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Last week, Apple announced new MacBook Pros, including a 15inch model that supports Intel's 6core 2.9GHz i9 processor. YouTube Dave Lee managed to get his hands on this topoftheline device early and run some tests, revealing that the laptop gets severely throttled due to thermal issues. 9to5Mac reports: Dave Lee this afternoon shared a new video on the Core i9 MacBook Pro he purchased, and according to his testing, the new machine is unable to maintain even its base clock speed after just a short time doing processor intensive work like video editing. "This CPU is an unlocked, overclockable chip but all of that CPU potential is wasted inside this chassis  or more so the thermal solution that's inside here," says Lee. He goes on to share some Premiere Pro render times that suggest the new 2018 MacBook Pro with Core i9 chip underperforms compared to a 2017 model with a Core i7 chip. It took 39 minutes for the 2018 MacBook Pro to render a video that the older model was able to rend
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The zeros of the random Laurent series $1/\mu  \sum_{j=1}^\infty c_j/z^j$, where each $c_j$ is an independent standard complex Gaussian, is known to correspond to the scaled eigenvalues of a particular additive rank 1 perturbation of a standard complex Gaussian matrix. For the corresponding random Maclaurin series obtained by the replacement $z \mapsto 1/z$, we show that these same zeros correspond to the scaled eigenvalues of a particular multiplicative rank 1 perturbation of a random unitary matrix. Since the correlation functions of the latter are known, by taking an appropriate limit the correlation functions for the random Maclaurin series can be determined. Only for $\mu \to \infty$ is a determinantal point process obtained. For the one and two point correlations, by regarding the Maclaurin series as the limit of a random polynomial, a direct calculation can also be given.
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We provide a Central Limit Theorem for the MongeKantorovich distance between two empirical distributions with size $n$ and $m$, $W_p(P_n,Q_m)$ for $p>1$ for observations on the real line, using a minimal amount of assumptions. We provide an estimate of the asymptotic variance which enables to build a two sample test to assess the similarity between two distributions. This test is then used to provide a new criterion to assess the notion of fairness of a classification algorithm.
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Kim Zetter, reporting for Motherboard: The nation's top voting machine maker has admitted in a letter to a federal lawmaker that the company installed remoteaccess software on electionmanagement systems it sold over a period of six years, raising questions about the security of those systems and the integrity of elections that were conducted with them. In a letter sent to Sen. Ron Wyden (DOR) in April and obtained recently by Motherboard, Election Systems and Software acknowledged that it had "provided pcAnywhere remote connection software ... to a small number of customers between 2000 and 2006," which was installed on the electionmanagement system ES&S sold them. The statement contradicts what the company told me and fact checkers for a story I wrote for the New York Times in February. At that time, a spokesperson said ES&S had never installed pcAnywhere on any election system it sold. "None of the employees, â¦ including longtenured employees, has any knowled
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An anonymous reader quotes a report from Gizmodo: Scientists' models show that sound waves seem to travel too quickly through the old, stable cores of continents, called "cratons," which extend deep into the mantle at depths around 120 to 150 kilometers (75 to 93 miles). Through observations, experiments, and modeling, one team figured that a potential way to explain the sound speed anomaly would be the presence of a lot of diamonds, a medium that allows for a faster speed of sound than other crystals. Perhaps the Earth is as much as 2 percent diamonds by volume, they found. Scientists have modeled the rock beneath continents through tomography, which you can think of as like an xray image, but using sound waves. But soundwave velocities of around 4.7 kilometers per second (about 10,513 mph) are faster than soundwave velocities in other kinds of minerals beneath the crust, according to the paper in the journal Geochemistry, Geophysics, Geosystems. The researchers realized that if th
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We present a simplified version of the threshold dynamics algorithm given in the work of Esedoglu and Otto (2015). The new version still allows specifying Nchoose2 possibly distinct surface tensions and Nchoose2 possibly distinct mobilities for a network with N phases, but achieves this level of generality without the use of retardation functions. Instead, it employs linear combinations of Gaussians in the convolution step of the algorithm. Convolutions with only two distinct Gaussians is enough for the entire network, maintaining the efficiency of the original thresholding scheme. We discuss stability and convergence of the new algorithm, including some counterexamples in which convergence fails. The apparently convergent cases include unequal surface tensions given by the Read \& Shockley model and its three dimensional extensions, along with equal mobilities, that are a very common choice in computational materials science.
