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Like many people, Alex Stamos, former Facebook chief security officer, thinks tech platforms like Facebook and Google have too much power. But he doesn't agree with the calls to break them up. And he argues that the very people who say Facebook and Google are too powerful are giving them more power by insisting they do more to control hate speech and propaganda. From a report: "That's a dangerous path," he warns. If democratic countries make tech firms impose limits on free speech, so will autocratic ones. Before long, the technology will enable "machinespeed, realtime moderation of everything we say online." In attempting to rein in Big Tech, we risk creating Big Brother. So what's the solution? I spoke to Stamos at his Stanford office to find out. Technology Review: So is the disinformation/propaganda problem mostly solved? Stamos: In a free society, you will never eliminate that problem. I think the most important thing [in the US] is the advertising transparency. With or without
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Ars technica takes a look at the Enhanced Tracking Protection (ETP) feature in Firefox 63. "Firefox has long had the ability to block all thirdparty cookies, but this is a crude solution, and many sites will break if all thirdparty cookies are prohibited. The new EPT option works as a more selective block on tracking cookies; thirdparty cookies still work in general, but those that are known to belong to tracking companies are blocked. For the most part, sites will retain their full functionality, just without undermining privacy at the same time. At least for now, however, Mozilla is defaulting this feature to off, so the company can get a better idea of the impact it has on the Web. In testing, the company has found the occasional site that breaks when tracking cookies are blocked. Over the next few months, Firefox developers will get a better picture of just how much breaks, and, if it's not too severe, the plan is to block trackers by default starting in early 2019.
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Ever since Microsoft settled on a cadence of two feature updates a year  one in April, one in October  the quality of its operating system (taking into consideration the volume of bugs that emerge every few days) has deteriorated, writes Peter Bright of ArsTechnica. From the story: The problem with Windows as a Service is quality. Previous issues with the feature and security updates have already shaken confidence in Microsoft's updating policy for Windows 10. While data is notably lacking, there is at the very least a popular perception that the quality of the monthly security updates has taken a dive with Windows 10 and that installation of the twiceannual feature updates as soon as they're available is madness. These complaints are longstanding, too. The unreliable updates have been a cause for concern since shortly after Windows 10's release. The latest problem has brought this to a head, with commentators saying that two feature updates a year is too many and Redmond should
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According to a press release posted today, Netflix is planning to raise $2 billion to help fund new content, including "content acquisitions, production and development, capital expenditures, investments, working capital and potential acquisitions and strategic transactions." TechCrunch reports: The funds will be raised in the form of senior unsecured notes, denominated in U.S. dollars and euros, it said. This debt offering is the sixth time in under four years that Netflix is raising $1 billion or more through bonds, noted Variety, which was among the first to report the news. As of September 30, Netflix's longterm debt had reached $8.34 billion, up 71% from $4.89 billion in the year ago quarter, it said during its last earnings, Variety's report also noted. Netflix recently explained during its Q3 2018 earnings that it needs to continue to invest in original programming in order to remain competitive. "Content companies such as WarnerMedia and Disney/Fox are moving to selfdistribut
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If it seems as though the app you deleted last week is suddenly popping up everywhere, it may not be mere coincidence. From a report: Companies that cater to app makers have found ways to game both iOS and Android, enabling them to figure out which users have uninstalled a given piece of software lately  and making it easy to pelt the departed with ads aimed at winning them back. Adjust, AppsFlyer, MoEngage, Localytics, and CleverTap are among the companies that offer uninstall trackers, usually as part of a broader set of developer tools. Their customers include TMobile US, Spotify Technology, and Yelp. Critics say they're a fresh reason to reassess online privacy rights and limit what companies can do with user data. "Most tech companies are not giving people nuanced privacy choices, if they give them choices at all," says Jeremy Gillula, tech policy director at the Electronic Frontier Foundation, a privacy advocate. Some providers say these tracking tools are meant to measure use
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Brendan Iribe, the cofounder and former CEO of Oculus, announced today that he is leaving Facebook. From a report: Iribe is leaving Facebook following some internal shakeups in the company's virtual reality arm last week that saw the cancellation of the company's next generation "Rift 2" PCpowered virtual reality headset, which he had been leading development of, a source close to the matter told TechCrunch. Iribe and the Facebook executive team had "fundamentally different views on the future of Oculus that grew deeper over time," and Iribe wasn't interested in a "race to the bottom" in terms of performance, we are told.
