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DAOC: Stable Clustering of Large NetworksSep 19 2019Clustering is a crucial component of many data mining systems involving the analysis and exploration of various data. Data diversity calls for clustering algorithms to be accurate while providing stable (i.e., deterministic and robust) results on arbitrary ... More
Spectral Analysis Of Weighted Laplacians Arising In Data ClusteringSep 13 2019Graph Laplacians computed from weighted adjacency matrices are widely used to identify geometric structure in data, and clusters in particular; their spectral properties play a central role in a number of unsupervised and semi-supervised learning algorithms. ... More
Multiple Lattice Rules for Multivariate $L_\infty$ Approximation in the Worst-Case SettingSep 05 2019We develop a general framework for estimating the $L_\infty(\mathbb{T}^d)$ error for the approximation of multivariate periodic functions belonging to specific reproducing kernel Hilbert spaces (RHKS) using approximants that are trigonometric polynomials ... More
Set of independencies and Tutte polynomial of matroids over a domainSep 01 2019In this work, we study matroids over a domain and several classical combinatorial and algebraic invariants related. We define their Grothendieck-Tutte polynomial $T_{\mathcal{M}}(x,y)$, extending the definition given by Fink and Moci in 2016, and we show ... More
On the Boundary Layer Equations with Phase Transition in the Kinetic Theory of GasesAug 30 2019Consider the steady Boltzmann equation with slab symmetry for a monatomic, hard sphere gas in a half space. At the boundary of the half space, it is assumed that the gas is in contact with its condensed phase. The present paper discusses the existence ... More
Spectral properties of graphs associated to the Basilica groupAug 28 2019We provide the foundation of the spectral analysis of the Laplacian on the orbital Schreier graphs of the basilica group, the iterated monodromy group of the quadratic polynomial $z^2-1$. This group is an important example in the class of self-similar ... More
Supercritical elliptic problems on the round sphere and nodal solutions to the Yamabe problem in projective spacesAug 21 2019Given an isoparametric function $f$ on the $n$-dimensional round sphere, we consider functions of the form $u=w\circ f$ to reduce the semilinear elliptic problem \[ -\Delta_{g_0}u+\lambda u=\lambda\ | u\ | ^{p-1}u\qquad\text{ on }\mathbb{S}^n \] with ... More
Optimal Control for Chemotaxis Systems and Adjoint-Based Optimization with Multiple-Relaxation-Time Lattice Boltzmann ModelsAug 11 2019This paper is devoted to continuous and discrete adjoint-based optimization approaches for optimal control problems governed by an important class of Nonlinear Coupled Anisotropic Convection-Diffusion Chemotaxis-type System (NCACDCS). This study is motivated ... More
Structure of Finite-Dimensional ProtoriAug 08 2019A Structure Theorem for Protori is derived for the category of finite-dimensional protori(compact connected abelian groups), which details the interplay between the properties of density, discreteness, torsion, and divisibility within a finite-dimensional ... More
Some Laplace transforms and integral representations for parabolic cylinder functions and error functionsJul 31 2019This paper uses the convolution theorem of the Laplace transform to derive new inverse Laplace transforms for the product of two parabolic cylinder functions in which the arguments may have opposite sign. These transforms are subsequently specialized ... More
Null-controllability of linear parabolic-transport systemsJul 22 2019Over the past two decades, the controllability of several examples of parabolic-hyperbolic systems has been investigated. The present article is the beginning of an attempt to find a unified framework that encompasses and generalizes the previous results. ... More
