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新葡京娱乐城大厅 www.widgetbakery.com Microsoft documents the limitations of Windows 10 on ARM
0220 OSnews 13This week, however, Microsoft finally published a more complete list of the limitations of Windows 10 on ARM. And that word  limitations  is interesting. This isn't how Windows 10 on ARM differs from Windows 10 on x86based systems. It's how it's more limited. None of these things really sound all that surprising to me, but you can bet these limitations  which seem technical in nature, not political  will lead to outcries among some people who buy ARMbased Windows 10 machines.
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The end of Microsoft's Windows Phone project has been a long time coming, and now there's another nail in the coffin. From a report: Microsoft is ending support for all push notifications for Windows Phone 7.5 and Windows Phone 8.0 starting Tuesday, February 20th. According to Microsoft's blog post, in addition to the discontinuation of push notifications, live tiles will no longer be updated and the find my phone feature will not work. It's important to note that this doesn't apply to newer devices.
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For over a year we've been treated to the fantasy that Windows 10 on ARM was the same as Windows 10 on x86. But it's a bit more nuanced than that. Paul Thurrott: 64bit apps will not work. Yes, Windows 10 on ARM can run Windows desktop applications. But it can only run 32bit (x86) desktop applications, not 64bit (x64) applications. (The documentation doesn't note this, but support for x64 apps is planned for a future release.) Certain classes of apps will not run. Utilities that modify the Windows user interface  like shell extensions, input method editors (IMEs), assistive technologies, and cloud storage apps  will not work in Windows 10 on ARM. It cannot use x86 drivers. While Windows 10 on ARM can run x86 Windows applications, it cannot utilize x86 drivers. Instead, it will require native ARM64 drivers instead. This means that hardware support will be much more limited than is the case with mainstream Windows 10 versions. In other words, it will likely work much like Windows 1
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Britons should be able to bid for 10,000 pound (roughly $14,000) to help them prosper amid huge changes to their working lives, a leading think tank suggests today. From a report: The Royal Society for the Arts (RSA) has released research proposing a radical new sovereign wealth fund, which would be invested to make a profit like similar public funds in Norway. The returns from the fund would be used to build a pot of money, to which workingage adults under55 would apply to receive a grant in the coming decade. People would have to set out how they intend to put the fivefigure payouts to good use, for example, by using the cash to undergo retraining, to start a new business, or to combine work with the care of elderly or sick relatives. It would be funded like the student grant system and wealthier individuals could be required to pay back more in tax as their earnings increase. Ultimately, the RSA paper suggests, the wealth fund would finance a Universal Basic Income (UBI) as the
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Ian Barker, writing for BetaNews: While US government agencies are continuing to improve their security performance over time, the contractors they employ are failing to meet the same standards according to a new report. The study by security rankings specialist BitSight sampled over 1,200 federal contractors and finds that the security rating for federal agencies was 15 or more points higher than the mean of any contractor sector. It finds more than eight percent of healthcare and wellness contractors have disclosed a data breach since January 2016. Aerospace and defense firms have the next highest breach disclosure rate at 5.6 percent. While government has made a concerted effort to fight botnets in recent months, botnet infections are still prevalent among the government contractor base, particularly for healthcare and manufacturing contractors. The study also shows many contractors are not following best practices for network encryption and email security.
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Let $D$ be a fundamental discriminant. We prove that under GRH almost all binary quadratic forms of discriminant $D<0$ represent a prime number smaller than $\sqrt{D}\log(D)^{2+\varepsilon}$ and every binary quadratic form of Discriminant $D$ represent a prime number smaller than $D\log(D)^{2+\varepsilon}$. As a corollary, this shows that almost all ideal classes in the ideal class group of $\mathbb{Q}(\sqrt{D})$ contains a prime ideal of norm not exceeding $\sqrt{D}\log(D)^{2+\epsilon}.$ This generalized the Minkowski's bound on the least integral ideals to the prime ideals in a given ideal class. We conjecture that this Minkowski's bound holds for every number fields.
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We consider the polyharmonic equations $\Delta^m u = \pm u^{\alpha}$ in $\mathbb R^n$ with $n \geqslant 1$, $m \geqslant 1$ and $\alpha \in \mathbb R$. We study the existence of entire nontrivial nonnegative solutions and/or entire positive solutions. In each case, we provide necessary and sufficient conditions on the exponent $\alpha$ to guarantee the existence of such classical solutions in $\mathbb R^n$.
