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We study the limiting behavior of the eigenvalues of KreinFellerOperators with respect to weakly convergent probability measures. Therefore, we give a representation of the eigenvalues as zeros of measure theoretic sine functions. Further, we make a proposition about the limiting behavior of the previously determined eigenfunctions. With the main results we finally determine the speed of convergence of eigenvalues and functions for sequences which converge to invariant measures on the Cantor set.
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This is a review of the geometry of quantum states using elementary methods and pictures. Quantum states are represented by a convex body, often in high dimensions. In the case of nqubits, the dimension is exponentially large in n. The space of states can be visualized, to some extent, by its simple cross sections: Regular simplexes, balls and hyperoctahedra. When the dimension gets large there is a precise sense in which the space of states resembles, almost in every direction, a ball. The ball turns out to be a ball of rather low purity states. We also address some of the corresponding, but harder, geometric properties of separable and entangled states and entanglement witnesses.
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This is a review of the geometry of quantum states using elementary methods and pictures. Quantum states are represented by a convex body, often in high dimensions. In the case of nqubits, the dimension is exponentially large in n. The space of states can be visualized, to some extent, by its simple cross sections: Regular simplexes, balls and hyperoctahedra. When the dimension gets large there is a precise sense in which the space of states resembles, almost in every direction, a ball. The ball turns out to be a ball of rather low purity states. We also address some of the corresponding, but harder, geometric properties of separable and entangled states and entanglement witnesses.
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An anonymous reader quotes a report from NBC New York: Colin Kroll, the cofounder of HQ Trivia and Vine, died of an accidental overdose, the city's medical examiner announced Tuesday. According to the autopsy results, Kroll died of "acute intoxication due to the combined effects of fentanyl, fluoroisobutyryl fentanyl, heroin, and cocaine." Kroll, 34, was found dead in his SoHo, Manhattan, apartment on Dec. 16, 2018. Police responded to a 911 call for a welfare check at the Spring Street apartment where they found Kroll unconscious and unresponsive in a bedroom of the apartment, a New York Police Department spokesman previously told NBC News. Kroll was named the chief executive of HQ Trivia, a phonebased trivia platform, in September. Prior to that, Kroll cofounded Vine, the popular shortform video service acquired in 2012 by Twitter. Vine was discontinued four years later.
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We construct a family of $(2,n)$almost Grassmannian structures of regularity $C^1$, each admitting a oneparameter group of strongly essential automorphisms, and each not flat on any neighborhood of the higherorder fixed point. This shows that Theorem 1.3 of [9] does not hold assuming only $C^1$ regularity of the structure (see also [2, Prop 3.5]).
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We describe the possible linear actions of a cyclic group $G = \mathbb{Z} /n$ on a complex torus, using the cyclotomic exact sequence for the group algebra $\mathbb{Z} [G]$. The main application is devoted to a structure theorem for BagneraDe Franchis Manifolds, but we also give an application to hypergeometric integrals.
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Risk estimation is at the core of many learning systems. The importance of this problem has motivated researchers to propose different schemes, such as cross validation, generalized cross validation, and Bootstrap. The theoretical properties of such estimates have been extensively studied in the lowdimensional settings, where the number of predictors $p$ is much smaller than the number of observations $n$. However, a unifying methodology accompanied with a rigorous theory is lacking in highdimensional settings. This paper studies the problem of risk estimation under the highdimensional asymptotic setting $n,p \rightarrow \infty$ and $n/p \rightarrow \delta$ ($\delta$ is a fixed number), and proves the consistency of three risk estimates that have been successful in numerical studies, i.e., leaveoneout cross validation (LOOCV), approximate leaveoneout (ALO), and approximate message passing (AMP)based techniques. A corner stone of our analysis is a bound that we obtain on the dis
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In this article, we introduce Brownian motion on stable looptrees using resistance techniques. We prove an invariance principle characterising it as the scaling limit of random walks on discrete looptrees, and prove precise local and global bounds on its heat kernel. We also conduct a detailed investigation of the volume growth properties of stable looptrees, and show that the random volume and heat kernel fluctuations are locally loglogarithmic, and globally logarithmic around leading terms of $r^{\alpha}$ and $t^{\frac{\alpha}{\alpha + 1}}$ respectively. These volume fluctuations are the same order as for the Brownian continuum random tree, but the upper volume fluctuations (and corresponding lower heat kernel fluctuations) are different to those of stable trees.