Null-controllability of linear parabolic-transport systemsJul 22 2019Sep 11 2019Over the past two decades, the controllability of several examples of parabolic-hyperbolic systems has been investigated. The present article is the beginning of an attempt to find a unified framework that encompasses and generalizes the previous results. ... More
Tracking Holistic Object RepresentationsJul 21 2019Recent advances in visual tracking are based on siamese feature extractors and template matching. For this category of trackers, latest research focuses on better feature embeddings and similarity measures. In this work, we focus on building holistic ... More
Tracking Holistic Object RepresentationsJul 21 2019Aug 06 2019Recent advances in visual tracking are based on siamese feature extractors and template matching. For this category of trackers, latest research focuses on better feature embeddings and similarity measures. In this work, we focus on building holistic ... More
Refined Enumeration of Symmetry Classes of Alternating Sign MatricesJun 18 2019We prove refined enumeration results on several symmetry classes as well as related classes of alternating sign matrices with respect to classical boundary statistics, using the six-vertex model of statistical physics. More precisely, we study vertically ... More
Matricial characterization of tournaments with maximum number of diamondsJun 11 2019A diamond is a $4$-tournament which consists of a vertex dominating or dominated by a $3$-cycle. Assuming the existence of skew-conference matrices, we give a complete characterization of $n$-tournaments with the maximum number of diamonds when $n\equiv0\pmod{4}$ ... More
A trust model for spreading gossip in social networksMay 23 2019We introduce here a multi-type bootstrap percolation model, which we call T-Bootstrap Percolation (T-BP), and apply it to study information propagation in social networks. In this model, a social network is represented by a graph G whose vertices have ... More
Efficient solutions for nonlocal diffusion problems via boundary-adapted spectral methodsMay 09 2019We introduce an efficient boundary-adapted spectral method for peridynamic diffusion problems with arbitrary boundary conditions. The spectral approach transforms the convolution integral in the peridynamic formulation into a multiplication in the Fourier ... More
Cuntz semigroups of ultraproduct C*-algebrasMay 08 2019We prove that the category of abstract Cuntz semigroups is bicomplete. As a consequence, the category admits products and ultraproducts. We further show that the scaled Cuntz semigroup of the (ultra)product of a family of C*-algebras agrees with the (ultra)product ... More
Quantification of thermally-driven flows in microsystems using Boltzmann equation in deterministic and stochastic contextsMay 03 2019When the flow is sufficiently rarefied, a temperature gradient, for example, between two walls separated by a few mean free paths, induces a gas flow---an observation attributed to the thermo-stress convection effects at microscale. The dynamics of the ... More
The Varchenko DeterminantApr 15 2019Varchenko introduced a distance function on chambers of a hyperplane arrangement which gives rise to a determinant indexed by chambers whose entry in position $(C,D)$ is the distance between $C$ and $D$, and proved that that determinant has a nice factorization: ... More
The Varchenko DeterminantApr 15 2019Aug 29 2019In 1993, Varchenko introduced a distance function on chambers of hyperplane arrangements that he called quantum bilinear form. That gave rise to a determinant, indexed by the chambers, whose entry in position $(C,D)$ is the distance between $C$ and $D$: ... More
MAT-free reflection arrangementsApr 12 2019We introduce the class of MAT-free hyperplane arrangements which is based on the Multiple Addition Theorem by Abe, Barakat, Cuntz, Hoge, and Terao. We also investigate the closely related class of MAT2-free arrangements based on a recent generalization ... More
Clark measures on the complex sphereApr 08 2019Let $B_d$ denote the unit ball of $\mathbb{C}^d$, $d\ge 1$. Given a holomorphic function $\varphi: B_d \to B_1$, we study the corresponding family $\sigma_\alpha[\varphi]$, $\alpha\in\partial B_1$, of Clark measures on the unit sphere $\partial B_d$. ... More