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The 2nd Circuit denies an immediate appeal in a case that challenges how news organizations used embedded photos of Tom Brady. The Hollywood Reporter: Back in February, a New York judge caused a bit of a freakout by issuing a copyright decision regarding the embedding of a copyrighted photo of NFL superstar Tom Brady. Now comes another surprise with potentially big ramifications to the future of embedding and inline linking: The 2nd Circuit Court of Appeals has denied an interlocutory appeal. Justin Goldman is the plaintiff in the lawsuit after finding the photo of the New England Patriots quarterback he shot and uploaded to Snapchat go viral. Many news organizations embedded social media posts that took Goldman's photo in stories about whether the Boston Celtics would recruit NBA star Kevin Durant with Brady's assistance. Breitbart, Heavy, Time, Yahoo, Vox Media, Gannett Company, Herald Media, Boston Globe Media Partners and New England Sports Network were defendants in the lawsuit,
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We show the nonpositivity of the EinsteinHilbert action for conformal flat Riemannian metrics. The action vanishes only when the metric is constant flat. This recovers an earlier result of FathizadehKhalkhali in the setting of spectral triples on noncommutative fourtorus. Furthermore, computations of the gradient flow and the scalar curvature of this space based on modular operator are given. We also show the GaussBonnet theorem for a parametrized class of nondiagonal metrics on noncommutative twotorus.
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We prove that finite lamplighter groups $\{\mathbb{Z}_2\wr\mathbb{Z}_n\}_{n\ge 2}$ with a standard set of generators embed with uniformly bounded distortions into any nonsuperreflexive Banach space, and therefore form a set of testspaces for superreflexivity. Our proof is inspired by the well known identification of Cayley graphs of infinite lamplighter groups with the horocyclic product of trees. We cover $\mathbb{Z}_2\wr\mathbb{Z}_n$ by three sets with a structure similar to a horocyclic product of trees, which enables us to construct wellcontrolled embeddings.
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The recent years have seen a beautiful breakthrough culminating in a comprehensive understanding of certain scaleinvariant properties of $n1$ dimensional sets across analysis, geometric measure theory, and PDEs. The present paper surveys the first steps of a program recently launched by the authors and aimed at the new PDE approach to sets with lower dimensional boundaries. We define a suitable class of degenerate elliptic operators, explain our intuition, motivation, and goals, and present the first results regarding absolute continuity of the emerging elliptic measure with respect to the surface measure analogous to the classical theorems of C. Kenig and his collaborators in the case of codimension one.
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We deal with the following nonlinear problem involving fractional $p$ and $q$Laplacians: \begin{equation*} (\Delta)^{s}_{p}u+(\Delta)^{s}_{q}u+u^{p2}u+u^{q2}u=\lambda h(x) f(u)+u^{q^{*}_{s}2}u \mbox{ in } \mathbb{R}^{N}, \end{equation*} where $s\in (0,1)$, $1<p<q<\frac{N}{s}$, $q^{*}_{s}=\frac{Nq}{Nsq}$, $\lambda>0$, $h>0$ is a bounded function and $f$ is a superlinear continuous function with subcritical growth. By using suitable variational arguments and ConcentrationCompactness Lemma, we prove the existence of a nontrivial solution for $\lambda$ sufficiently large.