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Statistics has made tremendous advances since the times of Fisher, Neyman, Jeffreys, and others, but the fundamental questions about probability and inference that puzzled our founding fathers still exist and might even be more relevant today. To overcome these challenges, I propose to look beyond the two dominating schools of thought and ask what do scientists need out of statistics, do the existing frameworks meet these needs, and, if not, how to fill the void? To the first question, I contend that scientists seek to convert their data, posited statistical model, etc., into calibrated degrees of belief about quantities of interest. To the second question, I argue that any framework that returns additive beliefs, i.e., probabilities, necessarily suffers from false confidencecertain false hypotheses tend to be assigned high probabilityand, therefore, risks making systematically misleading conclusions. This reveals the fundamental importance of nonadditive beliefs in the context
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Cloud providers have recently introduced lowpriority machines to reduce the cost of computations. Exploiting such opportunity for machine learning tasks is challenging inasmuch as lowpriority machines can elastically leave (through preemption) and join the computation at any time. In this paper, we design a new technique called coded elastic computing enabling distributed machine learning computations over elastic resources. The proposed technique allows machines to transparently leave the computation without sacrificing the algorithmlevel performance, and, at the same time, flexibly reduce the workload at existing machines when new machines join the computation. Thanks to the redundancy provided by encoding, our approach is able to achieve similar computational cost as the original (uncoded) method when all machines are present; the cost gracefully increases when machines are preempted and reduces when machines join. We test the performance of the proposed technique on two miniben
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We study the longterm qualitative behavior of randomly perturbed dynamical systems. More specifically, we look at limit cycles of certain stochastic differential equations (SDE) with Markovian switching, in which the process switches at random times among different systems of SDEs, when the switching is fast varying and the diffusion (white noise) term is slowly changing. The system is modeled by $$ dX^{\varepsilon,\delta}(t)=f(X^{\varepsilon,\delta}(t), \alpha^\varepsilon(t))dt+\sqrt{\delta}\sigma(X^{\varepsilon,\delta}(t), \alpha^\varepsilon(t))dW(t) , \ X^\varepsilon(0)=x, $$ where $\alpha^\varepsilon(t)$ is a finite state space, Markov chain with generator $Q/\varepsilon=\big(q_{ij}/\varepsilon\big)_{m_0\times m_0}$ with $Q$ being irreducible. The relative changing rates of the switching and the diffusion are highlighted by the two small parameters $\varepsilon$ and $\delta$. We associate to the system the averaged ordinary differential equation (ODE) \[ d\bar X(t)=\bar f(\bar X(t
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In this paper we consider minimizers for nonlocal energy functionals generalizing elastic energies that are connected with the theory of peridynamics \cite{Silling2000} or nonlocal diffusion models \cite{Rossi}. We derive nonlocal versions of the EulerLagrange equations under two sets of growth assumptions for the integrand. Existence of minimizers is shown for integrands with joint convexity (in the function and nonlocal gradient components). By using the convolution structure we show regularity of solutions for certain EulerLagrange equations. No growth assumptions are needed for the existence and regularity of minimizers results, in contrast with the classical theory.
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It is known that there exist CalabiYau structures on the complexifications of symmetric spaces of compact type. In this paper, we describe the CalabiYau structures of the complexified symmetric spaces in terms of the Schwarz's theorem in detail. We consider the case where the CalabiYau structure arises from the Riemannian metric corresponding to the Stenzel metric. In the complexified symmetric spaces equipped with such a CalabiYau structure, we give constructions of special Lagrangian submanifolds of any phase which are invariant under the actions of symmetric subgroups of the isometry group of the original symmetric space of compact type.
