Episciences.org
Not a member yet
6707 research outputs found
Sort by
A q-analog of Jacobi's two squares formula and its applications
No full textWe consider a -analog of the number of representations of an integer as a sum of two squares . This -analog is generated by the expansion of a product that was studied by Kronecker and Jordan. We generalize Jacobi's two squares formula from to . We characterize the signs in the coefficients of using the prime factors of . We use to characterize the integers which are the length of the hypotenuse of a primitive Pythagorean triangle
Serre-invariant stability conditions and Ulrich bundles on cubic threefolds
No full textWe prove a general criterion which ensures that a fractional Calabi--Yaucategory of dimension admits a unique Serre-invariant stabilitycondition, up to the action of the universal cover of. We apply this result to the Kuznetsov component of a cubic threefold . In particular, we show that all theknown stability conditions on are invariant with respect to theaction of the Serre functor and thus lie in the same orbit with respect to theaction of the universal cover of . As anapplication, we show that the moduli space of Ulrich bundles of rank on is irreducible, answering a question asked by Lahoz, Macr\`i andStellari.Comment: 32 page
Deconfined Global Types for Asynchronous Sessions
No full textMultiparty sessions with asynchronous communications and global types play animportant role for the modelling of interaction protocols in distributedsystems. In designing such calculi the aim is to enforce, by typing, goodproperties for all participants, maximising, at the same time, the acceptedbehaviours. Our type system improves the state-of-the-art by typing allasynchronous sessions and preserving the key properties of Subject Reduction,Session Fidelity and Progress when some well-formedness conditions aresatisfied. The type system comes together with a sound and complete typeinference algorithm. The well-formedness conditions are undecidable, but analgorithm checking an expressive restriction of them recovers the effectivenessof typing
Strongly Continuous Domains
No full textStrong Scott topology introduced by X. Xu and D. Zhao is a kind of newtopology which is finer than upper topology and coarser than Scott topology.Inspired by the topological characterizations of continuous domains andhypercontinuous domains, we introduce the concept of strongly continuousdomains and investigate some properties of strongly continuous domains. Inparticular, we give the definition of strong way-below relation and obtain acharacterization of strongly continuous domains via the strong way-belowrelation. We prove that the strong way-below relation on a strongly continuousdomain satisfies the interpolation property, and clarify the relationshipbetween strongly continuous domains and continuous domains, and therelationship between strongly continuous domains and hypercontinuous domains.We discuss the properties of strong Scott topology and strong Lawson topology,which is the common refinement of the strong Scott topology and the lowertopology, on a strongly continuous domain.Comment: 10 pages, 2 figure
Social media in the Global South: A Network Dataset of the Malian Twittersphere
No full textWith the expansion of mobile communications infrastructure, social mediausage in the Global South is surging. Compared to the Global North, populationsof the Global South have had less prior experience with social media fromstationary computers and wired Internet. Many countries are experiencingviolent conflicts that have a profound effect on their societies. As a result,social networks develop under different conditions than elsewhere, and our goalis to provide data for studying this phenomenon. In this dataset paper, wepresent a data collection of a national Twittersphere in a West African countryof conflict. While not the largest social network in terms of users, Twitter isan important platform where people engage in public discussion. The focus is onMali, a country beset by conflict since 2012 that has recently had a relativelyprecarious media ecology. The dataset consists of tweets and Twitter users inMali and was collected in June 2022, when the Malian conflict became moreviolent internally both towards external and international actors. In apreliminary analysis, we assume that the conflictual context influences howpeople access social media and, therefore, the shape of the Twittersphere andits characteristics. The aim of this paper is to primarily invite researchersfrom various disciplines including complex networks and social sciencesscholars to explore the data at hand further. We collected the dataset using ascraping strategy of the follower network and the identification ofcharacteristics of a Malian Twitter user. The given snapshot of the MalianTwitter follower network contains around seven million accounts, of which56,000 are clearly identifiable as Malian. In addition, we present the tweets.The dataset is available at: https://osf.io/mj2qt/Comment: 12 pages, 4 figure