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This paper is devoted to survey composition algebras and some of their applications. After overviewing the classical algebras of quaternions and octonions, both unital composition algebras (or Hurwitz algebras) and symmetric composition algebras will be dealt with. Their main properties, as well as their classifications, will be reviewed. Algebraic triality, through the use of symmetric composition algebras, will be considered too.
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We study the scheduling of computation tasks across $n$ workers in a large scale distributed learning problem. Computation speeds of the workers are assumed to be heterogeneous and unknown to the master, and redundant computations are assigned to workers in order to tolerate straggling workers. We consider sequential computation and instantaneous communication from each worker to the master, and each computation round, which can model a single iteration of the stochastic gradient descent algorithm, is completed once the master receives $k$ distinct computations from the workers. Our goal is to characterize the average completion time as a function of the computation load, which denotes the portion of the dataset available at each worker. We propose two computation scheduling schemes that specify the computation tasks assigned to each worker, as well as their computation schedule, i.e., the order of execution, and derive the corresponding average completion time in closedform. We also
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We investigate the connectivity of wireless sensor networks secured by the heterogeneous random pairwise key predistribution scheme. In contrast to the homogeneous scheme proposed by Chan et al., where each node is paired (offline) with $K$ other nodes chosen uniformly at random; herein, each node is classified as class$1$ with probability $\mu$ or class$2$ with probability $1\mu$, for $0<\mu<1$, independently. Then, each class$1$ (respectively, class$2$) node is paired (offline) with $K_1$ (respectively, $K_2$) other nodes selected uniformly at random. We consider the particular case when $K_1=1$ and $K_2=K$. The heterogeneous random pairwise scheme induces an inhomogeneous random Kout graph $\mathbb{H} (n;\mu,K_n)$, where $n$ denotes the number of nodes and $K_n$ denotes a scaling of $K$ with respect to the network size $n$. Hence, establishing the connectivity of wireless sensor networks secured by the heterogeneous random pairwise scheme maps to deriving conditions on h
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This paper deals with a homoskedastic errorsinvariables linear regression model and properties of the total least squares (TLS) estimator. We partly revise the consistency results for the TLS estimator previously obtained by the author [18]. We present complete and comprehensive proofs of consistency theorems. A theoretical foundation for construction of the TLS estimator and its relation to the generalized eigenvalue problem is explained. Particularly, the uniqueness of the estimate is proved. The Frobenius norm in the definition of the estimator can be substituted by the spectral norm, or by any other unitarily invariant norm; then the consistency results are still valid.
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In this paper we prove that when the geodesic flow of a compact or noncompact complete manifold without conjugate points is of the Anosov type, then the average along of the sectional curvature in planes tangent to the geodesic is negative away from zero for some uniform time. Moreover, in dimension two, if the manifold has no focal points, then the latter condition is sufficient to obtain that the geodesic flow is of Anosov type.
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We study weak solutions of the twodimensional (2D) filtered Euler equations whose vorticity is a finite Radon measure and velocity has locally finite kinetic energy, which is called the vortex sheet solution. The 2D filtered Euler equations are considered as a regularized 2D Euler equations with a spatial filtering and these equations have a unique global weak solution for vortex sheet initial data. On the other hand, the 2D Euler equations require a distinguished sign of initial vorticity for the existence of a global solution with vortex sheet initial data and its uniqueness remains an open question. In this paper, we prove that vortex sheet solutions of the 2D filtered Euler equations converge to those of the 2D Euler equations in the limit of the filtering parameter provided that initial vortex sheet has a distinguished sign. We also show that a simple application of our proof yields the convergence of the vortex method that is a point vortex approximation of vortex sheets. We mak
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It is known that every torsionfree abelian group of finite rank has a maximal completely decomposable summand that is unique up to isomorphism. We show that groups of infinite rank need not have maximal completely decomposable summands, but when they do, this summand is unique up to isomorphism.