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We demonstrate that a MeijerGfunctionbased resummation approach can be successfully applied to approximate the Borel sum of divergent series, and thus to approximate the Borel\'Ecalle summation of resurgent transseries in quantum field theory (QFT). The proposed method is shown to vastly outperform the conventional BorelPad\'e and BorelPad\'e\'Ecalle summation methods. The resulting MeijerG approximants are easily parameterized by means of a hypergeometric ansatz and can be thought of as a generalization to arbitrary order of the BorelHypergeometric method [Mera {\it et al.} Phys. Rev. Lett. {\bf 115}, 143001 (2015)]. Here we illustrate the ability of this technique in various examples from QFT, traditionally employed as benchmark models for resummation, such as: 0dimensional $\phi^4$ theory, $\phi^4$ with degenerate minima, selfinteracting QFT in 0dimensions, and the computation of one and twoinstanton contributions in the quantummechanical doublewell problem.
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In this paper we provide a dynamical characterization of isolated invariant continua which are global attractors for planar dissipative flows. As a consequence, a sufficient condition for an isolated invariant continuum to be either an attractor or a repeller is derived for general planar flows.
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We consider the category of perverse sheaves on a complex vector space smooth with respect to a stratification given by an arrangement of hyperplanes with real equations. As shown in an earlier wotk of two of the authors, this category can be described in terms of certain diagrams of vector spaces labelled by all the faces of the real arrangement (we call such diagrams hyperbolic sheaves). In this paper we calculate, in these terms, several fundamental operations of sheaf theory such as forming the space of vanishing cycles, specialization and the FourierSato transform.
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Highorder methods for conservation laws can be highly efficient if their stability is ensured. A suitable means mimicking estimates of the continuous level is provided by summationbyparts (SBP) operators and the weak enforcement of boundary conditions. Recently, there has been an increasing interest in generalised SBP operators both in the finite difference and the discontinuous Galerkin spectral element framework. However, if generalised SBP operators are used, the treatment of the boundaries becomes more difficult since some properties of the continuous level are no longer mimicked discretely  interpolating the product of two functions will in general result in a value different from the product of the interpolations. Thus, desired properties such as conservation and stability are more difficult to obtain. Here, new formulations are proposed, allowing the creation of discretisations using general SBP operators that are both conservative and stable. Thus, several shortcomings th
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We study McKeanVlasov stochastic control problems where both the cost functions and the state dynamics depend upon the joint distribution of the controlled state and the control process. Our contribution is twofold. On the one hand, we prove a suitable version of the Pontryagin stochastic maximum principle (in necessary and in sufficient form). On the other hand, we suggest a variational approach to study a weak formulation of these difficult control problems. In this context, we derive a necessary martingale optimality condition, and we establish a new connection between such problems and an optimal transport problem on path space.
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Given a pair of random variables $(X,Y)\sim P_{XY}$ and two convex functions $f_1$ and $f_2$, we introduce two bottleneck functionals as the lower and upper boundaries of the twodimensional convex set that consists of the pairs $\left(I_{f_1}(W; X), I_{f_2}(W; Y)\right)$, where $I_f$ denotes $f$information and $W$ varies over the set of all discrete random variables satisfying the Markov condition $W \to X \to Y$. Applying Witsenhausen and Wyner's approach, we provide an algorithm for computing boundaries of this set for $f_1$, $f_2$, and discrete $P_{XY}$, . In the binary symmetric case, we fully characterize the set when (i) $f_1(t)=f_2(t)=t\log t$, (ii) $f_1(t)=f_2(t)=t^21$, and (iii) $f_1$ and $f_2$ are both $\ell^\beta$ norm function for $\beta > 1$. We then argue that upper and lower boundaries in (i) correspond to Mrs. Gerber's Lemma and its inverse (which we call Mr. Gerber's Lemma), in (ii) correspond to estimationtheoretic variants of Information Bottleneck and Privacy
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We give an analog of a ChevalleySerre presentation for the Lie superalgebras W(n) and S(n) of Cartan type. These are part of a wider class of Lie superalgebras, the socalled tensor hierarchy algebras, denoted W(g) and S(g), where g denotes the KacMoody algebra A_r, D_r or E_r. Then W(A_{n1}) and S(A_{n1}) are the Lie superalgebras W(n) and S(n). The algebras W(g) and S(g) are constructed from the Dynkin diagram of the BorcherdsKacMoody superalgebras B(g) obtained by adding a single grey node (representing an odd null root) to the Dynkin diagram of g. We redefine the algebras W(A_r) and S(A_r) in terms of Chevalley generators and defining relations. We prove that all relations follow from the defining ones at level 2 and higher. The analogous definitions of the algebras in the D and Eseries are given. In the latter case the full set of defining relations is conjectured.
