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This paper deals with a homoskedastic errors-in-variables 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 non-compact 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 two-dimensional (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 torsion-free 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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Dell tries to make durable laptops more modern with updated Latitude rugged
10-23 Ars Technica 12204 -
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 Boltzmann-Shannon 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 (SS-RFM) model which addresses short-term 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 (RP-TM&CI) model which guarantees some continuity between representative periods, e.g. days, and introduces long-term 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 matrix-valued polynomials in $\mathcal{M}(2,\mathbb{C})$ in terms of the corresponding polynomials in $\mathbb{C}$. Further, we construct Green functions and B\"{o}ttcher-type functions for these matrix-valued 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 Levin-Wen 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 Calabi-Yau 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 non-polynomial 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 one-cut 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 finite-dimensional 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 theory---and 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 theory---even cyclic groups are surprisingly rich---and 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: Miyadera-Voigt perturbations, Desch-Schappacher perturbations, and more general Staffans-Weiss 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 integro-differential 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), 415-435] and [B.H. Haak, M. Haase, P.C. Kunstmann, Adv. Differential Equations 11 (2006), no. 2, 201-240].
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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 Yoneda-type 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), iodine-potassium 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 large-cardinal notion of $\Sigma_n$-supercompactness as a higher-level analog of the well-known 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 large-cardinal 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 Lorentz-Morrey 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 Lorentz-Morrey 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 $\frac{3n-2}{2n-1}<p \le 2 - \frac{1}{n}$; and in
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In this article we lay out the details of Fukaya's A $\infty$-structure of the Morse com-plexe 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 $\chi_A(D)\leq \lceil \frac{c-1}{g-1} \rceil +1$, which improves, substantially, the bound proposed by Bondy; iii) if $D$ has girth $g$ and there are integers $k$ and $p,$ with $k\geq g-1\geq p\geq 1$ such that $D$ contains no cycle of length $r$
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This paper derives non-central asymptotic results for non-linear 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 quasi-coherent sheaves are not exact unless the scheme is affine. This result can especially be applied to all quasi-projective schemes over commutative noetherian rings. The main tools of the proof are the Gabriel-Popescu embedding and Roos' characterization of Grothendieck categories satisfying Ab6 and Ab4*.
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Non-transversal intersection of the free and fixed boundary is shown to hold and a classification of blow-up solutions is given for obstacle problems generated by fully nonlinear uniformly elliptic operators in two dimensions which appear in the mean-field 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 first-passage percolation for nonhomogeneous Poisson point processes.
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In this paper, we propose a nonintrusive filter-based stabilization of reduced order models (ROMs) for uncertainty quantification (UQ) of the time-dependent Navier-Stokes equations in convection-dominated regimes. We propose a novel high-order ROM differential filter and use it in conjunction with an evolve-filter-relax algorithm to attenuate the numerical oscillations of standard ROMs. We also examine how stochastic collocation methods (SCMs) can be combined with the evolve-filter-relax algorithm for efficient UQ of fluid flows. We emphasize that the new stabilized SCM-ROM 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 two-dimensional 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 side-by-side. 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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Distance-regular graphs have many beautiful combinatorial properties. Distance-transitive graphs have very strong symmetries, and they are distance-regular, i.e. distance-transitivity implies distance-regularity. In this paper, we give similar results, i.e. for special $s$ and graphs with other restrictions we show that $s$-distance-transitivity implies distance-regularity.
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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 k-clique of each color, then G has at least 4(k-1) vertices. This confirms a conjecture of Bucic, Lidicky, Long, and Wagner (arXiv:1805.11278[math.CO]) and thereby solves the 2-dimensional case of their problem about partitions of discrete boxes with the k-piercing 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 well-known Ashbaugh-Beguria inequality about the ratio of the first two Dirichlet eigenvalues of the same domains and supports strongly a conjecture of Ashbaugh-Benguria.