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We derive limit distributions for certain empirical regularized optimal transport distances between probability distributions supported on a finite metric space and show consistency of the (naive) bootstrap. In particular, we prove that the empirical regularized transport plan itself asymptotically follows a Gaussian law. The theory includes the BoltzmannShannon entropy regularization and hence a limit law for the widely applied Sinkhorn divergence. Our approach is based on an application of the implicit function theorem to necessary and sufficient optimality conditions for the regularized transport problem. The asymptotic results are investigated in Monte Carlo simulations. We further discuss computational and statistical applications, e.g. confidence bands for colocalization analysis of protein interaction networks based on regularized optimal transport.
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This paper analyzes different models for evaluating investments in Energy Storage Systems (ESS) in power systems with high penetration of Renewable Energy Sources (RES). First of all, two methodologies proposed in the literature are extended to consider ESS investment: a unit commitment model that uses the System States (SS) method of representing time; and another one that uses a representative periods (RP) method. Besides, this paper proposes two new models that improve the previous ones without a significant increase of computation time. The enhanced models are the System States Reduced Frequency Matrix (SSRFM) model which addresses shortterm energy storage more approximately than the SS method to reduce the number of constraints in the problem, and the Representative Periods with Transition Matrix and Cluster Indices (RPTM&CI) model which guarantees some continuity between representative periods, e.g. days, and introduces longterm storage into a model originally designed on
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Estimating the number of sources received by an antenna array have been well known and investigated since the starting of array signal processing. Accurate estimation of such parameter is critical in many applications that involve prior knowledge of the number of received signals. Information theo retic approaches such as Akaikes information criterion (AIC) and minimum description length (MDL) have been used extensively even though they are complex and show bad performance at some stages. In this paper, a new algorithm for estimating the number of sources is presented. This algorithm exploits the estimated eigenvalues of the auto correlation coefficient matrix rather than the auto covariance matrix, which is conventionally used, to estimate the number of sources. We propose to use either of a two simply estimated decision statistics, which are the moving increment and moving standard deviation as metric to estimate the number of sources. Then process a simple calculation of the increm
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Let $G$ be a finite group and let $H_1,H_2<G$ be two subgroups. In this paper, we are concerned with the bipartite graph whose vertices are $G/H_1\cup G/H_2$ and a coset $g_1H_1$ is connected with another coset $g_2H_2$ if and only if $g_1H_1\cap g_2 H_2\neq\varnothing$. The main result of the paper establishes the existence of such graphs with large girth and large spectral gap. Lubotzky, Manning and Wilton use such graphs to construct certain infinite groups of interest in geometric group theory.
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This article gives a precise description of the Fatou sets and Julia sets of matrixvalued polynomials in $\mathcal{M}(2,\mathbb{C})$ in terms of the corresponding polynomials in $\mathbb{C}$. Further, we construct Green functions and B\"{o}ttchertype functions for these matrixvalued polynomials.
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A binary interface defect is any interface between two (not necessarily invertible) domain walls. We compute all possible binary interface defects in Kitaev's $\mathbb{Z}/p\mathbb{Z}$ model and all possible fusions between them. Our methods can be applied to any LevinWen model. We also give physical interpretations for each of the defects in the $\mathbb{Z}/p\mathbb{Z}$ model. These physical interpretations provide a new graphical calculus which can be used to compute defect fusion.
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We consider a programming language based on the lamplighter group that uses only composition and iteration as control structures. We derive generating functions and counting formulas for this language and special subsets of it, establishing lower and upper bounds on the growth rate of semantically distinct programs. Finally, we show how to sample random programs and analyze the distribution of runtimes induced by such sampling.
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We study the large N expansion of a family of matrix models related to topological strings on toric CalabiYau threefolds. These matrix models compute spectral observables of underlying operators obtained by quantizing the mirror curves. They have the form of a deformed O(2) matrix model, with a specific nonpolynomial potential involving the Faddeev quantum dilogarithm. Their planar limit is studied using a particular conformal mapping depending on two parameters, from which several universal results can be obtained. As expected, the spectral curves controlling the planar limit of the matrix models are the mirror curves themselves, which in our cases have genus 1. Our results encompass all those toric geometries with genus $1$ mirror where an explicit onecut matrix integral is known: local $P^2$, local $F_0$, local $F_2$, and degenerations of the resolved $C^3/Z_5$, the resolved $C^3/Z_6$ and the resolved $Y^{3,0}$ geometries amongst others.
