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We first propose two conjectural estimates on Diophantine approximation of logarithms of algebraic numbers. Next we discuss the state of the art and we give further partial results on this topic.
The material of this work is aimed at mathematics educators, as well as math specialists with a keen interest in progressions. In this paper, we study the subject of arithmetic, geometric, mixed, and harmonic progressions or sequences. Some…
The relationship of scientific knowledge development to technological development is widely recognized as one of the most important and complex aspects of technological evolution. This paper adds to our understanding of the relationship…
Participants in recent discussions of AI-related issues ranging from intelligence explosion to technological unemployment have made diverse claims about the nature, pace, and drivers of progress in AI. However, these theories are rarely…
A fundamental problem in technological studies is how to measure the evolution of technology. The literature has suggested several approaches to measuring the level of technology (or state-of-the-art) and changes in technology. However, the…
Machine learning models support decision-making, yet the reasons behind their predictions are opaque. Clear and reliable explanations help users make informed decisions and avoid blindly trusting model outputs. However, many existing…
The purpose of this short paper is to identify the mathematical essence of the superiorization methodology. This methodology has been developed in recent years while attempting to solve specific application-oriented problems. Consequently,…
We discuss the notion of linearization through examples, which include the Price map, PageRank, representation theory, the Euler characteristic and quantum invariants. We also review categorification, which adds an additional layer of…
We propose an algorithm for incremental learning of classifiers. The proposed method enables an ensemble of classifiers to learn incrementally by accommodating new training data. We use an effective mechanism to overcome the…
If you want to tell people the truth, make them laugh, otherwise they'll kill you. (source unclear) Machine learning and deep learning are the technologies of the day for developing intelligent automatic systems. However, a key hurdle for…
Analyzed models of learning, which take into account that: 1) the rate of increase of student's knowledge is proportional to the difference between levels of teacher's requirements and prior knowledge; 2) if the requirements are too high,…
These notes concern linear transformations on R^n and C^n, exponentials of linear transformations, and some related geometric questions.
Kotlarski's theorem (see H. Kotlarski. Bounded Induction and Satisfaction Classes. Mathematical Logic Quarterly, vol. 32, 31-34, 1986, P. 531--544.) formalized in $WKL_0$.
An increasingly large number of experiments study the labor productivity effects of automation technologies such as generative algorithms. A popular question in these experiments relates to inequality: does the technology increase output…
A brief exposition of the point of higher topos theory in (mathematical) physics, commissioned for the Encyclopedia of Mathematical Physics 2nd ed.
Robin's Conjecture is strengthened, deformed, and proved. Nicolas conjecture follows.
This article examines two approaches to verification, one based on using a logic for expressing properties of a system, and one based on showing the system equivalent to a simpler system that obviously has whatever property is of interest.…
Any act of problem-solving combines prior knowledge, local search, and a third element that is less often discussed: the extraction of information from search to update understanding. I propose a model of mathematical problem-solving as a…
We continue the work of [4, 2, 3], in which we discuss published assertions that are incorrect or incorrectly proven; that are severely limited or reduce to triviality; or that we improve upon.
We examine whether data generated by explanation techniques, which promote a process of self-reflection, can improve classifier performance. Our work is based on the idea that humans have the ability to make quick, intuitive decisions as…