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Maximal and minimal dynamic Petri net slicing
No full textContext: Petri net slicing is a technique to reduce the size of a Petri netto ease the analysis or understanding of the original Petri net. Objective:Presenting two new Petri net slicing algorithms to isolate those places andtransitions of a Petri net (the slice) that may contribute tokens to one ormore places given (the slicing criterion). Method: The two algorithms proposedare formalized. The maximality of the first algorithm and the minimality of thesecond algorithm are formally proven. Both algorithms, together with threeother state-of-the-art algorithms, have been implemented and integrated into asingle tool so that we have been able to carry out a fair empirical evaluation.Results: Besides the two new Petri net slicing algorithms, a public, free, andopen-source implementation of five algorithms is reported. The results of anempirical evaluation of the new algorithms and the slices they produce are alsopresented. Conclusions: The first algorithm collects all places and transitionsthat may contribute tokens (in any computation) to the slicing criterion, whilethe second algorithm collects the places and transitions needed to fire theshortest transition sequence that contributes tokens to some place in theslicing criterion. Therefore, the net computed by the first algorithm canreproduce any computation that contributes tokens to any place of interest. Incontrast, the second algorithm loses this possibility, but it often produces amuch more reduced subnet (which still can reproduce some computations thatcontribute tokens to some places of interest). The first algorithm is provenmaximal, and the second one is proven minimal
The Opportunity Costs of Neoclassical Economics
No full textThe notion of "opportunity cost" has been neglected in economics. The reason is that any such measure of cost is invisible, unobservable, and untestable. Yet the so-called 'competitive ideal' in neoclassical theory is based on claims of decreasing returns and substitutional tradeoffs in production, consumption and social relations, and therewith an exclusive focus on scarcity in economics. Within this view, collusion is suspect: it raises prices, reduces sales, and so harms social welfare. This is the baseline emphasis of neoclassical microeconomic theory. The opportunity costs of this framework involve a significant loss of perspective on actual economic phenomena, the potential value of which may far exceed that of orthodoxy. Here are several reasons why. First, the real world is interdependent and not decomposable into parts: all we do initiates effects spreading outward forever on everything. Second, our interconnected environment calls for a network or systems conception of economics in which substitution and complementarities coexist in nondecomposable tangles, obviating any institutional claim for the efficiency of competition over cooperation. Third, if all long-term production occurs with increasing returns, then the nature of economic relations solely reflects substitution for physical goods in short-term contexts; all long-term material outputsas well as all intangible tradesexhibit a complementary connection to make cooperation efficient. Fourth, the unbounded character of economic effects suggests an analytical bound derived from our rational limits, since we cannot see the full range of outcomes stemming from our decisions: planning horizons so enter this scene. Such 'horizon effects' suggest another important distinction in economics of 'atoms, bits and wits,' where atoms (the realm of physical things) are only subject to substitution assumptions in the short run, but shift to complementary interaction for all longer horizons. For bits (the realm of transactions involving information and all intangible outputs) and wits (that of horizon effects), both are realms characterized by complementary relations, so also yielding an economics in which cooperative systems are efficient and where competition cannot but fail by restricting output, knowledge and truth, while promoting a myopic culture in a dangerous self-destruct mode. This is the 'opportunity cost' of neoclassical economics: a world hurtling into a self-destructive failure due to its myopic culture spawned by rivalry, blind to its own pathologies and encouraged by an economics dogmatically closed to realistic conceptions due to competitive frames wrongly imposed in complementary realms, such as in academics, ecology, ethics and organizational learning. These costs far exceed the value realized by this approach. The paper explores these failures in more detail and describes the horizonal theory that would have emerged from the 1930s debates on cost had Hicks not walked away from increasing returns and had Hirshleifer not promoted a false 'rescue' endorsed by Alchian in 1968, when he declared decreasing returns "a general and universally valid law." Because of 'The Hicksian Getaway' in 1939-and 'The Hirshleifer Rescue' in 1962a rigid orthodoxy in economics emerged that was resistant to any alternative views, seeing them as a threat to its unearned dominance instead of as an opportunity to engage in new learning. A (supposedly) 'scientific' community was thus transformed to a closed domain of adherents strongly opposed to open debate and discussion. The curious character of this unheralded situation deserves closer attention than it has gotten thus far. That is the primary aim of this paper
Ramanujan's Quarterly Reports
No full textThis is a faithful reproduction of Ramanujan's Quarterly Reports from a handwritten copy by T.A. Satagopan in 1925
On Pseudo bi-starlike functions related with Fibonacci numbers
No full textIn this paper we define a new subclass -bi-pseudo-starlike functionsof related to shell-like curves connected with Fibonacci numbers anddetermine the initial Taylor-Maclaurin coefficients and for Further we determine theFekete-Szeg\"{o} result for the function class and for special cases,corollaries are stated which some of them are new and have not been studied sofar.Comment: 11. arXiv admin note: text overlap with arXiv:1810.06216 by other author
Generalized curvature tensor and the hypersurfaces of the Hermitian manifold for the class of Kenmotsu type