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To increase the reliability of simulations by particle methods for incompressible viscous flow problems, convergence studies and improvements of accuracy are considered for a fully explicit particle method for incompressible NavierStokes equations. The explicit particle method is based on a penalty problem, which converges theoretically to the incompressible NavierStokes equations, and is discretized in space by generalized approximate operators defined as a wider class of approximate operators than those of the smoothed particle hydrodynamics (SPH) and moving particle semiimplicit (MPS) methods. By considering an analytical derivation of the explicit particle method and truncation error estimates of the generalized approximate operators, sufficient conditions of convergence are conjectured.Under these conditions, the convergence of the explicit particle method is confirmed by numerically comparing errors between exact and approximate solutions. Moreover, by focusing on the trunca
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Herein, we focus on explicit constructions of $\ell\times\ell$ binary kernels with small scaling exponent for $\ell \le 64$. In particular, we exhibit a sequence of binary linear codes that approaches capacity on the BEC with quasilinear complexity and scaling exponent $\mu < 3$. To the best of our knowledge, such a sequence of codes was not previously known to exist. The principal challenges in establishing our results are twofold: how to construct such kernels and how to evaluate their scaling exponent. In a single polarization step, an $\ell\times\ell$ kernel $K_\ell$ transforms an underlying BEC into $\ell$ bitchannels $W_1,W_2,\ldots,W_\ell$. The erasure probabilities of $W_1,W_2,\ldots,W_\ell$, known as the polarization behavior of $K_\ell$, determine the resulting scaling exponent $\mu(K_\ell)$. We first introduce a class of selfdual binary kernels and prove that their polarization behavior satisfies a strong symmetry property. This reduces the problem of constructing $K_\
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A twotype version of the frog model on $\mathbb{Z}^d$ is formulated, where active type $i$ particles move according to lazy random walks with probability $p_i$ of jumping in each time step ($i=1,2$). Each site is independently assigned a random number of particles. At time 0, the particles at the origin are activated and assigned type 1 and the particles at one other site are activated and assigned type 2, while all other particles are sleeping. When an active type $i$ particle moves to a new site, any sleeping particles there are activated and assigned type $i$, with an arbitrary tiebreaker deciding the type if the site is hit by particles of both types in the same time step. We show that the event $G_i$ that type $i$ activates infinitely many particles has positive probability for all $p_1,p_2\in(0,1]$ ($i=1,2$). Furthermore, if $p_1=p_2$, then the types can coexist in the sense that $\mathbb{P}(G_1\cap G_2)>0$. We also formulate several open problems. For instance, we conjectur
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Let $M$ be a Tmotive. We introduce the notion of duality for $M$. Main results of the paper (we consider uniformizable $M$ over $F_q[T]$ of rank $r$, dimension $n$, whose nilpotent operator $N$ is 0): 1. Algebraic duality implies analytic duality (Theorem 5). Explicitly, this means that the lattice of the dual of $M$ is the dual of the lattice of $M$, i.e. the transposed of a Siegel matrix of $M$ is a Siegel matrix of the dual of $M$. 2. Let $n=r1$. There is a 1  1 correspondence between pure Tmotives (all they are uniformizable), and lattices of rank $r$ in $C^n$ having dual (Corollary 8.4).
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We derive a formula of ChernGaussBonnet type for the Euler characteristic of a four dimensional manifoldwithboundary in terms of the geometry of the LoewnerNirenberg singular Yamabe metric in a prescribed conformal class. The formula involves the renormalized volume and a boundary integral. It is shown that if the boundary is umbilic, then the sum of the renormalized volume and the boundary integral is a conformal invariant. Analogous results are proved for asymptotically hyperbolic metrics in dimension four for which the second elementary symmetric function of the eigenvalues of the Schouten tensor is constant. Extensions and generalizations of these results are discussed. Finally, a general result is proved identifying the infinitesimal anomaly of the renormalized volume of an asymptotically hyperbolic metric in terms of its renormalized volume coefficients, and used to outline alternate proofs of the conformal invariance of the renormalized volume plus boundary integral.
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In this paper, we present a general framework to construct recurrent fractal interpolation surfaces (RFISs) on rectangular grids. Then we introduce bilinear RFISs, which are easy to be generated while there are no restrictions on interpolation points and vertical scaling factors. We also obtain the box dimension of bilinear RFISs under certain constraints, where the main assumption is that vertical scaling factors have uniform sums under a compatible partition.
