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Reconstruction of a Riemannian manifold from noisy intrinsic distancesMay 17 2019We consider reconstruction of a manifold, or, invariant manifold learning, where a smooth Riemannian manifold $M$ is determined from intrinsic distances (that is, geodesic distances) of points in a discrete subset of $M$. In the studied problem the Riemannian ... More

NANUQ: A method for inferring species networks from gene trees under the coalescent modelMay 16 2019Species networks generalize the notion of species trees to allow for hybridization or other lateral gene transfer. Under the Network Multispecies Coalescent Model, individual gene trees arising from a network can have any topology, but arise with frequencies ... More

Some computability-theoretic reductions between principles around $\mathsf{ATR}_0$May 16 2019We study the computational content of various theorems with reverse mathematical strength around Arithmetical Transfinite Recursion ($\mathsf{ATR}_0$) from the point of view of computability-theoretic reducibilities, in particular Weihrauch reducibility. ... More

Simplicial splines for representation of density functionsMay 16 2019In the context of functional data analysis, probability density functions as non-negative functions are characterized by specific properties of scale invariance and relative scale which enable to represent them with the unit integral constraint without ... More

Sample Paths Estimates for Stochastic Fast-Slow Systems driven by Fractional Brownian MotionMay 16 2019We analyze the effect of additive fractional noise with Hurst parameter $H > \frac{1}{2}$ on fast-slow systems. Our strategy is based on sample paths estimates, similar to the approach by Berglund and Gentz in the Brownian motion case. Yet, the setting ... More

Generical behavior of flows strongly monotone with respect to high-rank conesMay 16 2019We consider a $C^{1,\alpha}$ smooth flow in $\mathbb{R}^n$ which is "strongly monotone" with respect to a cone $C$ of rank $k$, a closed set that contains a linear subspace of dimension $k$ and no linear subspaces of higher dimension. We prove that orbits ... More

On the harmonic extension approach to fractional powers in Banach spacesMay 16 2019We show that fractional powers of general sectorial operators on Banach spaces can be obtained by the harmonic extension approach. Moreover, for the corresponding second order ordinary differential equation with incomplete data describing the harmonic ... More

Noncommutative Joinings IIMay 16 2019This paper is a continuation of the authors' previous work on noncommutative joinings, and contains a study of relative independence of W$^*$-dynamical systems. We prove that, given any separable locally compact group $G$, an ergodic W$^{*}$-dynamical ... More

On Noncommutative JoiningsMay 16 2019This paper extends the classical theory of joinings of measurable dynamical systems to the noncommutative setting from several interconnected points of view. Among these is a particularly fruitful identification of joinings with equivariant quantum channels ... More

Fields of dimension one algebraic over a global or local field need not be of type $(C_{1})$May 16 2019Let $(K, v)$ be a Henselian discrete valued field with a quasifinite residue field. This paper proves the existence of an algebraic extension $E/K$ with the following properties: (i) $E$ has dimension dim$(E) \le 1$, i.e. the Brauer group Br$(E ^{\prime ... More

The direct image of generalized divisors and the Norm map between compactified JacobiansMay 16 2019Given a finite, flat morphism between embeddable noetherian schemes of pure dimension 1, we define the notion of direct and inverse image for generalized divisors and generalized line bundles. Moreover, in the case where we deal with projective curves ... More

General divergent stability conditions of dynamic systemsMay 16 2019New necessary and sufficient conditions are proposed for the stability investigation of dynamical systems using the flow and the divergence of the phase vector velocity. The obtained conditions generalize the well-known results of V.P. Zhukov and A. Rantzer. ... More

M{ö}bius orthogonality in density for zero entropy dynamical systemsMay 16 2019It is proved that whenever a zero entropy dynamical system $(X,T)$ has only countably many ergodic measures and $\mu$ stands for the arithmetic M{\"o}bius function, then there exists a subset $A$ of integers depending only on the system, of logarithmic ... More

Two-Stroke Relaxation OscillatorsMay 16 2019Two-stroke relaxation oscillations} consist of two distinct phases per cycle -- one slow and one fast -- which distinguishes them from the well-known van der Pol-type `four-stroke' relaxation oscillations. These type of oscillations can be found in singular ... More

Gelfand-Naimark-Stone duality for normal spaces and insertion theoremsMay 16 2019Gelfand-Naimark-Stone duality provides an algebraic counterpart of compact Hausdorff spaces in the form of uniformly complete bounded archimedean $\ell$-algebras. In [4] we extended this duality to completely regular spaces. In this article we use this ... More

