Related papers: Critical points via monodromy and local methods

We study the problem of directly optimizing arbitrary non-differentiable task evaluation metrics such as misclassification rate and recall. Our method, named MetricOpt, operates in a black-box setting where the computational details of the…

Many offline unsupervised change point detection algorithms rely on minimizing a penalized sum of segment-wise costs. We extend this framework by proposing to minimize a sum of discrepancies between segments. In particular, we propose to…

We deal with the following closely related problems: (i) For a germ of a reduced plane analytic curve, what is the minimal degree of an algebraic curve with a singular point analytically equivalent (isomorphic) to the given one? (ii) For a…

Answering a question posed by Adam Epstein, we show that the collection of conjugacy classes of polynomials admitting a parabolic fixed point and at most one infinite critical orbit is a set of bounded height in the relevant moduli space.…

This paper is concerned with the problem of representing and learning a linear transformation using a linear neural network. In recent years, there has been a growing interest in the study of such networks in part due to the successes of…

A new exact projective penalty method is proposed for the equivalent reduction of constrained optimization problems to nonsmooth unconstrained ones. In the method, the original objective function is extended to infeasible points by summing…

We study the canonical problem of maximizing a stochastic submodular function subject to a cardinality constraint, where the goal is to select a subset from a ground set of items with uncertain individual performances to maximize their…

This note will study complex polynomial maps of degree $n\ge 2$ with only one critical point.

The behavior under iteration of the critical points of polynomial maps plays an essential role in understanding its dynamics. We study the special case where the forward orbits of the critical points are finite. Thurston's theorem tells us…

We enhance the approximation capabilities of algebraic polynomials by composing them with homeomorphisms. This composition yields families of functions that remain dense in the space of continuous functions, while enabling more accurate…

Mixtures of $r$ independent distributions for two discrete random variables can be represented by matrices of nonnegative rank $r$. Likelihood inference for the model of such joint distributions leads to problems in real algebraic geometry…

In healthcare, the highest risk individuals for morbidity and mortality are rarely those with the greatest modifiable risk. By contrast, many machine learning formulations implicitly attend to the highest risk individuals. We focus on this…

Let $k$ be a finite field extension of the function field $\bfF_p(T)$ and $\bar{k}$ its algebraic closure. We count points in projective space $\Bbb P ^{n-1}(\bar{k})$ with given height and of fixed degree $d$ over the field $k$. If…

Autonomous systems are often required to operate in partially observable environments. They must reliably execute a specified objective even with incomplete information about the state of the environment. We propose a methodology to…

We examine the linear convergence rates of variants of the proximal point method for finding zeros of maximal monotone operators. We begin by showing how metric subregularity is sufficient for linear convergence to a zero of a maximal…

In this article, we consider the following capacitated covering problem. We are given a set $P$ of $n$ points and a set $\mathcal{B}$ of balls from some metric space, and a positive integer $U$ that represents the capacity of each of the…

It is well known that conventional simulation algorithms are inefficient for the statistical description of macroscopic systems exactly at the critical point due to the divergence of the corresponding relaxation time (critical slowing…

In this paper, we apply our minimax theory ([4], [5], [6]) with the one developed by A. Moameni in [2] to formalize a general scheme giving the multiplicity of critical points. Here is a sample of application of the scheme to a critical…

A general theory is provided delivering convergence of maximal cyclically monotone mappings containing the supports of coupling measures of sequences of pairs of possibly random probability measures on Euclidean space. The theory is based…

This is the first in a series of three papers where we study the integral manifolds of the charged three-body problem. The integral manifolds are the fibers of the map of integrals. Their topological type may change at critical values of…