Related papers: Monotone Function Intervals: Theory and Applicatio…

Consider a real-valued function that can only be observed with stochastic noise at a finite set of design points within a Euclidean space. We wish to determine whether there exists a convex function that goes through the true function…

The purpose of this paper is to study the dynamical behavior of the sequence produced by a forward-backward algorithm involving two random maximal monotone operators and a sequence of decreasing step sizes. Defining a mean monotone operator…

The potential applications of boundary functionals of random processes, such as the extreme values of these processes, the moment of first reaching a fixed level, the value of the process at the moment of reaching the level, the moment of…

Functions with uniform level sets can represent orders, preference relations or other binary relations and thus turn out to be a tool for scalarization that can be used, e.g., in multicriteria optimization, decision theory, mathematical…

We study efficient differentially private algorithms for estimating monotone statistics, i.e., statistics that are monotone under the addition of new observations. The starting point for our investigation is subsample-and-aggregate: a…

Using the Fitzpatrick function, we characterize the solutions for different classes of deterministic and stochastic differential equations driven by maximal monotone operators (or in particular subdifferential operators) as the minimum…

The concept of sequential choice functions is introduced and studied. This concept applies to the reduction of the problem of stable matchings with sequential workers to a situation where the workers are linear.

We establish a set of relations between several quite diverse types of weighted inequalities involving various integral operators and fairly general quasinorm-like functionals which we call sub-monotone. The main result enables one to solve…

We consider a class of monotone operators which are appropriate for symbolic representation and manipulation within a computer algebra system. Various structural properties of the class (e.g., closure under taking inverses, resolvents) are…

Operator $k$-tone functions on an open interval of the real line, which are higher order extensions of operator monotone and convex functions, are characterized via certain inequalities for the real and imaginary parts of analytic…

In this short note we prove a conjecture for the interval $(0,1)$, related to a logarithmically completely monotonic function, presented in \cite{BG}. Then, we extend by proving a more generalized theorem. At the end we pose an open problem…

We study the symmetry in short intervals of arithmetic functions with non-negative exponential sums.

This article studies the solutions of time-dependent differential inclusions which is motivated by their utility in the modeling of certain physical systems. The differential inclusion is described by a time-dependent set-valued mapping…

In this paper a special type of difference equations is investigated. The impulses start abruptly at some points and their action continue on given finite intervals. This type of equations is used to model a real process. An algorithm,…

A principal curve serves as a powerful tool for uncovering underlying structures of data through 1-dimensional smooth and continuous representations. On the basis of optimal transport theories, this paper introduces a novel principal curve…

Critical intermittency stands for a type of intermittent dynamics in iterated function systems, caused by an interplay of a superstable fixed point and a repelling fixed point. We consider critical intermittency for iterated function…

The Lebesgue property (order-continuity) of a monotone convex function on a solid vector space of measurable functions is characterized in terms of (1) the weak inf-compactness of the conjugate function on the order-continuous dual space,…

Regression analysis under the assumption of monotonicity is a well-studied statistical problem and has been used in a wide range of applications. However, there remains a lack of a broadly applicable methodology that permits information…

Adaptive confidence intervals for regression functions are constructed under shape constraints of monotonicity and convexity. A natural benchmark is established for the minimum expected length of confidence intervals at a given function in…

Monotone systems constitute one of the most important classes of dynamical systems used in mathematical biology modeling. The objective of this paper is to extend the notion of monotonicity to systems with inputs and outputs, a necessary…