Elliptic problems and holomorphic functions in Banach spacesApr 05 2019In the first part we show that a vector-valued almost separably valued function $f$ is holomorphic (harmonic) if and only if it is dominated by an $L^1_\mathrm{loc}$ function and there exists a separating set $W\subset X'$ such that $\langle f,x'\rangle$ ... More
Uniqueness and Stability for the Shock Reflection-Diffraction Problem for Potential FlowMar 29 2019Jul 21 2019When a plane shock hits a two-dimensional wedge head on, it experiences a reflection-diffraction process, and then a self-similar reflected shock moves outward as the original shock moves forward in time. The experimental, computational, and asymptotic ... More
Uniqueness and Stability for the Shock Reflection-Diffraction Problem for Potential FlowMar 29 2019Apr 30 2019When a plane shock hits a two-dimensional wedge head on, it experiences a reflection-diffraction process, and then a self-similar reflected shock moves outward as the original shock moves forward in time. The experimental, computational, and asymptotic ... More
Uniqueness and Stability for the Shock Reflection-Diffraction Problem for Potential FlowMar 29 2019When a plane shock hits a two-dimensional wedge head on, it experiences a reflection-diffraction process, and then a self-similar reflected shock moves outward as the original shock moves forward in time. The experimental, computational, and asymptotic ... More
Electrocommunication for weakly electric fishMar 27 2019This paper addresses the problem of the electro-communication for weakly electric fish. In particular we aim at sheding light on how the fish circumvent the jamming issue for both electro-communication and active electro-sensing. A real-time tracking ... More
Presentations of Transversal Valuated MatroidsMar 19 2019Given $d$ row vectors of $n$ tropical numbers, $d<n$, the tropical Stiefel map constructs a version of their row space, whose Pl\"ucker coordinates are tropical determinants. We explicitly describe the fibers of this map. From the viewpoint of matroid ... More
Protori and Torsion-Free Abelian GroupsMar 19 2019The Resolution Theorem for Compact Abelian Groups is applied to show that the profinite subgroups of a finite-dimensional compact connected abelian group (protorus) which induce tori quotients comprise a lattice under intersection (meet) and $+$ (join), ... More
Transfer operators, atomic decomposition and the BestiaryMar 16 2019Arbieto and S. recently used atomic decomposition to study transfer operators. We give a long list of old and new expanding dynamical systems for which those results can be applied, obtaining the quasi-compactness of transfer operator acting on Besov ... More
Transfer operators and atomic decompositionMar 16 2019Apr 16 2019We use the method of atomic decomposition and a new family of Banach spaces to study the action of transfer operators associated to piecewise-defined maps. It turns out that these transfer operators are quasi-compact even when the associated potential, ... More
Transfer operators and atomic decompositionMar 16 2019We use the method of atomic decomposition and a new family of Banach spaces to study the action of transfer operators associated to piecewise-defined maps. It turns out that these transfer operators are quasi-compact even when the associated potential, ... More
A mixed problem for the Laplace operator in a domain with moderately close holesMar 14 2019We investigate the behavior of the solution of a mixed problem in a domain with two moderately close holes. We introduce a positive parameter $\epsilon$ and we define a perforated domain $\Omega_{\epsilon}$ obtained by making two small perforations in ... More
Relative Dolbeault cohomologyMar 12 2019We review the notion of relative Dolbeault cohomology and prove that it is canonically isomorphic with the local (relative) cohomology of A. Grothendieck and M. Sato with coefficients in the sheaf of holomorphic forms. We deal with this cohomology from ... More
