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  • We study the worst-case convergence rates of the proximal gradient method for minimizing the sum of a smooth strongly convex function and a non-smooth convex function whose proximal operator is available. We establish the exact worst-case convergence rates of the proximal gradient method in this setting for any step size and for different standard performance measures: objective function accuracy, distance to optimality and residual gradient norm. The proof methodology relies on recent developments in performance estimation of first-order methods based on semidefinite programming. In the case of the proximal gradient method, this methodology allows obtaining exact and non-asymptotic worst-case guarantees that are conceptually very simple, although apparently new. On the way, we discuss how strong convexity can be replaced by weaker assumptions, while preserving the corresponding convergence rates. We also establish that the same fixed step size policy is optimal for all three performan

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  • This article describes the geometry of isomorphisms between complements of geometrically irreducible closed curves in the affine plane $\mathbb{A}^2$, over an arbitrary field, which do not extend to an automorphism of $\mathbb{A}^2$. We show that such isomorphisms are quite exceptional. In particular, they occur only when both curves are isomorphic to open subsets of the affine line $\mathbb{A}^1$, with the same number of complement points, over any field extension of the ground field. Moreover, the isomorphism is uniquely determined by one of the curves, up to left composition with an automorphism of $\mathbb{A}^2$, except in the case where the curve is isomorphic to the affine line $\mathbb{A}^1$ or to the punctured line $\mathbb{A}^1 \setminus \{0\}$. If one curve is isomorphic to $\mathbb{A}^1$, then both curves are in fact equivalent to lines. In addition, for any positive integer $n$, we construct a sequence of $n$ pairwise non-equivalent closed embeddings of $\mathbb{A}^1 \setmi

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  • Chief Security Officer described security report as a “very painful process.”

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  • Abraham Robinson's method for finding model completions is refined and and generalized for model companions and is applied to the theory of fields equipped with both a valuation and an automorphism.

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  • We consider finite model approximations of discrete-time partially observed Markov decision processes (POMDPs) under the discounted cost criterion. After converting the original partially observed stochastic control problem to a fully observed one on the belief space, the finite models are obtained through the uniform quantization of the state and action spaces of the belief space Markov decision process (MDP). Under mild assumptions on the components of the original model, it is established that the policies obtained from these finite models are nearly optimal for the belief space MDP, and so, for the original partially observed problem. The assumptions essentially require that the belief space MDP satisfies a mild weak continuity condition. We provide examples and introduce explicit approximation procedures for the quantization of the set of probability measures on the state space of POMDP (i.e., belief space).

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  • We derive some new finite sums involving the sequence $s_{2}\left(n\right),$ the sum of digits of the expansion of $n$ in base $2.$ These functions allow us to generalize some classical results obtained by Allouche, Shallit and others.

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  • Over a field of prime characteristic $p>2$, we prove that the cohomology rings of some pointed Hopf algebras of dimension $p^3$ are finitely generated. These are Hopf algebras arising in the ongoing classification of finite dimensional Hopf algebras in positive characteristic, and include bosonizations of Nichols algebras of Jordan type in a general setting as well as their liftings when $p=3$. Our techniques are applications of twisted tensor product resolutions and Anick resolutions in combination with May spectral sequences.

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  • Starting from measured data, we develop a method to compute the fine structure of the spectrum of the Koopman operator with rigorous convergence guarantees. The method is based on the observation that, in the measure-preserving ergodic setting, the moments of the spectral measure associated to a given observable are computable from a single trajectory of this observable. Having finitely many moments available, we use the classical Christoffel-Darboux kernel to separate the atomic and absolutely continuous parts of the spectrum, supported by convergence guarantees as the number of moments tends to infinity. In addition, we propose a technique to detect the singular continuous part of the spectrum as well as two methods to approximate the spectral measure with guaranteed convergence in the weak topology, irrespective of whether the singular continuous part is present or not. The proposed method is simple to implement and readily applicable to large-scale systems since the computational c

