Related papers: Minsky machines and algorithmic problems
Computer based techniques for recognizing finitely presented groups are quite powerful. Tools available for this purpose are outlined. They are available both in stand-alone programs and in more comprehensive systems. A general…
Abundant accumulation of digital histopathological images has led to the increased demand for their analysis, such as computer-aided diagnosis using machine learning techniques. However, digital pathological images and related tasks have…
This book introduces the mathematical foundations and techniques that lead to the development and analysis of many of the algorithms that are used in machine learning. It starts with an introductory chapter that describes notation used…
We introduce algorithms that use predictions from machine learning applied to the input to circumvent worst-case analysis. We aim for algorithms that have near optimal performance when these predictions are good, but recover the…
The technique known as group averaging provides powerful machinery for the study of constrained systems. However, it is likely to be well defined only in a limited set of cases. Here, we investigate the possibility of using a `renormalized'…
In this paper we study the differential systems on Leibniz algebroids. We introduce a class of almost metriplectic manifolds as a special case of Leibniz manifolds. Also, the notion of almost metriplectic algebroid is introduced. These…
Existing work on fairness typically focuses on making known machine learning algorithms fairer. Fair variants of classification, clustering, outlier detection and other styles of algorithms exist. However, an understudied area is the topic…
Symbolic integration deals with the evaluation of integrals in closed form. We present an overview of Risch's algorithm including recent developments. The algorithms discussed are suited for both indefinite and definite integration. They…
\pkg{multiplex} is a computer program that provides algebraic tools for the analysis of multiple network structures within the \proglang{R} environment. Apart from the possibility to create and manipulate multivariate data representing…
We survey both old and new developments in the theory of algorithms in real algebraic geometry -- starting from effective quantifier elimination in the first order theory of reals due to Tarski and Seidenberg, to more recent algorithms for…
This paper describes algorithms to deal with nested symbolic sums over combinations of harmonic series, binomial coefficients and denominators. In addition it treats Mellin transforms and the inverse Mellin transformation for functions that…
While the field of algorithmic fairness has brought forth many ways to measure and improve the fairness of machine learning models, these findings are still not widely used in practice. We suspect that one reason for this is that the field…
A novel formulation and training procedure for full Boltzmann machines in terms of a mixed binary quadratic feasibility problem is given. As a proof of concept, the theory is analytically and numerically tested on XOR patterns.
For a finite subgroup $G$ of the special unitary group $SU_2$, we study the centralizer algebra $Z_k(G) = End_G(V^{\otimes k})$ of $G$ acting on the $k$-fold tensor product of its defining representation $V= \mathbb{C}^2$. These subgroups…
Graphs are a natural representation of data from various contexts, such as social connections, the web, road networks, and many more. In the last decades, many of these networks have become enormous, requiring efficient algorithms to cut…
Statistical learning algorithms are finding more and more applications in science and technology. Atomic-scale modeling is no exception, with machine learning becoming commonplace as a tool to predict energy, forces and properties of…
Cylindrical Algebraic Decomposition (CAD) is a key tool in computational algebraic geometry, best known as a procedure to enable Quantifier Elimination over real-closed fields. However, it has a worst case complexity doubly exponential in…
This paper addresses the problem of decomposing a numerical semigroup into m-irreducible numerical semigroups. The problem originally stated in algebraic terms is translated, introducing the so called Kunz-coordinates, to resolve a series…
Machine learning techniques have been widely employed as effective tools in addressing various engineering challenges in recent years, particularly for the challenging task of microstructure-informed materials modeling. This work provides a…
This paper describes a program that solves elementary mathematical problems, mostly in metric space theory, and presents solutions that are hard to distinguish from solutions that might be written by human mathematicians. The program is…