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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 sub-problems. For each subproblem, the Nesterov's accelerated gradient descent algorithm or the Barzilai-Borwein (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 shrinkage-threshold technique directly without iterations. In addition, a modified Attouch-Peypouquet technique is used to accelerate the iterative computation. These lead to more effective algorithms than the Wirtinger flow (WF) algorithm and the Gauss-Newton (
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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 e-commerce. 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 quid-pro-quo. 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 open-source 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 open-source 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 D-modules 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 Khovanov-Lauda-Rouquier 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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Millions of dollars in funding and billions of dollars in valuations have made scooters the next big thing since the last big thing. From a report: When Michael Ramsey, an analyst for technology research firm Gartner, started in February to put together his 2018 "hype cycle" report for the future of transportation, he had plenty of topics to choose from: electric vehicles, flying cars, 5G, blockchain, and, of course, autonomous vehicles. But one type of transportation is conspicuously absent from the results of the report: electric scooters. "At the time, outside of California, these scooters were really not that common," Ramsey said. "That's how much has happened." As for autonomous vehicles, which have enjoyed years of hype as the next big thing, Ramsey labeled them sliding into "the trough of disillusionment," which Ramsey described as "when expectations don't meet the truth." In a matter of months, electric scooter startups have gone from tech oddity to global phenomenon. In some c
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Essential Products, a startup founded in 2015 by Android creator Andy Rubin, was started to create a smartphone with high-end design features that wasn't associated with a particular operating-system maker. Unfortunately, reaching that goal has been harder than anticipated as the company has laid off about 30 percent of its staff. Fortune reports: Cuts were particularly deep in hardware and marketing. The company's website indicates it has about 120 employees. A company spokesperson didn't confirm the extent of layoffs, but said that the decision was difficult for the firm to make and, "We are confident that our sharpened product focus will help us deliver a truly game changing consumer product." The firm was Rubin's first startup after leaving Google in 2014, which had acquired his co-founded firm, Android, in 2005. Essential's first phone came out in August 2017, a few weeks later than initially promised. It received mixed reviews, with most critics citing its lower quality and missi
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Zorro shares a report from The Mercury News: Not only did Facebook inflate ad-watching metrics by up to 900 percent (Warning: source may be paywalled, alternative source), it knew for more than a year that its average-viewership estimates were wrong and kept quiet about it, a new legal filing claims. A group of small advertisers suing the Menlo Park social media titan alleged in the filing that Facebook "induced" advertisers to buy video ads on its platform because advertisers believed Facebook users were watching video ads for longer than they actually were. That "unethical, unscrupulous" behavior by Facebook constituted fraud because it was "likely to deceive" advertisers, the filing alleged. The latest allegations arose out of a lawsuit that the advertisers filed against Mark Zuckerberg-led Facebook in federal court in 2016 over alleged inflation of ad-watching metrics. "Suggestions that we in any way tried to hide this issue from our partners are false," the company told The Wall S
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People's Facebook posts might predict whether they are suffering from depression, researchers reported this week. From a report: The researchers found that the words people used seemed to indicate whether they would later be diagnosed with depression. The findings offer a way to flag people who may be in need of help, but they also raise important questions about people's health privacy, the team reported in the Proceedings of the National Academy of Sciences. People who were later clinically diagnosed with depression used more "I" language, according to Johannes Eichstaedt of the University of Pennsylvania and his colleagues. They also used more words reflecting loneliness, sadness and hostility. "We observed that users who ultimately had a diagnosis of depression used more first-person singular pronouns, suggesting a preoccupation with the self," they wrote. That is an indicator of depression in some people. The team recruited 683 people who visited an emergency room for their study
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Three state treasurers and a top official from New York have joined a shareholders' motion to install an independent chairman at Facebook, claiming the move would improve governance and accountability. [...] The move comes as Facebook was presented with a new legal challenge. The technology company has been accused of misleading advertisers by inflating the viewing figures for videos on its site. A group of US advertisers launched a fraud claim against the social media giant on Tuesday, stating that it had overstated the average viewing time of advertising videos on the site by between 100 and 900pc before reporting them in 2016. All tech companies are pretty terrible as far as companies go, but Facebook really seems to be going out of its way to lead the pack. As far as I'm concerned, we shut it down. Would anyone really miss it?
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In the early days of what ultimately became Waymo, Google's self-driving car division (known at the time as "Project Chauffeur"), there were "more than a dozen accidents, at least three of which were serious," according to a new article in The New Yorker . From a report: The magazine profiled Anthony Levandowski, the former Google engineer who was at the center of the Waymo v. Uber trade secrets lawsuit. According to the article, back in 2011, Levandowski also modified the autonomous software to take the prototype Priuses on "otherwise forbidden routes." Citing an anonymous source, The New Yorker reports that Levandowski sat behind the wheel as the safety driver, along with Isaac Taylor, a Google executive. But while they were in the car, the Prius "accidentally boxed in another vehicle," a Camry. As The New Yorker wrote: "A human driver could easily have handled the situation by slowing down and letting the Camry merge into traffic, but Google's software wasn't prepared for this scena
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An anonymous reader shares a report: Sellers have been modifying lower end NVIDIA graphics cards and selling them more powerful cards online. In a recent version of the GPU-Z graphics card information utility, TechPowerUp has added the ability to now detect these fake NVIDIA cards. This new feature allows buyers of cards to detect if the card is actually a relabled NVIDIA G84, G86, G92, G94, G96, GT215, GT216, GT218, GF108, GF106, GF114, GF116, GF119, or GK106 GPU by displaying an exclamation point where the NVIDIA logo would normally appear and also prepends the string "[FAKE]" before the card's name.
