Related papers: Software for enumerative and analytic combinatoric…
Numerical and symbolic methods for optimization are used extensively in engineering, industry, and finance. Various methods are used to reduce problems of interest to ones that are amenable to solution by such software. We develop a…
Combinatorial group testing reduces screening costs and turnaround time but remains challenging to apply due to design complexity, varying applicability, and lack of implementation tools. Here we present PoolPy, a unified end-to-end…
Ordinary Differential Equations (ODE) are used throughout science where the capture of rates of change in states is sought. While both pieces of commercial and open software exist to study such systems, their efficient and accurate usage…
A unifying approach to software and hardware design generated by ideas of Idempotent Mathematics is discussed. The so-called idempotent correspondence principle for algorithms, programs and hardware units is described. A software project…
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…
In these lecture notes, a selection of frequently required statistical tools will be introduced and illustrated. They allow to post-process data that stem from, e.g., large-scale numerical simulations (aka sequence of random experiments).…
Bialgebrae provide an abstract framework encompassing the semantics of different kinds of computational models. In this paper we propose a bialgebraic approach to the semantics of logic programming. Our methodology is to study logic…
Developing robust representations of chemical structures that enable models to learn topological inductive biases is challenging. In this manuscript, we present a representation of atomistic systems. We begin by proving that our…
\texttt{aurel} is an open-source Python package designed to \emph{au}tomatically calculate \emph{rel}ativistic quantities. It uses an efficient, flexible and user-friendly caching and dependency-tracking system, ideal for managing the…
The lower and upper bound of any given algorithm is one of the most crucial pieces of information needed when evaluating the computational effectiveness for said algorithm. Here a novel method of Boolean Algebraic Programming for symbolic…
Background: Current nomogram can only be created for regression algorithm. Providing nomogram for any machine learning (ML) algorithms may accelerate model deployment in clinical settings or improve model availability. We developed an R…
This paper shows how the Bayesian network paradigm can be used in order to solve combinatorial optimization problems. To do it some methods of structure learning from data and simulation of Bayesian networks are inserted inside Estimation…
We introduce operational semantics into games. And based on the operational semantics, we establish a full algebra of games, including basic algebra of games, algebra of concurrent games, recursion and abstraction. The algebra can be used…
Symmetric functions provide one of the most efficient tools for combinatorial enumeration, in the context of objects that may be acted upon by permutations. Only assuming a basic knowledge of linear algebra, we introduce and describe the…
Broadly speaking, there are two kinds of semantics-aware assistant systems for mathematics: proof assistants express the semantic in logic and emphasize deduction, and computer algebra systems express the semantics in programming languages…
Driven by the unprecedented computational power available to scientific research, the use of computers in solid-state physics, chemistry and materials science has been on a continuous rise. This review focuses on the software used for the…
The software feyntrop for direct numerical evaluation of Feynman integrals is presented. We focus on the underlying combinatorics and polytopal geometries facilitating these methods. Especially matroids, generalized permutohedra and…
Symbolic execution is a powerful program analysis technique that allows for the systematic exploration of all program paths. Path explosion, where the number of states to track becomes unwieldy, is one of the biggest challenges hindering…
Methods for the computation of invariants and symmetries of nonlinear evolution, wave, and lattice equations are presented. The algorithms are based on dimensional analysis, and can be implemented in any symbolic language, such as…
Signals can be interpreted as composed of a rapidly varying component modulated by a slower varying envelope. Identifying this envelope is an essential operation in signal processing, with applications in areas ranging from seismology to…