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Using the theory of generalized hydrodynamics (GHD), we derive exact Eulerscale dynamical twopoint correlation functions of conserved densities and currents in inhomogeneous, nonstationary states of manybody integrable systems with weak spacetime variations. This extends previous works to inhomogeneous and nonstationary situations. Using GHD projection operators, we further derive formulae for Eulerscale twopoint functions of arbitrary local fields, purely from the data of their homogeneous onepoint functions. These are new also in homogeneous generalized Gibbs ensembles. The technique is based on combining a fluctuationdissipation theorem along with the exact solution by characteristics of GHD, and gives a recursive procedure able to generate $n$point correlation functions. Owing to the universality of GHD, the results are expected to apply to quantum and classical integrable field theory such as the sinhGordon model and the LiebLiniger model, spin chains such as the XXZ
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We consider a general form of a parabolic equation that generalizes both the standard parabolic $p$Laplace equation and the normalized version that has been proposed in stochastic game theory. We establish an equivalence between this equation and the standard $p$parabolic equation posed in a fictitious space dimension, valid for radially symmetric solutions. This allows us to find suitable explicit solutions for example of Barenblatt type, and as a consequence we settle the exact asymptotic behaviour of the Cauchy problem even for nonradial data. We also establish the asymptotic behaviour in a bounded domain. Moreover, we use the explicit solutions to establish the parabolic Harnack's inequality.
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Let $G$ be a linear algebraic group over a field $k$ of characteristic 0. We show that any two connected semisimple $k$subgroups of $G$ that are conjugate over an algebraic closure of $k$ are actually conjugate over a finite field extension of $k$ of degree bounded independently of the subgroups. Moreover, if $k$ is a real number field, we show that any two connected semisimple $k$subgroups of $G$ that are conjugate over the field of real numbers $\mathbb{R}$ are actually conjugate over a finite real extension of $k$ of degree bounded independently of the subgroups.
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We derive the porous medium equation from an interacting particle system which belongs to the family of exclusion processes, with nearest neighbor exchanges. The particles follow a degenerate dynamics, in the sense that the jump rates can vanish for certain configurations, and there exist blocked configurations that cannot evolve. In [Gon\c{c}alvesLandimToninelli '09] it was proved that the macroscopic density profile in the hydrodynamic limit is governed by the porous medium equation (PME), for initial densities uniformly bounded away from $0$ and $1$. In this paper we consider the more general case where the density can take those extreme values. In this context, the PME solutions display a richer behavior, like moving interfaces, finite speed of propagation and breaking of regularity. As a consequence, the standard techniques that are commonly used to prove this hydrodynamic limits cannot be straightforwardly applied to our case. We present here a way to generalize the \emph{relat
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We study a connection between mapping spaces of bimodules and of infinitesimal bimodules over an operad. As main application and motivation of our work, we produce an explicit delooping of the manifold calculus tower associated to the space of maps $D^{m}\rightarrow D^{n}$, $n\geq m$, avoiding any given multisingularity and coinciding with the standard inclusion near $\partial D^{m}$.
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Given $1 \leq p,q < \infty$ and $n\in\mathbb{N}_0$, let $H_n^p(H_n^q)$ denote the canonical finitedimensional biparameter dyadic Hardy space. Let $(V_n : n\in\mathbb{N}_0)$ denote either $\bigl(H_n^p(H_n^q) : n\in\mathbb{N}_0\bigr)$ or $\bigl( (H_n^p(H_n^q))^* : n\in\mathbb{N}_0\bigr)$. We show that the identity operator on $V_n$ factors through any operator $T : V_N\to V_N$ which has large diagonal with respect to the Haar system, where $N$ depends \emph{linearly} on $n$.
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In this paper we prove selfimprovement properties of strong Muckenhoupt and Reverse H\"older weights with respect to a general Radon measure on $\mathbb{R}^n$. We derive our result via a Bellman function argument. An important feature of our proof is that it uses only the Bellman function for the onedimensional problem for Lebesgue measure; with this function in hand, we derive dimension free results for general measures and dimensions.
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We show that the theory $T_{\log}$ of the asymptotic couple of the field of logarithmic transseries is distal. As distal theories are NIP (= the nonindependence property), this provides a new proof that $T_{\log}$ is NIP. Finally, we show that $T_{\log}$ is not strongly NIP, and in particular, it is not $\operatorname{dp}$minimal and it does not have finite $\operatorname{dp}$rank.
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A $\Bbbk$configuration is a set of points $\mathbb{X}$ in $\mathbb{P}^2$ that satisfies a number of geometric conditions. Associated to a $\Bbbk$configuration is a sequence $(d_1,\ldots,d_s)$ of positive integers, called its type, which encodes many of its homological invariants. We distinguish $\Bbbk$configurations by counting the number of lines that contain $d_s$ points of $\mathbb{X}$. In particular, we show that for all integers $m \gg 0$, the number of such lines is precisely the value of $\Delta \mathbf{H}_{m\mathbb{X}}(m d_s 1)$. Here, $\Delta \mathbf{H}_{m\mathbb{X}}()$ is the first difference of the Hilbert function of the fat points of multiplicity $m$ supported on $\mathbb{X}$.
