arXiv research

Estimates for plate eigenvalues with nonzero Poisson's ratio.

We give a normal form for families of 3-dimensional Poisson structures. This allows us to classify singularities with nonzero 1-jet and typical bifurcations. The Appendix contains corollaries on classification of families of integrable 1-forms on $R^3

Invention involves combination, or more precisely, ratios of composition. According to Thomas Edison, "Genius is one percent inspiration and 99 percent perspiration" is an example. In many situations, researchers and inventors already have a variety of data and manage to create something new by using it, but the key pr…

This paper considers the problem of estimating an unknown high dimensional signal from noisy linear measurements, {when} the signal is assumed to possess a \emph{group-sparse} structure in a {known,} fixed dictionary. We consider signals generated according to a natural probabilistic model, and establish new conditions…

New concept of effective isometries for compliant shells.

Stokes-Dirac structures are infinite-dimensional Dirac structures defined in terms of differential forms on a smooth manifold with boundary. These Dirac structures lay down a geometric framework for the formulation of Hamiltonian systems with a nonzero boundary energy flow. Simplicial triangulation of the underlaying m…

Paper introduces ENZ to measure significant coefficients in sparse recovery, improving over classical methods.

We review a simple model of closed economy, where the economic agents make money transactions and a saving criterion is present. We observe the Gibbs distribution for zero saving propensity, and non-Gibbs distributions otherwise. While the exact solution in the case of zero saving propensity is already known to be give…

We prove that the Kontsevich tetrahedral flow $\dot{\mathcal{P}} = \mathcal{Q}_{a:b} (\mathcal{P})$, the right-hand side of which is a linear combination of two differential monomials of degree four in a bi-vector $\mathcal{P}$ on an affine real Poisson manifold $N^n$, does infinitesimally preserve the space of Poisson…

Study connects weighted isoperimetric problems to nonlocal elliptic operator extensions.

This paper studies non-asymptotic model selection for the general case of arbitrary design matrices and arbitrary nonzero entries of the signal. In this regard, it generalizes the notion of incoherence in the existing literature on model selection and introduces two fundamental measures of coherence---termed as the wor…

We define a Poisson Algebra called the {\em swapping algebra} using the intersection of curves in the disk. We interpret a subalgebra of the fraction algebra of the swapping algebra -- called the {\em algebra of multifractions} -- as an algebra of functions on the space of cross ratios and thus as an algebra of functio…

The Jacobian Conjecture is proven for all Jacobian maps.

Estimates on Einstein manifolds improve Brownian motion behavior and curvature limits.

The performance of the Lasso is well understood under the assumptions of the standard linear model with homoscedastic noise. However, in several applications, the standard model does not describe the important features of the data. This paper examines how the Lasso performs on a non-standard model that is motivated by …

In this paper, we propose a new method of Bayesian measurement for spectral deconvolution, which regresses spectral data into the sum of unimodal basis function such as Gaussian or Lorentzian functions. Bayesian measurement is a framework for considering not only the target physical model but also the measurement model…

Unified theory solves strain compatibility and elasticity of origami metamaterials.

A study on the depth of graph neural networks on sparse graphs, revealing a dichotomy based on the Kesten-Stigum ratio.

Researchers find examples of real Bott manifolds with nonzero dual Stiefel-Whitney class wbar_{n-ahat(n)} for all n nonzero mod 4.

We define new coordinates for Fock-Goncharov's higher Teichmüller spaces for a surface with holes, which are the moduli spaces of representations of the fundamental group into a reductive Lie group $G$. Some additional data on the boundary leads to two closely related moduli spaces, the $\mathscr{X}$-space and the $\ma…

Study on knotting in very long polymer chains, finding Poisson distribution for prime knot types.

Ridge regression linked to Poisson resetting in statistical physics.

Let $(X,L_{X})$ be an $n$-dimensional polarized manifold. Let $D$ be a smooth hypersurface defined by a holomorphic section of $L_{X}$. We prove that if $D$ has a constant positive scalar curvature Kähler metric, $X \setminus D$ admits a complete scalar-flat Kähler metric, under the following three conditions: (i) $n \…

The nonzero level sets of a homogeneous, logarithmically homogeneous, or translationally homogeneous function are affine spheres if and only if the Hessian determinant of the function is a multiple of a power or an exponential of the function. In particular, the nonzero level sets of a homogeneous polynomial are proper…

In this paper we prove that given a volume, among all domains with smooth boundary in rank-1 symmetric spaces of noncompact type, geodesic balls maximizes the first nonzero Steklov eigenvalue. We also prove a comparison result for the first nonzero Steklov eigenvalue for domains in simply connected Riemannian manifolds…

New formulas for barrier options in stochastic volatility models with nonzero correlation.