Distribuation of CM points of an infinite series of complete Calabi-Yau moduli spacesMay 16 2019In the infinite series of complete families of Calabi-Yau manifolds $\tilde{f}_n: \tilde{\mathcal{X}}_n\rightarrow \mathfrak{M}_{n, n+3}$, where $n$ is an odd number, arising from cyclic covers of $\mathbb{P}^n$ branching along hyperplane arrangements ... More

Attractors and Attracting Neighborhoods for MultiflowsMay 15 2019We already know a great deal about dynamical systems with uniqueness in forward time. Indeed, flows, semiflows, and maps (both invertible and not) have been studied at length. A view that has proven particularly fruitful is topological: consider invariant ... More

D-finiteness, rationality, and heightMay 15 2019Motivated by a result of van der Poorten and Shparlinski for univariate power series, Bell and Chen prove that if a multivariate power series over a field of characteristic 0 is D-finite and its coefficients belong to a finite set then it is a rational ... More

Simultaneous occurrence of sliding and crossing limit cycles in piecewise linear planar vector fieldsMay 15 2019In the present study we consider planar piecewise linear vector fields with two zones separated by the straight line $x=0$. Our goal is to study the existence of simultaneous crossing and sliding limit cycles for such a class of vector fields. First, ... More

Asymptotic stability of robust heteroclinic networksMay 15 2019We provide conditions guaranteeing that certain classes of robust heteroclinic networks are asymptotically stable. We study the asymptotic stability of ac-networks --- robust heteroclinic networks that exist in smooth ${\mathbb Z}^n_2$-equivariant dynamical ... More

Isometric Immersions and the Waving of FlagsMay 15 2019In this article we propose a novel geometric model to study the motion of a physical flag. In our approach a flag is viewed as an isometric immersion from the square with values into $\mathbb R^3$ satisfying certain boundary conditions at the flag pole. ... More

When a spherical body of constant diameter is of constant width?May 15 2019{\bf Abstract.} Let $D$ be a convex body of diameter $\delta$, where $0 < \delta < \frac{\pi}{2}$, on the $d$-dimensional sphere. We prove that $D$ is of constant diameter $\delta$ if and only if it is of constant width $\delta$ in the following two cases. ... More

The group $J_4 \times J_4$ is recognizable by spectrumMay 15 2019The spectrum of a finite group is the set of its element orders. In this paper we prove that the direct product of two copies of the finite simple sporadic group $J_4$ is uniquely determined by its spectrum in the class of all finite groups.

Uniqueness of the measure of maximal entropy for singular hyperbolic flows in dimension 3 and more results on equilibrium statesMay 15 2019We prove that any 3-dimensional singular hyperbolic attractor admits for any H\"older continuous potential $V$ at most one equilibrium state for $V$ among regular measures. We give a condition on $V$ which ensures that no singularity can be an equilibrium ... More

Wave propagation and its stability for a class of discrete diffusion systemsMay 15 2019This paper is devoted to study the wave propagation and its stability for a class of two-component discrete diffusive systems. We first establish the existence of positive monotone monostable traveling wave fronts. Then, applying the techniques of weighted ... More

On formal groups and geometric quantizationMay 15 2019In the theory of geometric quantization, the (cobordism classes of) complex projective spaces, regarded as symplectic manifolds, are to the (cobordism classes of) complex projective spaces, regarded as almost complex manifolds, as elementary symmetric ... More

On ternary Egyptian fractions with prime denominatorMay 15 2019Given a positive integer $n$ we let $A_k(n)$ be the number of positive integers $a$ such that $\frac{a}{n}=\frac{1}{m_1}+\frac{1}{m_2}+\cdots+\frac{1}{m_k}$ for some $m_1,m_2,\ldots,m_k\in {\mathbb N}$. We show that $x(\log x)^3\ll \sum_{p\le x} A_3(p)\ll ... More

Counting and ordering periodic stationary solutions of lattice Nagumo equationsMay 15 2019We study the rich structure of periodic stationary solutions of Nagumo reaction diffusion equation on lattices. By exploring the relationship with Nagumo equations on cyclic graphs we are able to divide these periodic solutions into equivalence classes ... More

