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Mathematics

CM

[Communications in Mathematics]

CM

Communications in Mathematics

Communications in Mathematics—created in 2009—is the continuation of the journal Acta Mathematica et Informatica Universitatis Ostraviensis, founded in 1993, which became Acta Mathematica Universitatis Ostraviensis in 2003. Communications in Mathematics publishes research and review articles in English in all areas of pure and applied mathematics, mathematical physics and computer science.

  • Director of publication: Jan Lata
  • Editor-in-chief: Ivan Kaygorodov
  • Medium: electronic
  • Frequency: annual
  • Date created: 2009
  • Date of publication on Episciences: 2021
  • eISSN: 2336-1298
  • Subjects: mathematics
  • Languages of publication: English
  • Review process: single blind peer review
  • CC BY-SA 4.0 licence
  • Publisher: University of Ostrava
    • Address: Dvořákova 7, 701 03 Ostrava
    • Country: Czech Republic
  • Contact: cm AT episciences.org
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Latest articles

Structure of finite groups with restrictions on the set of conjugacy classes sizes

Let $N(G)$ be the set of conjugacy classes sizes of $G$. We prove that if $N(G)=\Omega\times \{1,n\}$ for specific set $\Omega$ of integers, then $G\simeq A\times B$ where $N(A)=\Omega$, $N(B)=\{1,n\}$, and $n$ is a power of prime.
Gorshkov, Ilya
February 03, 2023
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Various notions of (co)simplicial (pre)sheaves

The phrase "(co)simplicial (pre)sheaf" can be reasonably interpreted in multiple ways. In this survey we study how the various notions familiar to the author relate to one another. We end by giving some example applications of the most general of these notions.
Hosgood, Timothy
January 27, 2023
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Social Sciences and Humanities

J. Philos. Econ.

[Journal of Philosophical Economics]

J. Philos. Econ.

Journal of Philosophical Economics

Journal of Philosophical Economics is a social science journal founded in 2007. Published by Editura ASE, J. Philos. Econ. publishes one volume per year containing articles and book reviews in German, English or French.

  • Director of publication: Dr. Simona Bușoi
  • Editor-in-chief: Valentin Cojanu
  • Medium: print and electronic
  • Frequency: annual
  • Date created: 2007
  • Date of publication on Episciences: 2021
  • eISSN: 1844-8208
  • Subjects: Social sciences, Philosophy, Economic theory
  • Languages of publication: English, French, German
  • Review process: single blind peer review
  • CC BY-NC-SA 4.0 licence
  • Publisher: Editura ASE
    • Address: Academia de Studii Economice Bucuresti, Piata Romana 6, 010374 Bucuresti
    • Country: Romania
  • Contact: jpe AT episciences.org
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Towards a Theory of Conversation in Political Economy

The paper analyzes the nature of Political Economy as a modern conversational style, by defining its logical and rhetoric features. Successively, a wider historical and political context linked to the birth of the discipline is taken into account and thoroughly introduced in its implications for the interpretation of the role of such a discipline in modern life. Finally Political Economy is examined under the light of the educational effort it requires, as an anti- rhetoric method of inquiry and dialogue.
Faella, Gian Paolo
January 31, 2023
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Nietzsche and Fractal Geometry: a philosophical continuity

The purpose of this work is to highlight the epistemological proximity between Nietzsche’s philosophy of science and the underlying philosophical principles of fractal geometry, as illustrated in the main work of its creator, French mathematician Benoit Mandelbrot.This work also aims to find the end of this philosophical continuity, finding an important divergence between Nietzsche’s philosophy of risk taking and Mandelbrot’s legacy in risk management.
Gualario, Leandro
January 20, 2023
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Informatics and Applied Mathematics

TheoretiCS

TheoretiCS

Established in 2021, TheoretiCS covers all areas of Theoretical Computer Science (TCS). A joint effort of the TCS community, the journal is published by the TheoretiCS Foundation, a non-profit organisation based in Germany. The journal publishes research papers in English on an ongoing basis, including revised and extended versions of conference papers.