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  • An anonymous reader quotes a report from The Verge: Google's AI subsidiary DeepMind has unveiled the latest version of its Go-playing software, AlphaGo Zero. The new program is a significantly better player than the version that beat the game's world champion earlier this year, but, more importantly, it's also entirely self-taught. DeepMind says this means the company is one step closer to creating general purpose algorithms that can intelligently tackle some of the hardest problems in science, from designing new drugs to more accurately modeling the effects of climate change. The original AlphaGo demonstrated superhuman Go-playing ability, but needed the expertise of human players to get there. Namely, it used a dataset of more than 100,000 Go games as a starting point for its own knowledge. AlphaGo Zero, by comparison, has only been programmed with the basic rules of Go. Everything else it learned from scratch. As described in a paper published in Nature today, Zero developed its Go

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  • Cyclic sieving is a well-known phenomenon where certain interesting polynomials, especially $q$-analogues, have useful interpretations related to actions and representations of the cyclic group. We define sieving for an arbitrary group $G$ and study it for the dihedral group $I_2(n)$ of order $2n$. This requires understanding the generators of the representation ring of the dihedral group. For $n$ odd, we exhibit several instances of "dihedral sieving" which involve the generalized Fibonomial coefficients, recently studied by Amdeberhan, Chen, Moll, and Sagan.

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  • We introduce the local and global indices of Dirac operators for the rational Cherednik algebra $\mathsf{H}_{t,c}(G,\mathfrak{h})$, where $G$ is a complex reflection group acting on a finite-dimensional vector space $\mathfrak{h}$. We investigate precise relations between the (local) Dirac index of a simple module in the category $\mathcal{O}$ of $\mathsf{H}_{t,c}(G,\mathfrak{h})$, the graded $G$-character of the module, the Euler-Poincar\'e pairing, and the composition series polynomials for standard modules. In the global theory, we introduce integral-reflection modules for $\mathsf{H}_{t,c}(G,\mathfrak{h})$ constructed from finite-dimensional $G$-modules. We define and compute the index of a Dirac operator on the integral-reflection module and show that the index is, in a sense, independent of the parameter function $c$. The study of the kernel of these global Dirac operators leads naturally to a notion of dualised generalised Dunkl-Opdam operators.

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  • This paper investigates distributed optimization of dynamically coupled networks. We propose distributed algorithms to address two complementary cases: linear systems with controllable subsystems and nonlinear systems in the strict-feedback form. The proposed controllers are verified by two case studies on an optimal power flow problem and a multizone building temperature regulation problem, respectively.

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  • Dollar General Hits a Gold Mine in Rural America

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  • Amy Davidson Sorkin on Donald Trump’s bragging about his condolence call to the wife of Sergeant La David T. Johnson, who was killed in Niger.

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  • We describe the macroscopic behavior of evolutions by crystalline curvature of planar sets in a chessboard--like medium, modeled by a periodic forcing term. We show that the underlying microstructure may produce both pinning and confinement effects on the geometric motion.

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  • We find the number of compositions over finite abelian groups under two types of restrictions: (i) each part belongs to a given subset and (ii) small runs of consecutive parts must have given properties. Waring's problem over finite fields can be converted to type~(i) compositions, whereas Carlitz and locally Mullen compositions can be formulated as type~(ii) compositions. We use the multisection formula to translate the problem from integers to group elements, the transfer matrix method to do exact counting, and finally the Perron-Frobenius theorem to derive asymptotics. We also exhibit bijections involving certain restricted classes of compositions.

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  • We consider the problem of minimizing a convex function over the intersection of finitely many simple sets which are easy to project onto. This is an important problem arising in various domains such as machine learning. The main difficulty lies in finding the projection of a point in the intersection of many sets. Existing approaches yield an infeasible point with an iteration-complexity of $O(1/\varepsilon^2)$ for nonsmooth problems with no guarantees on the in-feasibility. By reformulating the problem through exact penalty functions, we derive first-order algorithms which not only guarantees that the distance to the intersection is small but also improve the complexity to $O(1/\varepsilon)$ and $O(1/\sqrt{\varepsilon})$ for smooth functions. For composite and smooth problems, this is achieved through a saddle-point reformulation where the proximal operators required by the primal-dual algorithms can be computed in closed form. We illustrate the benefits of our approach on a graph tr

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  • We study a nonlinear, nonhomogeneous elliptic equation with an asymmetric reaction term depending on a positive parameter, coupled with Robin boundary conditions. Under appropriate hypotheses on both the leading differential operator and the reaction, we prove that, if the parameter is small enough, the problem admits at least four nontrivial solutions: two of such solutions are positive, one is negative, and one is sign-changing. Our approach is variational, based on critical point theory, Morse theory, and truncation techniques.

