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Longtime Slashdot reader Noryungi writes: NASA will celebrate the 40th anniversary of the launch of the twin Voyager probes next month. So let us celebrate both the probes and the people who are still working on them, and nursing them in their final years. The New York Times fondly profiles Voyager's nine aging flightteam engineers who "may be the last people left on the planet who can operate the spacecraft's onboard computers, which have 235,000 times less memory and 175,000 times less speed than a 16gigabyte smartphone." NASA reports that now "Voyager 1 is in 'Interstellar space' and Voyager 2 is currently in the 'Heliosheath'  the outermost layer of the heliosphere where the solar wind is slowed by the pressure of interstellar gas. " But the Times notes that the probes "are running out of fuel. (Decaying plutonium supplies their power.) By 2030 at the latest, they will not have enough juice left to run a single experiment." NASA is now inviting the public to submit positiv
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An anonymous reader writes: This week the L.A. Times described a 17yearold from Virginia who'd spent several hours a day perfecting his technique in Microsoft Excel, "one of 150 students from 50 countries competing in the Microsoft Office Specialist World Championship" at the Disneyland Hotel in Anaheim. "At stake: cash, prizes and the clout that comes with being the best in the world at Excel, PowerPoint or Word. 'I'm going to do my best to bring it home for the United States,' John said as he prepared for the competition." Microsoft's VP of Worldwide Education said the event helps students "to become more employable to companies that build their businesses around the Microsoft suite." For example, the article points out, "Past winners have gone on to attend Ivy League colleges and even work at, yes, Microsoft... Delaware resident Anirudh Narayanan, 17, prepared all summer to compete in the Excel 2013 category, 'looking up obscure facts just in case I might need to know it during th
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An anonymous reader writes: An engineer at Google's Mountain View headquarters circulated a 3,400word essay internally that argued a "moral bias" exists at Google that's "shaming dissenters" and silencing their voices against "encroaching extremist and authoritarian policies." It attributes the gender gap in technology to biologybased differences in abilities (such as "speaking up" and "leading") and different personality traits (including "neuroticism"). Its suggested remedies include "Stop alienating conservatives" (calling it "noninclusive" and "bad business because conservatives tend to be higher in conscientiousness"), and it also suggests as a solution to "deemphasize empathy" (which "causes us to focus on anecdotes, favor individuals similar to us, and harbor other irrational and dangerous biases"). As the essay leaked over the weekend, former Google engineer Yonatan Zunger identified its anonymous author as "not someone senior," saying the author didn't seem to understand g
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pizzutz writes: Chrome's popular Web Developer plugin was briefly hijacked on Wednesday when an attacker gained control of the author's Google account and released a new version (0.49) which injected ads into web pages of more than a million users who downloaded the update. The version was quickly replaced with an uncompromised version (0.5) and all users are urged to update immediately. Lauren Weinstein has a broader warning: While the browser firms work extensively to build topnotch security and privacy controls into the browsers themselves, the unfortunate fact is that these can be undermined by addons, some of which are downright crooked, many more of which are sloppily written and poorly maintained. Ironically, some of these addon extensions and apps claim to be providing more security, while actually undermining the intrinsic security of the browsers themselves. Others (and this is an extremely common scenario) claim to be providing additional search or shopping functionali
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The convergence to equilibrium for renormalised solutions to nonlinear reactiondiffusion systems is studied. The considered reactiondiffusion systems arise from chemical reaction networks with mass action kinetics and satisfy the complex balanced condition. By applying the socalled entropy method, we show that if the system does not have boundary equilibria, then any renormalised solution converges exponentially to the complex balanced equilibrium with a rate, which can be computed explicitly up to a finite dimensional inequality. This inequality is proven via a contradiction argument and thus not explicitly. An explicit method of proof, however, is provided for a specific application modelling a reversible enzyme reaction by exploiting the specific structure of the conservation laws. Our approach is also useful to study the trend to equilibrium for systems possessing boundary equilibria. More precisely, to show the convergence to equilibrium for systems with boundary equilibria, we
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The author showed that any homogeneous algebraic Diophantine equation of the second order can be converted to a diagonal form using an integer nonorthogonal transformation maintaining asymptotic behavior of the number of its integer solutions. In this paper, we consider the transformation to the diagonal form of a wider class of algebraic secondorder Diophantine equations, and also we consider the conditions for converting higher order algebraic Diophantine equations to this form. The author found an asymptotic estimate for the number of integer solutions of the diagonal Thue equation of odd degree with an amount of variables greater than two, and also he got and asymptotic estimates of the number of integer solutions of other types of diagonal algebraic Diophantine equations.