Trees are nilrigidMay 15 2019We study cellular automata on the unoriented $k$-regular tree $T_k$, i.e. continuous maps acting on colorings $T_k$ which commute with all automorphisms of the tree. We prove that every CA that is asymptotically nilpotent, meaning every configuration ... More

Phase-locked states in oscillating neural networks and their role in neural communicationMay 15 2019The theory of communication through coherence (CTC) proposes that brain oscillations reflect changes in the excitability of neurons, and therefore the successful communication between two oscillating neural populations depends not only on the strength ... More

Cauchy and uniform temporal functions of globally hyperbolic cone fieldsMay 15 2019We study a class of time functions called uniform temporal functions in the general context of globally hyperbolic closed cone fields. We prove some existence results for uniform temporal functions, and prove the density of uniform temporal functions ... More

Generic Birkhoff SpectraMay 15 2019Suppose that $\Omega = \{0, 1\}^ {\mathbb {N}}$ and $ {\sigma}$ is the one-sided shift. The Birkhoff spectrum $ \displaystyle S_{f}( {\alpha})=\dim_{H}\Big \{ {\omega}\in {\Omega}:\lim_{N \to \infty} \frac{1}{N} \sum_{n=1}^N f(\sigma^n \omega) = \alpha ... More

Identifying conversion efficiency as a key mechanism underlying food webs evolution: A step forward, or backward?May 15 2019Body size or mass is generally seen as one of the main factors which structure food webs. A large number of evolutionary models have shown that indeed, the evolution of body size (or mass) can give rise to hierarchically organized trophic levels with ... More

An example of a symmetric homeomorphism of the real line with non-symmetric inversionMay 15 2019We show an example of a symmetric homeomorphism $h$ of the real line $\mathbb{R}$ onto itself such that $h^{-1}$ is not symmetric. This implies that the set of all symmetric self-homeomorphisms of $\mathbb{R}$ does not constitute a group under the composition. ... More

Revolving FractalsMay 15 2019Davis and Knuth in 1970 introduced the notion of revolving sequences, as representations of a Gaussian integer. Later, Mizutani and Ito pointed out a close relationship between a set of points determined by all revolving sequences and a self-similar set, ... More

Elementary numerical methods for double integralsMay 14 2019Approximations to the integral $\int_a^b\int_c^d f(x,y)\,dy\,dx$ are obtained under the assumption that the partial derivatives of the integrand are in an $L^p$ space, for some $1\leq p\leq\infty$. We assume ${\lVert f_{xy}\rVert}_p$ is bounded (integration ... More

Sliding Motions on SO(3), Sliding SubgroupsMay 14 2019We propose a sliding surface for systems on the Lie group $SO(3)\times \mathbb{R}^3$ . The sliding surface is shown to be a Lie subgroup. The reduced-order dynamics along the sliding subgroup have an almost globally asymptotically stable equilibrium. ... More

$\mathbb{P}^n$-functorsMay 14 2019We propose a new theory of (non-split) P^n-functors. These are F: A -> B for which the adjunction monad RF is a repeated extension of Id_A by powers of an autoequivalence H and three conditions are satisfied: the monad condition, the adjoints condition, ... More

Random walks on linear groups satisfying a Schubert conditionMay 14 2019We study random walks on $\mathrm{GL}_d(\mathbb{R})$ whose proximal dimension $r$ is larger than $1$ and whose limit set in the Grassmannian $\mathrm{Gr}_{r,d}(\mathbb{R})$ is not contained any Schubert variety. These random walks, without being proximal, ... More

Symplectic dominationMay 14 2019Let M be a compact oriented even-dimensional manifold. This note constructs a compact symplectic manifold S of the same dimension and a map f from S to M of strictly positive degree. The construction relies on two deep results: the first is a theorem ... More

Global existence and uniqueness of weak solutions to a generalized Camassa-Holm equationMay 14 2019In this paper, we prove the existence and uniqueness of global weak solutions, which satisfy the balance law in a weak sense, to a generalized Camassa-Holm equation. Due to the effects of forcing terms, the solution loses the conservation of $H^{1}$-energy. ... More

Sample Efficient Toeplitz Covariance EstimationMay 14 2019May 15 2019We study the sample complexity of estimating the covariance matrix $T$ of a distribution $\mathcal{D}$ over $d$-dimensional vectors, under the assumption that $T$ is Toeplitz. This assumption arises in many signal processing problems, where the covariance ... More