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Erd\"{o}s proved that for every infinite $X \subseteq \mathbb{R}^d$ there is $Y \subseteq X$ with $Y=X$, such that all pairs of points from $Y$ have distinct distances, and he gave partial results for general $a$ary volume. In this paper, we search for the strongest possible canonization results for $a$ary volume, making use of general modeltheoretic machinery. The main difficulty is for singular cardinals; to handle this case we prove the following. Suppose $T$ is a stable theory, $\Delta$ is a finite set of formulas of $T$, $M \models T$, and $X$ is an infinite subset of $M$. Then there is $Y \subseteq X$ with $Y = X$ and an equivalence relation $E$ on $Y$ with infinitely many classes, each class infinite, such that $Y$ is $(\Delta, E)$indiscernible. We also consider the definable version of these problems, for example we assume $X \subseteq \mathbb{R}^d$ is perfect (in the topological sense) and we find some perfect $Y \subseteq X$ with all distances distinct. Finally we
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Recently knapsack problems have been generalized from the integers to arbitrary finitely generated groups. The knapsack problem for a finitely generated group $G$ is the following decision problem: given a tuple $(g, g_1, \ldots, g_k)$ of elements of $G$, are there natural numbers $n_1, \ldots, n_k \in \mathbb{N}$ such that $g = g_1^{n_1} \cdots g_k^{n_k}$ holds in $G$? Myasnikov, Nikolaev, and Ushakov proved that for every (Gromov)hyperbolic group, the knapsack problem can be solved in polynomial time. In this paper, the precise complexity of the knapsack problem for hyperbolic group is determined: for every hyperbolic group $G$, the knapsack problem belongs to the complexity class $\mathsf{LogCFL}$, and it is $\mathsf{LogCFL}$complete if $G$ contains a free group of rank two. Moreover, it is shown that for every hyperbolic group $G$ and every tuple $(g, g_1, \ldots, g_k)$ of elements of $G$ the set of all $(n_1, \ldots, n_k) \in \mathbb{N}^k$ such that $g = g_1^{n_1} \cdots g_k^{n_
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This paper considers the minimization of the offloading delay for nonorthogonal multiple access assisted mobile edge computing (NOMAMEC). By transforming the delay minimization problem into a form of fractional programming, two iterative algorithms based on Dinkelbach's method and Newton's method are proposed. The optimality of both methods is proved and their convergence is compared. Furthermore, criteria for choosing between three possible modes, namely orthogonal multiple access (OMA), pure NOMA, and hybrid NOMA, for MEC offloading are established.
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Security updates have been issued by Arch Linux (curl, lib32curl, lib32libcurlcompat, lib32libcurlgnutls, libcurlcompat, and libcurlgnutls), Debian (blender, ffmpeg, and wordpress), Fedora (curl), Gentoo (tqdm), Oracle (kernel), Slackware (mutt), SUSE (xen), and Ubuntu (policykit1).
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In this paper, we propose that relations between high order moments of data distributions, for example between the skewness (S) and kurtosis (K), allow to point to theoretical models with understandable structural parameters. The illustrative data concerns two cases: (i) the distribution of income taxes and (ii) that of inhabitants, after aggregation over each city in each province of Italy in 2011. Moreover, from the ranksize relationship, for either S or K, in both cases, it is shown that one obtains the parameters of the underlying (hypothetical) modeling distribution: in the present cases, the 2parameter Beta function,  itself related to the YuleSimon distribution function, whence suggesting a growth model based on the preferential attachment process.
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We propose a compressive spectral collocation method for the numerical approximation of Partial Differential Equations (PDEs). The approach is based on a spectral SturmLiouville approximation of the solution and on the collocation of the PDE in strong form at random points, by taking advantage of the compressive sensing principle. The proposed approach makes use of a number of collocation points substantially less than the number of basis functions when the solution to recover is sparse or compressible. Focusing on the case of the diffusion equation, we prove that, under suitable assumptions on the diffusion coefficient, the matrix associated with the compressive spectral collocation approach satisfies the restricted isometry property of compressive sensing with high probability. Moreover, we demonstrate the ability of the proposed method to reduce the computational cost associated with the corresponding full spectral collocation approach while preserving good accuracy through numeric
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The Libor market model is a mainstay term structure model of interest rates for derivatives pricing, especially for Bermudan swaptions, and other exotic Libor callable derivatives. For numerical implementation the pricing of derivatives with Libor market models is mainly carried out with Monte Carlo simulation. The PDE grid approach is not particularly feasible due to Curse of Dimensionality. The standard Monte Carlo method for American/Bermudan swaption pricing more or less uses regression to estimate expected value as a linear combination of basis functions (Longstaff and Schwartz). However, Monte Carlo method only provides the lower bound for American option price. Another complexity is the computation of the sensitivities of the option, the socalled Greeks, which are fundamental for a trader's hedging activity. Recently, an alternative numerical method based on deep learning and backward stochastic differential equations appeared in quite a few researches. For European style optio
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We study Van den Bergh's noncommutative symmetric algebra $\mathbb{S}^{nc}(M)$ (over division rings) via Minamoto's theory of Fano algebras. In particular, we show $\mathbb{S}^{nc}(M)$ is coherent, and its proj category $\mathbb{P}^{nc}(M)$ is derived equivalent to the corresponding bimodule species. This generalizes the main theorem of \cite{minamoto}, which in turn is a generalization of Beilinson's derived equivalence. As corollaries, we show that $\mathbb{P}^{nc}(M)$ is hereditary and there is a structure theorem for sheaves on $\mathbb{P}^{nc}(M)$ analogous to that for $\mathbb{P}^1$.