No full textThis paper determined the components of the generalized curvature tensor forthe class of Kenmotsu type and established the mentioned class is{\eta}-Einstein manifold when the generalized curvature tensor is flat; theconverse holds true under suitable conditions. It also introduced the notion ofgeneralized {\Phi}-holomorphic sectional (G{\Phi}SH-) curvature tensor and thusfound the necessary and sufficient conditions for the class of Kenmotsu type tobe of constant G{\Phi}SH-curvature. In addition, the notion of{\Phi}-generalized semi-symmetric was introduced and its relationship with theclass of Kenmotsu type and {\eta}-Einstein manifold established. Furthermore,this paper generalized the notion of the manifold of constant curvature anddeduced its relationship with the aforementioned ideas. It finally showed thatthe class of Kenmotsu type exists as a hypersurface of the Hermitian manifoldand derived a relation between the components of the Riemannian curvaturetensors of the almost Hermitian manifold and its hypersurfaces
Full-deautonomisation of a class of second-order mappings in ancillary form
No full textWe present an application of the full-deautonomisation method to a class of secondorder mappings which, using an ancillary variable, can be cast into a form that greatly facilitates the study of their singularities. The ancillary approach was originally introduced to make it possible to construct discrete Painlevé equations associated with the affine Weyl group E (1) 8 by deautonomising a QRT mapping. The full-deautonomisation method has been shown to offer a practical technique for calculating the exact dynamical degree of a mapping, whereby allowing the detection of discrete integrability using only singularity analysis. We study the confinement property for a given singularity, for a wide class of mappings that includes the autonomous limit of the standard additive Painlevé equation with E (1) 8 symmetry. This leads to a class of non-autonomous mappings, which can be integrable or not, for which we obtain their exact dynamical degrees. The case of a non-confining singularity is also analysed and again we obtain the corresponding dynamical degrees
Stream processors and comodels
No full textIn 2009, Hancock, Pattinson and Ghani gave a coalgebraic characterisation ofstream processors drawing on ideas ofBrouwerian constructivism. Their stream processors have an intensionalcharacter; in this paper, we give a corresponding coalgebraic characterisationof extensional stream processors, i.e., the set of continuous functions. Our account sites both our result and that ofop. cit. within the apparatus of comodels for algebraic effects originatingwith Power-Shkaravska. Within this apparatus, the distinction betweenintensional and extensional equivalence for stream processors arises in thesame way as the the distinction between bisimulation and trace equivalence forlabelled transition systems and probabilistic generative systems
Data Layout from a Type-Theoretic Perspective
No full textThe specifics of data layout can be important for the efficiency offunctional programs and interaction with external libraries. In this paper, wedevelop a type-theoretic approach to data layout that could be used as a typedintermediate language in a compiler or to give a programmer more control. Ourstarting point is a computational interpretation of the semi-axiomatic sequentcalculus for intuitionistic logic that defines abstract notions of cells andaddresses. We refine this semantics so addresses have more structure to reflectpossible alternative layouts without fundamentally departing fromintuitionistic logic. We then add recursive types and explore example programsand properties of the resulting language.Comment: Invited paper for MFPS 2022 special issue of ENTIC
Skew characteristic polynomial of graphs and embedded graphs
No full textWe introduce a new one-variable polynomial invariant of graphs, which we callthe skew characteristic polynomial. For an oriented simple graph, this is justthe characteristic polynomial of its anti-symmetric adjacency matrix. Fornonoriented simple graphs the definition is different, but for a certain classof graphs (namely, for intersection graphs of chord diagrams), it gives thesame answer if we endow such a graph with an orientation induced by the chorddiagram. We prove that this invariant satisfies Vassiliev's -term relationsand determines therefore a finite type knot invariant. We investigate thebehaviour of the polynomial with respect to the Hopf algebra structure on thespace of graphs and show that it takes a constant value on any primitiveelement in this Hopf algebra. We also provide a two-variable extension of theskew characteristic polynomial to embedded graphs and delta-matroids. The-term relations for the extended polynomial prove that it determines afinite type invariant of multicomponent links
La reconnaissance de l'écriture pour les manuscrits documentaires du Moyen Âge
No full textHandwritten Text Recognition (HTR) techniques aim to accurately recognize sequences of characters in input manuscript images by training artificial intelligence models to capture historical writing features. Efficient HTR models can transform digitized manuscript collections into indexed and quotable corpora, providing valuable research insight for various historical inquiries. However, several challenges must be addressed, including the scarcity of relevant training corpora, the consequential variability introduced by different scribal hands and writing scripts, and the complexity of page layouts. This paper presents two models and one cross-model approach for automatic transcription of Latin and French medieval documentary manuscripts, particularly charters and registers, written between the 12th and 15th centuries and classified into two major writing scripts: Textualis (from the late-11th to 13th century) and Cursiva (from the 13th to the 15th century). The architecture of the models is based on a Convolutional Recurrent Neural Network (CRNN) coupled with a Connectionist Temporal Classification (CTC) loss. The training and evaluation of the models, involving 120k lines of text and almost 1M tokens, were conducted using three available ground-truth corpora : The e-NDP corpus, the Alcar-HOME database and the Himanis project. This paper describes the training architecture and corpora used, while discussing the main training challenges, results, and potential applications of HTR techniques on medieval documentary manuscripts