Related papers: Intro To Logarithms After The Meltdown
This thesis is devoted to the study of a calculus that describes the application of conditional rewriting rules and the obtained results at the same level of representation. We introduce the rewriting calculus, also called the rho-calculus,…
Can machine learning help discover new mathematical structures? In this article we discuss an approach to doing this which one can call "mathematical data science". In this paradigm, one studies mathematical objects collectively rather than…
Human cognition exhibits systematic compositionality, the algebraic ability to generate infinite novel combinations from finite learned components, which is the key to understanding and reasoning about complex logic. In this work, we…
Digital System Research has pioneered the mathematics and design for a new class of computing machine using residue numbers. Unlike prior art, the new breakthrough provides methods and apparatus for general purpose computation using several…
The method of using concepts and insight from quantum information theory in order to solve problems in reversible classical computing (introduced in Ref. [1]) have been generalized to irreversible classical computing. The method have been…
This paper first summarizes the foundations of stochastic calculus via regularization and constructs through this procedure It\^o and Stratonovich integrals. In the second part, a survey and new results are presented in relation with finite…
In this article the algorithm for transformation of logic functions which are given by truth tables is considered. The suggested algorithm allows the transformation of many-valued logic functions with the required number of variables and…
The resummation of logarithmically-enhanced terms to all perturbative orders is a prerequisite for many studies of QCD final-states. Until now such resummations have always been performed by hand, for a single observable at a time. In this…
Methods for the reduction of the complexity of computational problems are presented, as well as their connections to renormalization, scaling, and irreversible statistical mechanics. Several statistically stationary cases are analyzed; for…
Logs are widely used to record runtime information of software systems, such as the timestamp and the importance of an event, the unique ID of the source of the log, and a part of the state of a task's execution. The rich information of…
The aim of this chapter is twofold. First, we introduce the information loss problem; second, we provide a critical assessment by thoroughly inspecting the assumptions underlying its formulations. In particular, we argue that if we work in…
Reconstructing the logical network from the transition matrix is benefit for learning the logical meaning of the algebraic result from the algebraic representation of a BN. And so far there has no method to convert the matrix expression…
We introduce the structural resource lambda-calculus, a new formalism in which strongly normalizing terms of the lambda-calculus can naturally be represented, and at the same time any type derivation can be internally rewritten to its…
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…
The article contains an outline of a possible new direction for Computability Logic (see www.csc.villanova.edu/~japaridz/CL/ ), focused on computability without infinite memory or other impossible-to-possess computational resources. The new…
A non-deterministic call-by-need lambda-calculus \calc with case, constructors, letrec and a (non-deterministic) erratic choice, based on rewriting rules is investigated. A standard reduction is defined as a variant of left-most outermost…
A semantical embedding of input/output logic in classical higher-order logic is presented. This embedding enables the mechanisation and automation of reasoning tasks in input/output logic with off-the-shelf higher-order theorem provers and…
Algorithms are becoming more capable, and with that comes hic sunt dracones (here be dragons). The term symbolizes areas beyond our known maps. We use this term since we are stepping into an exciting, potentially dangerous, and unknown area…
Learning to Optimize (L2O) stands at the intersection of traditional optimization and machine learning, utilizing the capabilities of machine learning to enhance conventional optimization techniques. As real-world optimization problems…
In various areas of applied numerics, the problem of calculating the logarithm of a matrix A emerges. Since series expansions of the logarithm usually do not converge well for matrices far away from the identity, the standard numerical…