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    2D Syntax

    06-29 Hacker News 50
  • How good is the return? Try 44-fold—yep, that’s 4,400 percent

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  • ZeroKit for Realm: Easy End-To-End Encryption

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  • In his PyCon 2017 talk, Miguel Grinberg wanted to introduce asynchronous programming with Python to complete beginners. There is a lot of talk about asynchronous Python, especially with the advent of the asyncio module, but there are multiple ways to create asynchronous Python programs, many of which have been available for quite some time. In the talk, Grinberg took something of a step back from the intricacies of those solutions to look at what asynchronous processing means at a higher level.

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  • Voodoo Manufacturing (YC W17) Is Building a Robotic Factory – Join us

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  • DHS Chief: “Our enemies are adaptive, and we must be too.”

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  • After surveying 2.5 million dogs and 500,000 cats in the U.S. last year, a group of researchers found that about one in three were overweight or obese. "Looking over data from the last decade, the researchers say the new figures reveal a 169-percent increase in hefty felines and a 158-percent increase in chunky canines," reports Ars Technica. From the report: All the data is from researchers at Banfield, which runs a chain of veterinary hospitals across 42 states. The researchers surveyed animals that checked into one of Banfield's 975 locations, putting them through a five-point physical and visual exam. Animals were considered overweight if their ribs were not clearly visible or easily felt and if their waists were also hard to see. Pets were dubbed obese if their ribs couldn't be felt at all and they had no visible waist. As in humans, being overweight makes pets more prone to chronic health conditions. Also similar to humans, doctors blame pets' weight problems on overfeeding and l

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  • An anonymous reader quotes a report from The Guardian: Mayors of more than 7,400 cities across the world have vowed that Donald Trump's decision to withdraw from the Paris accord will spur greater local efforts to combat climate change. At the first meeting of a "global covenant of mayors," city leaders from across the US, Europe and elsewhere pledged to work together to keep to the commitments made by Barack Obama two years ago. Cities will devise a standard measurement of emission reductions to help them monitor their progress. They will also share ideas for delivering carbon-free transport and housing. Kassim Reed, the mayor of Atlanta, told reporters he had travelled to Europe to "send a signal" that US states and cities would execute the policies Obama committed to, whether the current White House occupants agreed or not. Reed, whose administration has promised that the city of Atlanta will use 100% renewable energy by 2035, said 75% of the US population and GDP lay in urban areas

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  • His ‘Petya’ Code Was Used in a Global Cyber Attack, Now He Wants to Help

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    Content Distribution Networks

    06-29 Hacker News 44

    Content Distribution Networks

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  • Ask HN: A good primer on cryptocurrencies?

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  • The LWN.net Weekly Edition for June 29, 2017 is available.

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  • Recently, Lennart Poettering announced a new tool called casync for efficiently distributing filesystem and disk images. Deployment of virtual machines or containers often requires such an image to be distributed for them. These images typically contain most or all of an entire operating system and its requisite data files; they can be quite large. The images also often need updates, which can take up considerable bandwidth depending on how efficient the update mechanism is. Poettering developed casync as an efficient tool for distributing such filesystem images, as well as for their updates.

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  • Steve Lohr, writing for the New York Times: A few years ago, Sean Bridges lived with his mother, Linda, in Wiley Ford, W.Va. Their only income was her monthly Social Security disability check. He applied for work at Walmart and Burger King, but they were not hiring. Yet while Mr. Bridges had no work history, he had certain skills. He had built and sold some stripped-down personal computers, and he had studied information technology at a community college. When Mr. Bridges heard IBM was hiring at a nearby operations center in 2013, he applied and demonstrated those skills. Now Mr. Bridges, 25, is a computer security analyst, making $45,000 a year. In a struggling Appalachian economy, that is enough to provide him with his own apartment, a car, spending money -- and career ambitions. "I got one big break," he said. "That's what I needed." Mr. Bridges represents a new but promising category in the American labor market: people working in so-called new-collar or middle-skill jobs. As the U

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  • We study representations of positive definite kernels $K$ in a general setting, but with view to applications to harmonic analysis, to metric geometry, and to realizations of certain stochastic processes. Our initial results are stated for the most general given positive definite kernel, but are then subsequently specialized to the above mentioned applications. Given a positive definite kernel $K$ on $S\times S$ where $S$ is a fixed set, we first study families of factorizations of $K$. By a factorization (or representation) we mean a probability space $\left(B,\mu\right)$ and an associated stochastic process indexed by $S$ which has $K$ as its covariance kernel. For each realization we identify a co-isometric transform from $L^{2}\left(\mu\right)$ onto $\mathscr{H}\left(K\right)$, where $\mathscr{H}\left(K\right)$ denotes the reproducing kernel Hilbert space of $K$. In some cases, this entails a certain renormalization of $K$. Our emphasis is on such realizations which are minimal in

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  • We show that Dranishnikov's asymptotic property C is preserved by direct products and the free product of discrete metric spaces. In particular, if $G$ and $H$ are groups with asymptotic property C, then both $G \times H$ and $G * H$ have asymptotic property C. We also prove that a group~$G$ has asymptotic property C if $1\to K\to G\to H\to 1$ is exact, if $\operatorname{asdim} K<\infty$, and if $H$ has asymptotic property C. The groups are assumed to have left-invariant proper metrics and need not be finitely generated. These results settle questions of Dydak and Virk, of Bell and Moran, and an open problem in topology from the Lviv Topological Seminar.

