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    Strongly Sublinear Algorithms for Testing Pattern Freeness

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    For a permutation π:[k][k]\pi:[k] \to [k], a function f:[n]Rf:[n] \to \mathbb{R}contains a π\pi-appearance if there exists 1i1<i2<<ikn1 \leq i_1 < i_2 < \dots < i_k\leq n such that for all s,t[k]s,t \in [k], f(is)<f(it)f(i_s) < f(i_t) if and only ifπ(s)<π(t)\pi(s) < \pi(t). The function is π\pi-free if it has no π\pi-appearances.In this paper, we investigate the problem of testing whether an input functionff is π\pi-free or whether ff differs on at least εn\varepsilon n valuesfrom every π\pi-free function. This is a generalization of the well-studiedmonotonicity testing and was first studied by Newman, Rabinovich,Rajendraprasad and Sohler (Random Structures and Algorithms 2019). We show thatfor all constants kNk \in \mathbb{N}, ε(0,1)\varepsilon \in (0,1), and permutationπ:[k][k]\pi:[k] \to [k], there is a one-sided error ε\varepsilon-testing algorithmfor π\pi-freeness of functions f:[n]Rf:[n] \to \mathbb{R} that makesO~(no(1))\tilde{O}(n^{o(1)}) queries. We improve significantly upon the previous bestupper bound O(n11/(k1))O(n^{1 - 1/(k-1)}) by Ben-Eliezer and Canonne (SODA 2018). Ouralgorithm is adaptive, while the earlier best upper bound is known to be tightfor nonadaptive algorithms.Comment: 28 pages, 2 figures; We thank anonymous reviewers for comments that helped us significantly improve the presentatio

    Diagonal F-splitting and Symbolic Powers of Ideals

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    Let JJ be any ideal in a strongly FF-regular, diagonally FF-split ring RRessentially of finite type over an FF-finite field. We show that Js+tτ(Jsϵ)τ(Jtϵ)J^{s+t}\subseteq \tau(J^{s - \epsilon}) \tau(J^{t-\epsilon}) for all s,t,ϵ>0s, t, \epsilon> 0 for which the formula makes sense. We use this to show a number of novelcontainments between symbolic and ordinary powers of prime ideals in thissetting, which includes all determinantal rings and a large class of toricrings in positive characteristic. In particular, we show that P(2hn)PnP^{(2hn)}\subseteq P^n for all prime ideals PP of height hh in such rings.Comment: Copy edited and formatted in the EpiGA journal's styleshee

    One Belt One Road : une nouvelle architecture des flux mondiaux sous influence chinoise

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    China’s One Belt One Road (OBOR) strategy was launched in September 2013 by Xi Jinping. It is a global transports infrastructure strategy that covers both land (road and rail) and sea roads by connecting ports from Asia to Europe through Africa. With a budget of more than 1,400 billion dollars, it is one of the most important strategies on a global scale. The purpose of this article is firstly to characterize this strategy, from its foundations to the actual enactment modalities. It is then to propose an interpretation based on a Braudelian reading in terms of world economy and hegemonic posture leading to the emergence of new asian global value chains.La stratégie chinoise One Belt One Road (OBOR) a été lancée en septembre 2013 par Xi Jinping. Il s’agit d’une stratégie globale de développement d’infrastructures, notamment de transport, et de coopérations. Elle concerne aussi bien les voies terrestres (routes et fer) que les voies maritimes par la connexion de ports depuis l’Asie jusqu’à l’Europe en passant par l’Afrique. Dotée d’un budget de plus de 1 400 milliards de dollars, elle est l’une des plus importantes stratégies initiées à l’échelle mondiale. L’objet de cet article, écrit en 2018, est d’abord de caractériser cette stratégie, depuis ses fondements jusqu’aux modalités de sa mise en acte. Il s’agit ensuite d’en proposer une interprétation fondée sur une lecture braudélienne en termes d’économie-monde et de posture hégémonique conduisant à l’émergence de nouvelles global value chains asiatiques

    Partial-dual genus polynomial as a weight system

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    We prove that the partial-dual genus polynomial considered as a function onchord diagrams satisfies the four-term relation. Thus it is a weight systemfrom the theory of Vassiliev knot invariants.Comment: Final version for publication in Communications in Mathematic

    On the primitive subspace of Lando framed graph bialgebra

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    Lando framed graph bialgebra is generated by framed graphs modulo 4-termrelations. We provide an explicit set of generators of its primitive subspaceand a description of the set of relations between the generators. We alsodefine an operation of leaf addition that endows the primitive subspace ofLando algebra with a structure of a module over the ring of polynomials in onevariable and construct a 4-invariant that satisfies a simple identity withrespect to the vertex-multiplication.Comment: 12 pages. Published versio

    Quantitative stability estimate for the inverse coefficients problem in linear elasticity

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    In this article we consider the inverse problem of reconstructing piece-wise Lamé coefficients from boundary measurements. We reformulate the inverse problem into a minimization one using a Kohn-Vogelius type functional. We study the stability of the parameters when the jump of the discontinuity is perturbed. Using tools of shape calculus, we give a quantitative stability result for local optimal solution.Dans cet article, nous considérons le problème inverse de reconstruction des coefficients de Lamé constants par morceaux à partir de mesures au bord. Nous reformulons le problème inverse en un problème de minimisation utilisant une fonctionnelle de type Kohn-Vogelius. Nous étudions la stabilité des paramètres lorsque le saut de la discontinuité est perturbé. En utilisant les outils du calcul de forme, nous donnons un résultat de stabilité quantitative pour une la solution optimale locale

    Foundations of probability-raising causality in Markov decision processes

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    This work introduces a novel cause-effect relation in Markov decisionprocesses using the probability-raising principle. Initially, sets of states ascauses and effects are considered, which is subsequently extended to regularpath properties as effects and then as causes. The paper lays the mathematicalfoundations and analyzes the algorithmic properties of these cause-effectrelations. This includes algorithms for checking cause conditions given aneffect and deciding the existence of probability-raising causes. As thedefinition allows for sub-optimal coverage properties, quality measures forcauses inspired by concepts of statistical analysis are studied. These includerecall, coverage ratio and f-score. The computational complexity for findingoptimal causes with respect to these measures is analyzed.Comment: arXiv admin note: substantial text overlap with arXiv:2201.0876

    All about unambiguous polynomial closure

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    We study a standard operator on classes of languages: unambiguous polynomialclosure. We prove that for every class C of regular languages satisfying mildproperties, the membership problem for its unambiguous polynomial closureUPol(C) reduces to the same problem for C. We also show that unambiguouspolynomial closure coincides with alternating left and right deterministicclosure. Moreover, we prove that if additionally C is finite, the separationand covering problems are decidable for UPol(C). Finally, we present anoverview of the generic logical characterizations of the classes built usingunambiguous polynomial closure

    Center of Mass Technique and Affine Geometry

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    The 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 protected nodes in exponential recursive trees

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    The exponential recursive trees model several kinds of networks. At each step of growing of these trees, each node independently attracts a new node with probability p, or fails to do with probability 1 − p. Here, we investigate the number of protected nodes, total path length of protected nodes, and a mean study of the protected node profile of such trees

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