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  • Kimura and Yoshida treated a model in which the finite variation part of a two-dimensional semimartingale is expressed by time-integration of latent processes. They proposed a correlation estimator between the latent processes and proved its consistency and asymptotic mixed normality. In this paper, we discuss the confidence interval of the correlation estimator to detect the correlation. %between latent processes. We propose two types of estimators for asymptotic variance of the correlation estimator and prove their consistency in a high frequency setting. Our model includes doubly stochastic Poisson processes whose intensity processes are correlated It\^o processes. We compare our estimators based on the simulation of the doubly stochastic Poisson processes.

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  • Perhaps we’re not alone in the universe; it’s just that everyone else is snoozing

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  • We generalise some well-known graph parameters to operator systems by considering their underlying quantum channels. In particular, we introduce the quantum complexity as the dimension of the smallest co-domain Hilbert space a quantum channel requires to realise a given operator system as its non-commutative confusability graph. We describe quantum complexity as a generalised minimum semidefinite rank and, in the case of a graph operator system, as a quantum intersection number. The quantum complexity and a closely related quantum version of orthogonal rank turn out to be upper bounds for the Shannon zero-error capacity of a quantum channel, and we construct examples for which these bounds beat the best previously known general upper bound for the capacity of quantum channels, given by the quantum Lov\'asz theta number.

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  • We consider the problem of computing the Fourier transform of high-dimensional vectors, distributedly over a cluster of machines consisting of a master node and multiple worker nodes, where the worker nodes can only store and process a fraction of the inputs. We show that by exploiting the algebraic structure of the Fourier transform operation and leveraging concepts from coding theory, one can efficiently deal with the straggler effects. In particular, we propose a computation strategy, named as coded FFT, which achieves the optimal recovery threshold, defined as the minimum number of workers that the master node needs to wait for in order to compute the output. This is the first code that achieves the optimum robustness in terms of tolerating stragglers or failures for computing Fourier transforms. Furthermore, the reconstruction process for coded FFT can be mapped to MDS decoding, which can be solved efficiently. Moreover, we extend coded FFT to settings including computing general

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  • This paper studies sheaf cohomology on coarse spaces.

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  • Ars staffers got as little as $0.76 and as much as $12.02. How much did you get?

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  • An anonymous reader quotes a report from The Guardian: The abundance of flying insects has plunged by three-quarters over the past 25 years, according to a new study that has shocked scientists. Insects are an integral part of life on Earth as both pollinators and prey for other wildlife and it was known that some species such as butterflies were declining. But the newly revealed scale of the losses to all insects has prompted warnings that the world is "on course for ecological Armageddon," with profound impacts on human society. The new data was gathered in nature reserves across Germany but has implications for all landscapes dominated by agriculture, the researchers said. The cause of the huge decline is as yet unclear, although the destruction of wild areas and widespread use of pesticides are the most likely factors and climate change may play a role. The scientists were able to rule out weather and changes to landscape in the reserves as causes, but data on pesticide levels has

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  • Over the moduli space of smooth curves, the double ramification cycle can be defined by pulling back the unit section of the universal jacobian along the Abel-Jacobi map. This breaks down over the boundary since the Abel-Jacobi map fails to extend. We construct a `universal' resolution of the Abel-Jacobi map, and thereby extend the double ramification cycle to the whole of the moduli of stable curves. In the non-twisted case, we show that our extension coincides with the cycle constructed by Li, Graber, Vakil via a virtual fundamental class on a space of rubber maps.

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  • Financial models are studied where each asset may potentially lose value relative to any other. Conditioning on non-devaluation, each asset can serve as proper num\'eraire and classical valuation rules can be formulated. It is shown when and how these local valuation rules can be aggregated to obtain global arbitrage-free valuation formulas.