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We describe the Lorentzian version of the KapovitchMillson phase space for polyhedra with $N$ faces. Starting with the Schwinger representation of the $\mathfrak{su}(1,1)$ Lie algebra in terms of a pair of complex variables (or spinor), we define the phase space for a spacelike vectors in the threedimensional Minkowski space $\mathbb{R}^{1,2}$. Considering $N$ copies of this space, quotiented by a closure constraint forcing the sum of those 3vectors to vanish, we obtain the phase space for Lorentzian polyhedra with $N$ faces whose normal vectors are spacelike, up to Lorentz transformations. We identify a generating set of $SU(1,1)$invariant observables, whose flow by the Poisson bracket generate both areapreserving and areachanging deformations. We further show that the areapreserving observables form a $\mathfrak{gl}_{N}(\mathbb{R})$ Lie algebra and that they generate a $GL_{N}(\mathbb{R})$ action on Lorentzian polyhedra at fixed total area. That action is cyclic and all Lore
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Licenseassisted access LTE (LAALTE) has been proposed to deal with the intense contradiction between tremendous mobile traffic demands and crowded licensed spectrums. In this paper, we investigate the coexistence mechanism for LAALTE based heterogenous networks (HetNets). A joint resource allocation and network access problem is considered to maximize the normalized throughput of the unlicensed band while guaranteeing the qualityofservice requirements of incumbent WiFi users. A twolevel learningbased framework is proposed to solve the problem by decomposing it into two subproblems. In the master level, a Qlearning based method is developed for the LAALTE system to determine the proper transmission time. In the slave one, a gametheory based learning method is adopted by each user to autonomously perform network access. Simulation results demonstrate the effectiveness of the proposed solution.
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We study the learnability of sums of independent integer random variables given a bound on the size of the union of their supports. For $\mathcal{A} \subset \mathbf{Z}_{+}$, a sum of independent random variables with collective support $\mathcal{A}$} (called an $\mathcal{A}$sum in this paper) is a distribution $\mathbf{S} = \mathbf{X}_1 + \cdots + \mathbf{X}_N$ where the $\mathbf{X}_i$'s are mutually independent (but not necessarily identically distributed) integer random variables with $\cup_i \mathsf{supp}(\mathbf{X}_i) \subseteq \mathcal{A}.$ We give two main algorithmic results for learning such distributions: 1. For the case $ \mathcal{A}  = 3$, we give an algorithm for learning $\mathcal{A}$sums to accuracy $\epsilon$ that uses $\mathsf{poly}(1/\epsilon)$ samples and runs in time $\mathsf{poly}(1/\epsilon)$, independent of $N$ and of the elements of $\mathcal{A}$. 2. For an arbitrary constant $k \geq 4$, if $\mathcal{A} = \{ a_1,...,a_k\}$ with $0 \leq a_1 < ... < a_k$,
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In order to actually do anything, a kernel module must gain access to functions and data structures in the rest of the kernel. Enabling and controlling that access is the job of the symbolexport mechanism. While the enabling certainly happens, the control part is not quite so clear; many developers view the nearly 30,000 symbols in current kernels that are available to all modules as being far too many. The symbol namespaces patch set from Martijn Coenen doesn't reduce that number, but it does provide a mechanism that might help to impose some order on exported symbols in general.
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The contributions of scalars and fermions to the null polygonal bosonic Wilson loops/gluon MHV scattering amplitudes in $\mathcal{N} = 4$ SYM are considered. We first examine the resummation of scalars at strong coupling. Then, we disentangle the form of the fermion contribution and show its strong coupling expansion. In particular, we derive the leading order with the appearance of a fermionantifermion bound state first and then effective multiple bound states thereof. This reproduces the string minimal area result and also applies to the Nekrasov instanton partition function $\mathcal{Z}$ of the $\mathcal{N}=2$ theories. Especially, in the latter case the method appears to be suitable for a systematic expansion.