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This paper deals with the problem of linear programming with inexact data represented by real closed intervals. Optimization problems with interval data arise in practical computations and they are of theoretical interest for more than forty years. We extend the concept of duality gap (DG), the difference between the primal and its dual optimal value, into interval linear programming. We consider two situations: First, DG is zero for every realization of interval parameters (the so called strongly zero DG) and, second, DG is zero for at least one realization of interval parameters (the so called weakly zero DG). We characterize strongly and weakly zero DG and its special case where the matrix of coefficients is real. We discuss computational complexity of testing weakly and strongly zero DG for commonly used types of interval linear programs and their variants with the real matrix of coefficients. We distinguish the NPhard cases and the cases that are efficiently decidable. Based on D
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We prove that the 2$n$1st homotopy groups of Ravenel's $X(n)$ spectra are cyclic for all $n$. This implies that the complex cobordism spectrum can be constructed by iteratively attaching coherently associative algebra cells to to the sphere spectrum in odd degrees. We also show that the complex cobordism spectrum can be constructed by iteratively attaching $E_k$algebra cells in odd degrees to a Thom spectrum over $\Omega^k SU(n)$, for any odd $k$ and $n=\frac{k1}{2}$. Along the way we prove some technical statements in the setting of quasicategories about the structure of $E_k$algebras built by structured cell attachments.
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In this work, we improve a previous minimalistic treegrass savanna model by taking into account water availability, in addition to fire, since both factors are known to be important for shaping savanna physiognomies along a climatic gradient. As in our previous models, we consider two nonlinear functions of grass and tree biomasses to respectively take into account grassfire feedbacks, and the response of trees to fire of a given intensity. The novelty is that rainfall is taken into account in the tree and grass growth functions and in the biomass carrying capacities. Then, we derive a qualitative analysis of the ODE model, showing existence of equilibria, and studying their stability conditions. We also construct a two dimension bifurcation diagram based on rainfall and fire frequency. This led to summarize different scenarios for the model including multistabilities that are proven possible. Next, to bring more realism in the model, pulsed fire events are modelled as part of an ID
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In the Brenier variational model for perfect fluids, the datum is the joint law of the initial and final positions of the particles. In this paper, we show that both the optimal action and the pressure field are H\"older continuous with respect to this datum metrized in MongeKantorovic distance.
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The Grassmannian $V_2(\mathbb{R}^{n+2})$ of oriented 2planes in $\mathbb R^{n+2}$ where $n\ge3$ carries a homogeneous parabolic contact structure of Grassmannian type. The main result of this article is that on $V_2(\mathbb{R}^{n+2})$ lives an elliptic complex of invariant differential operators of length 3 which starts with the 2Dirac operator and that the index of the complex is zero.
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Interference during the uplink training phase significantly deteriorates the performance of a massive MIMO system. The impact of the interference can be reduced by exploiting second order statistics of the channel vectors, e.g., to obtain minimum mean squared error estimates of the channel. In practice, the channel covariance matrices have to be estimated. The estimation of the covariance matrices is also impeded by the interference during the training phase. However, the coherence interval of the covariance matrices is larger than that of the channel vectors. This allows us to derive methods for accurate covariance matrix estimation by appropriate assignment of pilot sequences to users in consecutive channel coherence intervals.
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Deployment of Long Term Evolution (LTE) in unlicensed spectrum has been a candidate feature to meet the explosive growth of traffic demand since 3GPP release 13. To further explore the advantage of unlicensed bands, in this context the operation of both uplink and downlink has been supported and studied in the subsequent releases. However, it has been identified that scheduled uplink transmission performance in unlicensed spectrum is significantly degraded due to the double listenbeforetalk (LBT) requirements at both eNB when sending the uplink grant, and at the scheduled UEs before transmission. In this paper, in order to overcome this issue, a novel uplink transmission scheme, which does not require any grant, is proposed, and the details regarding the system design are provided. By modeling the dynamics in time of the LBT for both a system that employs a conventional uplink scheme, as well as the proposed scheme, it is verified through analytical evaluation that the double LBT sch
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An exact Lagrangian submanifold $L$ in the symplectization of standard contact $(2n1)$space with Legendrian boundary $\Sigma$ can be glued to itself along $\Sigma$. This gives a Legendrian embedding $\Lambda(L,L)$ of the double of $L$ into contact $(2n+1)$space. We show that the Legendrian isotopy class of $\Lambda(L,L)$ is determined by formal data: the manifold $L$ together with a trivialization of its complexified tangent bundle. In particular, if $L$ is a disk then $\Lambda(L,L)$ is the Legendrian unknot.
