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An Alternative Proof for the Expected Number of Distinct Consecutive Patterns in a Random Permutation
No full textLet be a uniformly chosen random permutation on . Using ananalysis of the probability that two overlapping consecutive -permutationsare order isomorphic, the authors of a recent paper showed that the expectednumber of distinct consecutive patterns of all lengths in is as . This exhibited the factthat random permutations pack consecutive patterns near-perfectly. We useentirely different methods, namely the Stein-Chen method of Poissonapproximation, to reprove and slightly improve their result.Comment: 11 page
Une évaluation expérimentale de choix des paramètres de prévisions SSA
No full textSix time series related to atmospheric phenomena are used as inputs for experiments offorecasting with singular spectrum analysis (SSA). Existing methods for SSA parametersselection are compared throughout their forecasting accuracy relatively to an optimal aposteriori selection and to a naive forecasting methods. The comparison shows that awidespread practice of selecting longer windows leads often to poorer predictions. It alsoconfirms that the choices of the window length and of the grouping are essential. Withthe mean error of rainfall forecasting below 1.5%, SSA appears as a viable alternative forhorizons beyond two weeks.Six séries temporelles ont servi pour des évaluations expérimentales, en fonction des paramètres choisis, d'exactitude de prévisions de phénomènes atmosphériques par la méthode d'analyse de spectre singulier (SSA). Les méthodes les plus connues de sélection automatique des ces paramètres ont été comparées avec une sélection optimale a posteriori et des méthodes de prévision naïves. On constate notamment qu'une pratique répandue d'utiliser des fenêtres plus larges conduit souvent à des prévisions de médiocre qualité. On confirme aussi que le choix du groupement est capital. Avec l'erreur moyenne observée en dessous de 1,5% de prévisions de pluviométrie pour des horizons au delà de deux semaines, la SSA apparaît comme une alternative viable à d'autres méthodes de prévision
Exploring Data Provenance in Handwritten Text Recognition Infrastructure: Sharing and Reusing Ground Truth Data, Referencing Models, and Acknowledging Contributions. Starting the Conversation on How We Could Get It Done
No full textThis paper discusses best practices for sharing and reusing Ground Truth in Handwritten Text Recognition infrastructures, as well as ways to reference and acknowledge contributions to the creation and enrichment of data within these systems. We discuss how one can place Ground Truth data in a repository and, subsequently, inform others through HTR-United. Furthermore, we want to suggest appropriate citation methods for ATR data, models, and contributions made by volunteers. Moreover, when using digitised sources (digital facsimiles), it becomes increasingly important to distinguish between the physical object and the digital collection. These topics all relate to the proper acknowledgement of labour put into digitising, transcribing, and sharing Ground Truth HTR data. This also points to broader issues surrounding the use of machine learning in archival and library contexts, and how the community should begin to acknowledge and record both contributions and data provenance
Terminal Embeddings in Sublinear Time
No full textRecently (Elkin, Filtser, Neiman 2017) introduced the concept of a {\itterminal embedding} from one metric space to another with aset of designated terminals . Such an embedding is said to havedistortion if is the smallest value such that there exists aconstant satisfying \begin{equation*} \forall x\in T\ \forall q\in X,\ C d_X(x, q) \le d_Y(f(x), f(q)) \le C \rhod_X(x, q) . \end{equation*} When are both Euclidean metrics with being -dimensional,recently (Narayanan, Nelson 2019), following work of (Mahabadi, Makarychev,Makarychev, Razenshteyn 2018), showed that distortion isachievable via such a terminal embedding with for. This generalizes the Johnson-Lindenstrauss lemma, which onlypreserves distances within and not to from the rest of space. Thedownside of prior work is that evaluating their embedding on some required solving a semidefinite program with constraints in~ variables and thus required some superlinear runtime. Our main contribution in this work is to give a newdata structure for computing terminal embeddings. We show how to pre-process to obtain an almost linear-space data structure that supports computing theterminal embedding image of any in sublinear time . To accomplish this, we leverage toolsdeveloped in the context of approximate nearest neighbor search
Optimal impulsive control of coffee berry borers in a berry age-structured epidemiological model
No full textThe coffee berry borer (CBB) Hypothenemus hampei (Coleoptera: Scolytidae) is the most important insect pest affecting coffee production worldwide and generating huge economic losses. As most of its life cycle occurs inside the coffee berry, its control is extremely difficult. To tackle this issue, we solve an optimal control problem based on a berry age-structured dynamical model that describes the infestation dynamics of coffee berries by CBB during a cropping season. This problem consists in applying a bio-insecticide at discrete times in order to maximise the economic profit of healthy coffee berries, while minimising the CBB population for the next cropping season. We derive analytically the first-order necessary optimality conditions of the control problem. Numerical simulations are provided to illustrate the effectiveness of the optimal control strategy