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We prove a factorization theorem for reproducing kernel Hilbert spaces whose kernel has a normalized complete NevanlinnaPick factor. This result relates the functions in the original space to pointwise multipliers determined by the NevanlinnaPick kernel and has a number of interesting applications. For example, for a large class of spaces including Dirichlet and DruryArveson spaces, we construct for every function $f$ in the space a pluriharmonic majorant of $f^2$ with the property that whenever the majorant is bounded, the corresponding function $f$ is a pointwise multiplier.
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We present a set of new energystable open boundary conditions for tackling the backflow instability in simulations of outflow/open boundary problems for incompressible flows. These boundary conditions are developed through two steps: (i) devise a general form of boundary conditions that ensure the energy stability by reformulating the boundary contribution into a quadratic form in terms of a symmetric matrix and computing an associated eigen problem; and (ii) require that, upon imposing the boundary conditions from the previous step, the scale of boundary dissipation should match a physical scale. These open boundary conditions can be recast into the form of a tractiontype condition, and therefore they can be implemented numerically using the splittingtype algorithm from a previous work. The current boundary conditions can effectively overcome the backflow instability typically encountered at moderate and high Reynolds numbers. These boundary conditions in general give rise to a n
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The purpose of this article is to show that there are many differential viscoelastic models for which the global existence of a regular solution is possible. Although the problem of global existence in the classic Oldroyd model is still open, we show that by adding a nonlinear contribution (proposed by R.G. Larson in 1984), it is possible to obtain more regular and global solutions, regardless of the size of the data (in the twodimensional and periodic case). Similarly, more complex appearance models such as those related to "pompom" polymers are interesting and mathematically richer: some "natural" bounds on the stress make it possible to obtain global results. On the other hand, in the last part, we show that other models clearly do not seem to fit into this framework, and do not even seem to have a global solution in time. These kinds of results allow to highlight the advantages and disadvantages of such or such viscoelastic fluid models. They can thus help rheologists and numeri
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Approximately regularized minimizer of the least squares functional with a nonsmooth, convex penalty term and an indicator function is considered to be produced iteratively by some nested primaldual algorithm. The algorithm is a proximalgradient linesearch based iterative procedure and is introduced as an iterative variational regularization method. Under the consideration of that the exact solution for the linear illposed inverse problem satisfies a variational source condition (VSC), convergence of the regularized solution of the minimization problem to the exact solution, and convergence of the iteratively regularized approximate minimizer by our primaldual algorithm to the exact solution are analysed separately. It is in the emphasis of this work that the regularization parameter obeys {\em Morozov`s discrepancy principle} (MDP) in order for the stability analysis of regularized solution. Furthermore, stability analysis of the algorithm requires us to define the additional par
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Let $f(x)$ be a degree $(2g+1)$ monic polynomial with coefficients in an algebraically closed field $K$ with $char(K)\ne 2$ and without repeated roots. Let $\mathfrak{R}\subset K$ be the $(2g+1)$element set of roots of $f(x)$. Let $\mathcal{C}: y^2=f(x)$ be an odd degree genus $g$ hyperelliptic curve over $K$. Let $J$ be the jacobian of $\mathcal{C}$ and $J[2]\subset J(K)$ the (sub)group of its points of order dividing $2$. We identify $\mathcal{C}$ with the image of its canonical embedding into $J$ (the infinite point of $\mathcal{C}$ goes to the identity element of $J$). Let $P=(a,b)\in \mathcal{C}(K)\subset J(K)$ and $M_{1/2,P}\subset J(K)$ the set of halves of $P$ in $J(K)$, which is $J[2]$torsor. In a previous work we established an explicit bijection between $M_{1/2,P}$ and the set of collections of square roots $$\mathfrak{R}_{1/2,P}:=\{\mathfrak{r}: \mathfrak{R} \to K\mid \mathfrak{r}(\alpha)^2=a\alpha \ \forall \alpha\in\mathfrak{R}; \ \prod_{\alpha\in\mathfrak{R}} \mathfra
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A new bound on quantum version of Wielandt inequality for positive (not necessarily completely positive) maps has been established. Also bounds for entanglement breaking and PPT channels are put forward which are better bound than the previous bounds known. We prove that a primitive positive map $\mathcal{E}$ acting on $\mathcal{M}_d$ that satisfies the Schwarz inequality becomes strictly positive after at most $2(d1)^2$ iterations. This is to say, that after $2(d1)^2$ iterations, such a map sends every positive semidefinite matrix to a positive definite one. This finding does not depend on the number of Kraus operators as the map may not admit any Kraus decomposition. The motivation of this work is to provide an answer to a question raised in the article \cite{Wielandt} by SanzGarc\'iaWolf and Cirac.