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We develop the rudiments of a finitedimensional representation theory of groups over idempotent semifields by considering linear actions on tropical linear spaces. This can be considered a tropical representation theory, a characteristic one modular representation theory, or a matroidal representation theoryand we draw from all three perspectives. After some general properties and constructions, including a weak tropical analogue of Maschke's theorem, we turn to a study of the regular representation of a finite group and its tropicalization. For abelian groups we find an interesting interplay between elementary number theory and matroid theoryeven cyclic groups are surprisingly richand we conclude with some possible first steps toward a tropical character theory.
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The main purpose of this paper is to investigate the concept of maximal $L^p$regularity for perturbed evolution equations in Banach spaces. We mainly consider three classes of perturbations: MiyaderaVoigt perturbations, DeschSchappacher perturbations, and more general StaffansWeiss perturbations. We introduce conditions for which the maximal $L^p$regularity can be preserved under these kind of perturbations. We give examples for a boundary perturbed heat equation in $L^r$spaces and a perturbed boundary integrodifferential equation. We mention that our results mainly extend those in the works: [P. C. Kunstmann and L. Weis, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 30 (2001), 415435] and [B.H. Haak, M. Haase, P.C. Kunstmann, Adv. Differential Equations 11 (2006), no. 2, 201240].
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Metagories are metrically enriched directed multigraphs with designated loops. Their structure assigns to every directed triangle in the graph a value which may be interpreted as the area of the triangle; alternatively, as the distance of a pair of consecutive arrows to any potential candidate for their composite. These values may live in an arbitrary commutative quantale. Generalizing and extending recent work by Aliouche and Simpson, we give a condition for the existence of an Yonedatype embedding which, in particular, gives the isometric embeddability of a metagory into a metrically enriched category. The generality of the value quantale allows for applications beyond the classical metric context.
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A recent result by J. \v{S}aroch and J. \v{S}\v{t}ov\'{\i}\v{c}ek asserts that there is a unique abelian model structure on the category of left $R$modules, for any associative ring $R$ with identity, whose (trivially) cofibrant and (trivially) fibrant objects are given by the classes of Gorenstein flat (resp., flat) and cotorsion (resp., Gorenstein cotorsion) modules. In this paper, we generalise this result to a certain relativisation of Gorenstein flat modules, which we call Gorenstein $\mathcal{B}$flat modules, where $\mathcal{B}$ is a class of right $R$modules. Using some of the techniques considered by \v{S}aroch and \v{S}\v{t}ov\'{\i}\v{c}ek, plus some other arguments coming from model theory, we determine some conditions for $\mathcal{B}$ so that the class of Gorenstein $\mathcal{B}$modules is closed under extensions. This will allow us to show approximation properties concerning these modules, and also to obtain a relative version of the model structure described before. M
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Recovery of multispecies oral biofilms is investigated following treatment by chlorhexidine gluconate (CHX), iodinepotassium iodide (IPI) and Sodium hypochlorite (NaOCl) both experimentally and theoretically. Experimentally, biofilms taken from two donors were exposed to the three antibacterial solutions (irrigants) for 10 minutes, respectively. We observe that (a) live bacterial cell ratios decline for a week after the exposure and the trend reverses beyond a week; after fifteen weeks, live bacterial cell ratios in biofilms fully return to their pretreatment levels; (b) NaOCl is shown as the strongest antibacterial agent for the oral biofilms; (c) multispecies oral biofilms from different donors showed no difference in their susceptibility to all the bacterial solutions. Guided by the experiment, a mathematical model for biofilm dynamics is developed, accounting for multiple bacterial phenotypes, quorum sensing, and growth factor proteins, to describe the nonlinear time evolutionary