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  • We investigate in this paper a Bickel-Rosenblatt test of goodness-of-fit for the density of the noise in an autoregressive model. Since the seminal work of Bickel and Rosenblatt, it is well-known that the integrated squared error of the Parzen-Rosenblatt density estimator, once correctly renormalized, is asymptotically Gaussian for independent and identically distributed (i.i.d.) sequences. We show that the result still holds when the statistic is built from the residuals of general stable and explosive autoregressive processes. In the univariate unstable case, we also prove that the result holds when the unit root is located at $-1$ whereas we give further results when the unit root is located at $1$. In particular, we establish that except for some particular asymmetric kernels leading to a non-Gaussian limiting distribution and a slower convergence, the statistic has the same order of magnitude. Finally we build a goodness-of-fit Bickel-Rosenblatt test for the true density of the no

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  • We explicitly describe the Cartier dual of the $l$-th Frobenius kernel $N_l$ of the deformation group scheme, which deforms the additive group scheme to the multiplicative group scheme. Then the Cartier dual of $N_l$ is given by a certain Frobenius type kernel of the Witt scheme. Here we assume that the base ring $A$ is a $Z_{(p)}/(p^n)$-algebra, where $p$ is a prime number. The obtained result generalizes a previous result by the author which assumes that $A$ is a ring of characteristic $p$.

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  • In this note, we analyze the classification problem for compact metrizable $G$-ambits for a countable discrete group $G$ from the point of view of descriptive set theory. More precisely, we prove that the topological conjugacy relation on the standard Borel space of compact metrizable $G$-ambits is Borel for every countable discrete group $G$.

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  • Using transversality and a dimension reduction argument, a result of A. Bezdek and W. Kuperberg is applied to polycylinders $\mathbb{D}^2\times \mathbb{R}^n$, showing that the optimal packing density is $\pi/\sqrt{12}$ in any dimension.

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  • In this paper we consider time dependent Schr\"odinger equations on the one-dimensional torus $\T := \R /(2 \pi \Z)$ of the form $\partial_t u = \ii {\cal V}(t)[u]$ where ${\cal V}(t)$ is a time dependent, self-adjoint pseudo-differential operator of the form ${\cal V}(t) = V(t, x) |D|^M + {\cal W}(t)$, $M > 1$, $|D| := \sqrt{- \partial_{xx}}$, $V$ is a smooth function uniformly bounded from below and ${\cal W}$ is a time-dependent pseudo-differential operator of order strictly smaller than $M$. We prove that the solutions of the Schr\"odinger equation $\partial_t u = \ii {\cal V}(t)[u]$ grow at most as $t^\e$, $t \to + \infty$ for any $\e > 0$. The proof is based on a reduction to constant coefficients up to smoothing remainders of the vector field $\ii {\cal V}(t)$ which uses Egorov type theorems and pseudo-differential calculus.

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  • This paper studies the small time behavior of the heat content for the Poisson kernel over a bounded open set $\dom\subset \Rd$, $d\geq 2$, of finite perimeter by working with the set covariance function. As a result, we obtain a third order expansion involving geometric features related to the underlying set $\dom$. We provide the explicit form of the third term for the unit ball when $d=2$ and $d=3$ and supply some results concerning the square $[-1,1]\times [-1,1]$.

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  • In this paper the author studies the isoperimetric problem in $\re^n$ with perimeter density $|x|^p$ and volume density $1.$ We settle completely the case $n=2,$ completing a previous work by the author: we characterize the case of equality if $0\leq p\leq 1$ and deal with the case $-\infty<p<-1$ (with the additional assumption $0\in\Omega$). In the case $n\geq 3$ we deal mainly with the case $-\infty<p<0,$ showing among others that the results in $2$ dimensions do not generalize for the range $-n+1<p<0.$

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  • We use the adelic language to show that any homomorphism between Jacobians of modular curves arises from a linear combination of Hecke modular correspondences. The proof is based on a study of the actions of $\mathrm{GL}_2$ and Galois on the \'etale cohomology of the tower of modular curves. We also make this result explicit for Ribet's twisting operators on modular abelian varieties.

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  • We consider support points of the class $S^0(\mathbb{D}^n)$ of normalized univalent mappings on the polydisc $\mathbb{D}^n$ with parametric representation and we prove sharp estimates for coefficients of degree 2.