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We describe the $C_2$equivariant homotopy type of the space of commuting ntuples in the stable unitary group in terms of Real Ktheory. The result is used to give a complete calculation of the homotopy groups of the space of commuting ntuples in the stable orthogonal group, as well as of the coefficient ring for commutative orthogonal Ktheory.
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A tight $r$tree $T$ is an $r$uniform hypergraph that has an edgeordering $e_1, e_2, \dots, e_t$ such that for each $i\geq 2$, $e_i$ has a vertex $v_i$ that does not belong to any previous edge and $e_iv_i$ is contained in $e_j$ for some $j<i$. Kalai conjectured in 1984 that every $n$vertex $r$uniform hypergraph with more than $\frac{t1}{r}\binom{n}{r1}$ edges contains every tight $r$tree $T$ with $t$ edges. A trunk $T'$ of a tight $r$tree $T$ is a tight subtree $T'$ of $T$ such that vertices in $V(T)\setminus V(T')$ are leaves in $T$. Kalai's Conjecture was proved in 1987 for tight $r$trees that have a trunk of size one. In a previous paper we proved an asymptotic version of Kalai's Conjecture for all tight $r$trees that have a trunk of bounded size. In this paper we continue that work to establish the exact form of Kalai's Conjecture for all tight $3$trees with at least $20$ edges that have a trunk of size two.
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We show that fractional Brownian motion(fBM) defined via Volterra integral representation with Hurst parameter $H\geq\frac{1}{2}$ is a quasisurely defined Wiener functional on classical Wiener space,and we establish the large deviation principle(LDP) for such fBM with respect to $(p,r)$capacity on classical Wiener space in Malliavin's sense.
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In this note we describe how some objects from generalized geometry appear in the qualitative analysis and numerical simulation of mechanical systems. In particular we discuss double vector bundles and Dirac structures. It turns out that those objects can be naturally associated to systems with constraints  we recall the mathematical construction in the context of so called implicit Lagrangian systems. We explain how they can be used to produce new numerical methods, that we call Dirac integrators. On a test example of a simple pendulum in a gravity field we compare the Dirac integrators with classical explicit and implicit methods, we pay special attention to conservation of constrains. Then, on a more advanced example of the Ziegler column we show that the choice of numerical methods can indeed affect the conclusions of qualitative analysis of the dynamics of mechanical systems. We also tell why we think that Dirac integrators are appropriate for this kind of systems by explaining
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Let $\C$ be an $(n+2)$angulated category with shift functor $\Sigma$ and $\X$ be a clustertilting subcategory of $\C$. Then we show that the quotient category $\C/\X$ is an $n$abelian category. If $\C$ has a Serre functor, then $\C/\X$ is equivalent to an $n$cluster tilting subcategory of an abelian category $\textrm{mod}(\Sigma^{1}\X)$. Moreover, we also prove that $\textrm{mod}(\Sigma^{1}\X)$ is Gorenstein of Gorenstein dimension at most $n$. As an application, we generalize recent results of JacobsenJ{\o}rgensen and KoenigZhu.
