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A proposal for a calculational program in fluid turbulence is presented. It is proposed that the fluid probability density functional has an attractor for its time-evolution, just as the dynamical system itself has. The evolution of the…

In this note we provide a full conjugacy and subdifferential calculus for convex convex-composite functions in finite-dimensional space. Our approach, based on infimal convolution and cone-convexity, is straightforward and yields the…

We consider spline estimates which preserve prescribed piecewise convex properties of the unknown function. A robust version of the penalized likelihood is given and shown to correspond to a variable halfwidth kernel smoother where the…

We present a general systematic formalism for describing dynamics of fluctuations in an arbitrary relativistic hydrodynamic flow, including their feedback (known as long-time hydrodynamic tails). The fluctuations are described by two-point…

Given an irrational rotation $T$ on $\M T$ we settle necessary and sufficient conditions on a step function $\phi$ and $t\in \M T$ for the existence of measurable solutions to the cohomogical equation $$\exp{(2i\pi\phi)}=\e{2i\pi t}f/f\rond…

Let $X\subset\mathbb{R}^n$ be a convex closed and semialgebraic set and let $f$ be a polynomial positive on $X$. We prove that there exists an exponent $N\geq 1$, such that for any $\xi\in\mathbb{R}^n$ the function…

Consider $n$ i.i.d. random elements on $C[0,1]$. We show that, under an appropriate strengthening of the domain of attraction condition, natural estimators of the extreme-value index, which is now a continuous function, and the normalizing…

We present an algorithm to approximate the solutions to variational problems where set of admissible functions consists of convex functions. The main motivator behind this numerical method is estimating solutions to Adverse Selection…

In performative prediction, predictions guide decision-making and hence can influence the distribution of future data. To date, work on performative prediction has focused on finding performatively stable models, which are the fixed points…

This paper considers online convex optimization with time-varying constraint functions. Specifically, we have a sequence of convex objective functions $\{f_t(x)\}_{t=0}^{\infty}$ and convex constraint functions…

We study the properties of the exponential functional $\int\_0^{+ \infty} e^{- X^{\uparrow} (t)}dt$ where $X^{\uparrow}$ is a spectrally one-sided L{\'e}vy process conditioned to stay positive. In particular, we study finiteness,…

Covariance regression analysis is an approach to linking the covariance of responses to a set of explanatory variables $X$, where $X$ can be a vector, matrix, or tensor. Most of the literature on this topic focuses on the "Fixed-$X$"…

We discuss conditions under which a convex cone $\K\subset \R^{\Omega}$ admits a probability $m$ such that $\sup_{k\in \K} m(k)\leq0$. Based on these, we also characterize linear functionals that admit the representation as finitely…

We consider the ergodicity and consensus problem for a discrete-time linear dynamic model driven by random stochastic matrices, which is equivalent to studying these concepts for the product of such matrices. Our focus is on the model where…

Varying-coefficient functional linear models consider the relationship between a response and a predictor, where the response depends not only the predictor but also an exogenous variable. It then accounts for the relation of the predictors…

Given a smooth function $f$, we develop a general approach to turn Monte Carlo samples with expectation $m$ into an unbiased estimate of $f(m)$. Specifically, we develop estimators that are based on randomly truncating the Taylor series…

A common goal in observational research is to estimate marginal causal effects in the presence of confounding variables. One solution to this problem is to use the covariate distribution to weight the outcomes such that the data appear…

We consider the question of existence of a unique invariant probability distribution which satisfies some evolutionary property. The problem arises from the random graph theory but to answer it we treat it as a dynamical system in the…

A scalar model of wet active matter in the presence of an imposed temperature gradient, or chemical potential gradient, is considered. It is shown that there is a convective instability driven by a (negative) activity parameter. In this…

Scale-space energy density function, $E(\mathbf{x}, \mathbf{r})$, is defined as the derivative of the two-point velocity correlation. The function E describes the turbulent kinetic energy density of scale r at a location x and can be…