Related papers: Real-number Computability from the Perspective of …
The Operator axioms have produced new real numbers with new operators. New operators naturally produce new equations and thus extend the traditional mathematical models which are selected to describe various scientific rules. So new…
It is said that beauty is in the eye of the beholder. But how exactly can we characterize such discrepancies in interpretation? For example, are there any specific features of an image that makes person A regard an image as beautiful while…
Differences between computer simulation of dynamical systems and laboratory experiments are common in teaching and research in engineering. Normally, numerical inaccuracy and the non-ideal behaviour of the devices involved in the experiment…
By the example of the proof of Minkowski's conjecture on critical determinant we give a category theory framework for interval computation.
Most existing implementations of multiple precision arithmetic demand that the user sets the precision {\em a priori}. Some libraries are said adaptable in the sense that they dynamically change the precision of each intermediate operation…
These Course Notes provide an introduction to mathematical proofs for undergraduate students transitioning from computational calculus to abstract mathematics. Topics include propositional logic, proof techniques, mathematical induction,…
The error function of real argument can be uniformly approximated to a given accuracy by a single closed-form expression for the whole variable range either in terms of addition, multiplication, division, and square root operations only, or…
The computer-assisted analysis is not currently a novelty, but a necessity in all areas of psychology. A number of studies that examine the limits of the computer assisted and analyzed interpretations, also its advantages. A series of…
Current and emerging trends such as cloud computing, fog computing, and more recently, multi-access edge computing (MEC) increase the interest in finding solutions to the verifiable computation problem. Furthermore, the number of…
In this paper we present the set of intervals as a normed vector space. We define also a four-dimensional associative algebra whose product gives the product of intervals in any cases. This approach allows to give a notion of divisibility…
Computational method for statistical measures of reliability, confidence, and assurance are available for infinite population size. If the population size is finite and small compared to the number of samples tested, these computational…
In this article we present very intuitive, easy to follow, yet mathematically rigorous, approach to the so called data fitting process. Rather than minimizing the distance between measured and simulated data points, we prefer to find such…
Comparison to traditionally accurate computing, approximate computing focuses on the rapidity of the satisfactory solution, but not the unnecessary accuracy of the solution. Approximate bisimularity is the approximate one corresponding to…
These course notes are about computing modular forms and some of their arithmetic properties. Their aim is to explain and prove the modular symbols algorithm in as elementary and as explicit terms as possible, and to enable the devoted…
We introduce a lightweight and accessible approach to computation over the real numbers, with the aim of clarifying both the underlying concepts and their relevance in modern research. The material is intended for a broad audience,…
We use the martingale-theoretic approach of game-theoretic probability to incorporate imprecision into the study of randomness. In particular, we define a notion of computable randomness associated with interval, rather than precise,…
Incremental computation aims to compute more efficiently on changed input by reusing previously computed results. We give a high-level overview of works on incremental computation, and highlight the essence underlying all of them, which we…
We expect an increase in the frequency and severity of cyber-attacks that comes along with the need for efficient security countermeasures. The process of attributing a cyber-attack helps to construct efficient and targeted mitigating and…
In this article we consider mathematical fundamentals of one method for proving inequalities by computer, based on the Remez algorithm. Using the well-known results of undecidability of the existence of zeros of real elementary functions,…
We introduce the continued logarithm representation of real numbers and prove results on the occurrence and frequency of digits with respect to this representation