Episciences.org
Not a member yet
6707 research outputs found
Sort by
On -ranks of topological spaces
No full textIn this paper, the concepts of -subset systems and -well-filteredspaces are introduced, which provide another uniform approach to -spaces,-well-filtered spaces (i.e., -admissibility) andwell-filtered spaces. We prove that the -well-filtered reflection of any space exists. Meanwhile, we propose the definition of -rank, whichis an ordinal that measures how many steps from a space to a-well-filtered space. Moreover, we derive that for any ordinal ,there exists a space whose -rank equals to . One immediatecorollary is that for any ordinal , there exists a space whose-rank (respectively, -rank) equals to
Structure of finite groups with restrictions on the set of conjugacy classes sizes
No full textLet be the set of conjugacy classes sizes of . We prove that if for specific set of integers, then where , , and is a power ofprime
Arena-Independent Finite-Memory Determinacy in Stochastic Games
No full textWe study stochastic zero-sum games on graphs, which are prevalent tools tomodel decision-making in presence of an antagonistic opponent in a randomenvironment. In this setting, an important question is the one of strategycomplexity: what kinds of strategies are sufficient or required to playoptimally (e.g., randomization or memory requirements)? Our contributionsfurther the understanding of arena-independent finite-memory (AIFM)determinacy, i.e., the study of objectives for which memory is needed, but in away that only depends on limited parameters of the game graphs. First, we showthat objectives for which pure AIFM strategies suffice to play optimally alsoadmit pure AIFM subgame perfect strategies. Second, we show that we can reducethe study of objectives for which pure AIFM strategies suffice in two-playerstochastic games to the easier study of one-player stochastic games (i.e.,Markov decision processes). Third, we characterize the sufficiency of AIFMstrategies through two intuitive properties of objectives. This work extends aline of research started on deterministic games to stochastic ones
On Mixed Cages
No full textMixed graphs have both directed and undirected edges. A mixed cage is aregular mixed graph of given girth with minimum possible order. In this papermixed cages are studied. Upper bounds are obtained by general constructionmethods and computer searches
Computing the Density of the Positivity Set for Linear Recurrence Sequences
No full textThe set of indices that correspond to the positive entries of a sequence ofnumbers is called its positivity set. In this paper, we study the density ofthe positivity set of a given linear recurrence sequence, that is the questionof how much more frequent are the positive entries compared to the non-positiveones. We show that one can compute this density to arbitrary precision, as wellas decide whether it is equal to zero (or one). If the sequence isdiagonalisable, we prove that its positivity set is finite if and only if itsdensity is zero. Further, arithmetic properties of densities are treated, inparticular we prove that it is decidable whether the density is a rationalnumber, given that the recurrence sequence has at most one pair of dominantcomplex roots. Finally, we generalise all these results to symbolic orbits oflinear dynamical systems, thereby showing that one can decide variousproperties of such systems, up to a set of density zero
A model of actors and grey failures
No full textExisting models for the analysis of concurrent processes tend to focus onfail-stop failures, where processes are either working or permanently stopped,and their state (working/stopped) is known. In fact, systems are often affectedby grey failures: failures that are latent, possibly transient, and may affectthe system in subtle ways that later lead to major issues (such as crashes,limited availability, overload). We introduce a model of actor-based systemswith grey failures, based on two interlinked layers: an actor model, given asan asynchronous process calculus with discrete time, and a failure model thatrepresents failure patterns to inject in the system. Our failure model capturesnot only fail-stop node and link failures, but also grey failures (e.g.,partial, transient). We give a behavioural equivalence relation based on weakbarbed bisimulation to compare systems on the basis of their ability to recoverfrom failures, and on this basis we define some desirable properties ofreliable systems. By doing so, we reduce the problem of checking reliabilityproperties of systems to the problem of checking bisimulation
Non-associative algebraic structures: classification and structure
No full textThese are detailed notes for a lecture on "Non-associative AlgebraicStructures: Classification and Structure" which I presented as a part of myAgrega\c{c}\~ao em Matem\'atica e Applica\c{c}\~oes (University of BeiraInterior, Covilh\~a, Portugal, 13-14/03/2023)
The Future of Heterodox Economics
No full textWe assess economics research and teaching frameworks in the United States by examining how knowledge is produced and ranked, the flaws and strengths of heterodox economic theory; and how students are trained, especially for careers in economic policy. We challenge the meaning of established terminology such as 'heterodoxy' and 'mainstream' by investigating their utility as a marker and to illuminate major barriers to the successful adoption of alternative economic theories in academia and the public discourse. Based on interviews with experienced economists working with heterodox paradigms in both mainstream and heterodox institutions, we identify three barriers 1) Neoclassical hegemony, 2) Weakness of heterodox theory, and 3) Pedagogy and training in economics
Non-Deterministic Functions as Non-Deterministic Processes (Extended Version)
No full textWe study encodings of the lambda-calculus into the pi-calculus in theunexplored case of calculi with non-determinism and failures. On the sequentialside, we consider lambdafail, a new non-deterministic calculus in whichintersection types control resources (terms); on the concurrent side, weconsider spi, a pi-calculus in which non-determinism and failure rest upon aCurry-Howard correspondence between linear logic and session types. We presenta typed encoding of lambdafail into spi and establish its correctness. Ourencoding precisely explains the interplay of non-deterministic and fail-proneevaluation in lambdafail via typed processes in spi. In particular, it showshow failures in sequential evaluation (absence/excess of resources) can beneatly codified as interaction protocols
Cohomology of moduli spaces via a result of Chenevier and Lannes
No full textWe use a classification result of Chenevier and Lannes for algebraicautomorphic representations together with a conjectural correspondence with-adic absolute Galois representations to determine the Eulercharacteristics (with values in the Grothendieck group of such representations)of and for and oflocal systems on for .Comment: 14 pages, minor revisio