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We introduce first the largecardinal notion of $\Sigma_n$supercompactness as a higherlevel analog of the wellknown Magidor's characterization of supercompact cardinals, and show that a cardinal is $C^{(n)}$extendible if and only if it is $\Sigma_{n+1}$supercompact. This yields a new characterization of $C^{(n)}$extendible cardinals which underlines their role as natural milestones in the region of the largecardinal hierarchy between the first supercompact cardinal and Vop\v{e}nka's Principle ($\rm{VP}$). We then develop a general setting for the preservation of $\Sigma_n$supercompact cardinals under class forcing iterations. As a result we obtain new proofs of the consistency of the GCH with $C^{(n)}$extendible cardinals (cf.~\cite{Tsa13}) and the consistency of $\rm{VP}$ with the GCH (cf.~\cite{Broo}). Further, we show that $C^{(n)}$extendible cardinals are preserved after forcing with standard Easton class forcing iterations for any $\Pi_1$definable possible behaviour of
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The aim of this paper is to present the global bounds for renormalized solutions to the following quasilinear elliptic problem: \begin{align*} \begin{cases} \div(A(x,\nabla u)) &= \mu \quad \text{in} \ \ \Omega, \\ u &=0 \quad \text{on} \ \ \partial \Omega, \end{cases} \end{align*} in LorentzMorrey spaces, where $\Omega \subset \mathbb{R}^n$ ($n \ge 2$), $\mu$ is a finite Radon measure, $A$ is a monotone Carath\'eodory vector valued function defined on $W^{1,p}_0(\Omega)$ and the $p$capacity uniform thickness condition is imposed on our domain. There have been research activities on the gradient estimates in LorentzMorrey spaces with various hypotheses. For instance, in \cite{55Ph1} Nguyen Cong Phuc proposed the Morrey global bounds of solution to this equation, but for the regular case $2\frac{1}{n}<p\le n$, in \cite{MP2018}, our first result provides us with the good$\lambda$ bounds of solution in Lorentz space for $\frac{3n2}{2n1}<p \le 2  \frac{1}{n}$; and in
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In this article we lay out the details of Fukaya's A $\infty$structure of the Morse complexe of a manifold possibily with boundary. We show that this A $\infty$structure is homotopically independent of the made choices. We emphasize the transversality arguments that some fiber product constructions make valid.
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We obtain an improved version of a recent result concerning the existence of nonnegative nonradial solutions $u\in D^{1,2}(\mathbb{R}^{N})\cap L^{2}(\mathbb{R}^{N},\left x\right ^{\alpha }dx)$ to the equation \[ \triangle u+\displaystyle\frac{A}{\left x\right ^{\alpha }}u=f\left( u\right) \quad \text{in }\mathbb{R}^{N},\quad N\geq 3,\quad A,\alpha >0, \] where $f$ is a continuous nonlinearity satisfying $f\left( 0\right) =0$.
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The dichromatic number of a digraph $D$, denoted by $\chi_A(D)$, is the minimum $k$ such that $D$ admits a $k$coloring of its vertex set in such a way that each color class is acyclic. In 1976, Bondy proved that the chromatic number of a digraph $D$ is at most its circumference, the length of a longest cycle. In this paper we will construct three graphs from $D$ whose chromatic numbers will bound $\chi_A(D)$. Moreover, we prove: i) for integers $k\geq 2$, $s\geq 1$ and $r_1, \ldots, r_s$ with $k\geq r_i\geq 0$ and $r_i\neq 1$ for each $i\in[s]$, that if all cycles in $D$ have length $r$ modulo $k$ for some $r\in\{r_1,\ldots,r_s\}$, then $\chi_A(D)\leq 2s+1;$ ii) if $D$ has girth $g$, the length of a shortest cycle, and circumference $c$, then $\chi_A(D)\leq \lceil \frac{c1}{g1} \rceil +1$, which improves, substantially, the bound proposed by Bondy; iii) if $D$ has girth $g$ and there are integers $k$ and $p,$ with $k\geq g1\geq p\geq 1$ such that $D$ contains no cycle of length $r$
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This paper derives noncentral asymptotic results for nonlinear integral functionals of homogeneous isotropic Gaussian random fields defined on hypersurfaces in $\mathbb{R}^d$. We obtain the rate of convergence for these functionals. The results extend recent findings for solid figures. We apply the obtained results to the case of sojourn measures and demonstrate different limit situations.
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For a noetherian scheme that has an ample family of invertible sheaves, we prove that direct products in the category of quasicoherent sheaves are not exact unless the scheme is affine. This result can especially be applied to all quasiprojective schemes over commutative noetherian rings. The main tools of the proof are the GabrielPopescu embedding and Roos' characterization of Grothendieck categories satisfying Ab6 and Ab4*.
