Related papers: Two characterizations of crooked functions
We study characteristics which might distinguish two-graphs by introducing different numerical measures on the collection of graphs on $n$ vertices. Two conjectures are stated, one using these numerical measures and the other using the deck…
We introduce COPT, a novel distance metric between graphs defined via an optimization routine, computing a coordinated pair of optimal transport maps simultaneously. This gives an unsupervised way to learn general-purpose graph…
This article shows that on a closed interval $[a,b]$ a continuous function may be approximated to an arbitrary degree of accuracy using scattered translates of the general multiquadric $(x^2+c^2)^{k-1/2}$.
We apply the techniques of computable model theory to the distance function of a graph. This task leads us to adapt the definitions of several truth-table reducibilities so that they apply to functions as well as to sets, and we prove…
The paper gives a constructive method, based on greedy algorithms, that provides for the classes of functions with small mixed smoothness the best possible in the sense of order approximation error for the $m$-term approximation with…
Some properties of generalized convexity for sets and for functions are identified in case of the reliability polynomials of two dual minimal networks. A method of approximating the reliability polynomials of two dual minimal network is…
We describe the structure of connected graphs with the minimum and maximum average distance, radius, diameter, betweenness centrality, efficiency and resistance distance, given their order and size. We find tight bounds on these graph…
Greb\'ik and Rocha [Fractional Isomorphism of Graphons, Combinatorica 42, pp 365-404 (2022)] extended the well studied notion of fractional isomorphism of graphs to graphons. We prove that fractionally isomorphic graphons can be…
We derive two conditional expectation bounds, which we use to simplify cryptographic security proofs. The first bound relates the expectation of a bounded random variable and the average of its conditional expectations with respect to a set…
We investigate regularity properties of generalized conjugate functions induced by a general coupling function and the associated generalized proximal mapping. Our main results provide verifiable conditions ensuring local single-valuedness,…
We obtain a factorization of the characteristic function of a contractive two-step iterated lifting in terms of the characteristic functions of constituent liftings of the iterated lifting and the Julia-Halmos matrix. We also give an…
We address a classical open question by H.Brezis and R.Ignat concerning the characterization of constant functions through double integrals that involve difference quotients. Our first result is a counterexample to the question in its full…
In this work, approximations for real two variables function $f$ which has continuous partial $(n-1)$-derivatives $(n \ge 1)$ and has the $n$--th partial derivative of bounded bivariation or absolutely continuous are established. Explicit…
The present article is an exposition of a theory of discrete convex functions on certain graph structures, developed by the author in recent years. This theory is a spin-off of discrete convex analysis by Murota, and is motivated by…
Signed graphs have their edges labeled either as positive or negative. Here we introduce two types of signed distance matrix for signed graphs. We characterize balance in signed graphs using these matrices and we obtain explicit formulae…
In this paper, we present two approximation algorithms for the directed multi-multiway cut and directed multicut problems. The so called region growing paradigm \cite{1} is modified and used for these two cut problems on directed graphs. By…
We analyze matrix convex functions of a fixed order defined on a real interval by differential methods as opposed to the characterization in terms of divided differences given by Kraus. We obtain for each order conditions for matrix…
We propose to differentiate a general curvature functional with two different approaches. In the first one we compute the derivative with the tools of shape optimization and in the second one we compute the derivative of a volumic…
We will show that a multifunction is strictly proto-differentiable at a point of its graph if and only if it is graphically strictly differentiable, i.e., the graph of the multifunction locally coincides, up to a change of coordinates, with…
A new notion of metric differentiability of set-valued functions at a point is introduced in terms of right and left limits of special set-valued metric divided differences of first order. A local metric linear approximant of a metrically…