A discontinuous Galerkin fast spectral method for multi-species full Boltzmann on streaming multi-processorsMar 12 2019When the molecules of a gaseous system are far apart, say in microscale gas flows where the surface to volume ratio is high and hence the surface forces dominant, the molecule-surface interactions lead to the formation of a local thermodynamically non-equilibrium ... More
On exact controllability of infinite-dimensional linear port-Hamiltonian systemsMar 09 2019Infinite-dimensional linear port-Hamiltonian systems on a one-dimensional spatial domain with boundary control are studied. This class of systems includes models of beams and waves as well as the transport equation and networks of nonhomogeneous transmission ... More
On exact controllability of infinite-dimensional linear port-Hamiltonian systemsMar 09 2019May 15 2019Infinite-dimensional linear port-Hamiltonian systems on a one-dimensional spatial domain with full boundary control and without internal damping are studied. This class of systems includes models of beams and waves as well as the transport equation and ... More
A discontinuous Galerkin fast spectral method for the multi-species Boltzmann equationMar 07 2019We introduce a fast Fourier spectral method for the multi-species Boltzmann collision operator. The method retains the riveting properties of the single-species fast spectral method (Gamba et al. SIAM J. Sci. Comput., 39 pp. B658--B674 2017) including: ... More
Anisotropy-based robust performance criteria for statistically uncertain linear continuous time invariant stochastic systemsMar 05 2019This paper is concerned with robust performance criteria for linear continuous time invariant stochastic systems driven by statistically uncertain random processes. The uncertainty is understood as the deviation of imprecisely known probability distributions ... More
Generalized semimodularity: order statisticsFeb 14 2019A notion of generalized $n$-semimodularity is introduced, which extends that of (sub/super)mod\-ularity in four ways at once. The main result of this paper, stating that every generalized $(n\colon\!2)$-semimodular function on the $n$th Cartesian power ... More
Sequentially Cohen-Macaulay matroidal idealsFeb 14 2019Let $R=K[x_1,...,x_n]$ be the polynomial ring in $n$ variables over a field $K$ and let $J$ be a matroidal ideal of degree $d$ in $R$. In this paper, we study the class of sequentially Cohen-Macaulay matroidal ideals. In particular, all sequentially Cohen-Macaulay ... More
Sequentially Cohen-Macaulay matroidal idealsFeb 14 2019Feb 17 2019Let $R=K[x_1,...,x_n]$ be the polynomial ring in $n$ variables over a field $K$ and let $J$ be a matroidal ideal of degree $d$ in $R$. In this paper, we study the class of sequentially Cohen-Macaulay matroidal ideals. In particular, all sequentially Cohen-Macaulay ... More
Sequentially Cohen-Macaulay matroidal idealsFeb 14 2019Apr 22 2019Let $R=K[x_1,...,x_n]$ be the polynomial ring in $n$ variables over a field $K$ and let $J$ be a matroidal ideal of degree $d$ in $R$. In this paper, we study the class of sequentially Cohen-Macaulay matroidal ideals. In particular, all sequentially Cohen-Macaulay ... More
Majority categoriesFeb 08 2019We introduce the notion of a majority category --- the categorical counterpart of varieties of universal algebras admitting a majority term. This notion can be thought to capture properties of the category of lattices, in a way that parallels how Mal'tsev ... More
Equivariant Kazhdan-Lusztig polynomials of thagomizer matroidsFeb 04 2019The equivariant Kazhdan-Lusztig polynomial of a matroid was introduced by Gedeon, Proudfoot, and Young. Gedeon conjectured an explicit formula for the equivariant Kazhdan-Lusztig polynomials of thagomizer matroids with an action of symmetric groups. In ... More
Subgroups of arbitrary even ordinary depthFeb 01 2019We show that for each positive integer $n$, there are a group $G$ and a subgroup $H$ such that the ordinary depth is $d(H, G) = 2n$. This answers the question posed by Lars Kadison (see [10]) whether even ordinary depth larger than $6$ can occur.