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Nontransversal intersection of the free and fixed boundary is shown to hold and a classification of blowup solutions is given for obstacle problems generated by fully nonlinear uniformly elliptic operators in two dimensions which appear in the meanfield theory of superconducting vortices.
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Consider an i.i.d. sample from an unknown density function supported on an unknown manifold embedded in a high dimensional Euclidean space. We tackle the problem of learning a distance between points, able to capture both the geometry of the manifold and the underlying density. We prove the convergence of this microscopic distance, as the sample size goes to infinity, to a macroscopic one that we call Fermat distance as it minimizes a path functional, resembling Fermat principle in optics. The proof boils down to the study of geodesics in Euclidean firstpassage percolation for nonhomogeneous Poisson point processes.
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In this paper, we propose a nonintrusive filterbased stabilization of reduced order models (ROMs) for uncertainty quantification (UQ) of the timedependent NavierStokes equations in convectiondominated regimes. We propose a novel highorder ROM differential filter and use it in conjunction with an evolvefilterrelax algorithm to attenuate the numerical oscillations of standard ROMs. We also examine how stochastic collocation methods (SCMs) can be combined with the evolvefilterrelax algorithm for efficient UQ of fluid flows. We emphasize that the new stabilized SCMROM framework is nonintrusive and can be easily used in conjunction with legacy flow solvers. We test the new framework in the numerical simulation of a twodimensional flow past a circular cylinder with a random viscosity that yields a random Reynolds number with mean $Re=100$.
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Distance Geometry Problem (DGP) and Nonlinear Mapping (NLM) are two well established questions: Distance Geometry Problem is about finding a Euclidean realization of an incomplete set of distances in a Euclidean space, whereas Nonlinear Mapping is a weighted Least Square Scaling (LSS) method. We show how all these methods (LSS, NLM, DGP) can be assembled in a common framework, being each identified as an instance of an optimization problem with a choice of a weight matrix. We study the continuity between the solutions (which are point clouds) when the weight matrix varies, and the compactness of the set of solutions (after centering). We finally study a numerical example, showing that solving the optimization problem is far from being simple and that the numerical solution for a given procedure may be trapped in a local minimum.
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A function $U:\left[ \omega_{1}\right] ^{2}\longrightarrow\omega$ is called $\left( 1,\omega_{1}\right) $\emph{weakly universal }if for every function $F:\left[ \omega_{1}\right] ^{2}\longrightarrow\omega$ there is an injective function $h:\omega_{1}\longrightarrow\omega_{1}$ and a function $e:\omega \longrightarrow\omega$ such that $F\left( \alpha,\beta\right) =e\left( U\left( h\left( \alpha\right) ,h\left( \beta\right) \right) \right) $ for every $\alpha,\beta\in\omega_{1}$. We will prove that it is consistent that there are no $\left( 1,\omega_{1}\right) $\emph{}weakly universal functions, this answers a question of Shelah and Stepr\={a}ns. In fact, we will prove that there are no $\left( 1,\omega_{1}\right) $\emph{}weakly universal functions in the Cohen model and after adding $\omega_{2}$ Sacks reals sidebyside. However, we show that there are $\left( 1,\omega _{1}\right) $\emph{}weakly universal functions in the Sacks model. In particular, the existence of such graphs is co
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Distanceregular graphs have many beautiful combinatorial properties. Distancetransitive graphs have very strong symmetries, and they are distanceregular, i.e. distancetransitivity implies distanceregularity. In this paper, we give similar results, i.e. for special $s$ and graphs with other restrictions we show that $s$distancetransitivity implies distanceregularity.
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We prove that if the edges of a graph G can be colored blue or red in such a way that every vertex belongs to a monochromatic kclique of each color, then G has at least 4(k1) vertices. This confirms a conjecture of Bucic, Lidicky, Long, and Wagner (arXiv:1805.11278[math.CO]) and thereby solves the 2dimensional case of their problem about partitions of discrete boxes with the kpiercing property. We also characterize the case of equality in our result.
