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On a general divisor problem related to a certain Dedekind zeta-function over a specific sequence of positive integers
No full textWe investigate the average behavior of coefficients of the Dirichlet series of positive integral power of the Dedekind zeta-function of a non-normal cubic extension of over a certain sequence of positive integers. More precisely, we prove an asymptotic formula with an error term for the sumwhere
Incorporating Crowdsourced Annotator Distributions into Ensemble Modeling to Improve Classification Trustworthiness for Ancient Greek Papyri
No full textPerforming classification on noisy, crowdsourced image datasets can provechallenging even for the best neural networks. Two issues which complicate theproblem on such datasets are class imbalance and ground-truth uncertainty inlabeling. The AL-ALL and AL-PUB datasets - consisting of tightly cropped,individual characters from images of ancient Greek papyri - are stronglyaffected by both issues. The application of ensemble modeling to such datasetscan help identify images where the ground-truth is questionable and quantifythe trustworthiness of those samples. As such, we apply stacked generalizationconsisting of nearly identical ResNets with different loss functions: oneutilizing sparse cross-entropy (CXE) and the other Kullback-Liebler Divergence(KLD). Both networks use labels drawn from a crowd-sourced consensus. Thisconsensus is derived from a Normalized Distribution of Annotations (NDA) basedon all annotations for a given character in the dataset. For the secondnetwork, the KLD is calculated with respect to the NDA. For our ensemble model,we apply a k-nearest neighbors model to the outputs of the CXE and KLDnetworks. Individually, the ResNet models have approximately 93% accuracy,while the ensemble model achieves an accuracy of > 95%, increasing theclassification trustworthiness. We also perform an analysis of the Shannonentropy of the various models' output distributions to measure classificationuncertainty. Our results suggest that entropy is useful for predicting modelmisclassifications
High order multiscale analysis of discrete integrable equations
No full textIn this article we present the results obtained applying the multiple scale expansion up to the order to a dispersive multilinear class of equations on a square lattice depending on 13 parameters. We show that the integrability conditions given by the multiple scale expansion give rise to 4 nonlinear equations, 3 of which seem to be new, depending at most on 2 parameters
Correctness Notions for Petri Nets with Identifiers
No full textA model of an information system describes its processes and how resourcesare involved in these processes to manipulate data objects. This paper presentsan extension to the Petri nets formalism suitable for describing informationsystems in which states refer to object instances of predefined types andresources are identified as instances of special object types. Severalcorrectness criteria for resource- and object-aware information systems modelsare proposed, supplemented with discussions on their decidability forinteresting classes of systems. These new correctness criteria can be seen asgeneralizations of the classical soundness property of workflow modelsconcerned with process control flow correctness
Constructive Separations and Their Consequences
No full textFor a complexity class and language , a constructive separation of gives an efficient algorithm (also called a refuter) to findcounterexamples (bad inputs) for every -algorithm attempting to decide .We study the questions: Which lower bounds can be made constructive? What arethe consequences of constructive separations? We build a case that"constructiveness" serves as a dividing line between many weak lower bounds weknow how to prove, and strong lower bounds against , , and . Putanother way, constructiveness is the opposite of a complexity barrier: it is aproperty we want lower bounds to have. Our results fall into three broadcategories. 1. Our first set of results shows that, for many well-known lower boundsagainst streaming algorithms, one-tape Turing machines, and query complexity,as well as lower bounds for the Minimum Circuit Size Problem, making theselower bounds constructive would imply breakthrough separations ranging from to even . 2. Our second set of results shows that for most major open problems in lowerbounds against , , and , including , ,, , and , any proof of the separationwould further imply a constructive separation. Our results generalize earlierresults for [Gutfreund, Shaltiel, and Ta-Shma, CCC 2005] and [Dolev, Fandina and Gutfreund, CIAC 2013]. 3. Our third set of results shows that certain complexity separations cannotbe made constructive. We observe that for all super-polynomially growingfunctions , there are no constructive separations for detecting high-time Kolmogorov complexity (a task which is known to be not in ) fromany complexity class, unconditionally.Comment: Abstract shortened to fit arXiv requirement
Center of Mass Technique and Affine Geometry
No full textThe notion of center of mass, which is very useful in kinematics, proves tobe very handy in geometry (see [1]-[2]). Countless applications of center ofmass to geometry go back to Archimedes. Unfortunately, the center of masscannot be defined for sets whose total mass equals zero. In the paper weimprove this disadvantage and assign to an n-dimensional affine space L overany field k the (n+1)-dimensional vector space over the field k of weightypoints and mass dipoles in L. In this space, the sum of weighted points withnonzero total mass is equal to the center of mass of these points equipped withtheir total mass. We present several interpretations of the space of weightypoints and mass dipoles in L, and a couple of its applications to geometry. Thepaper is self-contained and is accessible for undergraduate students.Comment: 43 pages, 6 figure
On the Satisfiability of Local First-Order Logics with Data