Isospectral deformations, the spectrum of Jacobi matrices, infinite continued fraction and difference operators. Application to dynamics on infinite dimensional systemsFeb 01 2019This paper is devoted to the study of some connections between coadjoint orbits in infinite dimensional Lie algebras, isospectral deformations and linearization of dynamical systems. We explain how results from deformation theory, cohomology groups and ... More
Embedding quadratization gadgets on Chimera and Pegasus graphsJan 23 2019We group all known quadratizations of cubic and quartic terms in binary optimization problems into six and seven unique graphs respectively. We then perform a minor embedding of these graphs onto the well-known Chimera graph, and the brand new Pegasus ... More
Pegasus: The second connectivity graph for large-scale quantum annealing hardwareJan 22 2019Pegasus is a graph which offers substantially increased connectivity between the qubits of quantum annealing hardware compared to the graph Chimera. It is the first fundamental change in the connectivity graph of quantum annealers built by D-Wave since ... More
Signed Network Structural Analysis and Applications with a Focus on Balance TheoryJan 21 2019We analyse signed networks from the perspective of balance theory which predicts structural balance as a global structure for signed social networks that represent groups of friends and enemies. The scarcity of balanced networks encouraged us to define ... More
Extending partial isometries of antipodal graphsJan 14 2019Aug 10 2019We prove EPPA (extension property for partial automorphisms) for all antipodal classes from Cherlin's list of metrically homogeneous graphs, thereby answering a question of Aranda et al. This paper should be seen as the first application of a new general ... More
Extending partial isometries of antipodal graphsJan 14 2019We prove EPPA (extension property for partial automorphisms) for all antipodal classes from Cherlin's list of metrically homogeneous graphs, thereby answering a question of Aranda et al. This paper should be seen as the first application of a new general ... More
Quadratization in discrete optimization and quantum mechanicsJan 14 2019A book about turning high-degree optimization problems into quadratic optimization problems that maintain the same global minimum (ground state). This book explores quadratizations for pseudo-Boolean optimization, perturbative gadgets used in QMA completeness ... More
On the controllability of the Navier-Stokes equation in a rectangle, with a little help of a distributed phantom forceJan 06 2019This note echoes the talk given by the second author during the Journ\'ees EDP 2018 in Obernai. Its aim is to provide an overview and a sketch of proof of the result obtained by the authors, concerning the controllability of the Navier-Stokes equation. ... More
A mesh-free method for interface problems using the deep learning approachJan 03 2019In this paper, we propose a mesh-free method to solve interface problems using the deep learning approach. Two interface problems are considered. The first one is an elliptic PDE with a discontinuous and high-contrast coefficient. While the second one ... More
EPPA for two-graphs and antipodal metric spacesDec 28 2018We prove that the class of two-graphs has the extension property for partial automorphisms (EPPA, or Hrushovski property), thereby answering a question of Macpherson. In other words, we show that the class of graphs has the extension property for switching ... More
Traveling waves for some nonlocal 1D Gross-Pitaevskii equations with nonzero conditions at infinityDec 20 2018We consider a nonlocal family of Gross-Pitaevskii equations with nonzero conditions at infinity in dimension one. We provide conditions on the nonlocal interaction such that there is a branch of traveling waves solutions with nonvanishing conditions at ... More
Traveling waves for some nonlocal 1D Gross-Pitaevskii equations with nonzero conditions at infinityDec 20 2018Jul 16 2019We consider a nonlocal family of Gross-Pitaevskii equations with nonzero conditions at infinity in dimension one. We provide conditions on the nonlocal interaction such that there is a branch of traveling waves solutions with nonvanishing conditions at ... More
Explicit Solutions for a Nonlinear Vector Model on the Triangular LatticeDec 16 2018Apr 13 2019We present a family of explicit solutions for a nonlinear classical vector model with anisotropic Heisenberg-like interaction on the triangular lattice.
Explicit solutions for a nonlinear vector model on the triangular latticeDec 16 2018We present a family of explicit solutions for a nonlinear classical vector model with anisotropic Heisenberg-like interaction on the triangular lattice.