In this paper, it is shown that every orientable closed 3-manifold maps with nonzero degree onto at most finitely many homeomorphically distinct irreducible non-geometric orientable closed 3-manifolds. Moreover, given any nonzero integer, as a mapping degree up to sign, every orientable closed 3-manifold maps with that…

F. Labourie [arXiv:1212.5015] characterized the Hitchin components for $\operatorname{PSL}(n, \mathbb{R})$ for any $n>1$ by using the swapping algebra, where the swapping algebra should be understood as a ring equipped with a Poisson bracket. We introduce the rank $n$ swapping algebra, which is the quotient of the swap…

New family of knots with epsilon invariant nonzero despite Upsilon and phi being zero.

Paper proves biharmonic hypersurfaces in nonzero space form have constant mean curvature.

we introduce a generalization of the $p$-Laplace operator to act on differential forms and generalize an estimate of Gallot-Meyer for the first nonzero eigenvalue on closed Riemannian manifolds.

This paper improves lower bounds for the first nonzero Steklov eigenvalue on compact manifolds.

The paper connects Lie bialgebras, Rota-Baxter Lie algebras, and their properties.

In this paper, we show that the peeling property still holds for Bondi-Sachs metrics with nonzero cosmological constant under the boundary condition given by Sommerfeld's radiation condition together with three nontrivial $Λ$-independent functions $B$, $a$, $b$. This should indicate the new boundary condition is natura…

Method improves regression models using unlabeled data.

In this paper, we develop a new approach to learning high-dimensional Poisson directed acyclic graphical (DAG) models from only observational data without strong assumptions such as faithfulness and strong sparsity. A key component of our method is to decouple the ordering estimation or parent search where the problems…

We present a Bayesian non-negative tensor factorization model for count-valued tensor data, and develop scalable inference algorithms (both batch and online) for dealing with massive tensors. Our generative model can handle overdispersed counts as well as infer the rank of the decomposition. Moreover, leveraging a repa…

We obtain a Kaehler Einstein structure on the nonzero cotangent bundle of a Riemannian manifold of positive constant sectional curvature. The obtained Kaehler Einstein structure cannot have constant holomorphic sectional curvature and is not locally symmetric.

The sinh-Gordon equation is solved on finite, symmetric graphs.

Given a compact Riemannian spin manifold with positive scalar curvature, we find a family of connections $\nabla^{A_t}$ for $t\in[0,1]$ on a trivial vector bundle of sufficiently high rank, such that the first eigenvalue of the twisted Dirac operator $D_{A_t}$ is nonzero and becomes arbitrarily small as $t\to1$. Howeve…

Large sample size brings the computation bottleneck for modern data analysis. Subsampling is one of efficient strategies to handle this problem. In previous studies, researchers make more fo- cus on subsampling with replacement (SSR) than on subsampling without replacement (SSWR). In this paper we investigate a kind of…

We derive intrinsic curvature and radius estimates for compact disks embedded in $\mathbb{R}^3$ with nonzero constant mean curvature and apply these estimates to study the global geometry of complete surfaces embedded in $\mathbb{R}^3$ with nonzero constant mean curvature.

Non-injectivity proven for trace map on character varieties.

We obtain a locally symmetric Kaehler Einstein structure on a tube in the nonzero cotangent bundle of a Riemannian manifold of positive constant sectional curvature. The obtained Kaehler Einstein structure cannot have constant holomorphic sectional curvature.

We construct a tangential map from a locally symmetric space of noncompact type to its dual compact type twin. By comparing the induced map in cohomology to a map defined by Matsushima, we conclude that in the equal rank case the map has a nonzero degree.

A novel multi-resolution cluster detection (MCD) method is proposed to identify irregularly shaped clusters in space. Multi-scale test statistic on a single cell is derived based on likelihood ratio statistic for Bernoulli sequence, Poisson sequence and Normal sequence. A neighborhood variability measure is defined to …

Let $X$ be a smooth manifold belonging to one of these three collections: acyclic manifolds (compact or not, possibly with boundary), compact connected manifolds (possibly with boundary) with nonzero Euler characteristic, integral homology spheres. We prove that $Diff(X)$ is Jordan. This means that there exists a const…

New concordance invariants phi and phi_j are defined and studied.