  • Director of publication: Thomas Schwentick
  • Editors-in-chief: Javier Esparza ; Uri Zwick
  • Medium: electronic
  • Frequency: continuous
  • Date created: 2021
  • Date of publication on Episciences: 2021
  • eISSN: 2751-4838
  • Subjects: Theoretical Computer Science
  • Language of publication: English
  • Review process: single blind peer review
  • CC BY 4.0 licence
  • Publisher: TheoretiCS Foundation e.V.
    • Address: c/o Thomas Schwentick – Schillingstr. 23, D-44139 Dortmund
    • Country: Germany
  • Contact: theoretics AT episciences.org
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Latest articles

Characterizing Positionality in Games of Infinite Duration over Infinite Graphs

We study turn-based quantitative games of infinite duration opposing two antagonistic players and played over graphs. This model is widely accepted as providing the adequate framework for formalizing the synthesis question for reactive systems. This important application motivates the question of strategy complexity: which valuations (or payoff functions) admit optimal positional strategies (without memory)? Valuations for which both players have optimal positional strategies have been characterized by Gimbert and Zielonka for finite graphs and by Colcombet and Niwi\'nski for infinite graphs. However, for reactive synthesis, existence of optimal positional strategies for the opponent (which models an antagonistic environment) is irrelevant. Despite this fact, not much is known about valuations for which the protagonist admits optimal positional strategies, regardless of the opponent. In this work, we characterize valuations which admit such strategies over infinite game graphs. Our characterization uses the vocabulary of universal graphs, which has also proved useful in understanding recent breakthrough results regarding the complexity of parity games. More precisely, we show that a valuation admitting universal graphs which are monotone and well-ordered is positional over all game graphs, and -- more surprisingly -- that the converse is also true for valuations admitting neutral colors. We prove the applicability and elegance of the framework by unifying a number of known positionality results, proving new ones, and establishing closure under lexicographical products. Finally, we discuss a class of prefix-independent positional objectives which is closed under countable unions.
Ohlmann, Pierre
January 31, 2023
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Conditional Dichotomy of Boolean Ordered Promise CSPs

Promise Constraint Satisfaction Problems (PCSPs) are a generalization of Constraint Satisfaction Problems (CSPs) where each predicate has a strong and a weak form and given a CSP instance, the objective is to distinguish if the strong form can be satisfied vs. even the weak form cannot be satisfied. Since their formal introduction by Austrin, Guruswami, and H\aa stad, there has been a flurry of works on PCSPs [BBKO19,KO19,WZ20]. The key tool in studying PCSPs is the algebraic framework developed in the context of CSPs where the closure properties of the satisfying solutions known as the polymorphisms are analyzed. The polymorphisms of PCSPs are much richer than CSPs. In the Boolean case, we still do not know if dichotomy for PCSPs exists analogous to Schaefer's dichotomy result for CSPs. In this paper, we study a special case of Boolean PCSPs, namely Boolean Ordered PCSPs where the Boolean PCSPs have the predicate $x \leq y$. In the algebraic framework, this is the special case of Boolean PCSPs when the polymorphisms are monotone functions. We prove that Boolean Ordered PCSPs exhibit a computational dichotomy assuming the Rich 2-to-1 Conjecture [BKM21] which is a perfect completeness surrogate of the Unique Games Conjecture. Assuming the Rich 2-to-1 Conjecture, we prove that a Boolean Ordered PCSP can be solved in polynomial time if for every $\epsilon>0$, it has polymorphisms where each coordinate has Shapley value at most $\epsilon$, else it is NP-hard. The algorithmic part of our dichotomy is based on a structural lemma that Boolean monotone functions with each coordinate having low Shapley value have arbitrarily large threshold functions as minors. The hardness part proceeds by showing that the Shapley value is consistent under a uniformly random 2-to-1 minor. Of independent interest, we show that the Shapley value can be inconsistent under an adversarial 2-to-1 minor.
Brakensiek, Joshua
January 25, 2023
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