Related papers: On Hessian limit directions along non-oscillating …

As a natural variant of domination in graphs, Dankelmann et al. [Domination with exponential decay, Discrete Math. 309 (2009) 5877-5883] introduce exponential domination, where vertices are considered to have some dominating power that…

We consider arbitrary trajectories subject to a coordinate-wise energy decrease: the sign of the derivative of each entry is never the same as that of the corresponding entry of the gradient of some energy function. We show that this simple…

We present a stochastic descent algorithm for unconstrained optimization that is particularly efficient when the objective function is slow to evaluate and gradients are not easily obtained, as in some PDE-constrained optimization and…

In this paper, we are interested in matrix valued orthogonal polynomials on the real line with respect to exponential weights. We obtain strong asymptotics as the degree tends to infinity in different regions of the complex plane, as well…

We give upper and lower bounds for the Hausdorff dimensions for a class of graph-directed measures when its underlying directed graph is the infinite N-ary tree. These measures are different from graph-directed self-similar measures driven…

We prove maximum and comparison principles for fractional discrete derivatives in the integers. Regularity results when the space is a mesh of length $h$, and approximation theorems to the continuous fractional derivatives are shown. When…

We consider functions $f(v)=\min_{A\in K}{Av}$ and $g(v)=\max_{A\in K}{Av}$, where $K$ is a finite set of nonnegative matrices and by "min" and "max" we mean coordinate-wise minimum and maximum. We transfer known results about properties of…

A navigation on a set of points $S$ is a rule for choosing which point to move to from the present point in order to progress toward a specified target. We study some navigations in the plane where $S$ is a non uniform Poisson point process…

In the inverse limit ${\hat{I}}_s$ of a tent map $f_s$ restricted to its core, the set $\mathcal{GR}$ of points whose path components are bi-infinite and bi-dense has full measure with respect to the measure induced on $\hat{I}_s$ by the…

For fully nonlinear $k$-Hessian operators on bounded strictly $(k-1)$-convex domains $\Omega$ in ${\mathbb R}^N$, a characterization of the principal eigenvalue associated to a $k$-convex and negative principal eigenfunction will be given…

We give an upper bound for the uniqueness transition on an arbitrary locally finite graph ${\cal G}$ in terms of the limit of the spectral radii $\rho\left[ H({\cal G}_t)\right]$ of the non-backtracking (Hashimoto) matrices for an…

We show that the problem of deciding whether a given graph $G$ has a well-balanced orientation $\vec{G}$ such that $d_{\vec{G}}^+(v)\leq \ell(v)$ for all $v \in V(G)$ for a given function $\ell:V(G)\rightarrow \mathbb{Z}_{\geq 0}$ is…

We derive new gradient flows of divergence functions in the probability space embedded with a class of Riemannian metrics. The Riemannian metric tensor is built from the transported Hessian operator of an entropy function. The new gradient…

Let g denote a real analytic function on an open subset U of Euclidean space, and let S denote the boundary points of U where g does not admit a local analytic extension. We show that if g is semialgebraic (respectively, globally…

In recent work Cortez and Petite defined odometer actions of discrete, finitely generated and residually finite groups G. In this paper we focus on the case where G is the discrete Heisenberg group. We prove a structure theorem for finite…

Consider a real valued function defined, but not differentiable at some point. We use sequences approaching the point of interest to define and study sequential concepts of secant and cord derivatives of the function at the point of…

There are presented sufficient conditions for existence of an infinite family of trajectories of an analytic gradient flow which converge to a critical point.

The $k$-Hessian operator $\sigma_k$ is the $k$-th elementary symmetric function of the eigenvalues of the Hessian. It is known that the $k$-Hessian equation $\sigma_k(D^2u)=f$ with Dirichlet boundary condition $u=0$ is variational; indeed,…

In this paper, we investigate a general class of stochastic gradient descent (SGD) algorithms, called Conditioned SGD, based on a preconditioning of the gradient direction. Using a discrete-time approach with martingale tools, we establish…

Let $\Omega$ in $R^M$ be a compact connected $M$-dimensional real analytic domain with boundary and $\phi$ be a primal navigation function; i.e. a real analytic Morse function on $\Omega$ with a unique minimum and with minus gradient vector…