Sample Efficient Toeplitz Covariance EstimationMay 14 2019We study the query complexity of estimating the covariance matrix $T$ of a distribution $\mathcal{D}$ over $d$-dimensional vectors, under the assumption that $T$ is Toeplitz. This assumption arises in many signal processing problems, where the covariance ... More

The Hadamard product in a crossed product C*-algebraMay 14 2019We show that for a C*-algebra A and a discrete group G with an action of G on A, the reduced crossed product C*-algebra possesses a natural generalization of the convolution product, which we suggest should be named the Hadamard product. We show that ... More

Embedding Deligne's category $\mathrm{Rep}(S_t)$ in the Heisenberg categoryMay 14 2019We define a faithful linear monoidal functor from the partition category, and hence from Deligne's category $\mathrm{Rep}(S_t)$, to the Heisenberg category. We show that the induced map on Grothendieck rings is injective and corresponds to the Kronecker ... More

Further improving of upper bound on a geometric Ramsey problemMay 14 2019We consider following geometric Ramsey problem: find the least dimension $n$ such that for any 2-coloring of edges of complete graph on the points $\{\pm 1\}^n$ there exists 4-vertex coplanar monochromatic clique. Problem was first analyzed by Graham ... More

A symplectic embedding of the cube with minimal sections and a question by SchlenkMay 14 2019I prove that the open unit cube can be symplectically embedded into a longer polydisc in such a way that the area of each section satisfies a sharp bound and the complement of each section is path-connected. This answers a variant of a question by F. ... More

A projection algorithm on the set of polynomials with two boundsMay 14 2019The motivation of this work stems from the numerical approximation of bounded functions by polynomials satisfying the same bounds. The present contribution makes use of the recent algebraic characterization found in [B. Despr\'es, Numer. Algorithms, 76(3), ... More

The Relative Canonical Ideal of the Artin-Schreier-Kummer-Witt family of curvesMay 14 2019We study the canonical model of the Artin-Schreier-Kummer-Witt flat family of curves over a ring of mixed characteristic. We first prove the relative version of a classical theorem by Petri, then use the model proposed by Bertin-M\'ezard to construct ... More

Busemann functions on the Wasserstein spaceMay 14 2019We study rays and co-rays in the Wasserstein space $P_p(\mathcal{X})$ ($p > 1$) whose ambient space $\mathcal{X}$ is a complete, separable, non-compact, locally compact length space. We show that rays in the Wasserstein space can be represented as probability ... More

Residuation in lattice effect algebrasMay 14 2019We introduce the concept of a quasiresiduated lattice and prove that every lattice effect algebra can be organized into a commutative quasiresiduated lattice with divisibility. Also conversely, every such a lattice can be converted into a lattice effect ... More

Asymptotic escape rates and limiting distributions for multimodal mapsMay 14 2019We consider multimodal maps with holes and study the evolution of the open systems with respect to equilibrium states for both geometric and H\"older potentials. For small holes, we show that a large class of initial distributions share the same escape ... More

Mean dimension and metric mean dimension for non-autonomous dynamical systemsMay 14 2019In this paper we extend the definitions of mean dimension and metric mean di-mension for non-autonomous dynamical systems. We show some properties of this extension and furthermore some applications to the mean dimension and metric mean dimension of single ... More

Persistence of Some Delayed Complex Balanced SystemsMay 14 2019Time-delay is very common phenomenon in real biological or industrial systems. This paper study persistence of complex balanced systems with any constant time-delayed. We give several of sufficient conditions for this kind of systems to be persistent. ... More

Global regularity of 2D tropical climate model with zero thermal diffusionMay 14 2019This article studies the global regularity problem of the two-dimensional zero thermal diffusion tropical climate model with fractional dissipation, given by $(-\Delta)^{\alpha}u$ in the barotropic mode equation and by $(-\Delta)^{\beta}v$ in the first ... More

Desingularizing positive scalar curvature 4-manifoldsMay 13 2019We show that the bordism group of closed 3-manifolds with positive scalar curvature (psc) metrics is trivial by explicit methods. Our constructions are derived from scalar-flat K{\"a}hler ALE surfaces discovered by Lock-Viaclovsky. Next, we study psc ... More

Morse index and stability of the planar N-vortex problemMay 13 2019This paper concerns the investigation of the stability properties of relative equilibria which are rigidly rotating vortex configurations sometimes called vortex crystals, in the N-vortex problem. Such a configurations can be characterized as critical ... More

