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The choice of a point set, to be used in numerical integration, determines, to a large extent, the error estimate of the integral. Point sets can be characterized by their discrepancy, which is a measure of its non-uniformity. Point sets…
Recent studies evaluate the value orientation of large language models (LLMs) using adapted social surveys, typically by prompting models with survey questions and comparing their responses to average human responses. This paper identifies…
We introduce the concept of disjunctive sum of squares for certifying nonnegativity of polynomials. Unlike the popular sum of squares approach where nonnegativity is certified by a single algebraic identity, the disjunctive sum of squares…
Nested dichotomies are used as a method of transforming a multiclass classification problem into a series of binary problems. A tree structure is induced that recursively splits the set of classes into subsets, and a binary classification…
This study explored the utilities of rationales generated by GPT-4.1 and GPT-5 in automated scoring using Prompt 6 essays from the 2012 Kaggle ASAP data. Essay-based scoring was compared with rationale-based scoring. The study found in…
Cluster analysis requires many decisions: the clustering method and the implied reference model, the number of clusters and, often, several hyper-parameters and algorithms' tunings. In practice, one produces several partitions, and a final…
We describe some approaches to explanations for observed outcomes in data management and machine learning. They are based on the assignment of numerical scores to predefined and potentially relevant inputs. More specifically, we consider…
We introduce a method for efficient multi-label text classification with large language models (LLMs), built on reformulating classification tasks as sequences of dichotomic (yes/no) decisions. Instead of generating all labels in a single…
In-vivo toxicological studies are characterized by multiple primary endpoints with quite different scales. Whereas guidelines and publications provide various statistical tests for normally distributed endpoints (such as organ weights) and…
The main purpose of this article is to study higher power mean values of generalized quadratic Gauss sums using estimates for character sums, analytic method and algebraic geometric methods. In this article, we prove two conjectures which…
For high volume data streams and large data warehouses, sampling is used for efficient approximate answers to aggregate queries over selected subsets. Mathematically, we are dealing with a set of weighted items and want to support queries…
A summation test is proposed to determine admissible types of gap penalties for logarithmic growth of the local alignment score. We also define a converging sequence of log moment generating functions that provide the constants associated…
In this paper we investigate the question of how much combined measurements can increase the accuracy of additive quantities. Therefore, we consider a set of measurements from a selection of all possible combinations of the $n$ labeled…
In this paper, we introduce concept of bipolar neutrosophic set and its some operations. Also, we propose score, certainty and accuracy functions to compare the bipolar neutrosophic sets. Then, we develop the bipolar neutrosophic weighted…
In this paper, we obtain a sharp upper bound for the sum of the first $k$-th eigenvalues for this Dirichlet problem of poly-Laplacian with any order, which is viewed as an extension of the result due to Cheng and Wei (Journal of…
Large Language Models (LLMs) can achieve inflated scores on multiple-choice tasks by exploiting inherent biases in option positions or labels, rather than demonstrating genuine understanding. This study introduces SCOPE, an evaluation…
Score-based divergences have been widely used in machine learning and statistics applications. Despite their empirical success, a blindness problem has been observed when using these for multi-modal distributions. In this work, we discuss…
Music similarity search is useful for a variety of creative tasks such as replacing one music recording with another recording with a similar "feel", a common task in video editing. For this task, it is typically necessary to define a…
The iterative method of Sinkhorn allows, starting from an arbitrary real matrix with non-negative entries, to find a so-called 'scaled matrix' which is doubly stochastic, i.e. a matrix with all entries in the interval (0, 1) and with all…
Keeping in mind the necessity of intelligent system in educational sector, this paper proposes a text analysis based automated approach for automatic evaluation of the descriptive answers in an examination. In particular, the research…