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Gabrielle Hamilton, April Bloomfield, and the Problem with Leaving Women to
10-18 THE NEW YORKER 10958 -
We propose an index for gapped quantum lattice systems that conserve a $\mathrm{U}(1)$-charge. This index takes integer values and it is therefore stable under perturbations. Our formulation is general, but we show that the index reduces to (i) an index of projections in the non-interacting case, (ii) the filling factor for translational invariant systems, (iii) the quantum Hall conductance in the two-dimensional setting without any additional symmetry. Example (ii) recovers the Lieb-Schultz-Mattis theorem, (iii) provides a new and short proof of quantization of Hall conductance in interacting many-body systems. Additionally, we provide a new proof of Bloch's theorem on the vanishing of ground state currents.
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Let $R=K[x_1,...,x_n]$ be the polynomial ring in $n$ variables over a field $K$ and $I$ be a monomial ideal generated in degree $d$. Bandari and Herzog conjectured that a monomial ideal $I$ is polymatroidal if and only if all its monomial localizations have a linear resolution. In this paper we give an affirmative answer to the conjecture in the following cases: $(i)$ ${\rm height}(I)=n-1$; $(ii)$ $I$ contains at least $n-3$ pure powers of the variables $x_1^d,...,x_{n-3}^d$; $(iii)$ $I$ is a monomial ideal in at most four variables.
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We look at the number $L(n)$ of $O$-sequences of length $n$. This interesting and naturally-defined sequence $L(n)$ was first investigated in a recent paper by commutative algebraists Enkosky and Stone, inspired by Huneke. In this note, we significantly improve both of their upper and lower bounds, by means of a very short partition-theoretic argument. In particular, it turns out that, for suitable positive constants $c_1$ and $c_2$ and all $n\ge 1$, $$e^{c_1\sqrt{n}}\le L(n)\le e^{c_2\sqrt{n}\log n}.$$ It remains an open problem to determine an exact asymptotic estimate for $L(n)$.
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We study the continuous-time evolution of the recombination equation of population genetics. This evolution is given by a differential equation that acts on a product probability space, and its solution can be described by a Markov chain on a set of partitions that converges to the finest partition. We study an explicit form of the law of this process by using a family of trees. We also describe the geometric decay rate to the finest partition and the quasi-stationary behavior of the Markov chain when conditioned on the event that the chain does not hit the limit.
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It is known that fuzzy set theory can be viewed as taking place within a topos. There are several equivalent ways to construct this topos, one is as the topos of \'{e}tal\'{e} spaces over the topological space $Y=[0,1)$ with lower topology. In this topos, the fuzzy subsets of a set $X$ are the subobjects of the constant \'{e}tal\'{e} $X\times Y$ where $X$ has the discrete topology. Here we show that the type-2 fuzzy truth value algebra is isomorphic to the complex algebra formed from the subobjects of the constant relational \'{e}tal\'{e} given by the type-1 fuzzy truth value algebra $\mathfrak{I}=([0,1],\wedge,\vee,\neg,0,1)$. More generally, we show that if $L$ is the lattice of open sets of a topological space $Y$ and $\mathfrak{X}$ is a relational structure, then the convolution algebra $L^\mathfrak{X}$ is isomorphic to the complex algebra formed from the subobjects of the constant relational \'{e}tal\'{e} given by $\mathfrak{X}$ in the topos of \'{e}tal\'{e} spaces over $Y$.
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For families of smooth complex projective varieties we show that normal functions arising from algebraically trivial cycle classes are algebraic, and defined over the field of definition of the family. As a consequence, we prove a conjecture of Charles and Kerr-Pearlstein, that zero loci of normal functions arising from algebraically trivial cycle classes are algebraic, and defined over the field of definition of the family. In particular, this gives a short proof of a special, algebraically motivated case of a result of Saito, Brosnan-Pearlstein, and Schnell, conjectured by Green-Griffiths, on zero loci of admissible normal functions.
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