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A connected graph G is called matching covered if every edge of G is contained in a perfect matching. Perfect matching width is a width parameter for matching covered graphs based on a branch decomposition. It was introduced by Norine and intended as a tool for the structural study of matching covered graphs, especially in the context of Pfaffian orientations. Norine conjectured that graphs of high perfect matching width would contain a large grid as a matching minor, similar to the result on treewidth by Robertson and Seymour. In this paper we obtain the first results on perfect matching width since its introduction. For the restricted case of bipartite graphs, we show that perfect matching width is equivalent to directed treewidth and thus the Directed Grid Theorem by Kawarabayashi and Kreutzer for directed \treewidth implies Norine's conjecture.
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Isogeometric Analysis allows highorder discretizations of boundary value problems using a number of degrees of freedom which is as small as for a loworder method. To be able to choose high spline degrees in practice, suitable numerical solvers are required. In nontrivial cases, the computational domain is typically decomposed into several patches, where for each patch a separate isogeometric discretization is chosen. If the discretization agrees on the interfaces between the patches, the coupling can be done in a conforming way. Otherwise, nonconforming discretizations (utilizing discontinuous Galerkin approaches) are required. The author and his coworkers have previously introduced multigrid solvers for Isogeometric Analysis. In the present paper, these results are extended to the nonconforming case. Moreover, it is shown that the solves get even more powerful if the proposed smoother is combined with a (standard) GaussSeidel smoother.
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We study the convergence of volumenormalized Betti numbers in BenjaminiSchramm convergent sequences of nonpositively curved manifolds with finite volume. In particular, we show that if $X$ is an irreducible symmetric space of noncompact type, $X \neq \mathbb H^3$, and $(M_n)$ is any BenjaminiSchramm convergent sequence of finite volume $X$manifolds, then the normalized Betti numbers $b_k(M_n)/vol(M_n)$ converge for all $k$. As a corollary, if $X$ has higher rank and $(M_n)$ is any sequence of distinct, finite volume $X$manifolds, the normalized Betti numbers of $M_n$ converge to the $L^2$ Betti numbers of $X$. This extends our earlier work with Nikolov, Raimbault and Samet, where we proved the same convergence result for uniformly thick sequences of compact $X$manifolds.
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This article analyses geometric constructions by origami when up to $n$ simultaneous folds may be done at each step. It shows that any arbitrary angle can be $m$sected if the largest prime factor of $m$ is $p\le n+2$. Also, the regular $m$gon can be constructed if the largest prime factor of $\phi(m)$ is $q\le n+2$, where $\phi$ is Euler's totient function.
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Type A Demazure atoms are pieces of Schur functions, or sets of tableaux whose weights sum to such functions. Inspired by colored vertex models of Borodin and Wheeler, we will construct solvable lattice models whose partition functions are Demazure atoms; the proof of this makes use of a YangBaxter equation for a colored fivevertex model. As a biproduct, we construct Demazure atoms on Kashiwara's $\mathcal{B}_\infty$ crystal and give new algorithms for computing LascouxSch\"utzenberger keys.
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Amplitudecoherent (AC) detection is an efficient detection technique that can simplify the receiver design while providing reliable symbol error rate (SER). Therefore, this work considers AC detector design and SER analysis using Mary amplitude shift keying (MASK) modulation over Rician fading channels. More specifically, we derive the optimum, nearoptimum and a suboptimum AC detectors and compare their SER to the coherent, noncoherent and the heuristic AC detectors. Moreover, the analytical SER of the heuristic detector is derived using two different approaches for single and multiple receiving antennas. One of the derived expressions is expressed in terms of a single integral that can be evaluated numerically, while the second approach gives a closedform analytical expression for the SER, which is also used to derive a simple formula for the asymptotic SER at high signaltonoise ratios (SNRs). The obtained analytical and simulation results show that the SER of the AC and coheren
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Recent progress in Zauner's conjecture has leveraged deep conjectures in algebraic number theory to promote numerical line packings to exact and verifiable solutions to the line packing problem. We introduce a numericaltoexact technique in the real setting that does not require such conjectures. Our approach is completely reproducible, matching Sloane's database of putatively optimal numerical line packings with Mathematica's builtin implementation of cylindrical algebraic decomposition. As a proof of concept, we promote a putatively optimal numerical packing of eight points in the real projective plane to an exact packing, whose optimality we establish in a forthcoming paper.