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  • The aim of this paper is to give fine asymptotics for random variables with moments of Gamma type. Among the examples we consider are random determinants of Laguerre and Jacobi beta ensembles with varying dimensions (the number of observed variables and the number of measurements vary and may be different). In addition to the Dyson threefold way of classical random matrix models (GOE, GUE, GSE), we study random determinants of random matrices of the so-called tenfold way, including the Bogoliubov-de Gennes and chiral ensembles from mesoscopic physics. We show that fixed-trace matrix ensembles can be analysed as well. Finally, we add fine asymptotics for the $p(n)$-dimensional volume of the simplex with $p(n)+1$ points in ${\Bbb R}^n$ distributed according to special distributions, which is strongly correlated to Gram matrix ensembles. We use the framework of mod-$\varphi$ convergence to obtain extended limit theorems, Berry-Esseen bounds, precise moderate deviations, large and moderate

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  • The deficiency of a group is the maximum over all presentations for that group of the number of generators minus the number of relators. Every finite group has non-positive deficiency. We show that every non-positive integer is the deficiency of a finite group -- in fact, of a finite $p$-group for every prime $p$. This completes Kotschick's classification of the integers which are deficiencies of fundamental groups of compact Kaehler manifolds.

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  • Anchored, floating turbines allow offshore wind installations in deep waters.

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  • The Semi-Algebraic framework for the approximate Canonical Polyadic (CP) decomposition via SImultaneaous matrix diagonalization (SECSI) is an efficient tool for the computation of the CP decomposition. The SECSI framework reformulates the CP decomposition into a set of joint eigenvalue decomposition (JEVD) problems. Solving all JEVDs, we obtain multiple estimates of the factor matrices and the best estimate is chosen in a subsequent step by using an exhaustive search or some heuristic strategy that reduces the computational complexity. Moreover, the SECSI framework retains the option of choosing the number of JEVDs to be solved, thus providing an adjustable complexity-accuracy trade-off. In this work, we provide an analytical performance analysis of the SECSI framework for the computation of the approximate CP decomposition of a noise corrupted low-rank tensor, where we derive closed-form expressions of the relative mean square error for each of the estimated factor matrices. These exp

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  • This paper concerns singular, complex projective, irreducible symplectic varieties. The generalized Beauville-Bogomolov form satisfies the Fujiki relations and has the same rank as in the smooth case. As a consequence, we see that these varieties admit only very special fibrations. Our results give new evidence that the correct definition of singular analogs of irreducible symplectic manifolds is the one from Greb-Kebekus-Peternell.

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    Browser security beyond sandboxing

    10-19 Hacker News 32

    Browser security beyond sandboxing

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  • Motivated mainly by the localization over an open bounded set $\Omega$ of $\mathbb R^n$ of solutions of the Schr\"odinger equations, we consider the Schr\"odinger equation over $\Omega$ with a very singular potential $V(x) \ge C d (x, \partial \Omega)^{-r}$ with $r\ge 2$ and a convective flow $\vec U$. We prove the existence and uniqueness of a very weak solution of the equation, when the right hand side datum $f(x)$ is in $L^1 (\Omega, d(\cdot, \partial \Omega))$, even if no boundary condition is a priori prescribed. We prove that, in fact, the solution necessarily satisfies (in a suitable way) the Dirichlet condition $u = 0$ on $\partial \Omega$. These results improve some of the results of the previous paper by the authors in collaboration with Roger Temam. In addition, we prove some new results dealing with the $m$-accretivity in $L^1 (\Omega, d(\cdot, \partial \Omega)^ \alpha)$, where $\alpha \in [0,1]$, of the associated operator, the corresponding parabolic problem and the study

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  • Tesla slams such abuse but expresses doubts regarding the men's claims.

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  • Estimator selection has become a crucial issue in non parametric estimation. Two widely used methods are penalized empirical risk minimization (such as penalized log-likelihood estimation) or pairwise comparison (such as Lepski's method). Our aim in this paper is twofold. First we explain some general ideas about the calibration issue of estimator selection methods. We review some known results, putting the emphasis on the concept of minimal penalty which is helpful to design data-driven selection criteria. Secondly we present a new method for bandwidth selection within the framework of kernel density density estimation which is in some sense intermediate between these two main methods mentioned above. We provide some theoretical results which lead to some fully data-driven selection strategy.