Aphids, Ants and Ladybirds: a mathematical model predicting their population dynamicsMay 13 2019The interaction between aphids, ants and ladybirds has been investigated from an ecological point of view since many decades, while there are no attempts to describe it from a mathematical point of view. This paper introduces a new mathematical model ... More

A Coupled Oscillator Model for the Origin of Bimodality and MultimodalityMay 13 2019Perhaps because of the elegance of the central limit theorem, it is often assumed that distributions in nature will approach singly-peaked, unimodal shapes reminiscent of the Gaussian normal distribution. However, many systems behave differently, with ... More

Local limit theorem in deterministic systemsMay 13 2019We show that for every ergodic and aperiodic probability preserving system, there exists a $\mathbb{Z}$ valued, square integrable function $f$ such that the partial sums process of the time series $\left\{f\circ T^i\right\}_{i=0}^\infty$ satisfies the ... More

Pseudorotations and Steenrod squaresMay 13 2019In this note we prove that if a closed monotone symplectic manifold $M$ of dimension $2n,$ satisfying a homological condition, that holds in particular when the minimal Chern number is $N>n,$ admits a Hamiltonian pseudorotation, then the quantum Steenrod ... More

Minimal Cohen-Macaulay Simplicial ComplexesMay 13 2019We define and study the notion of a minimal Cohen-Macaulay simplicial complex. We prove that any Cohen-Macaulay complex is shelled over a minimal one in our sense, and we give sufficient conditions for a complex to be minimal Cohen-Macaulay. We show that ... More

Dynamical invariants of toric correspondencesMay 13 2019We focus on various dynamical invariants associated to toric correspondences, using algebraic geometry or arithmetic. We find a formula for the dynamical degrees, relate the exponential growth of the degree sequences with a strict log-concavity condition ... More

Fefferman's Inequality and Unique Continuation Property of Elliptic Partial Differential EquationsMay 13 2019In this paper we prove a Fefferman's inequality for potentials belonging to a generalized Morrey space $ L^{p,\varphi} $ and a Stummel class $ \tilde{S}_{\alpha,p} $. Our result extends the previous Fefferman's inequality that was obtained in \cite{CF,F} ... More

Bivariate functions of bounded variation: Fractal dimension and fractional integralMay 13 2019In contrast to the univariate case, several definitions are available for the notion of bounded variation for a bivariate function. This article is an attempt to study the Hausdorff dimension and box dimension of the graph of a continuous function defined ... More

The Lie group of vertical bisections of a regular Lie groupoidMay 13 2019In this note we construct an infinite-dimensional Lie group structure on the group of vertical bisections of a regular Lie groupoid. We then identify the Lie algebra of this group and discuss regularity properties (in the sense of Milnor) for these Lie ... More

Mathematical analysis of complex SIR model with coinfection and density dependenceMay 13 2019An SIR model with the coinfection of the two infectious agents in a single host population is considered. The model includes the environmental carry capacity in each class of population. A special case of this model is analyzed and several threshold conditions ... More

Li-Yorke chaos in nonautonomous Hopf bifurcation patterns - IMay 13 2019We analyze the characteristics of the global attractor of a type of dissipative nonautonomous dynamical systems in terms of the Sacker and Sell spectrum of its linear part. The model gives rise to a pattern of nonautonomous Hopf bifurcation which can ... More

A Hales--Jewett type property of finite solvable groupsMay 13 2019A conjecture of Leader, Russell and Walters in Euclidean Ramsey theory says that a finite set is Ramsey if and only if it is congruent to a subset of a set whose symmetry group acts transitively. As they have shown the ``if" direction of their conjecture ... More

Physically-interpretable classification of network dynamics for complex collective motionsMay 13 2019Understanding complex network dynamics is a fundamental issue in various scientific and engineering fields. Network theory is capable of revealing the relationship between elements and their propagation; however, for complex collective motions, the network ... More

A new SSO-based Algorithm for the Bi-Objective Time-constrained task Scheduling Problem in Cloud Computing ServicesMay 13 2019Cloud computing distributes computing tasks across numerous distributed resources for large-scale calculation. The task scheduling problem is a long-standing problem in cloud-computing services with the purpose of determining the quality, availability, ... More

Componentwise linearity of projective varieties with almost maximal degreeMay 13 2019The degree of a projective subscheme has an upper bound in term of the codimension and the reduction number. If a projective variety has an almost maximal degree, that is, the degree equals to the upper bound minus one, then its Betti table has been described ... More