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We consider discrete time branching random walk on real line where the displacements of particles coming from the same parent are allowed to be dependent and jointly regularly varying. Using the one large bunch asymptotics, we derive large deviation for the extremal processes associated to the suitably scaled positions of particles in the $n$th generation where the genealogical tree satisfies KestenStigum condition. The large deviation limiting measure in this case is identified in terms of the cluster Poisson point process obtained in the underlying weak limit of the point processes. As a consequence of this, we derive large deviation for the rightmost particle in the $n$th generation giving the heavytailed analogue of recent work by Gantert and H\"{o}felsauer (2018).
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This paper addresses detecting anomalous patterns in images, timeseries, and tensor data when the location and scale of the pattern is unknown a priori. The multiscale scan statistic convolves the proposed pattern with the image at various scales and returns the maximum of the resulting tensor. Scale corrected multiscale scan statistics apply different standardizations at each scale, and the limiting distribution under the null hypothesisthat the data is only noiseis known for smooth patterns. We consider the problem of simultaneously learning and detecting the anomalous pattern from a dictionary of smooth patterns and a database of many tensors. To this end, we show that the multiscale scan statistic is a subexponential random variable, and prove a chaining lemma for standardized suprema, which may be of independent interest. Then by averaging the statistics over the database of tensors we can learn the pattern and obtain Bernsteintype error bounds. We will also provide a cons
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It has been recently established that a deterministic infinite horizon discounted optimal control problem in discrete time is closely related to a certain infinite dimensional linear programming problem and its dual. In the present paper, we use these results to establish necessary and sufficient optimality conditions for this optimal control problem and apply them to construct a near optimal control.
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In this paper we establish optimal local and global BesovLipschitz and TriebelLizorkin estimates for the solutions to linear hyperbolic partial differential equations. These estimates are based on local and global estimates for Fourier integral operators that span all possible scales (and in particular both Banach and quasiBanach scales) of BesovLipschitz spaces $B^s_{p,q}(\R^n)$, and certain Banach and quasiBanach scales of TriebelLizorkin spaces $F^s_{p,q}(\R^n)$
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We study some limit theorems for the law of a generalized onedimensional diffusion weighted and normalized by a nonnegative function of the local time evaluated at a parametrized family of random times (which we will call a clock). As the clock tends to infinity, we show that the initial process converges towards a new penalized process, which generally depends on the chosen clock. However, unlike with deterministic clocks, no specific assumptions are needed on the resolvent of the diffusion. We then give a path interpretation of these penalized processes via some universal $ \sigma $finite measures.
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This paper studies the asymptotic performance of maximumaposteriori estimation in the presence of prior information. The problem arises in several applications such as recovery of signals with nonuniform sparsity pattern from underdetermined measurements. With prior information, the maximumaposteriori estimator might have asymmetric penalty. We consider a generic form of this estimator and study its performance via the replica method. Our analyses demonstrate an asymmetric form of the decoupling property in the largesystem limit. Employing our results, we further investigate the performance of weighted zeronorm minimization for recovery of a nonuniform sparse signal. Our investigations illustrate that for a given distortion, the minimum number of required measurements can be significantly reduced by choosing weighting coefficients optimally.
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We provide in this work a robust solution theory for random rough differential equations of mean field type, with mean field interaction in both the drift and diffusivity. Propagation of chaos results for large systems of interacting rough differential equations are obtained as a consequence, with explicit optimal convergence rate. The development of these results requires the introduction of a new rough pathlike setting and an associated notion of controlled path. We use crucially Lions' approach to differential calculus on Wasserstein space along the way.
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The BoltzmannEnskog equation for a hard sphere gas is known to have so called microscopic solutions, i.e., solutions of the form of timeevolving empirical measures of a finite number of hard spheres. However, the precise mathematical meaning of these solutions should be discussed, since the formal substitution of empirical measures into the equation is not welldefined. Here we give a rigorous mathematical meaning to the microscopic solutions to the BoltzmannEnskog equation by means of a suitable series representation.