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  • We consider random Schr\"odinger operators with Dirichlet boundary conditions outside lattice approximations of a smooth Euclidean domain and study the behavior of its lowest-lying eigenvalues in the limit when the lattice spacing tends to zero. Under a suitable moment assumption on the random potential and regularity of the spatial dependence of its mean, we prove that the eigenvalues of the random operator converge to those of a deterministic Schr\"odinger operator. Assuming also regularity of the variance, the fluctuation of the random eigenvalues around their mean are shown to obey a multivariate central limit theorem. This extends the authors' recent work where similar conclusions have been obtained for bounded random potentials.

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  • We consider hyperelastic problems and their numerical solution using a conforming finite element discretization and iterative linearization algorithms. For these problems, we present equilibrated, weakly symmetric, $H(\rm{div)}$-conforming stress tensor reconstructions, obtained from local problems on patches around vertices using the Arnold--Falk--Winther finite element spaces. We distinguish two stress reconstructions, one for the discrete stress and one representing the linearization error. The reconstructions are independent of the mechanical behavior law. Based on these stress tensor reconstructions, we derive an a posteriori error estimate distinguishing the discretization, linearization, and quadrature error estimates, and propose an adaptive algorithm balancing these different error sources. We prove the efficiency of the estimate, and confirm it on a numerical test with analytical solution for the linear elasticity problem. We then apply the adaptive algorithm to a more applic

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  • The entropy is one of the fundamental states of a fluid and, in the viscous case, the equation that it satisfies is highly singular in the region close to the vacuum. In spite of its importance in the gas dynamics, the mathematical analyses on the behavior of the entropy near the vacuum region, were rarely carried out; in particular, in the presence of vacuum, either at the far field or at some isolated interior points, it was unknown if the entropy remains its boundedness. The results obtained in this paper indicate that the ideal gases retain their uniform boundedness of the entropy, locally or globally in time, if the vacuum occurs at the far field only and the density decays slowly enough at the far field. Precisely, we consider the Cauchy problem to the one-dimensional full compressible Navier-Stokes equations without heat conduction, and establish the local and global existence and uniqueness of entropy-bounded solutions, in the presence of vacuum at the far field only. It is als

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  • We address the following conjecture about the existence of common zeros for commuting vector fields in dimension three: let $X,Y$ be two $C^1$ commuting vector fields on a $3$-manifold $M$, and $U$ be a relatively compact open set where $Y$ does not vanish, then $X$ has zero Poincar\'e-Hopf index in $U$. We prove that conjecture when $X$ and $Y$ are of class $C^3$ and every periodic orbit of $Y$ along which $X$ and $Y$ are colinear is partially hyperbolic. We also prove the conjecture, still in the $C^3$ setting, and assuming that the flow $Y$ leaves invariant a transverse plane field. These results shed new light on the $C^3$ case of the conjecture and indeed we discuss a global strategy to attack this problem.

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  • We investigate the initial value problem for a defocusing nonlinear Schr\"odinger equation with weighted exponential nonlinearity $$ i\partial_t u+\Delta u=\frac{u}{|x|^b}(e^{\alpha|u|^2}-1); \qquad (t,x) \in \mathbb{R}\times\mathbb{R}^2, $$ where $0< b <1$ and $\alpha=2\pi(2-b)$. We establish local and global well-posedness in the subcritical and critical regimes.

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  • The processes of the averaged regression quantiles and of their modifications provide useful tools in the regression models when the covariates are not fully under our control. As an application we mention the probabilistic risk assessment in the situation when the return depends on some exogenous variables. The processes enable to evaluate the expected $\alpha$-shortfall ($0\leq\alpha\leq 1$) and other measures of the risk, recently generally accepted in the financial literature, but also help to measure the risk in environment analysis and elsewhere.

