Related papers: Complex Analysis as Catalyst
Meta-analysis is routinely performed in many scientific disciplines. This analysis is attractive since discoveries are possible even when all the individual studies are underpowered. However, the meta-analytic discoveries may be entirely…
In this paper, a new approximate syllogistic reasoning schema is described that expands some of the approaches expounded in the literature into two ways: (i) a number of different types of quantifiers (logical, absolute, proportional,…
This paper presents an analytical taxonomy that can suitably describe, rather than simply classify, techniques for data presentation. Unlike previous works, we do not consider particular aspects of visualization techniques, but their…
Abstraction logic is a new logic, serving as a foundation of mathematics. It combines features of both predicate logic and higher-order logic: abstraction logic can be viewed both as higher-order logic minus static types as well as…
Hysteresis can be defined from a dynamical systems perspective with respect to equilibrium points. Consequently, hysteresis naturally lends itself as a topic to illustrate and extend concepts in a dynamical systems course. A number of…
We present in this paper some fundamental tools for developing matrix analysis over the complex quaternion algebra. As applications, we consider generalized inverses, eigenvalues and eigenvectors, similarity, determinants of complex…
Presenting systems of differential equations in the form of diagrams has become common in certain parts of physics, especially electromagnetism and computational physics. In this work, we aim to put such use of diagrams on a firm…
Proposed is a new formal approach for solution of extreme multi-criteria problems transforming them into single-criterion mathematical models, without any additional information. Transforming rules are based on comparison standards and…
In this paper we study the complexity of solving a problem when a solution of a similar instance is known. This problem is relevant whenever instances may change from time to time, and known solutions may not remain valid after the change.…
We suggest new types and interpretation of complex and hypercomplex numbers for which the commutative, associative, and distributive laws and the norm axioms are trivially satisfied.
Multiplex networks offer an important tool for the study of complex systems and extending techniques originally designed for single--layer networks is an important area of study. One of the most important methods for analyzing networks is…
This article presents a general solution to the problem of computational complexity. First, it gives a historical introduction to the problem since the revival of the foundational problems of mathematics at the end of the 19th century.…
In resolving instances of a computational problem, if multiple instances of interest share a feature in common, it may be fruitful to compile this feature into a format that allows for more efficient resolution, even if the compilation is…
It is argued that the two problems of choosing characterizations and models of complex systems should not be considered independently. A particular criterion for these choices, oriented on the potential usefulness of the results, is…
Solving polynomial equations is a subtask of polynomial optimization. This article introduces systems of such equations and the main approaches for solving them. We discuss critical point equations, algebraic varieties, and solution counts.…
In recent years, ideas from statistics and scientific computing have begun to interact in increasingly sophisticated and fruitful ways with ideas from computer science and the theory of algorithms to aid in the development of improved…
A definition of what counts as an explanation of mathematical statement, and when one explanation is better than another, is given. Since all mathematical facts must be true in all causal models, and hence known by an agent, mathematical…
We characterize vertex algebras (in a suitable sense) as algebras over a certain graded co-operad. We also discuss some examples and categorical implications of this characterization.
We argue that parameterized complexity is a useful tool with which to study global constraints. In particular, we show that many global constraints which are intractable to propagate completely have natural parameters which make them…
With the increasing deployment of machine learning systems in practice, transparency and explainability have become serious issues. Contrastive explanations are considered to be useful and intuitive, in particular when it comes to…