Related papers: Intro To Logarithms After The Meltdown
Two general methods for establishing the logarithmic behavior of recursively defined sequences of real numbers are presented. One is the interlacing method, and the other one is based on calculus. Both methods are used to prove logarithmic…
This paper focuses on the application of soft computing in remanufacturing system, in which end-of-life products are disassembled into basic components and then remanufactured for both economic and environmental reasons. The disassembly…
One of the main uses of computers is to do statistical analysis of data. But, so far, the theory of statistics, and its noble mother, Probability theory, were all discovered and developed by lowly humans. No more! Computers can also develop…
Mathematical reasoning is regarded as a necessary ability for Language Models (LMs). Recent works demonstrate large LMs' impressive performance in solving math problems. The success is attributed to their Chain-of-Thought (CoT) reasoning…
Logically Constrained Term Rewriting Systems (LCTRSs) provide a general framework for term rewriting with constraints. We discuss a simple dependency pair approach to prove termination of LCTRSs. We see that existing techniques transfer to…
Nowadays, Machine Learning (ML) is seen as the universal solution to improve the effectiveness of information retrieval (IR) methods. However, while mathematics is a precise and accurate science, it is usually expressed by less accurate and…
The Collatz conjecture is explored using polynomials based on a binary numeral system. It is shown that the degree of the polynomials, on average, decreases after a finite number of steps of the Collatz operation, which provides a weak…
Logical relations (LR) have been around for many years, and today they are used in many formal results. However, it can be difficult to LR beginners to find a good place to start to learn. Papers often use highly specialized LRs that use…
Rigorous modelling of natural and industrial systems still conveys various challenges related to abstractions, methods to proceed with and easy-to-use tools to build, compose and reason on models. Operads are mathematical structures that…
Developing a 21st Century Global Library for Mathematics Research discusses how information about what the mathematical literature contains can be formalized and made easier to express, encode, and explore. Many of the tools necessary to…
For natural and artificial systems with some symmetry structure, computational understanding and manipulation can be achieved without learning by exploiting the algebraic structure. Here we describe this algebraic coordinatization method…
Resilience is a rehashed concept in natural hazard management - resilience of cities to earthquakes, to floods, to fire, etc. In a word, a system is said to be resilient if there exists a strategy that can drive the system state back to…
Integration by parts reduction is a standard component of most modern multi-loop calculations in quantum field theory. We present a novel strategy constructed to overcome the limitations of currently available reduction programs based on…
The purpose of this paper is to analyse, in the light of information theory and with the arsenal of (elementary) quantum mechanics (EPR correlations, copying machines, teleportation, mixing produced in sub-systems owing to a trace…
We deliver a call to arms for probabilistic numerical methods: algorithms for numerical tasks, including linear algebra, integration, optimization and solving differential equations, that return uncertainties in their calculations. Such…
Though technical advance of artificial intelligence and machine learning has enabled many promising intelligent systems, many computing tasks are still not able to be fully accomplished by machine intelligence. Motivated by the…
The evaporation of black holes into apparently thermal radiation poses a serious conundrum for theoretical physics: at face value, it appears that in the presence of a black hole quantum evolution is non-unitary and destroys information.…
Framing computation as the transformation of metastable memories, we explore its fundamental thermodynamic limits. The true power of information follows from a novel decomposition of nonequilibrium free energy derived here, which provides a…
Reconstructing a hypothetical recurrence equation from the first terms of an infinite sequence is a classical and well-known technique in experimental mathematics. We propose a variation of this technique which can succeed with fewer input…
This paper introduces a novel cryptographic approach based on the continuous logarithm in the complex circle, designed to address the challenges posed by quantum computing. By leveraging its multi-valued and spectral properties, this…