Related papers: Generalization of the Ball-Collision Algorithm

This paper offers a brief introduction to the framework of "general probabilistic theories", otherwise known as the "convex-operational" approach the foundations of quantum mechanics. Broadly speaking, the goal of research in this vein is…

Based on the definition of generalized partially bent functions, using the theory of linear transformation, the relationship among generalized partially bent functions over ring Z N, generalized bent functions over ring Z N and affine…

We discuss the algebraic renormalization of the Yang--Mills gauge field theory in the presence of translations. Due to the translations the algebra between Sorella's $\d$--operator, the exterior derivative and the BRST--operator closes.…

Accurate prediction of FIFA World Cup match outcomes holds significant value for analysts, coaches, bettors, and fans. This paper presents a machine learning framework specifically designed to forecast match winners in FIFA World Cup. By…

Probability estimation is one of the fundamental tasks in statistics and machine learning. However, standard methods for probability estimation on discrete objects do not handle object structure in a satisfactory manner. In this paper, we…

By introducing a parameter, we give a unified generalization of some quadrature rules, which not only unify the recent results about error bounds for generalized mid-point, trapezoid and Simpson's rules, but also give some new error bounds…

We present a simplified solution to orbit determination of a binary system from astrometric observations. An exact solution was found by Asada, Akasaka and Kasai by assuming no observational errors. We extend the solution considering…

Let $k$ be a field of characteristic $\neq 2$. We survey a general method of the field intersection problem of generic polynomials via formal Tschirnhausen transformation. We announce some of our recent results of cubic, quartic and quintic…

This paper extends and generalizes previous works on constructing combinatorial multivector fields from continuous systems (see [10]) and the construction of combinatorial vector fields from data (see [2]) by introducing an optimization…

A fundamental question in theoretical machine learning is generalization. Over the past decades, the PAC-Bayesian approach has been established as a flexible framework to address the generalization capabilities of machine learning…

We present a new framework for deriving bounds on the generalization bound of statistical learning algorithms from the perspective of online learning. Specifically, we construct an online learning game called the "generalization game",…

Existing generalization theories of supervised learning typically take a holistic approach and provide bounds for the expected generalization over the whole data distribution, which implicitly assumes that the model generalizes similarly…

In 1929 Heisenberg and Pauli laid the foundations of QFT by quantizing the fields (method of canonical quantization). This general theory of quantized fields has remained undisputed up to now. We show how the unmodified Heisenberg-Pauli…

Modern machine learning tasks often require considering not just one but multiple objectives. For example, besides the prediction quality, this could be the efficiency, robustness or fairness of the learned models, or any of their…

In this paper, we give two new generalizations of Clarkson-McCarthy with several operators, which depends on the unitary orbit technique developed by Bourin, Hadamard Three-lines Theorem and the duality argument developed by Ball, Carlen…

We develop a fractional extension of the classical binomial distribution and the associated Bernstein operator, formulated within the framework of the generalized binomial theorem (Hara and Hino [Bull.\ London Math.\ Soc. \textbf{42}…

We propose a generalization of Zhang's coefficient of determination to generalized linear geostatistical models and illustrate its application to river-blindness mapping. The generalized coefficient of determination has a more intuitive…

The problem of matching two sets of multiple elements, namely set-to-set matching, has received a great deal of attention in recent years. In particular, it has been reported that good experimental results can be obtained by preparing a…

We study a simple learning algorithm for binary classification. Instead of predicting with the best hypothesis in the hypothesis class, that is, the hypothesis that minimizes the training error, our algorithm predicts with a weighted…

Through the method of brick decomposition and the operations on essential topological lines, we generalize the line translation theorem of Beguin, Crovisier, Le Roux [BCL] in the case where the property of preserving a finite measure with…