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We rewrite classical topological definitions using the categorytheoretic notation of arrows and are led to concise reformulations in terms of simplicial categories and orthogonality of morphisms, which we hope might be of use in the formalisation of topology and in developing the tame topology of Grothendieck. Namely, we observe that topological and uniform spaces are simplicial objects in the same category, a category of filters, and that a number of elementary properties can be obtained by repeatedly passing to the left or right orthogonal (in the sense of Quillen model categories) starting from a simple class of morphisms, often a single typical (counter)example appearing implicitly in the definition. Examples include the notions of: compact, discrete, connected, and totally disconnected spaces, dense image, induced topology, and separation axioms, and, outside of topology, finite groups being nilpotent, solvable, torsionfree, pgroups, and primetop groups; injective and project
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In this paper, we consider the classic stochastic (dynamic) knapsack problem, a fundamental mathematical model in revenue management, with general timevarying random demand. Our main goal is to study the optimal policies, which can be obtained by solving the dynamic programming formulated for the problem, both qualitatively and quantitatively. It is wellknown that when the demand size is fixed and the demand distribution is stationary over time, the value function of the dynamic programming exhibits extremely useful first and second order monotonicity properties, which lead to monotonicity properties of the optimal policies. In this paper, we are able to verify that these results still hold even in the case that the price distributions are timedependent. When we further relax the demand size distribution assumptions and allow them to be arbitrary, for example in random batches, we develop a scheme for using value function of alternative unit demand systems to provide bounds to the v
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For a symplectic manifold admitting a metaplectic structure and for a Kuiper map, we construct a complex of differential operators acting on exterior differential forms with values in the dual of the Kostant's symplectic spinor bundle. Defining a Hilbert $C^*$structure on this bundle for a suitable $C^*$algebra, we obtain an elliptic $C^*$complex in the sense of MishchenkoFomenko. Its cohomology groups appear to be finitely generated projective Hilbert $C^*$modules.
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We study the functional calculus properties of generators of $C_{0}$groups under type and cotype assumptions on the underlying Banach space. In particular, we show the following. Let $iA$ generate a $C_{0}$group on a Banach space $X$ with type $p\in[1,2]$ and cotype $q\in[2,\infty)$. Then $A$ has a bounded $\mathcal{H}^{\infty}$calculus from $\mathrm{D}_{A}(\tfrac{1}{p}\tfrac{1}{q},1)$ to $X$, i.e. $f(A):\mathrm{D}_{A}(\tfrac{1}{p}\tfrac{1}{q},1)\to X$ is bounded for each bounded holomorphic function $f$ on a sufficiently large strip. As a corollary of our main theorem, for sectorial operators we quantify the gap between bounded imaginary powers and a bounded $\mathcal{H}^{\infty}$calculus in terms of the type and cotype of the underlying Banach space. For cosine functions we obtain similar results as for $C_{0}$groups. We extend our results to $R$bounded operatorvalued calculi, and we give an application to the theory of rational approximation of $C_{0}$groups.
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In this paper we study a system of boundary value problems involving weak pLaplacian on the Sierpi\'nski gasket in $\mathbb{R}^2$. Parameters $\lambda, \gamma, \alpha, \beta$ are real and $1<q<p<\alpha+\beta.$ Functions $a,b,h : \mathcal{S} \rightarrow \mathbb{R}$ are suitably chosen. For $p>1$ we show the existence of at least two nontrivial weak solutions to the system of equations for some $(\lambda,\gamma) \in \mathbb{R}^2.$
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Cooperative computation is a promising approach for localized data processing at the edge, e.g., for Internet of Things (IoT). Cooperative computation advocates that computationally intensive tasks in a device could be divided into subtasks, and offloaded to other devices or servers in close proximity. However, exploiting the potential of cooperative computation is challenging mainly due to the heterogeneous and timevarying nature of edge devices. Coded computation, which advocates mixing data in subtasks by employing erasure codes and offloading these subtasks to other devices for computation, is recently gaining interest, thanks to its higher reliability, smaller delay, and lower communication costs. In this paper, we develop a coded cooperative computation framework, which we name Coded Cooperative Computation Protocol (C3P), by taking into account the heterogeneous resources of edge devices. C3P dynamically offloads coded subtasks to helpers and is adaptive to timevarying res
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We consider the discrepancy of the integer lattice with respect to the collection of all translated copies of a dilated convex body having a finite number of flat, possibly nonsmooth, points in its boundary. We estimate the $L^{p}$ norm of the discrepancy with respect to the translation variable as the dilation parameter goes to infinity. If there is a single flat point with normal in a rational direction we obtain an asymptotic expansion for this norm. Anomalies may appear when two flat points have opposite normals. When all the flat points have normals in generic irrational directions, we obtain a smaller discrepancy. Our proofs depend on careful estimates for the Fourier transform of the characteristic function of the convex body.
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We collect three observations on the homology for Smale spaces defined by Putnam. The definition of such homology groups involves four complexes. It is shown here that a simple convergence theorem for spectral sequences can be used to prove that all complexes yield the same homology. Furthermore, we introduce a simplicial framework by which the various complexes can be understood as suitable "symmetric" Moore complexes associated to the simplicial structure. The last section discusses projective resolutions in the context of dynamical systems. It is shown that the projective cover of a Smale space is realized by the system of shift spaces and factor maps onto it.
