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The Volterra Integrable case. Novel analytical and numerical results
No full textIn the present paper we reconsider the integrable case of the Hamiltonian-species Volterra system, as it has been introduced by Vito Volterra in 1937and significantly enrich the results already published in the ArXiv in 2019 bytwo of the present authors (M. Scalia and O. Ragnisco). In fact, we present anew approach to the construction of conserved quantities and comment about thesolutions of the equations of motion; we display mostly new analytical andnumerical results, starting from the classical predator-prey model and arrivingat the general -species modelComment: 24 pages, 9 figures. This paper is a natural prosecution of the work arXiv:1903.03595 and presents different enrichments and enhancements of the results there appeared. In this second version several typos have been correcte
A higher-order transformation approach to the formalization and analysis of BPMN using graph transformation systems
No full textThe Business Process Modeling Notation (BPMN) is a widely used standardnotation for defining intra- and inter-organizational workflows. However, theinformal description of the BPMN execution semantics leads to differentinterpretations of BPMN elements and difficulties in checking behavioralproperties. In this article, we propose a formalization of the executionsemantics of BPMN that, compared to existing approaches, covers more BPMNelements while also facilitating property checking. Our approach is based on ahigher-order transformation from BPMN models to graph transformation systems.To show the capabilities of our approach, we implemented it as an open-sourceweb-based tool
Pre-measure spaces and pre-integration spaces in predicative Bishop-Cheng measure theory
No full textBishop's measure theory (BMT) is an abstraction of the measure theory of alocally compact metric space , and the use of an informal notion of aset-indexed family of complemented subsets is crucial to its predicativecharacter. The more general Bishop-Cheng measure theory (BCMT) is aconstructive version of the classical Daniell approach to measure andintegration, and highly impredicative, as many of its fundamental notions, suchas the integration space of -integrable functions , rely onquantification over proper classes (from the constructive point of view). Inthis paper we introduce the notions of a pre-measure and pre-integration space,a predicative variation of the Bishop-Cheng notion of a measure space and of anintegration space, respectively. Working within Bishop Set Theory (BST), andusing the theory of set-indexed families of complemented subsets andset-indexed families of real-valued partial functions within BST, we apply theimplicit, predicative spirit of BMT to BCMT. As a first example, we present thepre-measure space of complemented detachable subsets of a set with theDirac-measure, concentrated at a single point. Furthermore, we translate in ourpredicative framework the non-trivial, Bishop-Cheng construction of anintegration space from a given measure space, showing that a pre-measure spaceinduces the pre-integration space of simple functions associated to it.Finally, a predicative construction of the canonically integrable functions, as the completion of an integration space, is included
Temporal Sequencing of Documents
No full textWe outline an unsupervised method for temporal rank ordering of sets ofhistorical documents, namely American State of the Union Addresses and DEEDS, acorpus of medieval English property transfer documents. Our method relies uponeffectively capturing the gradual change in word usage via a bandwidth estimatefor the non-parametric Generalized Linear Models (Fan, Heckman, and Wand,1995). The number of possible rank orders needed to search through for costfunctions related to the bandwidth can be quite large, even for a small set ofdocuments. We tackle this problem of combinatorial optimization using theSimulated Annealing algorithm, which allows us to obtain the optimal documenttemporal orders. Our rank ordering method significantly improved the temporalsequencing of both corpora compared to a randomly sequenced baseline. Thisunsupervised approach should enable the temporal ordering of undated documentsets
Lie symmetry analysis of (2+1)-dimensional time fractional Kadomtsev-Petviashvili equation
No full textIn this paper, Lie symmetry analysis method is applied to the(2+1)-dimensional time fractional Kadomtsev-Petviashvili (KP) equation with themixed derivative of Riemann-Liouville time-fractional derivative andinteger-order -derivative. We obtained all the Lie symmetries admitted bythe KP equation and used them to reduce the (2+1)-dimensional fractionalpartial differential equation with Riemann-Liouville fractional derivative tosome (1+1)-dimensional fractional partial differential equations withErd\'{e}lyi-Kober fractional derivative or Riemann-Liouville fractionalderivative, thereby getting some exact solutions of the reduced equations. Inaddition, the new conservation theorem and the generalization of Noetheroperators are developed to construct the conservation laws for the equationstudied