Stabilized profunctors and stable species of structures
No full textWe introduce a bicategorical model of linear logic which is a novel variationof the bicategory of groupoids, profunctors, and natural transformations. Ourmodel is obtained by endowing groupoids with additional structure, called akit, to stabilize the profunctors by controlling the freeness of the groupoidaction on profunctor elements. The theory of generalized species of structures,based on profunctors, is refined to a new theory of \emph{stable species} ofstructures between groupoids with Boolean kits. Generalized species are incorrespondence with analytic functors between presheaf categories; in ourrefined model, stable species are shown to be in correspondence withrestrictions of analytic functors, which we characterize as being stable, tofull subcategories of stabilized presheaves. Our motivating example is theclass of finitary polynomial functors between categories of indexed sets, alsoknown as normal functors, that arises from kits enforcing free actions. We showthat the bicategory of groupoids with Boolean kits, stable species, and naturaltransformations is cartesian closed. This makes essential use of the logicalstructure of Boolean kits and explains the well-known failure of cartesianclosure for the bicategory of finitary polynomial functors between categoriesof set-indexed families and cartesian natural transformations. The paperadditionally develops the model of classical linear logic underlying thecartesian closed structure and clarifies the connection to stable domaintheory
Maker-Breaker domination number for Cartesian products of path graphs and
No full textWe study the Maker-Breaker domination game played by Dominator and Staller onthe vertex set of a given graph. Dominator wins when the vertices he hasclaimed form a dominating set of the graph. Staller wins if she makes itimpossible for Dominator to win, or equivalently, she is able to claim somevertex and all its neighbours. Maker-Breaker domination number () of a graph is defined to be the minimum number ofmoves for Dominator to guarantee his winning when he plays first (second). Weinvestigate these two invariants for the Cartesian product of any two graphs.We obtain upper bounds for the Maker-Breaker domination number of the Cartesianproduct of two arbitrary graphs. Also, we give upper bounds for theMaker-Breaker domination number of the Cartesian product of the complete graphwith two vertices and an arbitrary graph. Most importantly, we prove that for , equals , , , for , , and , respectively. For the disjoint union of s, we show that (), andthat equals ,, for , , and , respectively
Degree growth of lattice equations defined on a 3x3 stencil
No full textWe study complexity in terms of degree growth of one-component latticeequations defined on a stencil. The equations include two in Hirotabilinear form and the Boussinesq equations of regular, modified and Schwarziantype. Initial values are given on a staircase or on a corner configuration anddepend linearly or rationally on a special variable, for example, in which case we count the degree in of the iterates. Known integrable cases have linear growth if only one initialvalues contains , and quadratic growth if all initial values contain .Even a small deformation of an integrable equation changes the degree growthfrom polynomial to exponential, because the deformation will changefactorization properties and thereby prevent cancellations.Comment: 19 pages, to appear in "Open Communications in Nonlinear Mathematical Physics", Special Issue in Memory of Decio Lev
Negative flows and non-autonomous reductions of the Volterra lattice
No full textWe study reductions of the Volterra lattice corresponding to stationaryequations for the additional, noncommutative subalgebra of symmetries. It isshown that, in the case of general position, such a reduction is equivalent tothe stationary equation for a sum of the scaling symmetry and the negativeflows, and is written as -component difference equations of thePainlev\'e type generalizing the dP and dP equations. For thesereductions, we present the isomonodromic Lax pairs and derive the B\"acklundtransformations which form the lattice.Comment: 17 pages. This article is part of an OCNMP Special Issue in Memory of Professor Decio Lev
Integrable discretization of recursion operators and unified bilinear forms to soliton hierarchies
No full textIn this paper, we give a procedure for discretizing recursion operators byutilizing unified bilinear forms within integrable hierarchies. To illustratethis approach, we present unified bilinear forms for both the AKNS hierarchyand the KdV hierarchy, derived from their respective recursion operators.Leveraging the inherent connection between soliton equations and theirauto-B\"acklund transformations, we discretize the bilinear integrablehierarchies and derive discrete recursion operators. These discrete recursionoperators exhibit convergence towards the original continuous forms whensubjected to a standard limiting process.Comment: 16Page