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  • This work constructs a well-defined and operational form factor expansion in a model having a massless spectrum of excitations. More precisely, the dynamic two-point functions in the massless regime of the XXZ spin-1/2 chain are expressed in terms of properly regularised series of multiple integrals. These series are obtained by taking, in an appropriate way, the thermodynamic limit of the finite volume form factor expansions. The series are structured in way allowing one to identify directly the contributions to the correlator stemming from the conformal-type excitations on the Fermi surface and those issuing from the massive excitations (deep holes, particles and bound states). The obtained form factor series opens up the possibility of a systematic and exact study of asymptotic regimes of dynamical correlation functions in the massless regime of the XXZ spin $1/2$ chain. Furthermore, the assumptions on the microscopic structure of the model's Hilbert space that are necessary so as t

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  • The concentration of measure phenomenon in Gauss' space states that every $L$-Lipschitz map $f$ on $\mathbb R^n$ satisfies \[ \gamma_{n} \left(\{ x : | f(x) - M_{f} | \geqslant t \} \right) \leqslant 2 e^{ - \frac{t^2}{ 2L^2} }, \quad t>0, \] where $\gamma_{n} $ is the standard Gaussian measure on $\mathbb R^{n}$ and $M_{f}$ is a median of $f$. In this work, we provide necessary and sufficient conditions for when this inequality can be reversed, up to universal constants, in the case when $f$ is additionally assumed to be convex. In particular, we show that if the variance ${\rm Var}(f)$ (with respect to $\gamma_{n}$) satisfies $ \alpha L \leqslant \sqrt{ {\rm Var}(f) } $ for some $ 0<\alpha \leqslant 1$, then \[ \gamma_{n} \left(\{ x : | f(x) - M_{f} | \geqslant t \}\right) \geqslant c e^{ -C \frac{t^2}{ L^2} } , \quad t>0 ,\] where $c,C>0$ are constants depending only on $\alpha$.

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  • Once a Model City, Hong Kong Is in Trouble

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    Pattern-defeating quicksort

    06-29 Hacker News 22

    Pattern-defeating quicksort

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  • For an arbitrary finite permutation group $G$, subgroup of the symmetric group $S_\ell$, we determine the permutations involving only members of $G$ as $\ell$-patterns, i.e., avoiding all patterns in the set $S_\ell \setminus G$. The set of all $n$-permutations with this property constitutes again a permutation group. We consequently refine and strengthen the classification of sets of permutations closed under pattern involvement and composition that is due to Atkinson and Beals.

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  • In the paper, we prove an analogue of the Kato-Rosenblum theorem in a semifinite von Neumann algebra. Let $\mathcal{M}$ be a countably decomposable, properly infinite, semifinite von Neumann algebra acting on a Hilbert space $\mathcal{H}$ and let $\tau$ be a faithful normal semifinite tracial weight of $\mathcal M$. Suppose that $H$ and $H_1$ are self-adjoint operators affiliated with $\mathcal{M}$. We show that if $H-H_1$ is in $\mathcal{M}\cap L^{1}\left(\mathcal{M},\tau\right)$, then the ${norm}$ absolutely continuous parts of $H$ and $H_1$ are unitarily equivalent. This implies that the real part of a non-normal hyponormal operator in $\mathcal M$ is not a perturbation by $\mathcal{M}\cap L^{1}\left(\mathcal{M},\tau\right)$ of a diagonal operator. Meanwhile, for $n\ge 2$ and $1\leq p<n$, by modifying Voiculescu's invariant we give examples of commuting $n$-tuples of self-adjoint operators in $\mathcal{M}$ that are not arbitrarily small perturbations of commuting diagonal operato

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  • We improve the Peres-Schlag result on pinned distances in sets of a given Hausdorff dimension. In particular, for Euclidean distances, with $$\Delta^y(E) = \{|x-y|:x\in E\},$$ we prove that for any $E, F\subset{\Bbb R}^d$, there exists a probability measure $\mu_F$ on $F$ such that for $\mu_F$-a.e. $y\in F$, (1) $\dim_{{\mathcal H}}(\Delta^y(E))\geq\beta$ if $\dim_{{\mathcal H}}(E) + \frac{d-1}{d+1}\dim_{{\mathcal H}}(F) > d - 1 + \beta$; (2) $\Delta^y(E)$ has positive Lebesgue measure if $\dim_{{\mathcal H}}(E)+\frac{d-1}{d+1}\dim_{{\mathcal H}}(F) > d$; (3) $\Delta^y(E)$ has non-empty interior if $\dim_{{\mathcal H}}(E)+\frac{d-1}{d+1}\dim_{{\mathcal H}}(F) > d+1$. We also show that in the case when $\dim_{{\mathcal H}}(E)+\frac{d-1}{d+1}\dim_{{\mathcal H}}(F)>d$, for $\mu_F$-a.e. $y\in F$, $$ \left\{t\in{\Bbb R} : \dim_{{\mathcal H}}(\{x\in E:|x-y|=t\}) \geq \dim_{{\mathcal H}}(E)+\frac{d+1}{d-1}\dim_{{\mathcal H}}(F)-d \right\} $$ has positive Lebesgue measure. This des

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  • One major obstacle in applications of Stein's method for compound Poisson approximation is the availability of so-called magic factors (bounds on the solution of the Stein equation) with favourable dependence on the parameters of the approximating compound Poisson random variable. In general, the best such bounds have an exponential dependence on these parameters, though in certain situations better bounds are available. In this paper, we extend the region for which well-behaved magic factors are available for compound Poisson approximation in the Kolmogorov metric, allowing useful compound Poisson approximation theorems to be established in some regimes where they were previously unavailable. To illustrate the advantages offered by these new bounds, we consider applications to runs, reliability systems, Poisson mixtures and sums of independent random variables.

