande Valley
Isometric Flows Of G 2-Structures, Sergey Grigorian
School of Mathematical & Statistical Sciences Faculty Publications
We survey recent progress in the study of flows of isometric G 2-structures on seven-dimensional manifolds, that is, flows that preserve the metric, while modifying the G 2-structure. In particular, heat flows of isometric G 2-structures have been recently studied from several different perspectives, in particular in terms of 3-forms, octonions, vector fields, and geometric structures. We will give an overview of each approach, the results obtained, and compare the different perspectives.
Recursive And Viterbi Estimation For Semi-Markov Chains,
2021
University of South Australia, Campus Central - City West, GPO Box 2471
Recursive And Viterbi Estimation For Semi-Markov Chains, Robert J. Elliott, W. P. Malcolm
Journal of Stochastic Analysis
No abstract provided.
Mitigating The Externality Of Diseases Of Poverty Through Health Aid,
2021
The University of Texas Rio Grande Valley
Mitigating The Externality Of Diseases Of Poverty Through Health Aid, Kamal Jnawali, Michael G. Tyshenko, Tamer Oraby
School of Mathematical & Statistical Sciences Faculty Publications
Externality exists in healthcare when an individual benefits from others being healthy as it reduces the probability of getting sick from illness. Healthy workers are considered to be the more productive labourers leading to a country’s positive economic growth over time. Several research studies have modelled disease transmission and its economic impact on a single country in isolation. We developed a two-country diseaseeconomy model that explores disease transmission and crossborder infection of disease for its impacts. The model includes aspects of a worsening and rapid transmission of disease juxtaposed by positive impacts to the economy from tourism. We found that …
Using Lie Sphere Geometry To Study Dupin Hypersurfaces In R^N,
2021
College of the Holy Cross
Using Lie Sphere Geometry To Study Dupin Hypersurfaces In R^N, Thomas E. Cecil
Mathematics and Computer Science Department Faculty Scholarship
A hypersurface M in Rn or Sn is said to be Dupin if along each curvature surface, the corresponding principal curvature is constant. A Dupin hypersurface is said to be proper Dupin if each principal curvature has constant multiplicity on M, i.e., the number of distinct principal curvatures is constant on M. The notions of Dupin and proper Dupin hypersurfaces in Rn or Sn can be generalized to the setting of Lie sphere geometry, and these properties are easily seen to be invariant under Lie sphere transformations. This makes Lie sphere geometry an effective …
The N-Dimensional Quadratic Heisenberg Algebra As A “Non–Commutative” Sl(2,C),
2021
Universitá di Roma Tor Vergata, Via di Torvergata, Roma, Italy
The N-Dimensional Quadratic Heisenberg Algebra As A “Non–Commutative” Sl(2,C), Luigi Accardi, Andreas Boukas, Yun-Gang Lu
Journal of Stochastic Analysis
No abstract provided.
The Chromatic Quasisymmetric Class Function Of A Digraph,
2021
The University of Texas Rio Grande Valley
The Chromatic Quasisymmetric Class Function Of A Digraph, Jacob A. White
School of Mathematical & Statistical Sciences Faculty Publications
We introduce a quasisymmetric class function associated with a group acting on a double poset or on a directed graph. The latter is a generalization of the chromatic quasisymmetric function of a digraph introduced by Ellzey, while the former is a generalization of a quasisymmetric function introduced by Grinberg. We prove representation-theoretic analogues of classical and recent results, including F-positivity, and combinatorial reciprocity theorems. We deduce results for orbital quasisymmetric functions, and study a generalization of the notion of strongly flawless sequences.