Hypercomplex Generalizations of Gaussian-type MeasuresDec 15 2018The article is devoted to a new type of measures which are hypercomplex generalizations of Gaussian-type measures. The considered such measures are related with solutions of high order hyperbolic PDEs and related Markov processes. Their characteristic ... More
On ultrafilter extensions of first-order models and ultrafilter interpretationsDec 15 2018There exist two known canonical concepts of ultrafilter extensions of first-order models; one comes from modal logic and universal algebra, another one from model theory and algebra of ultrafilters, with ultrafilter extensions of semigroups as its main ... More
Some results relevant to embeddability of rings (especially group algebras) in division ringsDec 14 2018P. M. Cohn showed in 1971 that given a ring $R$, to describe, up to isomorphism, a division ring $D$ generated by a homomorphic image of $R$ is equivalent to specifying the set of square matrices over $R$ which map to singular matrices over $D,$ and he ... More
Some results relevant to embeddability of rings (especially group algebras) in division ringsDec 14 2018Jul 08 2019P. M. Cohn showed in 1971 that given a ring $R$, to describe, up to isomorphism, a division ring $D$ generated by a homomorphic image of $R$ is equivalent to specifying the set of square matrices over $R$ which map to singular matrices over $D,$ and he ... More
Riesz transform and vertical oscillation in the Heisenberg groupOct 31 2018Jan 20 2019We study the $L^{2}$-boundedness of the $3$-dimensional (Heisenberg) Riesz transform on intrinsic Lipschitz graphs in the first Heisenberg group $\mathbb{H}$. Inspired by the notion of vertical perimeter, recently defined and studied by Lafforgue, Naor, ... More
Traces and Extensions of Bounded Divergence-Measure Fields on Rough Open SetsOct 30 2018We prove that an open set $\Omega \subset \mathbb{R}^n$ can be approximated by smooth sets with uniformly bounded perimeters from the interior if and only if the open set $\Omega$ satisfies \begin{align*} &\qquad \qquad\qquad\qquad\qquad\qquad\qquad \mathscr{H}^{n-1}(\partial ... More
Expected Utility Maximization and Conditional Value-at-Risk Deviation-based Sharpe Ratio in Dynamic Stochastic Portfolio OptimizationOct 27 2018In this paper we investigate the expected terminal utility maximization approach for a dynamic stochastic portfolio optimization problem. We solve it numerically by solving an evolutionary Hamilton-Jacobi-Bellman equation which is transformed by means ... More
Null-controllability and control cost estimates for the heat equation on unbounded and large bounded domainsOct 26 2018We survey recent results on the control problem for the heat equation on unbounded and large bounded domains. First we formulate new uncertainty relations, respectively spectral inequalities. Then we present an abstract control cost estimate which improves ... More
Sharp estimates and homogenization of the control cost of the heat equation on large domainsOct 25 2018Dec 17 2018We prove new bounds on the control cost for the abstract heat equation, assuming a spectral inequality or uncertainty relation for spectral projectors. In particular, we specify quantitatively how upper bounds on the control cost depend on the constants ... More
Maximal $L^p$-regularity for perturbed evolution equations in Banach spacesOct 21 2018The main purpose of this paper is to investigate the concept of maximal $L^p$-regularity for perturbed evolution equations in Banach spaces. We mainly consider three classes of perturbations: Miyadera-Voigt perturbations, Desch-Schappacher perturbations, ... More
Matroidal representations of groupsOct 19 2018We develop the rudiments of a finite-dimensional representation theory of groups over idempotent semifields by considering linear actions on tropical linear spaces. This can be considered a tropical representation theory, a characteristic one modular ... More
Representation of relative sheaf cohomologyOct 15 2018We study the cohomology theory of sheaf complexes for open embeddings of topological spaces and related subjects. The theory is situated in the intersection of the general Cech theory and the theory of derived categories. That is to say, on the one hand ... More
Pattern Formation in a Slowly Flattening Spherical Cap: Delayed BifurcationOct 10 2018This article describes a reduction of a nonautonomous Brusselator reaction-diffusion system of partial differential equations on a spherical cap with time dependent curvature using the method of centre manifold reduction. Parameter values are chosen such ... More