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  • In this article we introduce the notion of a quasi-compatible system of Galois representations. The quasi-compatibility condition is a slight relaxation of the classical compatibility condition in the sense of Serre. The main theorem that we prove is the following: Let $M$ be an abelian motive, in the sense of Yves Andr\'e. Then the $\ell$-adic realisations of $M$ form a quasi-compatible system of Galois representations. (In fact, we actually prove something stronger. See theorem 5.1.) As an application, we deduce that the absolute rank of the $\ell$-adic monodromy groups of $M$ does not depend on $\ell$. In particular, the Mumford-Tate conjecture for $M$ does not depend on $\ell$.

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  • We study bipartite maps on the plane with one infinite face and one face of perimeter 2. At first we consider the problem of their enumeration an then study the connection between the combinatorial structure of a map and the degree of its definition field. The second problem is considered, when the number of edges is $p+1$, where $p$ is a prime.

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  • Model reduction methods for bilinear control systems are compared by means of practical examples of Liouville-von Neumann and Fokker--Planck type. Methods based on balancing generalized system Gramians and on minimizing an H2-type cost functional are considered. The focus is on the numerical implementation and a thorough comparison of the methods. Structure and stability preservation are investigated, and the competitiveness of the approaches is shown for practically relevant, large-scale examples.

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  • Modified human crania provide evidence for a new form of Neolithic skull cult

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  • In this paper, we study rational sections of the relative Picard scheme of a linear system on a smooth projective variety. We prove that if the linear system is basepoint-free and the locus of non-integral divisors has codimension at least two, then all rational sections of the relative Picard scheme come from restrictions of line bundles on the variety. As a consequence, we describe the group of sections of the Hitchin fibration for moduli spaces of Higgs bundles on curves.

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  • We identify phase noise as a bottleneck for the performance of digital self-interference cancellers that utilize a single auxiliary receiver---single-tap digital cancellers---and operate in multipath propagation environments. Our analysis demonstrates that the degradation due to phase noise is caused by a mismatch between the analog delay of the auxiliary receiver and the different delays of the multipath components of the self-interference signal. We propose a novel multi-tap digital self-interference canceller architecture that is based on multiple auxiliary receivers and a customized Normalized-Least-Mean-Squared (NLMS) filtering for self-interference regeneration. Our simulation results demonstrate that our proposed architecture is more robust to phase noise impairments and can in some cases achieve 10~dB larger self-interference cancellation than the single-tap architecture.

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  • A sharp upper bound for the maximum integer not belonging to an ideal of a numerical semigroup is given and the ideals attaining this bound are characterized. Then the result is used, through the so-called Feng-Rao numbers, to bound the generalized Hamming weights of algebraic-geometry codes. This is further developed for Hermitian codes and the codes on one of the Garcia-Stichtenoth towers, as well as for some more general families.

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  • In this contribution we consider the sequence $\{Q_{n}^{\lambda }\}_{n\geq 0} $ of monic polynomials orthogonal with respect to the following inner product involving differences \begin{equation*} \langle p,q\rangle _{\lambda }=\int_{0}^{\infty }p\left( x\right) q\left(x\right) d\psi ^{(a)}(x)+\lambda \,\Delta p(c)\Delta q(c), \end{equation*} where $\lambda \in \mathbb{R}_{+}$, $\Delta $ denotes the forward difference operator defined by $\Delta f\left( x\right) =f\left( x+1\right) -f\left(x\right) $, $\psi ^{(a)}$ with $a>0$ is the well known Poisson distribution of probability theory \begin{equation*} d\psi ^{(a)}(x)=\frac{e^{-a}a^{x}}{x!}\quad \text{at }x=0,1,2,\ldots , \end{equation*} and $c\in \mathbb{R}$ is such that the spectrum of $\psi ^{(a)}$ is contained in an interval $I$ and $I\cap (c,c+1)=\varnothing $. We derive its corresponding hypergeometric representation. The ladder operators associated with these polynomials are obtained, and the linear difference equation of sec

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  • Recently, new classes of positive and measurable functions, $\mathcal{M}(\rho)$ and $\mathcal{M}(\pm \infty)$, have been defined in terms of their asymptotic behaviour at infinity, when normalized by a logarithm (Cadena et al., 2015, 2016, 2017). Looking for other suitable normalizing functions than logarithm seems quite natural. It is what is developed in this paper, studying new classes of functions of the type $\displaystyle \lim_{x\rightarrow \infty}\log U(x)/H(x)=\rho <\infty$ for a large class of normalizing functions $H$. It provides subclasses of $\mathcal{M}(0)$ and $\mathcal{M}(\pm\infty)$.

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  • It has recently been established that, in a non-demolition measurement of an observable $\mathcal{N}$ with a finite point spectrum, the density matrix of the system approaches an eigenstate of $\mathcal{N}$, i.e., it "purifies" over the spectrum of $\mathcal{N}$. We extend this result to observables with general spectra. It is shown that the spectral density of the state of the system converges to a delta function exponentially fast, in an appropriate sense. Furthermore, for observables with absolutely continuous spectra, we show that the spectral density approaches a Gaussian distribution over the spectrum of $\mathcal{N}$. Our methods highlight the connection between the theory of non-demolition measurements and classical estimation theory.