Pre-crossed modules and rack homology
No full textWe define a homology theory for pre-crossed modules that specifies to rackhomology in the case when the pre-crossed module is freely generated by a rack
A Nivat Theorem for Weighted Alternating Automata over Commutative Semirings
No full textThis paper connects the classes of weighted alternating finite automata(WAFA), weighted finite tree automata (WFTA), and polynomial automata (PA). First, we investigate the use of trees in the run semantics for weightedalternating automata and prove that the behavior of a weighted alternatingautomaton can be characterized as the composition of the behavior of a weightedfinite tree automaton and a specific tree homomorphism, if weights are takenfrom a commutative semiring. Based on this, we give a Nivat-like characterization for weighted alternatingautomata. Moreover, we show that the class of series recognized by weightedalternating automata is closed under inverses of homomorphisms, but not underhomomorphisms. Additionally, we give a logical characterization of weightedalternating automata, which uses weighted MSO logic for trees. Finally, weinvestigate the strong connection between weighted alternating automata andpolynomial automata. We prove: A weighted language is recognized by a weightedalternating automaton iff its reversal in recognized by a polynomial automaton.Using the corresponding result for polynomial automata, we are able to provethat the ZERONESS problem for weighted alternating automata with weights takenfrom the rational numbers decidable.Comment: Extended version of a paper at GandALF 2021, see arXiv:2109.08323. Submitted to GandALF 2021 Special Issue on LMCS First revision: Typos & grammar, slight changes in structure, additional explanations, new lmcs.cl
On Young diagrams of maximum dimension
No full textWe study the problem of finding Young diagrams of maximum dimension, i. e.those with the largest number of Young tableaux of their shapes. Consider aclass of Young diagrams that differ from a symmetric diagram by no more thanone box in each row and column. It is proven that when moving boxes to symmetric positions , the original diagram istransformed into another diagram of the same size, but with a greater or equaldimension. A conjecture is formulated that generalizes the above fact to thecase of arbitrary Young diagrams. Based on this conjecture, we developed analgorithm applied to obtain new Young diagrams of sizes up to 42 thousand boxeswith large and maximum dimensions
Synchronizability of Communicating Finite State Machines is not Decidable
No full textA system of communicating finite state machines is synchronizable if its sendtrace semantics, i.e.the set of sequences of sendings it can perform, is thesame when its communications are FIFO asynchronous and when they are justrendez-vous synchronizations. This property was claimed to be decidable inseveral conference and journal papers for either mailboxes or peer-to-peercommunications, thanks to a form of small model property. In this paper, weshow that this small model property does not hold neither for mailboxcommunications, nor for peer-to-peer communications, therefore the decidabilityof synchronizability becomes an open question. We close this question forpeer-to-peer communications, and we show that synchronizability is actuallyundecidable. We show that synchronizability is decidable if the topology ofcommunications is an oriented ring. We also show that, in this case,synchronizability implies the absence of unspecified receptions and orphanmessages, and the channel-recognizability of the reachability set.Comment: Long versio
Overlap Algebras as Almost Discrete Locales
No full textBoolean locales are "almost discrete", in the sense that a spatial Booleanlocale is just a discrete locale (that is, it corresponds to the frame of opensubsets of a discrete space, namely the powerset of a set). This basic fact,however, cannot be proven constructively, that is, over intuitionistic logic,as it requires the full law of excluded middle (LEM). In fact, discrete localesare never Boolean constructively, except for the trivial locale. So, what is analmost discrete locale constructively? Our claim is that Sambin's overlapalgebras have good enough features to deserve to be called that. Namely, theyinclude the class of discrete locales, they arise as smallest strongly densesublocales (of overt locales), and hence they coincide with the Boolean localesif LEM holds