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We study (smooth, complex) Fano 4folds X having a rational contraction of fiber type, that is, a rational map X>Y that factors as a sequence of flips followed by a contraction of fiber type. The existence of such a map is equivalent to the existence of a nonzero, nonbig movable divisor on X. Our main result is that if Y is not P^1 or P^2, then the Picard number rho(X) of X is at most 18, with equality only if X is a product of surfaces. We also show that if a Fano 4fold X has a dominant rational map X>Z, regular and proper on an open subset of X, with dim(Z)=3, then either X is a product of surfaces, or rho(X) is at most 12. These results are part of a program to study Fano 4folds with large Picard number via birational geometry.
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This paper is the continuation of the study on discrete harmonic analysis related to Jacobi expansions initiated in [1]. Considering the operator $\mathcal{J}^{(\alpha,\beta)}=J^{(\alpha,\beta)}I$, where $J^{(\alpha,\beta)}$ is the threeterm recurrence relation for the normalized Jacobi polynomials and $I$ is the identity operator, we focus on the study of weighted inequalities for the Riesz transform associated with it.
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The Wasserstein distances are a set of metrics on probability distributions supported on $\mathbb{R}^d$ with applications throughout statistics and machine learning. Often, such distances are used in the context of variational problems, in which the statistician employs in place of an unknown measure a proxy constructed on the basis of independent samples. This raises the basic question of how well measures can be approximated in Wasserstein distance. While it is known that an empirical measure comprising i.i.d. samples is rateoptimal for general measures, no improved results were known for measures possessing smooth densities. We prove the first minimax rates for estimation of smooth densities for general Wasserstein distances, thereby showing how the curse of dimensionality can be alleviated for sufficiently regular measures. We also show how to construct discretely supported measures, suitable for computational purposes, which enjoy improved rates. Our approach is based on novel bo
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This paper advocates a pair of strategies in nonorthogonal multiple access (NOMA) in unmanned aerial vehicles (UAVs) communications, where multiple UAVs play as new aerial communications platforms for serving terrestrial NOMA users. A new multiple UAVs framework with invoking stochastic geometry technique is proposed, in which a pair of practical strategies are considered: 1) UAVCentric strategy for offloading actions and 2) UserCentric strategy for providing emergency communications. In order to provide practical insights for the proposed NOMA assisted UAV framework, an imperfect successive interference cancelation (ipSIC) scenario is taken into account. For both UAVCentric strategy and UserCentric strategy, we derive new exact expressions for the coverage probability. We also derive new analytical results for orthogonal multiple access (OMA) for providing a benchmark scheme. The derived analytical results in both UserCentric strategy and UAVCentric strategy explicitly indicate
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We compute the DonaldsonThomas invariants of a local elliptic surface with section. We introduce a new computational technique which is a mixture of motivic and toric methods. This allows us to write the partition function for the invariants in terms of the topological vertex. Utilizing identities for the topological vertex proved in arXiv:1603.05271, we derive product formulas for the partition functions. The connected version of the partition function is written in terms of Jacobi forms. In the special case where the elliptic surface is a K3 surface, we get a derivation of the KatzKlemmVafa formula for primitive curve classes which is independent of the computation of KawaiYoshioka.
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The classic Fatou lemma states that the lower limit of a sequence of integrals of functions is greater or equal than the integral of the lower limit. It is known that Fatou's lemma for a sequence of weakly converging measures states a weaker inequality because the integral of the lower limit is replaced with integral of the lower limit in two parameters, where the second parameter is the argument of the functions. This paper provides sufficient conditions when Fatou's lemma holds in its classic form for a sequence of weakly converging measures. The functions can take both positive and negative values. The paper also provides similar results for sequences of setwise converging measures. It also provides Lebesgue's and monotone convergence theorem for sequences of weakly and setwise converging measures. The obtained results are used to prove broad sufficient conditions for the validity of optimality equations for averagecosts Markov decision processes.