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The stochastic variational approach for geophysical fluid dynamics was introduced by Holm (Proc Roy Soc A, 2015) as a framework for deriving stochastic parameterisations for unresolved scales. The key feature of transport noise is that it respects the Kelvin circulation theorem. This paper applies the variational stochastic parameterisation in a twolayer quasigeostrophic model for a $\beta$plane channel flow configuration. The parameterisation is tested by comparing it with a deterministic high resolution eddyresolving solution that has reached statistical equilibrium. We describe a stochastic timestepping scheme for the twolayer model and discuss its consistency in time. Then we describe a procedure for estimating the stochastic forcing to approximate unresolved components using data from the high resolution deterministic simulation. We compare an ensemble of stochastic solutions at lower resolution with the numerical solution of the deterministic model. These computations quant
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Elliptic boundary value problems which are posed on a random domain can be mapped to a fixed, nominal domain. The randomness is thus transferred to the diffusion matrix and the loading. This domain mapping method is quite efficient for theory and practice, since only a single domain discretization is needed. Nonetheless, it is not useful for applying multilevel accelerated methods to efficiently deal with the random parameter. This issues from the fact that the domain discretization needs to be fine enough in order to avoid indefinite diffusion matrices. To overcome this obstruction, we are going to couple the finite element method with the boundary element method. In this article, we verify the required regularity with respect to the random perturbation field, derive the coupling formulation, and show by numerical results that the approach is feasible.
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We study several classes of nonassociative algebras as possible candidates for deformation quantization in the direction of a Poisson bracket that does not satisfy Jacobi identities. We show that in fact alternative deformation quantization algebras require the Jacobi identities on the Poisson bracket and, under very general assumptions, are associative. At the same time, flexible deformation quantization algebras exist for any Poisson bracket.
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PseudoRiemannian metrics with LeviCivita connection in the projective class of a given torsion free affine connection can be obtained from (and are equivalent to) the maximal rank solutions of a certain overdetermined projectively invariant differential equation often called the metrizability equation. Dropping this rank assumption we study the solutions to this equation given less restrictive generic conditions on its prolonged system. In this setting we find that the solution stratifies the manifold according to the strict signature (pointwise) of the solution and does this in way that locally generalizes the stratification of a model, where the model is, in each case, a corresponding Lie group orbit decomposition of the sphere. Thus the solutions give curved generalizations of such embedded orbit structures. We describe the smooth nature of the strata and determine the geometries of each of the different strata types; this includes a metric on the open strata that becomes singular
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Knowing the connectivity and line parameters of the underlying electric distribution network is a prerequisite for solving any grid optimization task. Although distribution grids lack observability and comprehensive metering, inverters with advanced cyber capabilities currently interface solar panels and energy storage devices to the grid. Smart inverters have been widely used for grid control and optimization, yet the fresh idea here is to engage them towards network topology inference. Being an electric circuit, a distribution grid can be intentionally probed by instantaneously perturbing inverter injections. Collecting and processing the incurred voltage deviations across nodes can potentially unveil the grid topology even without knowing loads. Using grid probing data and under an approximate grid model, the tasks of topology recovery and line status verification are posed respectively as nonconvex estimation and detection problems. Leveraging the features of the Laplacian matrix
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Regularization has become a primary tool for developing reliable estimators of the covariance matrix in highdimensional settings. To curb the curse of dimensionality, numerous methods assume that the population covariance (or inverse covariance) matrix is sparse, while making no particular structural assumptions on the desired pattern of sparsity. A highlyrelated, yet complementary, literature studies the specific setting in which the measured variables have a known ordering, in which case a banded population matrix is often assumed. While the banded approach is conceptually and computationally easier than asking for "patternless sparsity," it is only applicable in very specific situations (such as when data are measured over time or onedimensional space). This work proposes a generalization of the notion of bandedness that greatly expands the range of problems in which banded estimators apply. We develop convex regularizers occupying the broad middle ground between the former appro
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Graphene is locally twodimensional but not flat. Nanoscale ripples appear in suspended samples and rollingup often occurs when boundaries are not fixed. We address this variety of graphene geometries by classifying all groundstate deformations of the hexagonal lattice with respect to configurational energies including two and threebody terms. As a consequence, we prove that all groundstate deformations are either periodic in one direction, as in the case of ripples, or rolled up, as in the case of nanotubes.
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We consider the problem of constructing a cyclic listing of all bitstrings of length $2n+1$ with Hamming weights in the interval $[n+1\ell,n+\ell]$, where $1\leq \ell\leq n+1$, by flipping a single bit in each step. This is a farranging generalization of the wellknown middle two levels problem (the case $\ell=1$). We provide a solution for the case $\ell=2$ and solve a relaxed version of the problem for general values of $\ell$, by constructing cycle factors for those instances. Our proof uses symmetric chain decompositions of the hypercube, a concept known from the theory of posets, and we present several new constructions of such decompositions. In particular, we construct four pairwise edgedisjoint symmetric chain decompositions of the $n$dimensional hypercube for any $n\geq 12$.