Visibility of Cartesian products of Cantor setsMay 12 2019Let $K_{\lambda}$ be the attractor of the following IFS \begin{equation*} \{f_1(x)=\lambda x, f_2(x)=\lambda x+1-\lambda\}, \;\;0<\lambda<1/2. \end{equation*} Given $\alpha \geq 0$, we say the line $y=\alpha x$ is visible through $K_{\lambda}\times K_{\lambda}$ ... More

On subspace convex-cyclic operatorsMay 12 2019Let $\mathcal{H}$ be an infinite dimensional real or complex separable Hilbert space. We introduce a special type of a bounded linear operator $T$ and its important relation with invariant subspace problem on $\mathcal{H}$: operator $T$ is said to be ... More

On the Hofer-Zehnder conjectureMay 12 2019We prove that if a Hamiltonian diffeomorphism on a closed monotone symplectic manifold with semisimple quantum homology has a finite number of contractible periodic points then the sum of the ranks of the local Floer homologies at its contractible fixed ... More

The nonlinear stability regime of the viscous Faraday wave problemMay 12 2019This paper concerns the dynamics of a layer of incompressible viscous fluid lying above a vertically oscillating rigid plane and with an upper boundary given by a free surface. We consider the problem with gravity and surface tension for horizontally ... More

Historic behavior in non-hyperbolic homoclinic classesMay 12 2019We show that $C^1$-generically for diffeomorphisms of manifolds of dimension $d\geq3$, a homoclinic class containing saddles of different indices has a residual subset where the orbit of any point has historic behavior.

Historic behavior in non-hyperbolic homoclinic classesMay 12 2019May 14 2019We show that $C^1$-generically for diffeomorphisms of manifolds of dimension $d\geq3$, a homoclinic class containing saddles of different indices has a residual subset where the orbit of any point has historic behavior.

An Analysis of a Fishing Model with Nonlinear Harvesting FunctionMay 12 2019In this study, considering the importance of how to exploit renewable natural resources, we analyze a fishing model with nonlinear harvesting function in which the players at the equilibrium point do a static game with complete information that, according ... More

Arithmetic on Moran setsMay 12 2019Let $(\mathcal{M}, c_k,n_k)$ be a class of Moran sets. We assume that the convex hull of any $E\in (\mathcal{M}, c_k,n_k)$ is $[0,1]$. Let $A,B$ be two non-empty sets in $\mathbb{R}$. Suppose that $f$ is a continuous function defined on an open set $U\subset ... More

Real moduli space of stable rational curves revistedMay 11 2019We give a description of the operad formed by the real locus of the moduli space of stable genus zero curves with marked points $\overline{{\mathcal M}_{0,{n+1}}}({\mathbb R})$ in terms of a homotopy quotient of an operad of associative algebras. We use ... More

Solving Empirical Risk Minimization in the Current Matrix Multiplication TimeMay 11 2019Many convex problems in machine learning and computer science share the same form: \begin{align*} \min_{x} \sum_{i} f_i( A_i x + b_i), \end{align*} where $f_i$ are convex functions on $\mathbb{R}^{n_i}$ with constant $n_i$, $A_i \in \mathbb{R}^{n_i \times ... More

Effective counting of simple closed geodesics on hyperbolic surfacesMay 11 2019We prove a quantitative estimate, with a power saving error term, for the number of simple closed geodesics of length at most $L$ on a closed hyperbolic surface of genus $g$. The proof relies on the exponential mixing rate for the Teichm\"{u}ller geodesic ... More

An O(1) Algorithm for the Numerical Evaluation of the Prolate Spheroidal Wave Functions of Order 0May 11 2019The standard algorithm for the numerical evaluation of the prolate spheroidal wave function $\mathsf{Ps}\hskip.05em{}_{n}(x;\gamma^2)$ of order $0$, bandlimit $\gamma > 0$ and characteristic exponent $n$ has running time which grows with both $n$ and ... More

Minimality and stable Bernouliness in dimension 3May 11 2019In 3-dimensional manifolds, we prove that generically in$Diff^1_m(M)$, the existence of a minimal expanding invariant foliation implies stable Bernoulliness.