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We review and extend several recent results on the existence of the ground state for the nonlinear Schr\"odinger (NLS) equation on a metric graph. By ground state we mean a minimizer of the NLS energy functional constrained to the manifold of fixed $L^2$norm. In the energy functional we allow for the presence of a potential term, of deltainteractions in the vertices of the graph, and of a powertype focusing nonlinear term. We discuss both subcritical and critical nonlinearity. Under general assumptions on the graph and the potential, we prove that a ground state exists for sufficiently small mass, whenever the constrained infimum of the quadratic part of the energy functional is strictly negative.
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Some new results provide opportunities to ensure the exponential convergence to a unique quasistationary distribution in the total variation norm, for quite general strong Markov processes. Specifically, nonreversible processes with discontinuous trajectories are concerned, which seems to be a substantial breakthrough. Considering jumps driven by Poisson Point Processes in four different applications, we intend to illustrate the potential of these results and motivate an original yet apparently very technical criterion. Such criterion is expected to be much easier to verify than an implied property essential for our proof, namely a comparison of the asymptotic extinction rate between different initial conditions. Keywords : continuoustime and continuousspace Markov process , jumps , quasistationary distribution , survival capacity , Qprocess , Harris recurrence
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SQUID (Superconducting QUantum Interference Device) metamaterials, subject to a timeindependent (dc) flux gradient and driven by a sinusoidal (ac) flux field, support chimera states that can be generated with zero initial conditions. The dc flux gradient and the amplitude of the ac flux can control the number of desynchronized clusters of such a generated chimera state (i.e., its `heads') as well as their location and size. The combination of three measures, i.e., the synchronization parameter averaged over the period of the driving flux, the incoherence index, and the chimera index, is used to predict the generation of a chimera state and its multiplicity on the parameter plane of the dc flux gradient and the ac flux amplitude. Moreover, the fullwidth halfmaximum of the distribution of the values of the synchronization parameter averaged over the period of the ac driving flux, allows to distinguish chimera states from nonchimera, partially synchronized states.
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Inspired by a similar analysis for the vacuum conformal Einstein field equations by Paetz [Ann. H. Poincar\'e 16, 2059 (2015)], in this article we show how to construct a system of quasilinear wave equations for the geometric fields associated to the conformal Einstein field equations coupled to matter models whose energymomentum tensor has vanishing trace. In this case, the equation of conservation for the energymomentum tensor is conformally invariant. Our analysis includes the construction of a subsidiary evolution system which allows to prove the propagation of the constraints. We discuss how the underlying structure behind these systems of equations is the integrability conditions satisfied by the conformal field equations. The main result of our analysis is that both the evolution and subsidiary equations for the geometric part of the conformal Einsteintracefree matter field equations close without the need of any further assumption on the matter models other than the vanishin
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Self dual symmetric Rspaces have special curves, called circles, introduced by Burstall, Donaldson, Pedit and Pinkall in 2011, whose definition does not involve the choice of any Riemannian metric. We characterize the elements of the big transformation group G of a self dual symmetric Rspace M as those diffeomorphisms of M sending circles in circles. Besides, although these curves belong to the realm of the invariants by G, we manage to describe them in Riemannian geometric terms: Given a circle c in M, there is a maximal compact subgroup K of G such that c, except for a projective reparametrization, is a diametrical geodesic in M (or equivalently, a diagonal geodesic in a maximal totally geodesic flat torus of M), provided that M carries the canonical symmetric Kinvariant metric. We include examples for the complex quadric and the split standard or isotropic Grassmannians.