Complexity results for modal logic with recursion via translations and tableaux
No full textThis paper studies the complexity of classical modal logics and of theirextension with fixed-point operators, using translations to transfer resultsacross logics. In particular, we show several complexity results formulti-agent logics via translations to and from the -calculus and modallogic, which allow us to transfer known upper and lower bounds. We also usethese translations to introduce terminating and non-terminating tableau systemsfor the logics we study, based on Kozen's tableau for the -calculus andthe one of Fitting and Massacci for modal logic. Finally, we describe thesetableaux with -calculus formulas, thus reducing the satisfiability of eachof these logics to the satisfiability of the -calculus, resulting in ageneral 2EXP upper bound for satisfiability testing.Comment: arXiv admin note: text overlap with arXiv:2209.1037
The concept of relation in methodological individualism and holism: a reply to a functionalist critique
No full textIn an article entitled "Agency, functionalism and all that. A Sraffian view", published in the Journal of Philosophical Economics, Professor Cesaratto (2024) has proposed a functionalist methodology to study the relation between agency and structure. In doing so, he made some criticisms of an article of ours that had previously appeared in the same journal in issue XV, entitled "Towards a unity of sense: a critical analysis of the concept of relation in methodological individualism and holism in economics" (Ianulardo and Stella, 2022). We take Cesaratto's critique as an invitation to a dialogue on the methodology of the social sciences, and we would like to clarify some aspects in response to his critique. In essence, we clarify that our article consisted of two parts, which we can call pars destruens and pars construens, respectively. In the first, we show that while the determinate identity of the individual postulated by methodological individualism cannot stand without reference to difference, the relational methodology postulated by methodological holism requires its terms (i.e. individuals) to stand as a relation. In the second part, we make it clear that the sense of unity to which we have referred is not represented by an actual community, but by the drive towards unity that is common to all individuals when they intend to form a social entity (group, class, nation, party, institution etc.). Every unification makes it possible to shed new light on the moments that led to it. In this sense, we have spoken of a teleological perspective, since the end point allows us to re-signify the intermediate moments that led to it
Long increasing subsequences and non-algebraicity
No full textWe use a recent result of Alin Bostan to prove that the generating functionsof two infinite sequences of permutation classes are not algebraic.Comment: 9 page
On the Complexity of Target Set Selection in Simple Geometric Networks
No full textWe study the following model of disease spread in a social network. At first,all individuals are either infected or healthy. Next, in discrete rounds, thedisease spreads in the network from infected to healthy individuals such that ahealthy individual gets infected if and only if a sufficient number of itsdirect neighbors are already infected. We represent the social network as agraph. Inspired by the real-world restrictions in the current epidemic,especially by social and physical distancing requirements, we restrictourselves to networks that can be represented as geometric intersection graphs.We show that finding a minimal vertex set of initially infected individuals tospread the disease in the whole network is computationally hard, already onunit disk graphs. Hence, to provide some algorithmic results, we focusourselves on simpler geometric graph classes, such as interval graphs and gridgraphs.Comment: This is an extended and revised version of a preliminary conference report that was presented in WAW 202
Orbit-Finite-Dimensional Vector Spaces and Weighted Register Automata
No full textWe develop a theory of vector spaces spanned by orbit-finite sets. Using thistheory, we give a decision procedure for equivalence of weighted registerautomata, which are the common generalization of weighted automata and registerautomata for infinite alphabets. The algorithm runs in exponential time, and inpolynomial time for a fixed number of registers. As a special case, we candecide, with the same complexity, language equivalence for unambiguous registerautomata, which improves previous results in three ways: (a) we allow for ordercomparisons on atoms, and not just equality; (b) the complexity isexponentially better; and (c) we allow automata with guessing.Comment: Journal Version for TheoretiC