Related papers: Counting Self-Dual Interval Orders
In a nutshell, submodular functions encode an intuitive notion of diminishing returns. As a result, submodularity appears in many important machine learning tasks such as feature selection and data summarization. Although there has been a…
The idea of generating integrals analogous to generating functions is first introduced in this paper. A new proof of the well-known Finite Harmonic Series Theorem in Analysis and Analytical Number Theory is then obtained by the method of…
In this work we present strategies for (optimal) measurement selection in model-based sequential diagnosis. In particular, assuming a set of leading diagnoses being given, we show how queries (sets of measurements) can be computed and…
A new 1D search method is proposed for minimizing an arbitrary real valued function. The algorithm is a modification of the interval halving method which is based on dividing the interval of uncertainty by three points into four equal…
This article discusses nonconforming finite element methods for convex minimization problems and systematically derives dual mixed formulations. Duality relations lead to simple error estimates that avoid an explicit treatment of…
In this paper we consider the rank generating function of a separable permutation $\pi$ in the weak Bruhat order on the two intervals $[\text{id}, \pi]$ and $[\pi, w_0]$, where $w_0 = n,(n-1),..., 1$. We show a surprising result that the…
Recent works have developed new projection-free first-order methods based on utilizing linesearches and normal vector computations to maintain feasibility. These oracles can be cheaper than orthogonal projection or linear optimization…
In this paper we have investigated enumeration orders of elements of r.e. sets enumerated by means of Turing machines. We have defined a reducibility based on enumeration orders named "Enumeration Order Reducibility" on computable functions…
We propose a quadrature-based formula for computing the exponential function of matrices with a non-oscillatory integral on an infinite interval and an oscillatory integral on a finite interval. In the literature, existing quadrature-based…
We establish the functional relations between generating series of higher-order free cumulants and moments in higher-order free probability, solving an open problem posed fifteen years ago by Collins, Mingo, \'Sniady and Speicher. We…
We continue our study on counting irreducible polynomials over a finite field with prescribed coefficients. We set up a general combinatorial framework using generating functions with coefficients from a group algebra which is generated by…
The influence of class orderings in the evaluation of incremental learning has received very little attention. In this paper, we investigate the impact of class orderings for incrementally learned classifiers. We propose a method to compute…
We describe an algorithm for the sequential sampling of entries in multiway contingency tables with given constraints. The algorithm can be used for computations in exact conditional inference. To justify the algorithm, a theory relates…
In this paper, we present methods of obtaining single moments of order statistics arising from posibly dependent and non-identically distributed discrete random variables. We derive exact and approximate formulas convenient for numerical…
This article gives some properties of intervals in $\mathbb{R}$ and discusses some problems involving intervals for which the concept of outer measure on $\mathbb{R}$ provides a more efficient solution than an elementary approach. The outer…
The aim of this article is to define some new families of the special numbers. These numbers provide some further motivation for computation of combinatorial sums involving binomial coefficients and the Euler kind numbers of negative order.…
Accurate uncertainty quantification is necessary to enhance the reliability of deep learning models in real-world applications. In the case of regression tasks, prediction intervals (PIs) should be provided along with the deterministic…
This paper analyzes the performance of sequential importance sampling algorithms for estimating the number of perfect matchings in bipartite graphs. Precise bounds on the number of samples required to yield an accurate estimate are derived.…
There have been several efforts to extend distributional semantics beyond individual words, to measure the similarity of word pairs, phrases, and sentences (briefly, tuples; ordered sets of words, contiguous or noncontiguous). One way to…
We study the number of linear extensions of a partial order with a given proportion of comparable pairs of elements, and estimate the maximum and minimum possible numbers. We also consider a random interval partial order on $n$ elements,…