Emergence of Subcritical Bifurcations in a System of Randomly Coupled Supercritical Andronov-Hopf Oscillators: A Potential Mechanism for Neural Network Type SwitchingMay 10 2019Cortical systems such as the visual cortex exhibit behaviors that change according to behavioral and stimulus context. It is still unknown what mechanisms underlie this adaptive processing in cortical circuitry. In this paper, we present a model of randomly ... More

Corrigendum to: Oscillatory motions in restricted $N$-body problems [J. Differential Equations 265 (2018) 779-803]May 10 2019We consider the planar restricted $N$-body problem where the $N-1$ primaries are assumed to be in a central configuration whereas the infinitesimal particle escapes to infinity in a parabolic orbit. We prove the existence of transversal intersections ... More

Finite time stability for the Riemann problem with extremal shocks for a large class of hyperbolic systemsMay 10 2019In this paper on hyperbolic systems of conservation laws in one space dimension, we give a complete picture of stability for all solutions to the Riemann problem which contain only extremal shocks. We study stability of the Riemann problem amongst a large ... More

A Subspace Framework for ${\mathcal H}_\infty$-Norm MinimizationMay 10 2019We deal with the minimization of the ${\mathcal H}_\infty$-norm of the transfer function of a parameter-dependent descriptor system over the set of admissible parameter values. Subspace frameworks are proposed for such minimization problems where the ... More

Low-Complexity Tilings of the PlaneMay 10 2019A two-dimensional configuration is a coloring of the infinite grid Z^2 with finitely many colors. For a finite subset D of Z^2, the D-patterns of a configuration are the colored patterns of shape D that appear in the configuration. The number of distinct ... More

Dynamics of the Morse Oscillator: Analytical Expressions for Trajectories, Action-Angle Variables, and Chaotic DynamicsMay 10 2019We consider the one degree-of-freedom Hamiltonian system defined by the Morse potential energy function (the "Morse oscillator"). We use the geometry of the level sets to construct explicit expressions for the trajectories as a function of time, their ... More

A monotone Lagrangian casebookMay 10 2019We present an array of new calculations in Lagrangian Floer theory which demonstrate observations relating to symplectic reduction, grading periodicity, and the closed-open map. We also illustrate Perutz's symplectic Gysin sequence and the quilt theory ... More

Real gas flows issued from a sourceMay 10 2019Stationary adiabatic flows of real gases issued from a source of given intensity are studied. Thermodynamic states of gases are described by Legendrian or Lagrangian manifolds. Solutions of Euler equations are given implicitly for any equation of state ... More

Generic point equivalence and Pisot numbersMay 10 2019Let $\beta >1$ be an integer or generally a Pisot number. Put $T(x) = \{ \beta x \}$ on $[0,1]$ and let $S: [0,1]\to [0,1]$ be a piecewise linear transformation whose slopes have the form $\pm \beta^m$ with positive integers $m$. We give sufficient conditions ... More

On Topologically Controlled Model Reduction for Discrete-Time SystemsMay 10 2019In this document the author proves that several problems in data-driven numerical approximation of dynamical systems in $\mathbb{C}^n$, can be reduced to the computation of a family of constrained matrix representations of elements of the group algebra ... More

Almost-sure exponential mixing of passive scalars by the stochastic Navier-Stokes equationsMay 09 2019We deduce almost-sure exponentially fast mixing of passive scalars advected by solutions of the stochastically-forced 2D Navier-Stokes equations and 3D hyper-viscous Navier-Stokes equations in $\mathbb T^d$ subjected to non-denegenerate $H^\sigma$-regular ... More

The Dirichlet problem for fully nonlinear degenerate elliptic equations with a singular nonlinearityMay 09 2019We investigate the homogeneous Dirichlet problem in uniformly convex domains for a large class of degenerate elliptic equations with singular zero order term. In particular we establish sharp existence and uniqueness results of positive viscosity solutions. ... More

Single site factors of Gibbs measuresMay 09 2019It has been an open problem to identify classes of Gibbs measures less regular then H\"older continuous on the full shift which are closed under factor maps. In this article we show that in fact all of the classical uniqueness regimes (Bowen, Walters, ... More

$N_\infty$-operads and associahedraMay 09 2019We provide a new combinatorial approach to studying the collection of N-infinity-operads in G-equivariant homotopy theory for G a finite cyclic group. In particular, we show that for G the cyclic group of order p^n the natural order on the collection ... More

Splitting hairs with transcendental entire functionsMay 09 2019Many authors have studied the dynamics of functions in the \emph{Eremenko-Lyubich class} $\mathcal{B}$; this class consists of those transcendental entire functions for which the set of singular values is bounded. With the additional assumption that the ... More