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We deal with the following question of Dolgachev : is the Cremona group generated by involutions ? Answer is yes in dimension $2$ (CerveauDeserti). We give an upper bound of the minimal number $\mathfrak{n}_\varphi$ of involutions we need to write a birational self map $\varphi$ of $\mathbb{P}^2_\mathbb{C}$. We prove that de Jonqui\`eres maps of $\mathbb{P}^3_\mathbb{C}$ and maps of small bidegree of $\mathbb{P}^3_\mathbb{C}$ can be written as a composition of involutions of $\mathbb{P}^3_\mathbb{C}$ and give an upper bound of $\mathfrak{n}_\varphi$ for such maps $\varphi$. We get similar results in particular for automorphisms of $(\mathbb{P}^1_\mathbb{C})^n$, automorphisms of $\mathbb{P}^n_\mathbb{C}$, tame automorphisms of $\mathbb{C}^n$, monomial maps of $\mathbb{P}^n_\mathbb{C}$, and elements of the subgroup generated by the standard involution of $\mathbb{P}^n_\mathbb{C}$ and $\mathrm{PGL}(n+1,\mathbb{C})$.
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We construct (generalized) cross ratios on Furstenberg boundaries (or flag manifolds) of higher rank symmetric spaces of noncompact type. We show several basic properties of it; including continuity, the connection to translation lengths of hyperbolic elements, and the behavior under products. Moreover, we motivate that these are suitable generalizations of cross ratios on ideal boundaries of rank one symmetric spaces, by proving that every continuous cross ratiopreserving map on the maximal Furstenberg boundary (or full flag manifold) is induced by an isometry, after multiplying metrics on de Rham factors by positive constants. If the symmetric space is irreducible this yields a onetoone correspondence of isometries and continuous cross ratiopreserving maps.
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Let $k$ be a field and let $\Lambda$ be a finite dimensional $k$algebra. We prove that every bounded complex $V^\bullet$ of finitely generated $\Lambda$modules has a welldefined versal deformation ring $R(\Lambda,V^\bullet)$ which is a complete local commutative Noetherian $k$algebra with residue field $k$. We also prove that nice twosided tilting complexes between $\Lambda$ and another finite dimensional $k$algebra $\Gamma$ preserve these versal deformation rings. Additionally, we investigate stable equivalences of Morita type between selfinjective algebras in this context. We apply these results to the derived equivalence classes of the members of a particular family of algebras of dihedral type that were introduced by Erdmann and shown by Holm to be not derived equivalent to any block of a group algebra.
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Several useful variancereduced stochastic gradient algorithms, such as SVRG, SAGA, Finito, and SAG, have been proposed to minimize empirical risks with linear convergence properties to the exact minimizers. The existing convergence results assume uniform data sampling with replacement. However, it has been observed that random reshuffling can deliver superior performance. No formal proofs or guarantees of exact convergence exist for variancereduced algorithms under random reshuffling. This paper resolves this open convergence issue and provides the first theoretical guarantee of linear convergence under random reshuffling for SAGA; the argument is also adaptable to other variancereduced algorithms. Under random reshuffling, the paper further proposes a new amortized variancereduced gradient (AVRG) algorithm with constant storage requirements compared to SAGA and with balanced gradient computations compared to SVRG. The balancing in computations are attained by amortizing the full g
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Domain decomposition based time integrators allow the usage of parallel and distributed hardware, making them wellsuited for the temporal discretization of parabolic systems, in general, and degenerate parabolic problems, in particular. The latter is due to the degenerate equations' finite speed of propagation. In this study, a rigours convergence analysis is given for such integrators without assuming any restrictive regularity on the solutions or the domains. The analysis is conducted by first deriving a new variational framework for the domain decomposition, which is applicable to the two standard degenerate examples. That is, the $p$Laplace and the porous medium type vector fields. Secondly, the decomposed vector fields are restricted to the underlying pivot space and the time integration of the parabolic problem can then be interpreted as an operators splitting applied to a dissipative evolution equation. The convergence results then follow by employing elements of the approxima
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We consider a spherical pendulum whose suspension point performs highfrequency oscillations. We derive the averaged over these oscillations Hamiltonian of the problem. We assume that these oscillations are such that the averaged Hamiltonian is invariant with respect to rotations about the vertical direction. Under this assumption we give complete description of bifurcations of phase portraits of the averaged system.
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We study two rational Fano threefolds with an action of the icosahedral group $\mathfrak{A}_5$. The first one is the famous Burkhardt quartic threefold, and the second one is the double cover of the projective space branched in the Barth sextic surface. We prove that both of them are $\mathfrak{A}_5$Fano varieties that are $\mathfrak{A}_5$birationally superrigid. This gives two new embeddings of the group $\mathfrak{A}_5$ into the space Cremona group.