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For a given graph $G$, the least integer $k\geq 2$ such that for every Abelian group $\mathcal{G}$ of order $k$ there exists a proper edge labeling $f:E(G)\rightarrow \mathcal{G}$ so that $\sum_{x\in N(u)}f(xu)\neq \sum_{x\in N(v)}f(xv)$ for each edge $uv\in E(G)$ is called the \textit{group twin chromatic index} of $G$ and denoted by $\chi'_g(G)$. This graph invariant is related to a few wellknown problems in the field of neighbor distinguishing graph colorings. We conjecture that $\chi'_g(G)\leq \Delta(G)+3$ for all graphs without isolated edges, where $\Delta(G)$ is the maximum degree of $G$, and provide an infinite family of connected graph (trees) for which the equality holds. We prove that this conjecture is valid for all trees, and then apply this result as the base case for proving a general upper bound for all graphs $G$ without isolated edges: $\chi'_g(G)\leq 2(\Delta(G)+{\rm col}(G))5$, where ${\rm col}(G)$ denotes the coloring number of $G$. This improves the best known u
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This paper establishes by employing analytic and probabilistic techniques estimates concerning the {\it heat content} for the fractional Schr\"odinger operator $\F+\ind$ with $0<\alpha\leq 2$ in $\Rd$, $d\geq 2$ and $\dom$ a Lebesgue measure set satisfying some regularity conditions.
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We argue that the scattering of gravitons in ordinary Einstein gravity possesses a hidden conformal symmetry at tree level in any number of dimensions. The presence of this conformal symmetry is indicated by the dilaton soft theorem in string theory, and it is reminiscent of the conformal invariance of gluon treelevel amplitudes in four dimensions. To motivate the underlying prescription, we demonstrate that formulating the conformal symmetry of gluon amplitudes in terms of momenta and polarization vectors requires manifest reversal and cyclic symmetry. Similarly, our formulation of the conformal symmetry of graviton amplitudes relies on a manifestly permutation symmetric form of the amplitude function.
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We consider a stochastic flow $\phi_t(x,\omega)$ in $\mathbb{R}^n$ with initial point $\phi_0(x,\omega)=x$, driven by a single $n$dimensional Brownian motion, and with an outward radial drift of magnitude $\frac{ F(\\phi_t(x)\)}{\\phi_t(x)\}$, with $F$ nonnegative, bounded and Lipschitz. We consider initial points $x$ lying in a ball of positive distance from the origin. We show that there exist constants $C^*,c^*>0$ not depending on $n$, such that if $F>C^*n$ then the image of the initial ball under the flow has probability 0 of hitting the origin. If $0\leq F<c^*n/\log n$, then the image of the ball has positive probability of hitting the origin.
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Schrijver identified a family of vertex critical subgraphs of the Kneser graphs called the stable Kneser graphs $SG_{n,k}$. Bj\"{o}rner and de Longueville proved that the neighborhood complex of the stable Kneser graph $SG_{n,k}$ is homotopy equivalent to a $k$sphere. In this article, we prove that the homotopy type of the neighborhood complex of the Kneser graph $KG_{2,k}$ is a wedge of $(k+4)(k+1)+1$ spheres of dimension $k$. We construct a maximal subgraph $S_{2,k}$ of $KG_{2,k}$, whose neighborhood complex is homotopy equivalent to the neighborhood complex of $SG_{2,k}$. Further, we prove that the neighborhood complex of $S_{2,k}$ deformation retracts onto the neighborhood complex of $SG_{2,k}$.
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The Killing tensor equation is a first order differential equation on symmetric covariant tensors that generalises to higher rank the usual Killing vector equation on Riemannian manifolds. We view this more generally as an equation on any manifold equipped with an affine connection, and in this setting derive its prolongation to a linear connection. This connection has the property that parallel sections are in 11 correspondence with solutions of the Killing equation. Moreover this connection is projectively invariant and is derived entirely using the projectively invariant tractor calculus which reveals also further invariant structures linked to the prolongation.
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Let $X$ and $Y$ be finite complexes. When $Y$ is a nilpotent space, it has a rationalization $Y \to Y_{(0)}$ which is wellunderstood. Sullivan showed that the induced map $[X,Y] \to [X,Y_{(0)}]$ on sets of mapping classes is finitetoone. The sizes of the preimages need not be bounded; we show, however, that as the complexity (in a suitable sense) of a rational mapping class increases, these sizes are polynomially bounded. This "torsion" information about $[X,Y]$ is in some sense orthogonal to rational homotopy theory but is nevertheless an invariant of the rational homotopy type of $Y$ in at least some cases. The notion of complexity is geometric and we also prove a conjecture of Gromov regarding the number of mapping classes that have Lipschitz constant at most $L$.
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Shannon's mathematical theory of communication defines fundamental limits on how much information can be transmitted between the different components of any manmade or biological system. This paper is an informal but rigorous introduction to the main ideas implicit in Shannon's theory. An annotated reading list is provided for further reading.