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Google acquired DeepMind for $500 million in 2014, and its AI programs later beat the world's best player in Go, as well as the top AI chess programs. But when its AlphaStar system beat two top Starcraft II players  was it cheating? Longtime Slashdot reader AmiMoJo quotes BoingBoing: It claimed the AI was limited to what human players can physically do, putting its achievement in the realm of strategic analysis rather than finger twitchery. But there's a problem: it was often tracked clicking with superhuman speed and efficiency. Aleksi Pietikainen writes "It is deeply unsatisfying to have prominent members of this research project make claims of humanlike mechanical limitations when the agent is very obviously breaking them and winning its games specifically because it is demonstrating superhuman execution." "It wasn't an entirely fair fight," argues Ars Technica, noting the limitations DeepMind placed on its AI "seem to imply that AlphaStar could take 50 actions in a single s
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This week HackerRank reported Java is now only the second most popular programming language, finally dropping behind JavaScript in the year 2018. Now longtime Slashdot reader shanen asks about the rumors that Java is dead  or is it? Can you convince me that Java isn't as dead as it seems? It's just playing dead and will spring to life? This week one Java news site argued that Javabased Minecraft has in fact "spawned a new generation of Java developers," citing an interview with Red Hat's JBoss Middleware CTO. (And he adds that "It's still the dominant programming language in the enterprise, so whether you're building enterprise clients, services or something in between, Java likely features in there somewhere.") Yet the original submission drew some interesting comments: "The licensing scheme for Java kills it..." "Java programs still are 'the alien on your desktop'. They suck in many ways. Users have learned to avoid them and install 'real programs' instead..." But what do Sl
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The FBI confiscated six drones in Atlanta for flying too close to the football stadium where the Super Bowl will be played Sunday, Reuters reports: Drone flight was prohibited on Saturday and from 10 a.m. until 5:30 p.m. EST on Sunday for one nautical mile (2 km) around the MercedesBenz Stadium and up to an altitude of 1,000 feet (305 meters), the Federal Aviation Administration said. The FAA will establish temporary flight restriction that prohibits drones within a 30nauticalmile radius of the stadium and up to 17,999 feet in altitude from 5:30 p.m. to 11:59 p.m. EST on Sunday, the agency said. .. Drones "are a big concern," said Nick Annan, Homeland Security Investigations special agent in charge. "There are a few other things that are in place to mitigate drones," he added without elaborating. Operators who send drones into restricted areas around the MercedesBenz Stadium could face more than $20,000 in civil penalties and criminal prosecution, according to the FAA. Drone pil
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An AIenhanced tool that suggests code snippets for Python developers in real time just raised $17 million in VC funding to expand its R&D team "with a focus on accelerating developer productivity." An anonymous reader quotes VentureBeat: "Our mission is to bring the latest advancements in AI and machine learning (ML) to make writing code fluid, effortless, and more enjoyable," explained [founder Adam] Smith. "Developers using Kite can focus their productive energy toward solving the next big technical challenges, instead of searching the web for code examples illustrating mundane and frequently repeated code patterns...." Instead of relying on the cloud to run its AI engine, Kite now runs locally on a user's computer, letting developers use it offline and without having to upload any code. (Kite still trains its machine learning models with thousands of publicly available code sources from highly rated developers.) Furthermore, running locally allows Kite to fully operate with
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More than a year after Facebook commercially launched Express WiFi in five markets, it is ready to bring the connectivity service to the sixth: Ghana. From a report: In partnership with telecom operator Vodafone Ghana, Facebook today launched Express WiFi, part of Internet.org initiative, in the suburban communities of the Western African nation. The service, available locally in Nima, James Town, Kanda, Pig Farm, and Abossey Okine in the capital city Accra, will aim to offer "carriergrade WiFi" to people living in some remote communities that lack fiber optic cables. Ever since India booted Free Basics in early 2016, Facebook has seemingly grown cautious about its connectivity efforts. The company has stopped updating the social media page and press page of Internet.org. Last year, we learned that Facebook had quietly pulled Internet.org from a handful of emerging markets. In recent months, however, it has quietly expanded Internet.org to two new markets  Morocco (in North Afr
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Longtime Slashdot reader darkwing_bmf writes: In an exclusive interview with Popular Mechanics, SpaceX founder Elon Musk explains why stainless steel is the best material to build rocket ships, beating carbon fiber in cost, durability and even weight. "As far as we know, this marks the first time the material has been used in spacecraft construction since some early, illfated attempts during the Atlas program in the late 1950s," reports Popular Mechanics. "It took me quite a bit of effort to convince the team to go in this direction..." Musk tells them. But among the other benefits "It has a high melting point. Much higher than aluminum, and although carbon fiber doesn't melt, the resin gets destroyed at a certain temperature... But steel, you can do 1500, 1600 degrees Fahrenheit."