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  • This paper develops upper and lower bounds on the influence measure in a network, more precisely, the expected number of nodes that a seed set can influence in the independent cascade model. In particular, our bounds exploit nonbacktracking walks, Fortuin-Kasteleyn-Ginibre (FKG) type inequalities, and are computed by message passing implementation. Nonbacktracking walks have recently allowed for headways in community detection, and this paper shows that their use can also impact the influence computation. Further, we provide a knob to control the trade-off between the efficiency and the accuracy of the bounds. Finally, the tightness of the bounds is illustrated with simulations on various network models.

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  • We present a motivating example for matrix multiplication based on factoring a data matrix. Traditionally, matrix multiplication is motivated by applications in physics: composing rigid transformations, scaling, sheering, etc. We present an engaging modern example which naturally motivates a variety of matrix manipulations, and a variety of different ways of viewing matrix multiplication. We exhibit a low-rank non-negative decomposition (NMF) of a "data matrix" whose entries are word frequencies across a corpus of documents. We then explore the meaning of the entries in the decomposition, find natural interpretations of intermediate quantities that arise in several different ways of writing the matrix product, and show the utility of various matrix operations. This example gives the students a glimpse of the power of an advanced linear algebraic technique used in modern data science.

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  • Let $\varphi$ be a hyperbolic outer automorphism of a non-abelian free group $F_N$ such that $\varphi$ and $\varphi^{-1}$ admit absolute train track representatives. We prove that $\varphi$ acts on the space of projectivized geodesic currents on $F_N$ with generalized uniform North-South dynamics.

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  • A numerical semigroup is a subset of N containing 0, closed under addition and with finite complement in N. An important example of numerical semigroup is given by the Weierstrass semigroup at one point of a curve. In the theory of algebraic geometry codes, Weierstrass semigroups are crucial for defining bounds on the minimum distance as well as for defining improvements on the dimension of codes. We present these applications and some theoretical problems related to classification, characterization and counting of numerical semigroups.

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  • Solving the linear elasticity and Stokes equations by an optimal domain decomposition method derived algebraically involves the use of non standard interface conditions. The one-level domain decomposition preconditioners are based on the solution of local problems. This has the undesired consequence that the results are not scalable, it means that the number of iterations needed to reach convergence increases with the number of subdomains. This is the reason why in this work we introduce, and test numerically, two-level preconditioners. Such preconditioners use a coarse space in their construction. We consider the nearly incompressible elasticity problems and Stokes equations, and discretise them by using two finite element methods, namely, the hybrid discontinuous Galerkin and Taylor-Hood discretisations.

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  • We review the notion of Gieseker stability for torsion-free Higgs sheaves. This notion is a natural generalization of the classical notion of Gieseker stability for torsion-free coherent sheaves. We prove some basic properties that are similar to the classical ones for torsion-free coherent sheaves over projective algebraic manifolds. In particular, we show that Gieseker stability for torsion-free Higgs sheaves can be defined using only Higgs subsheaves with torsion-free quotients; and we show that a classical relation between Gieseker stability and Mumford-Takemoto stability extends naturally to Higgs sheaves. We also prove that a direct sum of two Higgs sheaves is Gieseker semistable if and only if the Higgs sheaves are both Gieseker semistable with equal normalized Hilbert polynomial and we prove that a classical property of morphisms between Gieseker semistable sheaves also holds in the Higgs case; as a consequence of this and the existing relation between Mumford-Takemoto stabilit

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  • We look at the elliptic curve E(q), where q is a fixed rational number. A point (p,r) on E(q) is called a rational point if both p and r are rational numbers. We introduce the concept of conjugate points and show that not both can be rational points.

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  • We consider the problem of sampling an edge almost uniformly from an unknown graph, $G = (V, E)$. Access to the graph is provided via queries of the following types: (1) uniform vertex queries, (2) degree queries, and (3) neighbor queries. We describe an algorithm that returns a random edge $e \in E$ using $\tilde{O}(n / \sqrt{\varepsilon m})$ queries in expectation, where $n = |V|$ is the number of vertices, and $m = |E|$ is the number of edges, such that each edge $e$ is sampled with probability $(1 \pm \varepsilon)/m$. We prove that our algorithm is optimal in the sense that any algorithm that samples an edge from an almost-uniform distribution must perform $\Omega(n / \sqrt{m})$ queries.

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  • We calculate explicitly an adelic quotient group for an excellent Noetherian normal integral two-dimensional separated scheme. An application to an irreducible normal projective algebraic surface over a field is given.

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  • A sequence $\left(x_1,x_2,\ldots,x_{2n}\right)$ of even length is a repetition if $\left(x_1,\ldots,x_n\right) = \left(x_{n+1},\ldots,x_{2n}\right)$. We prove existence of a constant $C < 10^{4 \cdot 10^7}$ such that given any planar drawing of a graph $G$, and a list $L(v)$ of $C$ permissible colors for each vertex $v$ in $G$, there is a choice of a permissible color for each vertex such that the sequence of colors of the vertices on any facial simple path in $G$ is not a repetition.

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  • Given a rigid C*-tensor category C with simple unit and a probability measure $\mu$ on the set of isomorphism classes of its simple objects, we define the Poisson boundary of $(C,\mu)$. This is a new C*-tensor category P, generally with nonsimple unit, together with a unitary tensor functor $\Pi: C \to P$. Our main result is that if P has simple unit (which is a condition on some classical random walk), then $\Pi$ is a universal unitary tensor functor defining the amenable dimension function on C. Corollaries of this theorem unify various results in the literature on amenability of C*-tensor categories, quantum groups, and subfactors.