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  • Dyslexia: scientists claim cause of condition may lie in the eyes

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    Documenting the Web together

    10-18 Hacker News 57

    Documenting the Web together

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    DragonFly BSD 5.0

    10-17 LWN 58

    DragonFly BSD 5.0 has been released. "Preliminary HAMMER2 support has been released into the wild as-of the 5.0 release. This support is considered EXPERIMENTAL and should generally not yet be used for production machines and important data. The boot loader will support both UFS and HAMMER2 /boot. The installer will still use a UFS /boot even for a HAMMER2 installation because the /boot partition is typically very small and HAMMER2, like HAMMER1, does not instantly free space when files are deleted or replaced. DragonFly 5.0 has single-image HAMMER2 support, with live dedup (for cp's), compression, fast recovery, snapshot, and boot support. HAMMER2 does not yet support multi-volume or clustering, though commands for it exist. Please use non-clustered single images for now."

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    DragonFlyBSD 5.0 released

    10-17 OSnews 60

    DragonFlyBSD 5.0 is the first release with preliminary boot support for HAMMER2, the project's new filesystem. Preliminary HAMMER2 support has been released into the wild as-of the 5.0 release. This support is considered EXPERIMENTAL and should generally not yet be used for production machines and important data. The boot loader will support both UFS and HAMMER2 /boot. The installer will still use a UFS /boot even for a HAMMER2 installation because the /boot partition is typically very small and HAMMER2, like HAMMER1, does not instantly free space when files are deleted or replaced.

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  • Adding a tail to a cockroach-inspired robot helps it flip itself over with ease

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  • A Palo Alto startup that stopped trying to be an "Android killer" last year after raising $185 million has apparently pivoted to developing autonomous vehicle technology. From a report: The company now known as Cyngn has changed its name from Cyanogen and recently got a permit to test its self-driving tech on California roads, according to a report Wednesday on Axios. It's being led by Lior Tal, the former chief operating officer who took over as CEO last fall when Kirt McMaster left. The rest of the startup's current team of about 30 people appear to have joined since the strategy shift, Axios reported, citing LinkedIn records. Some of them are former Facebook people, like Tal, and alumni of automakers who include Mercedes-Benz. No new funding has been disclosed for the reinvented company. It lists on its website investors who backed it before it pivoted, including Andreessen Horowitz, Benchmark Capital, Redpoint Ventures, Index Ventures, Qualcomm and Chinese social networking company

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  • That’s “not how it works,” FCC commissioner tells the president.

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  • It can operate at a record 1,400 ˚C, enabling the use of liquid metals for thermal storage.

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    GitHub Discover

    10-12 Hacker News 80

    GitHub Discover

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    Competitive Self-Play

    10-12 Hacker News 90

    Competitive Self-Play

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    Eloquent JavaScript, 3rd edition

    10-12 Hacker News 77

    Eloquent JavaScript, 3rd edition

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  • The California Department of Motor Vehicles is changing its rules to allow companies to test autonomous vehicles without a driver behind the wheel -- and to let the public use autonomous vehicles. From a report: The DMV released a revised version of its regulations and has started a 15-day public comment period, ending October 25, 2017. California law requires the DMV to work on regulations to cover testing and public use of autonomous vehicles, and the regulator said that this is the first step. "We are excited to take the next step in furthering the development of this potentially life-saving technology in California," the state's Transportation Secretary, Brian Kelly, said in a statement. California's DMV took pains in its announcement to highlight that it wasn't trying to overstep the National Highway Traffic Safety Administration, which has the final say on developing and enforcing compliance with Federal Motor Vehicle Safety Standards. Rather, the California regulations, are goin

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  • The quote seems clear, but now he’s changing his tune.

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  • Jon Brodkin reports via Ars Technica: A Federal Communications Commission decision to eliminate price caps imposed on some business broadband providers should be struck down, advocacy groups told federal judges last week. The FCC failed to justify its claim that a market can be competitive even when there is only one Internet provider, the groups said. Led by Chairman Ajit Pai, the FCC's Republican majority voted in April of this year to eliminate price caps in a county if 50 percent of potential customers "are within a half mile of a location served by a competitive provider." That means business customers with just one choice are often considered to be located in a competitive market and thus no longer benefit from price controls. The decision affects Business Data Services (BDS), a dedicated, point-to-point broadband link that is delivered over copper-based TDM networks by incumbent phone companies like AT&T, Verizon, and CenturyLink. But the FCC's claim that "potential competit