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We study a modified version of a preypredator system with modified LeslieGower and Holling type II functional response studied by M.A. AzizAlaoui and M. DaherOkiye. The modification consists in incorporating a refuge for preys, and substantially complicates the dynamics of the system. We also investigate a stochastic perturbation of the system.
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Menasco showed that a nonsplit, prime, alternating link that is not a 2braid is hyperbolic in $S^3$. We prove a similar result for links in closed thickened surfaces $S \times I$. We define a link to be fully alternating if it has an alternating projection from $S\times I$ to $S$ where the interior of every complementary region is an open disk. We show that a prime, fully alternating link in $S\times I$ is hyperbolic. Similar to Menasco, we also give an easy way to determine primeness in $S\times I$. A fully alternating link is prime in $S\times I$ if and only if it is "obviously prime". Furthermore, we extend our result to show that a prime link with fully alternating projection to an essential surface embedded in an orientable, hyperbolic 3manifold has a hyperbolic complement.
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According to a report in The New York Times (Warning: source may be paywalled), Ajit Pai and the FCC approved a set of rules in 2017 to allow television broadcasters to increase the number of stations they own. Weeks after the rules were approved, Sinclair Broadcasting announced a $3.9 billion deal to buy Tribune Media. PC Gamer reports: The deal was made possible by the new set of rules, which subsequently raised some eyebrows. Notably, the FCC's inspector general is reportedly investigating if Pai and his aides abused their position by pushing for the rule changes that would make the deal possible, and timing them to benefit Sinclair. The extent of the investigation is not clear, nor is how long it will take. However, it does bring up the question of whether Pai had coordinated with Sinclair, and it could force him to publicly address the topic, which he hasn't really done up to this point. Legislators first pushed for an investigation into this matter last November. At the time, a s
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The shallow water equations (SWE) are a widely used model for the propagation of surface waves on the oceans. In particular, the SWE are used to model the propagation of tsunami waves in the open ocean. We consider the associated data assimilation problem of optimally determining the initial conditions for the onedimensional SWE in an unbounded domain from a small set of observations of the sea surface height and focus on how the structure of the observation operator affects the convergence of the gradient approach employed to solve the data assimilation problem computationally. In the linear case we prove a theorem that gives sufficient conditions for convergence to the true initial conditions. It asserts that at least two observation points must be used and at least one pair of observation points must be spaced more closely than half the effective minimum wavelength of the energy spectrum of the initial conditions. Our analysis is confirmed by numerical experiments for both the line
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A growing number of Coinbase customers are complaining that the cryptocurrency exchange withdrew unauthorized money out of their accounts. From a report: In some cases, this drained their linked bank accounts below zero, resulting in overdraft charges. In a typical anecdote posted on Reddit, one user said they purchased Bitcoin, Ether, and Litecoin for a total of $300 on February 9th. A few days later, the transactions repeated five times for a total of $1,500, even though the user had not made any more purchases. That was enough to clear out this user's bank account, they said, resulting in fees. [...] Coinbase representatives have been responding to similar complaints on Reddit for about two weeks, but the volume of complaints seems to have spiked over the last 24 hours. Similar complaints have popped up on forums and Twitter.
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TorrentFreak: As entertainment companies and Internet services spar over the boundaries of copyright law, the EFF is urging the US Copyright Office to keep "copyright's safe harbors safe." In a petition just filed with the office, the EFF warns that innovation will be stymied if Congress goes ahead with a plan to introduce proactive 'piracy' filters at the expense of the DMCA's current safe harbor provisions. [...] "Major media and entertainment companies and their surrogates want Congress to replace today's DMCA with a new law that would require websites and Internet services to use automated filtering to enforce copyrights. "Systems like these, no matter how sophisticated, cannot accurately determine the copyright status of a work, nor whether a use is licensed, a fair use, or otherwise noninfringing. Simply put, automated filters censor lawful and important speech," the EFF warns.
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Linux Journal takes a look at the newly announced LinuxBoot project. LWN covered a related talk back in November. "Modern firmware generally consists of two main parts: hardware initialization (early stages) and OS loading (late stages). These parts may be divided further depending on the implementation, but the overall flow is similar across boot firmware. The late stages have gained many capabilities over the years and often have an environment with drivers, utilities, a shell, a graphical menu (sometimes with 3D animations) and much more. Runtime components may remain resident and active after firmware exits. Firmware, which used to fit in an 8 KiB ROM, now contains an OS used to boot another OS and doesn't always stop running after the OS boots. LinuxBoot replaces the late stages with a Linux kernel and initramfs, which are used to load and execute the next stage, whatever it may be and wherever it may come from. The Linux kernel included in LinuxBoot is called the 'boot ke
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