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  • Phased antenna arrays are widely used for direction-of-arrival (DoA) estimation. For low-cost applications, signal power or received signal strength indicator (RSSI) based approaches can be an alternative. However, they usually require multiple antennas, a single antenna that can be rotated, or switchable antenna beams. In this paper we show how a multi-mode antenna (MMA) can be used for power-based DoA estimation. Only a single MMA is needed and neither rotation nor switching of antenna beams is required. We derive an estimation scheme as well as theoretical bounds and validate them through simulations. It is found that power-based DoA estimation with an MMA is feasible and accurate.

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  • In this paper we prove the existence of an exponentially localized stationary solution for a two-dimensional cubic Dirac equation. It appears as an effective equation in the description of nonlinear waves for some Condensed Matter (Bose-Einstein condensates) and Nonlinear Optics (optical fibers) systems. The nonlinearity is of Kerr-type, that is of the form |$\psi$| 2 $\psi$ and thus not Lorenz-invariant. We solve compactness issues related to the critical Sobolev embedding H 1 2 (R 2 , C 2) $\rightarrow$ L 4 (R 2 , C 4) thanks to a particular radial ansatz. Our proof is then based on elementary dynamical systems arguments. Contents

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  • We derive Stein approximation bounds for functionals of uniform random variables, using chaos expansions and the Clark-Ocone representation formula combined with derivation and finite difference operators. This approach covers sums and functionals of both continuous and discrete independent random variables. For random variables admitting a continuous density, it recovers classical distance bounds based on absolute third moments, with better and explicit constants. We also apply this method to multiple stochastic integrals that can be used to represent U-statistics, and include linear and quadratic functionals as particular cases.

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  • In this paper, we investigate the performance analysis and synthesis of distributed system throttlers (DST). A throttler is a mechanism that limits the flow rate of incoming metrics, e.g., byte per second, network bandwidth usage, capacity, traffic, etc. This can be used to protect a service's backend/clients from getting overloaded, or to reduce the effects of uncertainties in demand for shared services. We study performance deterioration of DSTs subject to demand uncertainty. We then consider network synthesis problems that aim to improve the performance of noisy DSTs via communication link modifications as well as server update cycle modifications.

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  • Superdiffusions corresponding to differential operators of the form $\LL u+\beta u-\alpha u^{2}$ with large mass creation term $\beta$ are studied. Our construction for superdiffusions with large mass creations works for the branching mechanism $\beta u-\alpha u^{1+\gamma},\ 0<\gamma<1,$ as well. Let $D\subseteq\mathbb{R}^{d}$ be a domain in $\R^d$. When $\beta$ is large, the generalized principal eigenvalue $\lambda_c$ of $L+\beta$ in $D$ is typically infinite. Let $\{T_{t},t\ge0\}$ denote the Schr\"odinger semigroup of $L+\beta$ in $D$ with zero Dirichlet boundary condition. Under the mild assumption that there exists an $0<h\in C^{2}(D)$ so that $T_{t}h$ is finite-valued for all $t\ge 0$, we show that there is a unique $\mathcal{M}_{loc}(D)$-valued Markov process that satisfies a log-Laplace equation in terms of the minimal nonnegative solution to a semilinear initial value problem. Although for super-Brownian motion (SBM) this assumption requires $\beta$ be less than quadr

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  • We prove that the three-dimensional Iwasawa manifold $X$, viewed as a locally holomorphically trivial fibration by elliptic curves over its two-dimensional Albanese torus, is self-dual in the sense that the base torus identifies canonically with its dual torus under a sesquilinear duality, the Jacobian torus of $X$, while the fibre identifies with itself. To this end, we derive elements of Hodge theory for arbitrary sGG manifolds, introduced in earlier joint work of the author with L. Ugarte, to construct in an explicit way the Albanese torus and map of any sGG manifold. These definitions coincide with the classical ones in the special K\"ahler and $\partial\bar\partial$ cases. The generalisation to the larger sGG class is made necessary by the Iwasawa manifold being an sGG, non-$\partial\bar\partial$, manifold. The main result of this paper can be seen as a complement from a different perspective to the author's very recent work where a non-K\"ahler mirror symmetry of the Iwasawa mani

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  • Compactness is one of the most versatile tools in the analysis of nonlinear PDEs and systems. Usually, compactness is established by means of some embedding theorem between functional spaces. Such theorems, in turn, rely on appropriate estimates for a function and its derivatives. While a similar result based on simultaneous estimates for the Malliavin and weak Sobolev derivatives is available for the Wiener-Sobolev spaces, it seems that it has not yet been widely used in the analysis of highly nonlinear parabolic problems with stochasticity. In the present work we apply this result in order to study compactness, existence of global solutions, and, as a by-product, the convergence of a semi-discretisation scheme for a prototypical degenerate PDE-SDE coupling.