An explicit saturating set leads to approximate controllability for Navier--Stokes equations in $\mathrm{3D}$ Cylinders under Lions boundary conditionsOct 10 2018A saturating set consisting eigenfunctions of Stokes operator in general 3D Cylinders is proposed. The explicit saturating set leads to the approximate controllability for Navier--Stokes equations in $\mathrm{3D}$ cylinders under Lions boundary conditions. ... More
A CFSG-free diameter bound for permutation subgroupsOct 05 2018Oct 21 2018Helfgott and Seress have proved the existence of a quasipolynomial upper bound on the diameter of transitive permutation subgroups. In this paper we remove the dependence on CFSG from that result, by using the algorithm solving the string isomorphism ... More
Method of automorphic functions for an inverse problem of antiplane elasticitySep 28 2018A nonlinear inverse problem of antiplane elasticity for a multiply connected domain is examined. It is required to determine the profile of $n$ uniformly stressed inclusions when the surrounding infinite body is subjected to antiplane uniform shear at ... More
The Lattice of Profinite Subgroups of ProtoriSep 27 2018Compact connected abelian groups, or protori, have intrinsic structural characteristics that present for the entire category. In the case of finite-dimensional torus-free protori, The Resolution Theorem for Compact Abelian Groups sets the stage for demonstrating ... More
A Discontinuous Galerkin Fast Spectral Method for the Full Boltzmann Equation with General Collision KernelsSep 26 2018Nov 02 2018The Boltzmann equation, an integro-differential equation for the molecular distribution function in the physical and velocity phase space, governs the fluid flow behavior at a wide range of physical conditions, including compressible, turbulent, as well ... More
Stationary distributions and condensation in autocatalytic CRNSep 19 2018Jun 21 2019We investigate a broad family of non weakly reversible stochastically modeled reaction networks (CRN), by looking at their steady-state distributions. Most known results on stationary distributions assume weak reversibility and zero deficiency. We first ... More
Stationary distributions and condensation in autocatalytic CRNSep 19 2018Dec 14 2018We investigate a broad family of non weakly reversible stochastically modeled reaction networks (CRN), by looking at their steady-state distributions. Most known results on stationary distributions assume weak reversibility and zero deficiency. We first ... More
Global exact controllability of bilinear quantum systems oncompact graphs and energetic controllabilitySep 17 2018Feb 07 2019In this work, we consider the bilinear Schr\"odinger equation on compact graphs. We study new hypotheses leading to the global exact controllability of the equation in suitable Sobolev's spaces. Afterwards, we introduce the "energetic controllability", ... More
The Main Decomposition of Finite-Dimensional ProtoriSep 12 2018A protorus is a compact connected abelian group. We use a result on finite rank torsion-free abelian groups and Pontryagin Duality to considerably generalize a well-known factorization of a finite-dimensional protorus into a product of a torus and a torus-free ... More
On the asymptotic structure of steady Stokes and Navier-Stokes flows around a rotating two-dimensional bodySep 10 2018We establish pointwise decay estimates for the velocity field of a steady two-dimensional Stokes flow around a rotating body via a new approach rather than analysis adopted in the previous literature. The novelty is to analyze the singular behavior of ... More
Cauchy Fluxes and Gauss-Green Formulas for Divergence-Measure Fields over General Open SetsSep 04 2018Jan 18 2019We establish the interior and exterior Gauss-Green formulas for divergence-measure fields in $L^p$ over general open sets, motivated by the rigorous mathematical formulation of the physical principle of balance law via the Cauchy flux in the axiomatic ... More
The gamma construction and asymptotic invariants of line bundles over arbitrary fieldsSep 04 2018Sep 25 2018We extend results on asymptotic invariants of line bundles on complex projective varieties to projective varieties over arbitrary fields. To do so over imperfect fields, we prove a scheme-theoretic version of the gamma construction of Hochster and Huneke ... More