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A second fundamental form is introduced for arbitrary closed subsets of Euclidean space, extending the same notion introduced by J. Fu for sets of positive reach. We extend well known integralgeometric formulas to this general setting and we provide a structural result in terms of second fundamental forms of submanifolds of class $2$ that is new even for sets of positive reach. In the case of a large class of minimal submanifolds, which include viscosity solutions of the minimal surface system and rectifiable stationary varifolds of arbitrary codimension and higher multiplicities, we prove the area formula for the generalized Gauss map in terms of the discriminant of the second fundamental form and, adapting techniques from the theory of viscosity solutions of elliptic equations to our geometric setting, we conclude a natural secondorderdifferentiability property almost everywhere. Moreover the trace of the second fundamental form is proved to be zero for stationary integral varifol
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Given a graph $G$, denote by $\Delta$, $\bar{d}$ and $\chi^\prime$ the maximum degree, the average degree and the chromatic index of $G$, respectively. A simple graph $G$ is called {\it edge$\Delta$critical} if $\chi^\prime(G)=\Delta+1$ and $\chi^\prime(H)\le\Delta$ for every proper subgraph $H$ of $G$. Vizing in 1968 conjectured that if $G$ is edge$\Delta$critical, then $\bar{d}\geq \Delta1+ \frac{3}{n}$. We show that $$ \begin{displaystyle} \avd \ge \begin{cases} 0.69241\D0.15658 \quad\,\: \mbox{ if } \Delta\geq 66, 0.69392\D0.20642\quad\;\,\mbox{ if } \Delta=65, \mbox{ and } 0.68706\D+0.19815\quad\! \quad\mbox{if } 56\leq \Delta\leq64. \end{cases} \end{displaystyle} $$ This result improves the best known bound $\frac{2}{3}(\Delta +2)$ obtained by Woodall in 2007 for $\Delta \geq 56$. Additionally, Woodall constructed an infinite family of graphs showing his result cannot be improved by wellknown Vizing's Adjacency Lemma and other known edgecoloring techniques. To over come
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We obtain a structure theorem for the group of holomorphic automorphisms of a conformally K\"ahler, EinsteinMaxwell metric, extending the classical results of Matsushima~\cite{M}, Licherowicz~\cite{L} and Calabi~\cite{calabi} in the K\"ahlerEinstein, cscK, and extremal K\"ahler cases. Combined with previous results of LeBrun~\cite{LeB1}, ApostolovMaschler~\cite{AM} and FutakiOno~\cite{FO}, this completes the classification of the conformally K\"ahler, EinsteinMaxwell metrics on $\mathbb{{CP}}^1 \times \mathbb{{CP}}^1$. We also use our result in order to introduce a (relative) Mabuchi energy in the more general context of $(K, q, a)$extremal K\"ahler metrics in a given K\"ahler class, and show that the existence of $(K, q, a)$extremal K\"ahler metrics is stable under small deformation of the K\"ahler class, the Killing vector field $K$ and the normalization constant $a$.
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Mobile communication technology has been rapidly evolving ever since its first introduction in the late 1980s. The development witnessed is not just in the refinement of the radio access techniques, but also in the progression towards offering sophisticated features and services to the mobile phone users. To fulfill this evergrowing user demand and market trends, frequency ranges in millimeter wave bands are envisioned for wireless radio transmission. To respond to this trends, the EUfunded mmMAGIC project has been launched and its main objective is to design and develop radio access techniques operating in 6100 GHz bands. When it comes to developing technologies for systems operating these frequency ranges, a major challenge encountered will be in terms of its radio access network integration. Unquestionably, issues at various aspects of physical layer design, channel modelling, architecture, network functions and deployment will be encountered; problems in multinode and multiant
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The betweenness structure of a finite metric space $M = (X, d)$ is a pair $\mathcal{B}(M) = (X,\beta_M)$, where $\beta_M = \{(x, y, z)\in X^3 : d(x, z) = d(x, y) + d(y, z)\}$ is the socalled betweenness relation of $M$. The adjacency graph of a betweenness structure $\mathcal{B} = (X,\beta)$ is the simple graph $G(\mathcal{B}) = (X, E)$ where the edges are such pairs of distinct points for which no third point lies between them. A connected graph is \emph{uniquely representable} if it is the adjacency graph of a unique betweenness structure. It was known before that trees are uniquely representable. In this paper, we give a full characterisation of uniquely representable graphs by showing that they coincide with the socalled Husimi trees.
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Based on the concept and properties of $C^{*}$algebras, the paper introduces a concept of $C_{*}$class functions. Then by using these functions in $C^{*}$algebra valued modular metric spaces of moeini et al. [14], some common fixed point theorems for selfmappings are established. Also, to support of our results an application is provided for existence and uniqueness of solution for a system of integral equations.