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An anonymous reader quotes TechCrunch: In September of last year, Elon Musk promised to make fixing service times a priority. On an earnings call, he outlined two ways they're working on it: more spare parts at service centers, and giving Tesla cars the ability to automatically get the process started by calling a tow truck as soon as it detects an issue. Said Elon on the call: The next thing we want to add is if a car detects something wrong  like a flat tire or a drive unit failure  that before the car has even come to a halt, there's a tow truck and service loaner on the way. False alarm? Don't want a tow truck to show up? You'll be able to cancel it through the indash display. Musk didn't provide a time frame for when this feature would become available.
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Potential functions can be used as generating potentials of relevant geometric structures for a Riemannian manifold such as the Riemannian metric and affine connections. We study wether this procedure can also be applied to tensors of rank four and find a negative answer. We study this from the perspective of solving the inverse problem and also from an intrinsic point of view.
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This paper deals with singularities of genus 2 curves on a general (d_1,d_2)polarized abelian surface (S,L). In analogy with Chen's results concerning rational curves on K3 surfaces [Ch1,Ch2], it is natural to ask whether all such curves are nodal. We prove that this holds true if and only if d_2 is not divisible by 4. In the cases where d_2 is a multiple of 4, we exhibit genus 2 curves in L that have a triple, 4tuple or 6tuple point. We show that these are the only possible types of unnodal singularities of a genus 2 curve in L. Furthermore, with no assumption on d_1 and d_2, we prove the existence of at least a nodal curve in L. As a corollary, we obtain nonemptiness of all Severi varieties on general abelian surfaces and hence generalize [KLM, Thm 1.1] to nonprimitive polarizations.
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We discuss the extent to which solutions to onephase free boundary problems can be characterized according to their topological complexity. Our questions are motivated by fundamental work of Luis Caffarelli on free boundaries and by striking results of T. Colding and W. Minicozzi concerning finitely connected, embedded, minimal surfaces. We review our earlier work on the simplest case, onephase free boundaries in the plane in which the positive phase is simply connected. We also prove a new, purely topological, effective removable singularities theorem for free boundaries. At the same time, we formulate some open problems concerning the multiply connected case and make connections with the theory of minimal surfaces and semilinear variational problems.
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Fuglede's conjecture in $\mathbb{Z}_{p}^{d}$, $p$ a prime, says that a subset $E$ tiles $\mathbb{Z}_{p}^{d}$ by translation if and only if $E$ is spectral, meaning any complexvalued function $f$ on $E$ can be written as a linear combination of characters orthogonal with respect to $E$. We disprove Fuglede's conjecture in $\mathbb{Z}_p^4$ for all odd primes $p$, by using logHadamard matrices to exhibit spectral sets of size $2p$ which do not tile, extending the result of Aten et al. that the conjecture fails in $\mathbb{Z}_p^4$ for primes $p \equiv 3 \pmod 4$ and in $\mathbb{Z}_p^5$ for all odd primes $p$. We also prove the conjecture in $\mathbb{Z}_2^4$, resolving all cases of fourdimensional vector spaces over prime fields. We give an example showing that our simple proof method does not extend to higher dimensions. However, we include a link to a computer program which the authors have used to verify that, nevertheless, the conjecture holds in $\mathbb{Z}_2^5$ and $\mathbb{Z}_2^6$
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A consumer DNA testing company has given the FBI access to its two million
0202 MIT Technology 1509 
Antielementarity is a strong way of ensuring that a class of structures , in a given firstorder language, is not closed under elementary equivalence with respect to any infinitary language of the form $\mathscr{L}_{\infty\lambda}$. We prove that many naturally defined classes are antielementary, including the following: $\bullet$ the class of all lattices of finitely generated convex $\ell$subgroups of members of any class of $\ell$groups containing all Archimedean $\ell$groups; $\bullet$ the class of all semilattices of finitely generated $\ell$ideals of members of any nontrivial quasivariety of $\ell$groups; $\bullet$ the class of all Stone duals of spectra of MValgebrasthis yields a negative solution for the MVspectrum Problem; $\bullet$ the class of all semilattices of finitely generated twosided ideals of rings; $\bullet$ the class of all semilattices of finitely generated submodules of modules; $\bullet$ the class of all monoids encoding the nonstable K$_0$theory of
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