Related papers: Electronic Appendix to "Input Invariants"

We continue studying essential inputs of trees and automata. Strongly essential inputs of trees are introduced and studied. Various examples for application in Computer Science are shown.

We show that the basic results on the paper referred in the title [J. Phys. A: Math. Gen. v. 35 (2002) 5333-5345], concerning the derivation of the Ermakov invariant from Noether symmetry methods, are not new.

This lecture note focuses on comparing the notions of invariance and home spaces in Transition Systems and more particularly, in Petri Nets. We also describe how linear algebra relates to these basic notions in Computer Science, how it can…

Introduction to Machine learning covering Statistical Inference (Bayes, EM, ML/MaxEnt duality), algebraic and spectral methods (PCA, LDA, CCA, Clustering), and PAC learning (the Formal model, VC dimension, Double Sampling theorem).

A number of topics in analysis are discussed, with emphasis on basic principles. There is some overlap with "Elements of linear and real analysis" (arXiv:math/0108030), with numerous changes in content and presentation since then.

We perform certain alternating binomial summations with parameters that occur in the analysis of algorithms. A combination of integral and special function and special number representations is used. The results are sufficiently general to…

This note corrects some omissions in section 2 of the paper "Lipschitz connectivity and filling invariants in solvable groups and buildings."

E-learning in higher education is exponentially increased during the past decade due to its inevitable benefits in critical situations like natural disasters, and pandemic. The reliable, fair, and seamless execution of online exams in…

In this paper, we study an adaptive finite element method for a class of a nonlinear eigenvalue problems that may be of nonconvex energy functional and consider its applications to quantum chemistry. We prove the convergence of adaptive…

This note corrects Example 3.2 in Two-Variable Wiman-Valiron Theory and PDEs by the authors which appeared in Ann. Acad. Sci. Fenn Math. (35) (2010), 571-580.

This text consists of additions to the book "Foundations of Garside Theory", EMS Tracts in Mathematics, vol. 22 (2015) -- see introduction and table of contents in arXiv:1309.0796 -- namely skipped proofs and solutions to selected…

Error invariants are assertions that over-approximate the reachable program states at a given position in an error trace while only capturing states that will still lead to failure if execution of the trace is continued from that position.…

Background: Biological networks have a growing importance for the interpretation of high-throughput omics data. Integrative network analysis makes use of statistical and combinatorial methods to extract smaller subnetwork modules, and…

Corrected versions of the numerically invariant expressions for the affine and Euclidean signature of a planar curve proposed by E.Calabi et. al are presented. The new formulas are valid for fine but otherwise arbitrary partitions of the…

Intelligibility and accurate uncertainty estimation are crucial for reliable decision-making. In this paper, we propose EviNAM, an extension of evidential learning that integrates the interpretability of Neural Additive Models (NAMs) with…

Machine learning plays a role in many deployed decision systems, often in ways that are difficult or impossible to understand by human stakeholders. Explaining, in a human-understandable way, the relationship between the input and output of…

In [1], we have presented the theoretical background for finding the Elementary Invariants for a 3D system of first order rational differential equations (1ODEs). We have also provided an algorithm to find such Invariants. Here we introduce…

Short review article on quantum computation accepted for Supplement III, Encyclopaedia of Mathematics (publication expected Summer 2001). See also http://www.wkap.nl/series.htm/ENM

We study some classes of semi-linear differential equations including both well-posed and ill-posed cases that can generate cocycles (or cocycle correspondences with generating cocycles). Under exponential dichotomy condition with other…

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…