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In this paper, we study partial actions of groups on $R$algebras, where $R$ is a commutative ring. We describe the partial actions of groups on the indecomposable algebras with enveloping actions. Then we work on algebras that can be decomposed as product of indecomposable algebras and we give a description of the partial actions of groups on these algebras in terms of global actions.
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In this paper, we develop a procedure for the detection of the contours of thermal bridges from thermographic images, in order to study the energetic performance of buildings. Two main steps of the above method are: the enhancement of the thermographic images by an optimized version of the mathematical algorithm for digital image processing based on the theory of sampling Kantorovich operators, and the application of a suitable thresholding based on the analysis of the histogram of the enhanced thermographic images. Finally, an accuracy improvement of the parameter that defines the thermal bridge is obtained.
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The study of the birational properties of algebraic $k$tori began in the sixties and seventies with work of Voskresenkii, Endo, Miyata, ColliotTh\'el\`ene and Sansuc. There was particular interest in determining the rationality of a given algebraic $k$tori. As rationality problems for algebraic varieties are in general difficult, it is natural to consider relaxed notions such as stable rationality, or even retract rationality. Work of the above authors and later Saltman in the eighties determined necessary and sufficient conditions to determine when an algebraic torus is stably rational, respectively retract rational in terms of the integral representations of its associated character lattice. An interesting question is to ask whether a stably rational algebraic $k$torus is always rational. In the general case, there exist examples of nonrational stably rational $k$varieties. Algebraic $k$tori of dimension $r$ are classified up to isomorphism by conjugacy classes of finite subgr
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The Riemann ZetaFunction is the most studied Lfunction; it's zeroes give information about the prime numbers. We can associate Lfunctions to a wide array of objects, and in general, the zeroes of these Lfunctions give information about those objects. For arbitrary Lfunctions, the order of vanishing at the central point is of particular important. For example, the Birch and SwinnertonDyer conjecture states that the order of vanishing at the central point of an elliptic curve Lfunction is the rank of the MordellWeil group of that elliptic curve. The KatzSarnak Density Conjecture states that this order vanishing and other behavior are wellmodeled by random matrices drawn from the classical compact groups. In particular, the conjecture states that an average order vanishing over a family of Lfunctions can be bounded using only a given weight function and a chosen test function, phi. The conjecture is known for many families when the test functions are suitably restricted. It is
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Gaussian states are at the heart of quantum mechanics and play an essential role in quantum information processing. In this paper we provide explicit formulas for the expansion of a general Gaussian symbol in terms of elementary Gaussian functions. For this purpose we introduce the notion of a "phase space frame" associated with a WeylHeisenberg frame.
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Let $G$ be any connected and simply connected complex semisimple Lie group, equipped with a standard holomorphic multiplicative Poisson structure. We show that the Hamiltonian flows of all the FominZelevinsky twisted generalized minors on every double Bruhat cell of $G$ are complete in the sense that all of their integral curves are defined on ${\mathbb{C}}$. It follows that the KoganZelevinsky integrable systems on $G$ are all complete, generalizing the result of Gekhtman and Yakimov for the case of $SL(n, {\mathbb{C}})$. We in fact construct a class of complete Hamiltonian flows and complete integral systems related to any {\it generalized Bruhat cell} which is defined using an arbitrary sequence of elements in the Weyl group of $G$, and we obtain the results for double Bruhat cells through the socalled open {\it FominZelevinsky embeddings} of (reduced) double Bruhat cells to generalized Bruhat cells. The FominZelevinsky embeddings are proved to be Poisson, and they provide glob
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Reducible codes for the rank metric were introduced for cryptographic purposes. They have fast encoding and decoding algorithms, include maximum rank distance (MRD) codes and can correct many rank errors beyond half of their minimum rank distance, which makes them suitable for errorcorrection in network coding. In this paper, we study their security behaviour against information leakage on networks when applied as coset coding schemes, giving the following main results: 1) we give lower and upper bounds on their generalized rank weights (GRWs), which measure worstcase information leakage to the wiretapper, 2) we find new parameters for which these codes are MRD (meaning that their first GRW is optimal), and use the previous bounds to estimate their higher GRWs, 3) we show that all linear (over the extension field) codes whose GRWs are all optimal for fixed packet and code sizes but varying length are reducible codes up to rank equivalence, and 4) we show that the information leaked
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It is known that for any knot $K$ every (meridionally) tracefree $SL_2(C)$representation of the knot group $G(K)$ gives an $SL_2(C)$representation of the fundamental group $\pi_1(\Sigma_2K)$ of the 2fold branched covering $\Sigma_2K$ of the 3sphere branched along $K$. In this paper, we show by using a notion called a ghost character of a knot that for the (4,5)torus knot $T_{4,5}$ the fundamental group $\pi_1(\Sigma_2T_{4,5})$ has an $SL(2,C)$representation which cannot be given by any tracefree $SL_2(C)$representation of $G(T_{4,5})$.