No full textWe study first-order logic over unordered structures whose elements carry afinite number of data values from an infinite domain. Data values can becompared wrt.\ equality. As the satisfiability problem for this logic isundecidable in general, we introduce a family of local fragments. They restrictquantification to the neighbourhood of a given reference point that is boundedby some radius. Our first main result establishes decidability of thesatisfiability problem for the local radius-1 fragment in presence of one"diagonal relation". On the other hand, extending the radius leads toundecidability. In a second part, we provide the precise decidability andcomplexity landscape of the satisfiability problem for the existentialfragments of local logic, which are parameterized by the number of data valuescarried by each element and the radius of the considered neighbourhoods.Altogether, we draw a landscape of formalisms that are suitable for thespecification of systems with data and open up new avenues for future research
Semantics, Specification Logic, and Hoare Logic of Exact Real Computation
No full textWe propose a simple imperative programming language, ERC, that featuresarbitrary real numbers as primitive data type, exactly. Equipped with adenotational semantics, ERC provides a formal programming language-theoreticfoundation to the algorithmic processing of real numbers. In order to capturemulti-valuedness, which is well-known to be essential to real numbercomputation, we use a Plotkin powerdomain and make our programming languagesemantics computable and complete: all and only real functions computable incomputable analysis can be realized in ERC. The base programming languagesupports real arithmetic as well as implicit limits; expansions supportadditional primitive operations (such as a user-defined exponential function).By restricting integers to Presburger arithmetic and real coercion to the`precision' embedding , we arrive at afirst-order theory which we prove to be decidable and model-complete. Based onsaid logic as specification language for preconditions and postconditions, weextend Hoare logic to a sound (w.r.t. the denotational semantics) andexpressive system for deriving correct total correctness specifications.Various examples demonstrate the practicality and convenience of our languageand the extended Hoare logic
Expertise économique et grandes infrastructures : l’analyse coûts- avantages du Lyon-Turin de 2019
No full textThis paper reviews the contribution of experts to the appraisal of large infrastructures, looking at the evaluation performed in 2019 in Italy by the Ministry of Infrastructures and Transports on the Lyon-Turin railway project. This evaluation had been initiated in a particular context, linked to a visible policy agenda and while the construction of the tunnel had already begun. The appraisal has produced surprising results, mostly counterintuitive and heavily criticized. We analyse these results and show how they can be valid, in that they would not result from inconsistency in the method but from the peculiar features of the project (low initial demand, high mode transfer compared with initial traffic, high road tax and toll levels). We also check the validity of some paradoxical results of the assessment. Moreover, the public debate has been made more difficult due to an inconsistency in EU evaluation Guidelines. Also, we analyse mechanisms that affect the credibility of experts and we find that the influence of experts in the public debate has little to see with the inherent consistency of the methods used.Cet article examine la contribution des experts à l’évaluation économique des grands projets à la lumière de l’évaluation du Lyon-Turin réalisée en Italie en 2019. Cette évaluation est née dans un contexte particulier caractérisé par une commande politique manifeste et pour un chantier entamé. L’évaluation, globalement négative, a produit des résultats inattendus, contre-intuitifs et fortement critiqués. Nous analysons ces résultats et mettons en évidence qu’ils apparaissent valides et dépendent des caractéristiques extrêmement particulières du projet : faible trafic initial, forte hypothèse de report modal, fiscalité et péages routiers élevés. Nous expliquons aussi certains résultats paradoxaux de l’analyse. En outre, le débat technique a été rendu particulièrement difficile en raison d’une incohérence dans les modalités de calcul préconisées par le Guide méthodologique de l’Union Européenne. Nous analysons ensuite les mécanismes de légitimation et de délégitimation de l’expertise économique à l’œuvre dans cet épisode. Une conclusion est que ce n’est pas la qualité du calcul économique qui en détermine l’acceptation et l’influence dans le débat public
Values That Are Explicitly Present in Fairy Tales: Comparing Samples from German, Italian and Portuguese Traditions
No full textLooking at how social values are represented in fairy tales can give insightsabout the variations in communication of values across cultures. We study howvalues are communicated in fairy tales from Portugal, Italy and Germany using atechnique called word embedding with a compass to quantify vocabularydifferences and commonalities. We study how these three national traditionsdiffer in their explicit references to values. To do this, we specify a list ofvalue-charged tokens, consider their word stems and analyse the distancebetween these in a bespoke pre-trained Word2Vec model. We triangulate andcritically discuss the validity of the resulting hypotheses emerging from thisquantitative model. Our claim is that this is a reusable and reproduciblemethod for the study of the values explicitly referenced in historical corpora.Finally, our preliminary findings hint at a shared cultural understanding andthe expression of values such as Benevolence, Conformity, and Universalismacross the studied cultures, suggesting the potential existence of apan-European cultural memory.Comment: In Proceedings of the Joint 3rd International Conference on Natural Language Processing for Digital Humanities and 8th International Workshop on Computational Linguistics for Uralic Language