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  •  

    The Rise of the Thought Leader

    06-29 Hacker News 22

    The Rise of the Thought Leader

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  • We present the Round Handle Problem, proposed by Freedman and Krushkal. It asks whether a collection of links, which contains the Generalised Borromean Rings, are slice in a 4-manifold R constructed from adding round handles to the four ball. A negative answer would contradict the union of the surgery conjecture and the s-cobordism conjecture for 4-manifolds with free fundamental group.

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  • We introduce a system of harmonic oscillators in a magnetic field perturbed by a stochastic dynamics conserving energy but not canonical momentum. We show that its thermal conductivity diverges in dimension 1 and 2, while it remains finite in dimension 3. We compute the current-current time correlation function, that decays like $t^{-\frac{1}{2}-\frac{d}{4}}$. This implies a finite conductivity in $d \ge 3$. For $d=1$, this order of the decay is different from the one without the magnetic field. This is the first rigorous result showing the macroscopic super-diffusive behavior of energy for a microscopic model without conservation of canonical momentum.

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  • In 1962 E. H. Rauch established the existence of points in the moduli space of Riemann surfaces not having a neighbourhood homeomorphic to a ball. These points are called here topologically singular. We give a different proof of the results of Rauch and also determine the topologically singular and non-singular points in the branch locus of some equisymmetric families of Riemann surfaces.

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  • The network structure (or topology) of a dynamical network is often unavailable or uncertain. Hence, in this paper we consider the problem of network reconstruction. Network reconstruction aims at inferring the topology of a dynamical network using measurements obtained from the network. This paper rigorously defines what is meant by solvability of the network reconstruction problem. Subsequently, we provide necessary and sufficient conditions under which the network reconstruction problem is solvable. Finally, using constrained Lyapunov equations, we establish novel network reconstruction algorithms, applicable to general dynamical networks. We also provide specialized algorithms for specific network dynamics, such as the well-known consensus and adjacency dynamics.

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  • We study shortest paths and their distances on a subset of a Euclidean space, and their approximation by their equivalents in a neighborhood graph defined on a sample from that subset. In particular, we recover and extend the results that Bernstein et al. (2000), developed in the context of manifold learning, and those of Karaman and Frazzoli (2011), developed in the context of robotics. We do the same with curvature-constrained shortest paths and their distances, establishing what we believe are the first approximation bounds for them.

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  • It is proved that for any Dunford-Schwartz operator $T$ acting in the space $l_\infty$ and for each $x\in c_0 $ there exists an element $\widehat x \in c_0 $ such that $\| \frac 1n \sum_{k=0}^{n-1}T^k(x) - \widehat x \|_\infty \to 0$.

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  • A notion of up and down Grover walks on simplicial complexes are proposed and their properties are investigated. These are abstract Szegedy walks, which is a special kind of unitary operators on a Hilbert space. The operators introduced in the present paper are usual Grover walks on graphs defined by using combinatorial structures of simplicial complexes. But the shift operators are modified so that it can contain information of orientations of each simplex in the simplicial complex. It is well-known that the spectral structures of this kind of unitary operators are completely determined by its discriminant operators. It has strong relationship with combinatorial Laplacian on simplicial complexes and geometry, even topology, of simplicial complexes. In particular, theorems on a relation between spectrum of up and down discriminants and orientability, on a relation between symmetry of spectrum of discriminants and combinatorial structure of simplicial complex are given. Some examples, b

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  • Current State-of-the-Art High Throughput Satellite systems provide wide-area connectivity through multi-beam architectures. However, due to the tremendous system throughput requirements that next generation Satellite Communications expect to achieve, traditional 4-colour frequency reuse schemes, i.e., two frequency bands with two orthogonal polarisations, are not sufficient anymore and more aggressive solutions as full frequency reuse are gaining momentum. These approaches require advanced interference management techniques to cope with the significantly increased inter-beam interference, like multicast precoding and Multi User Detection. With respect to the former, several peculiar challenges arise when designed for SatCom systems. In particular, to maximise resource usage while minimising delay and latency, multiple users are multiplexed in the same frame, thus imposing to consider multiple channel matrices when computing the precoding weights. In this paper, we focus on this aspect

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  • We show that for any claw-free graph $G$ and any graph $H$, $\gamma(G\square H)\geq \frac{2}{3}\gamma(G)\gamma(H)$, where $\gamma(G)$ is the domination number of $G$.

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  • The Supreme Court of Canada ruled against Google on Wednesday in a closely-watched intellectual property case over whether judges can apply their own country's laws to all of the internet. From a report: In a 7-2 decision, the court agreed a British Columbia judge had the power to issue an injunction forcing Google to scrub search results about pirated products not just in Canada, but everywhere else in the world too. Those siding with Google, including civil liberties groups, had warned that allowing the injunction would harm free speech, setting a precedent to let any judge anywhere order a global ban on what appears on search engines. The Canadian Supreme Court, however, downplayed this objection and called Google's fears "theoretical." "This is not an order to remove speech that, on its face, engages freedom of expression values, it is an order to de-index websites that are in violation of several court orders. We have not, to date, accepted that freedom of expression requires the