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Let $A$ be a commutative Noetherian ring containing a field $K$ of characteristic zero and let $R= A[X_1, \ldots, X_m]$. Consider $R$ as standard graded with $\deg A=0$ and $\deg X_i=1$ for all $i$. We present a few results about the behavior of the graded components of local cohomology modules $H_I^i(R)$ where $I$ is an arbitrary homogeneous ideal in $R$. We mostly restrict our attention to the Vanishing, Tameness and Rigidity problems.
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We complement the characterization of the graph products of cyclic groups $G(\Gamma, \mathfrak{p})$ admitting a Polish group topology of [9] with the following result. Let $G = G(\Gamma, \mathfrak{p})$, then the following are equivalent: (i) there is a metric on $\Gamma$ which induces a separable topology in which $E_{\Gamma}$ is closed; (ii) $G(\Gamma, \mathfrak{p})$ is embeddable into a Polish group; (iii) $G(\Gamma, \mathfrak{p})$ is embeddable into a nonArchimedean Polish group. We also construct leftinvariant separable group ultrametrics for $G = G(\Gamma, \mathfrak{p})$ and $\Gamma$ a closed graph on the Baire space, which is of independent interest.
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Weighted singular value decomposition (WSVD) of a quaternion matrix and with its help determinantal representations of the quaternion weighted MoorePenrose inverse have been derived recently by the author. In this paper, using these determinantal representations, explicit determinantal representation formulas for the solution of the restricted quaternion matrix equations, ${\bf A}{\bf X}{\bf B}={\bf D}$, and consequently, ${\bf A}{\bf X}={\bf D}$ and ${\bf X}{\bf B}={\bf D}$ are obtained within the framework of the theory of columnrow determinants. We consider all possible cases depending on weighted matrices.
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It is wellknown that polynomials decompose into spherical harmonics. This result is called separation of variables or the Fischer decomposition. In the paper we prove the Fischer decomposition for spinor valued polynomials in $k$ vector variables of ${\mathbb R}^m$ under the stable range condition $m\geq 2k$. Here the role of spherical harmonics is played by monogenic polynomials, that is, polynomial solutions of the Dirac equation in $k$ vector variables.
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In analysis of multicomponent complex systems, such as neural systems, identifying groups of units that share similar functionality will aid understanding of the underlying structures of the system. To find such a grouping, it is useful to evaluate to what extent the units of the system are separable. Separability or inseparability can be evaluated by quantifying how much information would be lost if the system were partitioned into subsystems, and the interactions between the subsystems were hypothetically removed. A system of two independent subsystems are completely separable without any loss of information while a system of strongly interacted subsystems cannot be separated without a large loss of information. Among all the possible partitions of a system, the partition that minimizes the loss of information, called the Minimum Information Partition (MIP), can be considered as the optimal partition for characterizing the underlying structures of the system. Although the MIP would
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Recent studies have revealed that multisoliton solutions of the nonlinear Schr\"odinger equation, as carriers of information, offer a promising solution to the problem of nonlinear signal distortions in fiber optic channels. In any nonlinear Fourier transform based transmission methodology seeking to modulate the discrete spectrum of the multisolitons, choice of an appropriate windowing function is an important design issue on account of the unbounded support of such signals. Here, we consider the rectangle function as the windowing function for the multisolitonic signal and provide the exact solution of the associated ZakharovShabat scattering problem for the windowed/doublytruncated multisoliton potential. This method further allows us to avoid prohibitive numerical computations normally required in order to accurately quantify the effect of timedomain windowing on the nonlinear Fourier spectrum of the multisolitonic signals. The method devised in this work also applies to ge
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For a class of partially observed diffusions, sufficient conditions are given for the map from initial condition of the signal to filtering distribution to be contractive with respect to Wasserstein distances, with rate which has no dependence on the dimension of the statespace and is stable under tensor products of the model. The main assumptions are that the signal has affine drift and constant diffusion coefficient, and that the likelihood functions are logconcave. Contraction estimates are obtained from an $h$process representation of the transition probabilities of the signal reweighted so as to condition on the observations.
