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Inconsistent values are commonly encountered in real-world applications, which can negatively impact data analysis and decision-making. While existing research primarily focuses on identifying the smallest removal set to resolve…
This note explores reach set computations for perturbed delay differential equations (DDEs). The perturbed DDEs of interest in this note is a class of DDEs whose dynamics are subject to perturbations, and their solutions feature the local…
Human labeled datasets, along with their corresponding evaluation algorithms, play an important role in boundary detection. We here present a psychophysical experiment that addresses the reliability of such benchmarks. To find better…
Differential equations and numerical methods are extensively used to model various real-world phenomena in science and engineering. With modern developments, we aim to find the underlying differential equation from a single observation of…
Spectral properties and transition to instability in neutral delay differential equations are investigated in the limit of large delay. An approximation of the upper boundary of stability is found and compared to an analytically derived…
Quantum state discrimination is an important problem in many information processing tasks. In this work we are concerned with finding its best possible sample complexity when the states are preprocessed by a quantum channel that is required…
A nearly logarithmic lower bound on the randomized competitive ratio for the metrical task systems problem is presented. This implies a similar lower bound for the extensively studied k-server problem. The proof is based on Ramsey-type…
We study linear regressions in a context where the outcome of interest and some of the covariates are observed in two different datasets that cannot be matched. Traditional approaches obtain point identification by relying, often…
We consider on-line density estimation with a parameterized density from the exponential family. The on-line algorithm receives one example at a time and maintains a parameter that is essentially an average of the past examples. After…
Local existence properties of initial boundary value problems associated with a new type of systems of differential equations with "maxima" are investigated.
In this work we obtain sufficient conditions for the existence of bounded solutions of a resonant multi-point second-order boundary value problem, with a fully differential equation. The noninvertibility of the linear part is overcome by a…
This work establishes computable bounds between f-divergences for probability measures within a generalized quasi-$\varepsilon_{(M,m)}$-neighborhood framework. We make the following key contributions. (1) a unified characterization of local…
Given a subset of real numbers $A$ with small product $AA$ we obtain a new upper bound for the additive energy of $A$. The proof uses a natural observation that level sets of convolutions of the characteristic function of $A$ have small…
New lower bounds involving sum, difference, product, and ratio sets for $A\subset \C$ are given.
We obtain a double exponential bound in Brauer's generalisation of van der Waerden's theorem, which concerns progressions with the same colour as their common difference. Such a result has been obtained independently and in much greater…
We consider an initial value problem for a nonlinear parabolic equation with memory under nonlinear nonlocal boundary condition. In this paper we study classical solutions. We establish the existence of a local maximal solution. It is shown…
We obtain new upper and lower bounds on the number of unit perimeter triangles spanned by points in the plane. We also establish improved bounds in the special case where the point set is a section of the integer grid.
In this note we consider boundary point principles for partial differential inequalities of elliptic type. Firstly, we highlight the difference between conditions required to establish classical strong maximum principles and classical…
We provide several Tauberian theorems for Laplace transforms with local pseudofunction boundary behavior. Our results generalize and improve various known versions of the Ingham-Fatou-Riesz theorem and the Wiener-Ikehara theorem. Using…
Estimation of the degree of stability and the bounds of solutions to non-autonomous nonlinear systems present major concerns in numerous applied problems. Yet, current techniques are frequently yield overconservative conditions which are…