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Mathematics
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Theory of Algorithms and Recursion Theory
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Theory of Algorithms and Recursion Theory

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Mathematics and Computer Science".

Deadline for manuscript submissions: closed (30 May 2023) | Viewed by 6226

Special Issue Editor

Prof. Dr. Shamil Ishmukhametov

E-Mail Website
Guest Editor
Institute of Computational Mathematics and Information Technology, Kazan Federal University, Kremlevskya St. 35, 420008 Kazan, Russia
Interests: information security; mathmatical logic; elaboration of cryptographical algorithms

Special Issue Information

Dear Colleagues,

The theory of algorithms is a part of computer science connected to the development of fast effective algorithms for various classes of tasks of Mathematics and its applications to practical aspects of human activity, such as information defense, searching and sorting algorithms in database systems, machine learning, etc.

Theoretical aspects of the theory of algorithms include such directions as classification of algorithms by their complexity, study of unsolvable problems, elaboration of special algorithms for quantum computers, and so on.

This Special Issue looks for novel developments in both theoretical and practical aspects of the theory of algorithms, including:

  • Complexity theory of algorithms;
  • Recursion theory and algebraic aspects of algorithms structures;
  • Elaboration of fast algorithms for practical tasks in computer science;
  • Cryptographic algorithms for reliable cyphering of crucial data;
  • Algorithms for breaking computer ciphers;
  • Novel algorithms for quantum computers.

Prof. Dr. Shamil Ishmukhametov
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • effective algorithms
  • recursion theory
  • classification of algorithms
  • polynomial algorithms
  • cyphering algorithms
  • quantum algorithms

Published Papers (3 papers)

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Research

25 pages, 478 KiB  
Article
On Correspondences between Feedforward Artificial Neural Networks on Finite Memory Automata and Classes of Primitive Recursive Functions
by Vladimir A. Kulyukin
Mathematics 2023, 11(12), 2620; https://doi.org/10.3390/math11122620 - 08 Jun 2023
Cited by 1 | Viewed by 1986
Abstract
When realized on computational devices with finite quantities of memory, feedforward artificial neural networks and the functions they compute cease being abstract mathematical objects and turn into executable programs generating concrete computations. To differentiate between feedforward artificial neural networks and their functions as [...] Read more.
When realized on computational devices with finite quantities of memory, feedforward artificial neural networks and the functions they compute cease being abstract mathematical objects and turn into executable programs generating concrete computations. To differentiate between feedforward artificial neural networks and their functions as abstract mathematical objects and the realizations of these networks and functions on finite memory devices, we introduce the categories of general and actual computabilities and show that there exist correspondences, i.e., bijections, between functions computable by trained feedforward artificial neural networks on finite memory automata and classes of primitive recursive functions. Full article
(This article belongs to the Special Issue Theory of Algorithms and Recursion Theory)
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14 pages, 1776 KiB  
Article
Thermodynamic Interpretation of a Machine-Learning-Based Response Surface Model and Its Application to Pharmacodynamic Synergy between Propofol and Opioids
by Hsin-Yi Wang, Jing-Yang Liou, Chen Lin, Chien-Kun Ting, Wen-Kuei Chang, Men-Tzung Lo and Chien-Chang Chen
Mathematics 2022, 10(10), 1651; https://doi.org/10.3390/math10101651 - 12 May 2022
Cited by 1 | Viewed by 1387
Abstract
Propofol and fentanyl are commonly used agents for the induction of anesthesia, and are often associated with hemodynamic disturbances. Understanding pharmacodynamic impacts is vital for parasympathetic and sympathetic tones during the anesthesia induction period. Inspired by the thermodynamic interaction between drug concentrations and [...] Read more.
Propofol and fentanyl are commonly used agents for the induction of anesthesia, and are often associated with hemodynamic disturbances. Understanding pharmacodynamic impacts is vital for parasympathetic and sympathetic tones during the anesthesia induction period. Inspired by the thermodynamic interaction between drug concentrations and effects, we established a machine-learning-based response surface model (MLRSM) to address this predicament. Then, we investigated and modeled the biomedical phenomena in the autonomic nervous system. Our study prospectively enrolled 60 patients, and the participants were assigned to two groups randomly and equally. Group 1 received propofol first, followed by fentanyl, and the drug sequence followed an inverse procedure in Group 2. Then, we extracted and analyzed the spectrograms of electrocardiography (ECG) and pulse photoplethysmography (PPG) signals after induction of propofol and fentanyl. Eventually, we utilized the proposed MLRSM to evaluate the relationship between anesthetics and the integrity/balance of sympathetic and parasympathetic activity by employing the power of high-frequency (HF) and low-frequency (LF) bands and PPG amplitude (PPGA). It is worth emphasizing that the proposed MLRSM exhibits a similar mathematical form to the conventional Greco model, but with better computational performance. Furthermore, the MLRSM has a theoretical foundation and flexibility for arbitrary numbers of drug combinations. The modeling results are consistent with the previous literature. We employed the bootstrap algorithm to inspect the results’ consistency and measure the various statistical fluctuations. Then, the comparison between the modeling and the bootstrapping results was used to validate the statistical stability and the feasibility of the proposed MLRSM. Full article
(This article belongs to the Special Issue Theory of Algorithms and Recursion Theory)
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16 pages, 303 KiB  
Article
Computation and Hypercomputation
by Andrew Powell
Mathematics 2022, 10(6), 997; https://doi.org/10.3390/math10060997 - 20 Mar 2022
Cited by 1 | Viewed by 2181
Abstract
This paper shows some of the differences and similarities between computation and hypercomputation, the similarities relating to the complexity of propositional computation and the differences being the propositions that can be decided computationally or hypercomputationally. The methods used are ordinal Turing machines with [...] Read more.
This paper shows some of the differences and similarities between computation and hypercomputation, the similarities relating to the complexity of propositional computation and the differences being the propositions that can be decided computationally or hypercomputationally. The methods used are ordinal Turing machines with infinitely long programs and diagonalization out of computing complexity classes. The main results are the characterization of inequalities of run time complexities of serial, indeterministic serial and parallel computers and hypercomputers and the specification of a hierarchy of hypercomputers that can hypercompute the truths of all propositions in the standard class model of set theory, the von Neumann hierarchy of pure sets. Full article
(This article belongs to the Special Issue Theory of Algorithms and Recursion Theory)
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