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In this paper, we prove an isoperimetric inequality for lower order eigenvalues of the Dirichlet Laplacian in bounded domains of a Euclidean space which strengthens the wellknown AshbaughBeguria inequality about the ratio of the first two Dirichlet eigenvalues of the same domains and supports strongly a conjecture of AshbaughBenguria.
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Comon's conjecture on the equality of the rank and the symmetric rank of a symmetric tensor, and Strassen's conjecture on the additivity of the rank of tensors are two of the most challenging and guiding problems in the area of tensor decomposition. We survey the main known results on these conjectures, and, under suitable bounds on the rank, we prove them, building on classical techniques used in the case of symmetric tensors, for mixed tensors. Finally, we improve the bound for Comon's conjecture given by flattenings by producing new equations for secant varieties of Veronese and Segre varieties.
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In this paper, we develop a new computational approach which is based on minimizing the difference of two convex functionals (DC) to solve a broader class of phase retrieval problems. The approach splits a standard nonlinear least squares minimizing function associated with the phase retrieval problem into the difference of two convex functions and then solves a sequence of convex minimization subproblems. For each subproblem, the Nesterov's accelerated gradient descent algorithm or the BarzilaiBorwein (BB) algorithm is used. In the setting of sparse phase retrieval, a standard $\ell_1$ norm term is added into the minimization mentioned above. The subproblem is approximated by a proximal gradient method which is solved by the shrinkagethreshold technique directly without iterations. In addition, a modified AttouchPeypouquet technique is used to accelerate the iterative computation. These lead to more effective algorithms than the Wirtinger flow (WF) algorithm and the GaussNewton (
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An anonymous reader shares a report: Amazon cracked down on fake reviews two years ago by prohibiting shoppers from getting free products directly from merchants in exchange for writing reviews. It was a major turning point for the world's largest online retailer, which had previously seen "incentivized reviews" as a key way for consumers to discover new products. Amazon changed course because it realized some merchants were using such reviews to game its search algorithm, undermining faith in the customer feedback that helps drive ecommerce. Amazon instead used its "Vine" program, in which Amazon serves as a middleman between prolific Amazon reviewers and vendors eager for exposure. Amazon would still allow freebies in exchange for feedback so long as there was no direct contact between its retail partners and reviewers, theoretically lessening the chance of quidproquo. Amazon would select shoppers eligible for the program, and Amazon vendors would pay a fee and provide free produc
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An anonymous reader quotes a report from Bloomberg: Apple on Wednesday began allowing users in the U.S. to download a copy of all of the data that they have stored with the company from a single online portal. U.S. users will be able to download data such as all of their address book contacts, calendar appointments, music streaming preferences and details about past Apple product repairs. Previously, customers could get their data by contacting Apple directly. In May, when Apple first launched the online privacy portal, it only allowed U.S. users to either correct their data or delete their Apple accounts.
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OpenSourceAllTheWay writes: There are many fantastic opensource tools out there for everything from scanning documents to making interactive music to creating 3D assets for games. Many of these tools have an Achilles heel though  while the code quality is great and the tool is fully functional, the user interface (UI) and user experience (UX) are typically significantly inferior to what you get in competing commercial tools. In an nutshell, with open source, the code is great, the tool is free, there is no DRM/activation/telemetry bullshit involved in using the tool, but you very often get a weak UI/UX with the tool that  unfortunately  ultimately makes the tool far less of a joy to use daily than should be the case. A prime example would be the FOSS 3D tool Blender, which is great technically, but ultimately flops on its face because of a poorly designed UI that is a decade behind commercial 3D software. So here is the question: should opensource developer teams for larger FOS
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This paper is the first step in the project of categorifying the bialgebra structure on the half of quantum group $U_{q}(\mathfrak{g})$ by using geometry and Hall algebras. We equip the category of Dmodules on the moduli stack of objects of the category $Rep_{\mathbb{C}}(Q)$ of representations of a quiver with the structure of an algebra object in the category of stable $\infty$categories. The data for this construction is provided by an extension of the Waldhausen construction for the category $Rep_{\mathbb{C}}(Q)$. We discuss the connection to the KhovanovLaudaRouquier categorification of half of the quantum group $U_{q}(\mathfrak{g})$ associated to the quiver $Q$ and outline our approach to the categorification of the bialgebra structure.
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