Related papers: A new mathematical symbol : the termirial
In many applications of the probabilistic method, one looks to study phenomena that occur ``with high probability''. More recently however, in an attempt to understand some of the most fundamental problems in combinatorics, researchers have…
A new notation has been introduced for the quantum information theory. By this notation,some calculations became simple in quantum information theory such as quantum swapping, quantum teleportation.
Learning to create, use, and evaluate models is a central element of becoming a scientist. In physics, we often begin an analysis of a complex system with highly simplified or toy models. In introductory physics classes, we tend to use them…
Ordinary binary multiplication of natural numbers can be generalized in a non-trivial way to a ternary operation by considering discrete volumes of lattice hexagons. With this operation, a natural notion of `3-primality' -- primality with…
Adequate uncertainty representation and quantification have become imperative in various scientific disciplines, especially in machine learning and artificial intelligence. As an alternative to representing uncertainty via one single…
This paper introduces a novel approach to understanding Galois theory, one of the foundational areas of algebra, through the lens of machine learning. By analyzing polynomial equations with machine learning techniques, we aim to streamline…
In recent years, neural systems have demonstrated highly effective learning ability and superior perception intelligence. However, they have been found to lack effective reasoning and cognitive ability. On the other hand, symbolic systems…
Symbolic equations are at the core of scientific discovery. The task of discovering the underlying equation from a set of input-output pairs is called symbolic regression. Traditionally, symbolic regression methods use hand-designed…
We survey a collective achievement of a group of researchers: the PCP Theorems. They give new definitions of the class \np, and imply that computing approximate solutions to many \np-hard problems is itself \np-hard. Techniques developed to…
This article aims to develop a new account of scientific explanation for computer simulations. To this end, two questions are answered: what is the explanatory relation for computer simulations? and what kind of epistemic gain should be…
This is a short review of some recent results obtained by the author. These results are related the problem of obtaining polynomial identities (computational formulas) for some matrix functions by means of the known polarization theorem,…
Problems for the graduate students who want to improve problem-solving skills in geometry. Every problem has a short elegant solution -- this gives a hint which was not available when the problem was discovered.
Neurosymbolic Programming (NP) techniques have the potential to accelerate scientific discovery. These models combine neural and symbolic components to learn complex patterns and representations from data, using high-level concepts or known…
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.…
A primary goal of physics is to create mathematical models that allow both predictions and explanations of physical phenomena. We weave maths extensively into our physics instruction beginning in high school, and the level and complexity of…
There is merely a short note on the selected issues of neutrino electromagnetic properties with focus on effects of new physics. The meaning of "new physics" is twofold: 1) a massive neutrino have nonzero electromagnetic properties that can…
One of the outstanding problems of philosophy of science and mathematics today is whether there is just "one" unique mathematics or the same can be bifurcated into "pure" and "applied" categories. A novel solution for this problem is…
We obtain new trigonometric identities, which are some product-to-sum type formulas for the higher derivative of the cotangent and cosecant functions. Further, from specializations of our formulas, we derive not only various known…
Symbolic regression is emerging as a promising machine learning method for learning succinct underlying interpretable mathematical expressions directly from data. Whereas it has been traditionally tackled with genetic programming, it has…
One of the hurdles in teaching undergraduate thermodynamics is a plethora of complicated partial derivative identities. Students suffer from difficulties in deriving, justifying, or interpreting the identities, misconceptions about partial…