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Solving a largescale system of linear equations is a key step at the heart of many algorithms in machine learning, scientific computing, and beyond. When the problem dimension is large, computational and/or memory constraints make it desirable, or even necessary, to perform the task in a distributed fashion. In this paper, we consider a common scenario in which a taskmaster intends to solve a largescale system of linear equations by distributing subsets of the equations among a number of computing machines/cores. We propose an accelerated distributed consensus algorithm, in which at each iteration every machine updates its solution by adding a scaled version of the projection of an error signal onto the nullspace of its system of equations, and where the taskmaster conducts an averaging over the solutions with momentum. The convergence behavior of the proposed algorithm is analyzed in detail and analytically shown to compare favorably with the convergence rate of alternative distribu
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The unitary Cayley graph of $\mathbb{Z} /n \mathbb{Z}$, denoted $X_{\mathbb{Z} / n \mathbb{Z}}$, has vertices $0,1, \dots, n1$ with $x$ adjacent to $y$ if $xy$ is relatively prime to $n$. We present results on the tightness of the known inequality $\gamma(X_{\mathbb{Z} / n \mathbb{Z}})\leq \gamma_t(X_{\mathbb{Z} / n \mathbb{Z}})\leq g(n)$, where $\gamma$ and $\gamma_t$ denote the domination number and total domination number, respectively, and $g$ is the arithmetic function known as Jacobsthal's function. In particular, we construct integers $n$ with arbitrarily many distinct prime factors such that $\gamma(X_{\mathbb{Z} / n \mathbb{Z}})\leq\gamma_t(X_{\mathbb{Z} / n \mathbb{Z}})\leq g(n)1$. Extending work of Meki\v{s}, we give lower bounds for the domination numbers of direct products of complete graphs. We also present a simple conjecture for the exact values of the upper domination numbers of direct products of balanced, complete multipartite graphs and prove the conjecture in ce
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In this paper we focus on the solution of shifted quasiseparable systems and of more general parameter dependent matrix equations with quasiseparable representations. We propose an efficient algorithm exploiting the invariance of the quasiseparable structure under diagonal shifting and inversion. This algorithm is applied to compute various functions of matrices. Numerical experiments show that this approach is fast and numerically robust.
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This work develops a fully decentralized variancereduced learning algorithm for ondevice intelligence where nodes store and process the data locally and are only allowed to communicate with their immediate neighbors. In the proposed algorithm, there is no need for a central or master unit while the objective is to enable the dispersed nodes to learn the {\em exact} global model despite their limited localized interactions. The resulting algorithm is shown to have low memory requirement, guaranteed linear convergence, robustness to failure of links or nodes, scalability to the network size, and privacypreserving properties. Moreover, the decentralized nature of the solution makes largescale machine learning problems more tractable and also scalable since data is stored and processed locally at the nodes.
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Let $\Phi_1$ and $\Phi_2$ be nondecreasing functions from $\mathbb{R_+}=(0,\infty)$ onto itself. For $i=1,2$ and $\gamma \in \mathbb{R}$, define the Orlicz class $L_{\Phi_{i}}(\mathbb{R_+})$ to be the set of Lebesguemeasurable functions $f$ on $\mathbb{R_+}$ such that \begin{equation*} \int_{\mathbb{R_+}} \Phi_{i} \left( k(Tf)(t) \right) t^{\gamma}dt < \infty \end{equation*} for some $k>0$. Our goal in this paper is to find conditions on $\Phi_1$, $\Phi_2$, $\gamma$ and an operator $T$ so that the assertions \begin{equation} T : L_{\Phi_2,t^{\gamma}}(\mathbb{R_+}) \rightarrow L_{\Phi_1,t^{\gamma}}(\mathbb{R_+}), \tag{I} \end{equation} and \begin{equation}\label{modularA} \int_{\mathbb{R_+}} \Phi_1 \left( (Tf)(t) \right)t^{\gamma}dt \leq K \int_{\mathbb{R_+}} \Phi_2 \left( Kf(s) \right)s^{\gamma}ds, \tag{M} \end{equation} in which $K>0$ is independent of $f$, say, simple on $\mathbb{R_+}$, are equivalent and to then find necessary and sufficient conditions in order that
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Suppose $\varphi$ is a holomorphic self map of the unit disk and $C_\varphi$ is a composition operator with symbol $\varphi$ that fixes the origin and $0<\varphi'(0)<1$. This work explores sufficient conditions that ensure all holomorphic solutions of Schr\"oder equation for the composition operator $C_\varphi$ belong to a Blochtype space $\mathcal{B}_\alpha$ for some $\alpha>0$. The results from composition operators have been extended to weighted composition operators in the second part of this work.
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We consider a compact CR manifold with a transversal CR locally free circle action endowed with a rigid positive CR line bundle. We prove that a certain weighted FourierSzeg\H{o} kernel of the CR sections in the high tensor powers admits a full asymptotic expansion. As a consequence, we establish an equivariant Kodaira embedding theorem.
