Related papers: On the Complexity of Real Functions
This paper is a reflexion on the computability of natural language semantics. It does not contain a new model or new results in the formal semantics of natural language: it is rather a computational analysis of the logical models and…
Quantum theory (QT) has been confirmed by numerous experiments, yet we still cannot fully grasp the meaning of the theory. As a consequence, the quantum world appears to us paradoxical. Here we shed new light on QT by being based on two…
Several philosophical issues in connection with computer simulations rely on the assumption that results of simulations are trustworthy. Examples of these include the debate on the experimental role of computer simulations \cite{Parker2009,…
The derivatives with respect to order {\nu} for the Bessel functions of argument x (real or complex) are studied. Representations are derived in terms of integrals that involve the products pairs of Bessel functions, and in turn series…
Complexity is a multi-faceted phenomenon, involving a variety of features including disorder, nonlinearity, and self-organisation. We use a recently developed rigorous framework for complexity to understand measures of complexity. We…
While looking for abductive explanations of a given set of manifestations, an ordering between possible solutions is often assumed. The complexity of finding/verifying optimal solutions is already known. In this paper we consider the…
Complexity theory as practiced by physicists and computational complexity theory as practiced by computer scientists both characterize how difficult it is to solve complex problems. Here it is shown that the parameters of a specific model…
We investigate replicable learning algorithms. Ideally, we would like to design algorithms that output the same canonical model over multiple runs, even when different runs observe a different set of samples from the unknown data…
For a smooth, closed $n$-manifold $M$, we define an upper semi-continuous integer-valued complexity function on $H^1(M;{\mathbb R})$ using Morse theory. This measures how far an integral class is from being a fiber of a fibration. The fact…
We answer the following question posed by Lechuga: Given a simply-connected space $X$ with both $H_*(X,\qq)$ and $\pi_*(X)\otimes \qq$ being finite-dimensional, what is the computational complexity of an algorithm computing the cup-length…
We study how well a real number can be approximated by sums of two or more rational numbers with denominators up to a certain size.
We seek random versions of some classical theorems on complex approximation by polynomials and rational functions, as well as investigate properties of random compact sets in connection to complex approximation.
Complexity theory provides a wealth of complexity classes for analyzing the complexity of decision and counting problems. Despite the practical relevance of enumeration problems, the tools provided by complexity theory for this important…
We show how the complexity of higher-order functional programs can be analysed automatically by applying program transformations to a defunctionalized versions of them, and feeding the result to existing tools for the complexity analysis of…
A good process model is expected not only to reflect the behavior of the process, but also to be as easy to read and understand as possible. Because preferences vary across different applications, numerous measures provide ways to reflect…
A property, or statistical functional, is said to be elicitable if it minimizes expected loss for some loss function. The study of which properties are elicitable sheds light on the capabilities and limitations of point estimation and…
Complexity of patterns is a key information for human brain to differ objects of about the same size and shape. Like other innate human senses, the complexity perception cannot be easily quantified. We propose a transparent and universal…
Inspired by Quantum Mechanics, we reformulate Hilbert's tenth problem in the domain of integer arithmetics into problems involving either a set of infinitely-coupled non-linear differential equations or a class of linear Schr\"odinger…
Quantum theory (QT) has been confirmed by numerous experiments, yet we still cannot fully grasp the meaning of the theory. As a consequence, the quantum world appears to us paradoxical. Here we shed new light on QT by having it follow from…
Extended real-valued functions are often used in optimization theory, but in different ways for infimum problems and for supremum problems. We present an approach to extended real-valued functions that works for all types of problems and…