The gamma construction and asymptotic invariants of line bundles over arbitrary fieldsSep 04 2018Aug 12 2019We extend results on asymptotic invariants of line bundles on complex projective varieties to projective varieties over arbitrary fields. To do so over imperfect fields, we prove a scheme-theoretic version of the gamma construction of Hochster and Huneke ... More
The spectrum of the Laplacian in a domain bounded by a flexible polyhedron in $\mathbb R^d$ does not always remain unaltered during the flexSep 02 2018Being motivated by the theory of flexible polyhedra, we study the Dirichlet and Neumann eigenvalues for the Laplace operator in special bounded domains of Euclidean $d$-space. The boundary of such a domain is an embedded simplicial complex which allows ... More
The spectrum of the Laplacian in a domain bounded by a flexible polyhedron in $\mathbb R^d$ does not always remain unaltered during the flexSep 02 2018Mar 16 2019Being motivated by the theory of flexible polyhedra, we study the Dirichlet and Neumann eigenvalues for the Laplace operator in special bounded domains of Euclidean $d$-space. The boundary of such a domain is an embedded simplicial complex which allows ... More
On the Formalization of Higher Inductive Types and Synthetic Homotopy TheoryAug 31 2018The goal of this dissertation is to present synthetic homotopy theory in the setting of homotopy type theory. We will present various results in this framework, most notably the construction of the Atiyah-Hirzebruch and Serre spectral sequences for cohomology, ... More
Model Predictive Control for Regular Linear SystemsAug 29 2018The present work extends known finite-dimensional constrained optimal control realizations to the realm of well-posed regular linear infinite-dimensional systems modelled by partial differential equations. The structure-preserving Cayley-Tustin transformation ... More
Equivariant Kazhdan-Lusztig polynomials of $q$-niform matroidsAug 23 2018Sep 01 2018We introduce $q$-analogues of uniform matroids, which we call $q$-niform matroids. While uniform matroids admit actions of symmetric groups, $q$-niform matroids admit actions of finite general linear groups. We show that the equivariant Kazhdan-Lusztig ... More
Entropy on normed semigroups (A unifying approach to entropy)Aug 11 2018We present a unifying approach to the study of entropies in Mathematics, such as measure entropy, topological entropy, algebraic entropy, set-theoretic entropy. We take into account discrete dynamical systems, that is, pairs $(X,T)$, where $X$ is the ... More
Entropy on normed semigroups (Towards a unifying approach to entropy)Aug 11 2018Aug 29 2019We present a unifying approach to the study of entropies in Mathematics, such as measure entropy, topological entropy, algebraic entropy, set-theoretic entropy. We take into account discrete dynamical systems, that is, pairs $(X,T)$, where $X$ is the ... More
Rigidity of proper colorings of $\mathbb{Z}^d$Aug 10 2018Dec 31 2018A proper $q$-coloring of a domain in $\mathbb{Z}^d$ is a function assigning one of $q$ colors to each vertex of the domain such that adjacent vertices are colored differently. Sampling a proper $q$-coloring uniformly at random, does the coloring typically ... More
Distinguishing Numbers and GeneralizationsAug 03 2018The distinguishing number of a graph was introduced by Albertson and Collins as a measure of the amount of symmetry contained in the graph. Tymoczko extended this definition to faithful group actions on sets; taking the set to be the vertex set of a graph ... More
Distinguishing Numbers and GeneralizationsAug 03 2018Apr 07 2019The distinguishing number of a graph was introduced by Albertson and Collins as a measure of the amount of symmetry contained in the graph. Tymoczko extended this definition to faithful group actions on sets; taking the set to be the vertex set of a graph ... More
Multiplicity of bounded solutions to the $k$-Hessian equation with a Matukuma-type sourceJul 31 2018The aim of this paper is to deal with the $k$-Hessian counterpart of the Laplace equation involving a nonlinearity studied by Matukuma. Namely, our model is the problem \begin{equation*} (1)\;\;\;\begin{cases} S_k(D^2u)= \lambda \frac{|x|^{\mu-2}}{(1+|x|^2)^{\frac{\mu}{2}}} ... More
A combinatorial proof of the extension property for partial isometriesJul 28 2018Aug 28 2018We present a short and self-contained proof of the extension property for partial isometries of the class of all finite metric spaces.