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In this paper we estimate both the Hurst and the stable indices of a Hselfsimilar stable process. More precisely, let $X$ be a $H$sssi (selfsimilar stationary increments) symmetric $\alpha$stable process. The process $X$ is observed at points $\frac{k}{n}$, $k=0,\ldots,n$. Our estimate is based on $\beta$variations with $\frac{1}{2}<\beta<0$. We obtain consistent estimators, with rate of convergence, for several classical $H$sssi $\alpha$stable processes (fractional Brownian motion, wellbalanced linear fractional stable motion, Takenaka's processes, L\'evy motion). Moreover, we obtain asymptotic normality of our estimators for fractional Brownian motion and L\'evy motion. \end{abstract} {\bf{Keywords:}} Hsssi processes; stable processes; selfsimilarity parameter estimator; stability parameter estimator.
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This paper investigates the optimal power allocation scheme for sum throughput maximization of nonorthogonal multiple access (NOMA) system with $\alpha$fairness. In contrast to the existing fairness NOMA models, $\alpha$fairness can only utilize a single scalar to achieve different user fairness levels. Two different channel state information at the transmitter (CSIT) assumptions are considered, namely, statistical and perfect CSIT. For statistical CSIT, fixed target data rates are predefined, and the power allocation problem is solved for sum throughput maximization with $\alpha$fairness, through characterizing several properties of the optimal power allocation solution. For perfect CSIT, the optimal power allocation is determined to maximize the instantaneous sum rate with $\alpha$fairness, where user rates are adapted according to the instantaneous channel state information (CSI). In particular, a simple alternate optimization (AO) algorithm is proposed, which is demonstrated t
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Last night out of the blue, we received an email from AMD, sharing some of the specifications for the forthcoming Ryzen Threadripper CPUs to be announced today. Up until this point, we knew a few things  Threadripper would consist of two Zeppelin dies featuring AMD's latest Zen core and microarchitecture, and would essentially double up on the HEDT Ryzen launch. Double dies means double pretty much everything: Threadripper would support up to 16 cores, up to 32 MB of L3 cache, quadchannel memory support, and would require a new socket/motherboard platform called X399, sporting a massive socket with 4094pins (and also marking an LGA socket for AMD). By virtue of being sixteen cores, AMD is seemingly carving a new consumer category above HEDT/HighEnd Desktop, which weâve coined the 'Super HighEnd Desktop', or SHED for short. AMD is listing the top of the line Threadripper 1950X for 999 dollars, which gives you 16 cores and 32 threads, with a base frequency of 3.4Ghz (and a turbo
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An anonymous reader quotes a report from MarketWatch: Fresh off its biggest Prime Day yet, the Whole Foods Market bid, and a slew of announcements including Amazon Wardrobe, Amazon.com Inc. was the subject of two investor calls Thursday that raised concerns that it is getting too big. In one case, hedgefund manager Douglas Kass said government intervention could be imminent. "I am shorting Amazon today because I have learned that there are currently early discussions and due diligence being considered in the legislative chambers in Washington DC with regard to possible antitrust opposition to Amazon's business practices, pricing strategy and expansion announcements already made (as well as being aimed at expansion strategies being considered in the future," wrote Kass, head of Seabreeze Partners Management. "My understanding is that certain Democrats in the Senate have instituted the very recent and preliminary investigation of Amazon's possible adverse impact on competition," he said
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Trailrunner7 shares a report from On the Wire: A group of House Democrats has introduced a bill that would formalize a policy of the United States not sharing cyber intelligence with Russia. The proposed law is a direct response to comments President Donald Trump made earlier this week after he met with Russian President Vladimir Putin. After the meeting, Trump said on Twitter that he and Putin had discussed forming an "impenetrable Cyber Security unit" to prevent future attacks, including election hacking. The idea was roundly criticized by security and foreign policy experts and within a few hours Trump walked it back, saying it was just an idea and couldn't actually happen. But some legislators are not taking the idea of information sharing with Russia as a hypothetical. On Wednesday, Rep. Ted Lieu (DCalif.), Rep. Brendan Boyle (DPa.), and Rep. Ruben Gallego (DAriz.) introduced the No Cyber Cooperation With Russia Act to ensure that the U.S. doesn't hand over any cybersecurity in
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An anonymous reader shares a report: The ACLU has begun to worry that artificial intelligence is discriminatory based on race, gender and age. So it teamed up with computer science researchers to launch a program to promote applications of AI that protect rights and lead to equitable outcomes. MIT Technology Review reports that the initiative is the latest to illustrate general concern that the increasing reliance on algorithms to make decisions in the areas of hiring, criminal justice, and financial services will reinforce racial and gender biases. A computer program used by jurisdictions to help with paroling prisoners that ProPublica found would go easy on white offenders while being unduly harsh to black ones.