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  • We study a boundary value problem related to the search of standing waves for the nonlinear Schr\"odinger equation (NLS) on graphs. Precisely we are interested in characterizing the standing waves of NLS posed on the {\it double-bridge graph}, in which two semi-infinite half-lines are attached at a circle at different vertices. At the two vertices the so-called Kirchhoff boundary conditions are imposed. The configuration of the graph is characterized by two lengths, $L_1$ and $L_2$, and we are interested in the existence and properties of standing waves of given frequency $\omega$. For every $\omega>0$ only solutions supported on the circle exist (cnoidal solutions), and only for a rational value of $L_1/L_2$; they can be extended to every $\omega\in \mathbb{R}$. We study, for $\omega<0$, the solutions periodic on the circle but with nontrivial components on the half-lines. The problem turns out to be equivalent to a nonlinear boundary value problem in which the boundary conditio

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  • In this paper we show, using Deligne-Lusztig theory and Kawanaka's theory of generalised Gelfand-Graev representations, that the decomposition matrix of the special linear and unitary group in non defining characteristic can be made unitriangular with respect to a basic set that is stable under the action of automorphisms.

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  • The increasing penetration of inverter based renewable generation (RG) in the form of solar photo-voltaic (PV) or wind has introduced numerous operational challenges and uncertainties. According to the standards, these generators are made to trip offline if their operating requirements are not met. In an RG-rich system, this might alter the system dynamics and/or cause shifting of the equilibrium points to the extent that a cascaded tripping scenario is manifested. The present work attempts at avoiding such scenarios by estimating the constrained stability region (CSR) inside which the system must operate using maximal level set of a Lyapunov function estimated through sum of squares (SOS) technique. A time-independent conservative approximation of the LVRT constraint is initially derived for a classical model of the power system. The proposed approach is eventually validated by evaluating the stability of a 3 machine test system with trip-able RG.

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  • We derive quantitative estimates proving the propagation of chaos for large stochastic systems of interacting particles. We obtain explicit bounds on the relative entropy between the joint law of the particles and the tensorized law at the limit. We have to develop for this new laws of large numbers at the exponential scale. But our result only requires very weak regularity on the interaction kernel in the negative Sobolev space $\dot W^{-1,\infty}$, thus including the Biot-Savart law and the point vortices dynamics for the 2d incompressible Navier-Stokes.

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  • We study an extension of Bernstein's theorem to the setting of quantum groups. For a d-tuple of free, identically distributed random variables we consider a problem of preservation of freeness under the action of a quantum subset of the free orthogonal quantum group. For a subset not contained in the hyperoctahedral quantum group we prove that preservation of freeness characterizes Wigner's semicircle law. We show that freeness is always preserved if the quantum subset is contained in the hyperoctahedral quantum group. We provide examples of quantum subsets which show that our result is an extension of results known in the literature.

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  • The "noncommutative graphs" which arise in quantum error correction are a special case of the quantum relations introduced in [N. Weaver, Quantum relations, Mem. Amer. Math. Soc. 215 (2012), v-vi, 81-140]. We use this perspective to interpret the Knill-Laflamme error-correction conditions [E. Knill and R. Laflamme, Theory of quantum error-correcting codes, Phys. Rev. A 55 (1997), 900-911] in terms of graph-theoretic independence, to give intrinsic characterizations of Stahlke's noncommutative graph homomorphisms [D. Stahlke, Quantum source-channel coding and non-commutative graph theory, arXiv:1405.5254] and Duan, Severini, and Winter's noncommutative bipartite graphs [R. Duan, S. Severini, and A. Winter, Zero-error communication via quantum channels, noncommutative graphs, and a quantum Lovasz number, IEEE Trans. Inform. Theory 59 (2013), 1164-1174], and to realize the noncommutative confusability graph associated to a quantum channel as the pullback of a diagonal relation. Our framew

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  • The Verma modules over the quantum groups $\mathrm U_q(\mathfrak{gl}_{l + 1})$ for arbitrary values of $l$ are analysed. The explicit expressions for the action of the generators on the elements of the natural basis are obtained. The corresponding representations of the quantum loop algebras $\mathrm U_q(\mathcal L(\mathfrak{sl}_{l + 1}))$ are constructed via Jimbo's homomorphism. This allows us to find certain representations of the positive Borel subalgebras of $\mathrm U_q(\mathcal L(\mathfrak{sl}_{l + 1}))$ as degenerations of the shifted representations. The latter are the representations used in the construction of the so-called $Q$-operators in the theory of quantum integrable systems. The interpretation of the corresponding simple quotient modules in terms of representations of the $q$-deformed oscillator algebra is given.

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  • It is well known that the real spectrum of any commutative unital ring, and the {\ell}-spectrum of any Abelian lattice-ordered group with order-unit, are all completely normal spectral spaces. We prove the following results: (1) Every real spectrum can be embedded, as a spectral subspace, into some {\ell}-spectrum. (2) Not every real spectrum is an {\ell}-spectrum. (3) A spectral subspace of a real spectrum may not be a real spectrum. (4) Not every {\ell}-spectrum can be embedded, as a spectral subspace, into a real spectrum. (5) There exists a completely normal spectral space which cannot be embedded , as a spectral subspace, into any {\ell}-spectrum. The commutative unital rings and Abelian lattice-ordered groups in (2), (3), (4) all have cardinality $\aleph 1 , while the spectral space of (4) has a basis of car-dinality $\aleph 2. Moreover, (3) solves a problem by Mellor and Tressl.

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