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Multiple linear regression is a basic statistical tool, yielding a prediction formula with the input variables, slopes, and an intercept. But is it really easy to see which terms have the largest effect, or to explain why the prediction of…
The chase is a sound, complete, but possibly non-terminating algorithm for reasoning with existential rules (aka. tuple-generating dependencies), a highly expressive knowledge representation language. Although the procedure appears simple,…
The study of essential and strongly essential variables in functions defined on finite sets is a part of $k$-valued logic. We extend the main definitions from functions to terms. This allows us to apply concepts and results of Universal…
Using the theory of $(\varphi, \Gamma)$-modules we generalizes Greenberg's construction of the $\Cal L$-invariant to semistable representations
A refinement of the multinomial distribution is presented where the number of inversions in the sequence of outcomes is tallied. This refinement of the multinomial distribution is its joint distribution with the number of inversions in the…
Stepwise refinement of algebraic specifications is a well known formal methodology for program development. However, traditional notions of refinement based on signature morphisms are often too rigid to capture a number of relevant…
Although being powerful, the differential transform method yet suffers from a drawback which is how to compute the differential transform of nonlinear non-autonomous functions that can limit its applicability. In order to overcome this…
The alternative version of Hamiltonian formalism for higher-derivative theories is proposed. As compared with the standard Ostrogradski approach it has the following advantages: (i) the Lagrangian, when expressed in terms of new variables…
While there are many applications of ML to scientific problems that look promising, visuals can be deceiving. Using numerical analysis techniques, we rigorously quantify the accuracy, convergence rates, and generalization bounds of certain…
A multidimensional generalization of the Bernstein class of functions and the properties of functions of the introduced class are examined. In particular, a new proof of the integral representation of Bernstein functions of many variables…
We investigate the behaviour of elliptic Feynman integrals under modular transformations. This has a practical motivation: Through a suitable modular transformation we can achieve that the nome squared is a small quantity, leading to fast…
We define involution algebroids which generalise Lie algebroids to the abstract setting of tangent categories. As a part of this generalisation the Jacobi identity which appears in classical Lie theory is replaced by an identity similar to…
This document reports on the use of an algebraic, visual, formal approach to the specification of patterns for the formalization of the GoF design patterns. The approach is based on graphs, morphisms and operations from category theory and…
The Bindlib library for OCaml provides a set of tools for the manipulation of data structures with variable binding. It is very well suited for the representation of abstract syntax trees, and has already been used for the implementation of…
In this paper, we give a new characterization of generalized Browder's theorem by considering equality between the generalized Drazin-meromorphic Weyl spectrum and the generalized Drazin-meromorphic spectrum. Also, we generalize Cline's…
A new class of integrable mappings and chains is introduced. Corresponding $(1+2)$ integrable systems invariant with respect to such discrete transformations are presented in an explicit form. Their soliton-type solutions are constructed in…
Many current challenges involve understanding the complex dynamical interplay between the constituents of systems. Typically, the number of such constituents is high, but only limited data sources on them are available. Conventional…
We discuss a new method of integration over matrix variables based on a suitable gauge choice in which the angular variables decouple from the eigenvalues at least for a class of two-matrix models. The calculation of correlation functions…
The study of variability in software development has become increasingly important in recent years. A common mechanism to represent the variability in a product line is by means of feature models. However, the relationship between these…
As a generalization of Riemann-Liouville integral, we introduce integral transformations of convergent power series which can be applied to hypergeometric functions with several variables.