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  • Facebook is going to ship a standalone VR headset called Oculus Go next year. The headset, which won't require a PC or phone to run, will be available early next year for $199. From a report: Facebook CEO Mark Zuckerberg officially announced the new product during his keynote speech at Facebook's fourth Oculus Connect virtual reality (VR) developer conference in San Jose, Calif. Wednesday, where he framed the device as an important step towards bringing VR to the masses. "We want to get a billion people in virtual reality," Zuckerberg said. Facebook VP of VR Hugo Barra said that the company developed custom lenses for the headset, which allow for a wide field of view. The display is a fast-switch LCD screen with a resolution of 2560x1440 pixels, and it comes with integrated headphones. The company will be shipping first headsets to developers in November.

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  • A great starter kit for newbies, if you can stand the lack of good music playback.

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  • Masha Gessen on how Donald Trump’s threat against NBC is part of a pattern of attempts to sabotage freedom of the press.

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  • An anonymous reader quotes a report from Engadget: 10.9 million U.S. driver's licenses were stolen in the massive breach that Equifax suffered in mid-May, according to a new report by The Wall Street Journal. In addition, WSJ has revealed that the attackers got a hold of 15.2 million UK customers' records, though only 693,665 among them had enough info in the system for the breach to be a real threat to their privacy. Affected customers provided most of the driver's licenses on file to verify their identities when they disputed their credit-report information through an Equifax web page. That page was one of the entry points the attackers used to gain entry into the credit reporting agency's system.

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  • Cthulhu: Organizing Go Code in a Scalable Repo

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  • Jia Tolentino on the sexual-assault allegations against Harvey Weinstein and the way powerful men like Weinstein wield power dynamics to prey on women.

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  • We generalize the definition of CM cycles beyond the small and big CM ones studied by various authors and give a uniform formula for the CM values of Green functions associated to these special cycles in general using the idea of regularized theta lifts.

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  • We prove near-tight concentration of measure for polynomial functions of the Ising model under high temperature. For any degree $d$, we show that a degree-$d$ polynomial of a $n$-spin Ising model exhibits exponential tails that scale as $\exp(-r^{2/d})$ at radius $r=\tilde{\Omega}_d(n^{d/2})$. Our concentration radius is optimal up to logarithmic factors for constant $d$, improving known results by polynomial factors in the number of spins. We demonstrate the efficacy of polynomial functions as statistics for testing the strength of interactions in social networks in both synthetic and real world data.

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  • By Langlands and Deligne we know that the local constants are extendible functions. Therefore, to give an explicit formula of the local constant of an induced representation of a local Galois group of a non-Archimedean local field $F$ of characteristic zero, we have to compute the lambda function $\lambda_{K/F}$ for a finite extension $K/F$. In this paper, when a finite extension $K/F$ is Galois, we give a formula for $\lambda_{K/F}$.

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  • Laman graphs model planar frameworks which are rigid for a general choice of distances between the vertices. There are finitely many ways, up to isometries, to realize a Laman graph in the plane. In a recent paper we provide a recursion formula for this number of realizations using ideas from algebraic and tropical geometry. Here, we present a concise summary of this result focusing on the main ideas and the combinatorial point of view.

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  • This paper gives a classification of all pairs $(\mathfrak g, \mathfrak h)$ with $\mathfrak g$ a simple real Lie algebra and $\mathfrak h < \mathfrak g$ a reductive subalgebra for which there exists a minimal parabolic subalgebra $\mathfrak p < \mathfrak g$ such that $\mathfrak g = \mathfrak h + \mathfrak p$ as vector sum.

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  • Geometric aspects play an important role in the construction and analysis of structure-preserving numerical methods for a wide variety of ordinary and partial differential equations. Here we review the development and theory of symplectic integrators for Hamiltonian ordinary and partial differential equations, of dynamical low-rank approximation of time-dependent large matrices and tensors, and its use in numerical integrators for Hamiltonian tensor network approximations in quantum dynamics.