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An anonymous reader writes: Recently, I asked Slashdot what you thought about paying for things online using plastic, and the security of using plastic in general; thank you all for your many and varied responses, they're all much appreciated and gave me things to consider. However, I got quite a few responses that puzzled me: People claiming that paying for things with cash, and carrying any amount of cash around at all, was somehow dangerous, that I'd be "robbed," and that I shouldn't carry cash at all, only plastic. I'm GenY; I've walked around my entire life, in all sorts of places, and have never been approached or robbed by anyone, so I'm more than a little puzzled by that. So now I ask you, Slashdotters: Why do you think carrying cash is so dangerous? Where do you live/spend your time that you worry so much about being robbed? Have you been robbed before, and that's why you feel this way? I'm not going to stop carrying cash in my wallet but I'd like to understand why it is
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New submitter Kant shares a report from Electrek: The auto industry is once again attempting to slow down the rollout of electric vehicles. Virtually all automakers, except for Tesla of course, have sent a letter to the Chinese government in an attempt to have them drastically weaken their zeroemission vehicle mandate. As we previously reported, China, the world's biggest car market, has somewhat of an aggressive ZEV mandate that would force automakers to have zeroemission vehicles (ZEVs) represent 8% of new car sales as soon as 2018 and quickly ramp up to 12% by 2020. Now Germany's WirtschaftsWoche magazine (via Auto News) reports that the American Automotive Policy Council (AAPC), which represents Chrysler/Fiat, Ford, and GM, the European Automobile Manufacturers Association (ACEA), which represents all major European automakers, the Japan Automobile Manufacturers Association (JAMA) and the Korea Automobile Manufacturers Association (KAMA), have all sent a joint letter to China's M
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New submitter elmohound writes: A recent paper in Nature describes how gene editing was used to store a digital movie into a bacterial population. The choice of subject is a nice hommage to Muybridge's 1887 photos. From a report via Scientific American: "The technical achievement, reported on July 12 in Nature, is a step towards creating cellular recording systems that are capable of encoding a series of events, says Seth Shipman, a synthetic biologist at Harvard Medical School in Boston, Massachusetts. To develop such a system, however, his team would need to establish a method for recording hundreds of events in a cell. Shipman and his colleagues, including Harvard geneticist George Church, harnessed the CRISPRCas immune system best known for enabling researchers to alter genomes with relative ease and accuracy. Shipman's team exploited the ability to capture snippets of DNA from invading viruses and store them in an organized array in the host genome. In nature, those snippets then
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From version to version, I always love to play around with the kernel. And it has always been a great lack in guides and documentation on how to build Mac OSX's kernel, XNU. For those of you that already have tried compiling XNU for Mac OSX 10.12 (Sierra), you probably noticed that earlier build guides like ssen's blog  Building xnu for OS X 10.11 El Capitan don't work anymore. However, many thanks to ssen to put in time to write a guide. The problem is that Apple introduced something named Circular dependency with the libdispatch library and the kernel headers. So the order of the build process just got really important.
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MojoKid writes: AMD first teased its Ryzen Threadripper series of highend desktop (HEDT) processors back in midMay, but is now sharing additional details on the first two products in the family. Both processors are based on the 14nm Zen core, make use of AMD's new Socket TR4 interface, support quadchannel DDR memory, and feature a total of 64 PCIe lanes. In addition, both processors will come from the factory unlocked. Ryzen Threadripper 1920X will have 12 Cores, 24 Threads, and 3.5/4.0 GHz (Base Clock/Precision Boost) clock speeds. Ryzen Threadripper 1950X will have 16 Cores, 32 Threads, and 3.4/4.0 GHz (Base Clock/Precision Boost) clock speeds. Pricing is set at $799 and $999, respectively, with availability in early August, though Dell's Alienware gaming PC division will have systems shipping with the new chip starting this month. AMD also put the new chips up against Intel's Core i77900X 10core CPU in a Cinebench benchmark run in a video demo, and the 12core Threadripper chip
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According to a letter obtained by NBC News, U.S. border officers aren't allowed to look at any data stored only in the "cloud"  including social media data  when they search U.S. travelers' phones. "The letter (PDF), sent in response to inquiries by Sen. Ron Wyden, (DOre.), and verified by Wyden's office, not only states that CBP doesn't search data stored only with remote cloud services, but also  apparently for the first time  declares that it doesn't have that authority in the first place." From the report: In April, Wyden and Sen. Rand Paul, RKy., introduced legislation to make it illegal for border officers to search or seize cellphones without probable cause. Privacy advocates and former Homeland Security lawyers have said they are alarmed by how many phones are being searched. The CBP letter, which is attributed to Kevin McAleenan, the agency's acting commissioner, is dated June 20, four months after Wyden asked the Department of Homeland Security (PDF), CBP's parent a
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