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For more than half a century lattices in Lie groups played an important role in geometry, number theory and group theory. Recently the notion of Invariant Random Subgroups (IRS) emerged as a natural generalization of lattices. It is thus intriguing to extend results from the theory of lattices to the context of IRS, and to study lattices by analyzing the compact space of all IRS of a given group. This article focuses on the interplay between lattices and IRS, mainly in the classical case of semisimple analytic groups over local fields.
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We derive exact formulas for the expectation value of local observables in a onedimensional gas of bosons with pointwise repulsive interactions (LiebLiniger model). Starting from a recently conjectured expression for the expectation value of vertex operators in the sinhGordon field theory, we derive explicit analytic expressions for the onepoint $K$body correlation functions $\langle (\Psi^\dagger)^K(\Psi)^K\rangle$ in the LiebLiniger gas, for arbitrary integer $K$. These are valid for all excited states in the thermodynamic limit, including thermal states, generalized Gibbs ensembles and nonequilibrium steady states arising in transport settings. Our formulas display several physically interesting applications: most prominently, they allow us to compute the full counting statistics for the particlenumber fluctuations in a short interval. Furthermore, combining our findings with the recently introduced generalized hydrodynamics, we are able to study multipoint correlation fun
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In recent years, considerable interest has been drawn by the analysis of geometric functionals for the excursion sets of random eigenfunctions on the unit sphere (spherical harmonics). In this paper, we extend those results to proper subsets of the sphere $\mathbb{S}^2$, i.e., spherical caps, focussing in particular on the excursion area. Precisely, we show that the asymptotic behavior of the excursion area is dominated by the socalled secondorder chaos component, and we exploit this result to establish a Quantitative Central Limit Theorem, in the high energy limit. These results generalize analogous findings for the full sphere; their proofs, however, requires more sophisticated techniques, in particular a careful analysis (of some independent interest) for smooth approximations of the indicator function for spherical caps subsets.
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Lorenzo FranceschiBicchierai of Motherboard has a chilling story on how hackers flip seized Instagram handles and cryptocurrency in a shady, buzzing underground market for stolen accounts and usernames. Their victim's weakness? Phone numbers. He writes: First, criminals call a cell phone carrier's tech support number pretending to be their target. They explain to the company's employee that they "lost" their SIM card, requesting their phone number be transferred, or ported, to a new SIM card that the hackers themselves already own. With a bit of social engineering  perhaps by providing the victim's Social Security Number or home address (which is often available from one of the many data breaches that have happened in the last few years)  the criminals convince the employee that they really are who they claim to be, at which point the employee ports the phone number to the new SIM card. Game over.
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Control and estimation on largescale social networks often necessitate the availability of models for the interactions amongst the agents in the network. However characterizing accurate models of social interactions pose new challenges due to their inherent complexity and unpredictability. Moreover, model uncertainty on the interaction dynamics becomes more pronounced for largescale networks. For certain classes of social networks, in the meantime, the layering structure allows a compositional approach for modeling as well as control and estimation. The layering can be induced in the network, for example, due to the presence of distinct social types and other indicators, such as geography and financial ties. In this paper, we present a compositional approach to determine performance guarantees on layered networks with inherent model uncertainties induced by the network. To this end, we use a factorization approach to determine robust stability and performance of the composite network
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For arbitrary radial weights $w$ and $u$, we study the integration operator between the growth spaces $H_w^\infty$ and $H_u^\infty$ on the complex plane. Also, we investigate the differentiation operator on the Hardy growth spaces $H_w^p$, $0<p<\infty$, defined on the unit disk or on the complex plane. As in the case $p=\infty$, the logconvex weights $w$ play a special role in the problems under consideration.
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The antimaximum principle for the homogeneous Dirichlet problem to $\Delta_p = \lambda u^{p2}u + f(x)$ with positive $f \in L^\infty(\Omega)$ states the existence of a critical value $\lambda_f > \lambda_1$ such that any solution of this problem with $\lambda \in (\lambda_1, \lambda_f)$ is strictly negative. In this paper, we give a variational upper bound for $\lambda_f$ and study its properties. As an important supplementary result, we investigate the branch of ground state solutions of the considered boundary value problem on $(\lambda_1,\lambda_2)$.
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