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  • We prove that for a strongly pseudoconvex domain $D\subset\mathbb C^n$, the infinitesimal Carath\'{e}odory metric $g_C(z,v)$ and the infinitesimal Kobayashi metric $g_K(z,v)$ coincide if $z$ is sufficiently close to $bD$ and if $v$ is sufficiently close to being tangential to $bD$. Also, we show that every two close points of $D$ sufficiently close to the boundary and whose difference is almost tangential to $bD$ can be joined by a (unique up to reparameterization) complex geodesic of $D$ which is also a holomorphic retract of $D$. The same continues to hold if $D$ is a worm domain, as long as the points are sufficiently close to a strongly pseudoconvex boundary point. We also show that a strongly pseudoconvex boundary point of a worm domain can be globally exposed; this has consequences for the behavior of the squeezing function.

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  • Inspired by code vertex operator algebras (VOAs) and their representation theory, we define code algebras, a new class of commutative non-associative algebras constructed from binary linear codes. Let $C$ be a binary linear code of length $n$. A basis for the code algebra $A_C$ consists of $n$ idempotents and a vector for each non-constant codeword of $C$. We show that code algebras are almost always simple and, under mild conditions on their structure constants, admit an associating bilinear form. We determine the Pierce decomposition and the fusion rules for the idempotents in the basis, and we give a construction to find additional idempotents, called the $s$-map, which comes from the code structure. For a general code algebra, we classify the eigenvalues and eigenvectors of the smallest examples of the $s$-map construction, and hence show that certain code algebras are axial algebras. We give some examples, including that for a Hamming code $H_8$ where the code algebra $A_{H_8}$ is

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  • The correspondence between Gorenstein Fano toric varieties and reflexive polytopes has been generalized by Ilten and S\"u{\ss} to a correspondence between Gorenstein Fano complexity-one $T$-varieties and Fano divisorial polytopes. Motivated by the finiteness of reflexive polytopes in fixed dimension, we show that over a fixed base polytope, there are only finitely many Fano divisorial polytopes, up to equivalence. We classify two-dimensional Fano divisorial polytopes, recovering Huggenberger's classification of Gorenstein del Pezzo $\mathbb{K}^*$-surfaces. Furthermore, we show that any three-dimensional Fano divisorial polytope is equivalent to one involving only eight functions.

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  • Given a Moebius homeomorphism $f : \partial X \to \partial Y$ between boundaries of proper, geodesically complete CAT(-1) spaces $X,Y$, we describe an extension $\hat{f} : X \to Y$ of $f$, called the circumcenter map of $f$, which is constructed using circumcenters of expanding sets. The extension $\hat{f}$ is shown to coincide with the $(1, \log 2)$-quasi-isometric extension constructed in [biswas3], and is locally $1/2$-Holder continuous. When $X,Y$ are complete, simply connected manifolds with sectional curvatures $K$ satisfying $-b^2 \leq K \leq -1$ for some $b \geq 1$ then the extension $\hat{f} : X \to Y$ is a $(1, (1 - \frac{1}{b})\log 2)$-quasi-isometry. Circumcenter extension of Moebius maps is natural with respect to composition with isometries.

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  • It can operate at a record 1,400 ˚C, enabling the use of liquid metals for thermal storage.

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  • Broken packets: IP fragmentation is flawed

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  • We extend the inner product from bosonic Fock space to a pairing between suitable antifunctionals on the symmetric algebra. Our account is illustrated by the (Gaussian) half-form pairing between positive polarizations in the form needed for geometric quantization.

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  • Ian Crouch on the new trailer for “Star Wars: The Last Jedi,” which, amid the bleakness, contains a speck of light.

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    Cornered Yanks Win Again

    10-11 THE NEW YORKER 72

    Roger Angell writes about the excitement of the New York Yankees’ win against the Cleveland Indians at home.

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  • Bryan Fuller (Hannibal, American Gods) will reboot obscure 80s anthology, Amazing Stories.

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  • Richard Brody reviews “Faces Places,” a documentary film directed by Agnès Varda and JR, in which the duo travels to small, nostalgia-infused towns in France.

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    Bubble – Visual Programming

    10-11 Hacker News 73

    Bubble – Visual Programming

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