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Here's a 34c3 conference report in CSO suggesting that the BSDs are losing developers. "von Sprundel says he easily found around 115 kernel bugs across the three BSDs, including 30 for FreeBSD, 25 for OpenBSD, and 60 for NetBSD. Many of these bugs he called 'lowhanging fruit.' He promptly reported all the bugs, but six months later, at the time of his talk, many remained unpatched. 'By and large, most security flaws in the Linux kernel don't have a long lifetime. They get found pretty fast,' von Sprundel says. 'On the BSD side, that isn't always true. I found a bunch of bugs that have been around a very long time.' Many of them have been present in code for a decade or more."
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We derive in this paper a family of conserved energies for the one dimensional GrossPitaevskii equation in the small energy case, which describe all the $H^s$, $s>\frac 12$ regularities of the solutions. We endow the energy space with a metric to make it a complete metric space and study its topological property.
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This paper is concerned with the highfrequency homogenization of bubbly phononic crystals. It is a followup of the works [H. Ammari et al., Subwavelength phononic bandgap opening in bubbly media, J. Diff. Eq., 263 (2017), 56105629] which shows the existence of a subwavelength band gap. This phenomena can be explained by the periodic inference of cell resonance which is due to the high contrast in both the density and bulk modulus between the bubbles and the surrounding medium. In this paper, we prove that the first Bloch eigenvalue achieves its maximum at the corner of the Brillouin zone. Moreover, by computing the asymptotic of the Bloch eigenfunctions in the periodic structure near that critical frequency, we demonstrate that these eigenfunctions can be decomposed into two parts: one part is slowly varying and satisfies a homogenized equation, while the other is periodic across each elementary crystal cell and is varying. They rigorously justify, in the nondilute case, the obse
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Richard Fontana explores the intersection of containers and copyleft licensing on opensource.com. "One imperfect way of framing the question is whether GPLlicensed code, when combined in some sense with proprietary code, forms a single modified work such that the proprietary code could be interpreted as being subject to the terms of the GPL. While we haven’t yet seen much of that concern directed to Linux containers, we expect more questions to be raised as adoption of containers continues to grow. But it’s fairly straightforward to show that containers do not raise new or concerning GPL scope issues."
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We study convex integration solutions in the context of the modelling of shapememory alloys. The purpose of the article is twofold, treating both rigidity and flexibility properties: Firstly, we relate the maximal regularity of convex integration solutions to the presence of lower bounds in variational models with surface energy. Hence, variational models with surface energy could be viewed as a selection mechanism allowing for or excluding convex integration solutions. Secondly, we present the first numerical implementations of convex integration schemes for the model problem of the geometrically linearised twodimensional hexagonaltorhombic phase transformation. We discuss and compare the two algorithms from [RZZ16] and [RZZ17].
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We define strict and weak duality involutions on 2categories, and prove a coherence theorem that every bicategory with a weak duality involution is biequivalent to a 2category with a strict duality involution. For this purpose we introduce "2categories with contravariance", a sort of enhanced 2category with a basic notion of "contravariant morphism", which can be regarded either as generalized multicategories or as enriched categories. This enables a universal characterization of duality involutions using absolute weighted colimits, leading to a conceptual proof of the coherence theorem.
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The YangLee edge singularity is investigated by the determinant method of the conformal field theory. The critical dimension Dc, for which the scale dimension of scalar Delta_phi is vanishing, is discussed by this determinant method. The result is incorporated in the Pade analysis of epsilon expansion, which leads to an estimation of the value Delta_phi between three and six dimensions. The structure of the minors is viewed from the fixed points.
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Recently \cite{Ramos2017a} presented a subspace system identification algorithm for 2D purely stochastic state space models in the general Roesser form. However, since the exact problem requires an oblique projection of $Y_f^h$ projected onto $W_p^h$ along $\widehat{X}_f^{vh}$, where $W_p^h= \begin{bmatrix}\widehat{X}_p^{vh} \\ Y_p^h \end{bmatrix}$, this presents a problem since $\{\widehat{X}_p^{vh},\widehat{X}_f^{vh}\}$ are unknown. In the above mentioned paper, the authors found that by doing an orthogonal projection $Y_f^h/Y_p^h$, one can identify the future horizontal state matrix $\widehat{X}_f^{h}$ with a small bias due to the initial conditions that depend on $\{\widehat{X}_p^{vh},\widehat{X}_f^{vh}\}$. Nevertheless, the results on modeling 2D images were very good despite lack of knowledge of $\{\widehat{X}_p^{vh},\widehat{X}_f^{vh}\}$. In this note we delve into the bias term and prove that it is insignificant, provided $i$ is chosen large enough and the vertical and horizo
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By an influential theorem of Boman, a function $f$ on an open set $U$ in $\mathbb R^d$ is smooth ($\mathcal C^\infty$) if and only if it is \emph{arcsmooth}, i.e., $f\circ c$ is smooth for every smooth curve $c : \mathbb R \to U$. In this paper we investigate the validity of this result on closed sets. Our main focus is on sets which are the closure of their interior, socalled \emph{fat} sets. We obtain an analogue of Boman's theorem on fat closed sets with H\"older boundary and on fat closed subanalytic sets with the property that every boundary point has a basis of neighborhoods each of which intersects the interior in a connected set. If $X \subseteq \mathbb R^d$ is any such set and $f : X \to \mathbb R$ is arcsmooth, then $f$ extends to a smooth function defined in $\mathbb R^d$. As a consequence we also get a version of the BochnakSiciak theorem on all such sets: if $f : X \to \mathbb R$ is arcsmooth and real analytic along all real analytic curves in $X$, then $f$ extends to
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The Coulomb branch indices of ArgyresDouglas theories on $L(k,1)\times S^{1}$ are recently identified with matrix elements of modular transforms of certain $2d$ vertex operator algebras in a particular limit. A one parameter generalization of the modular transformation matrices of $(2N+3,2)$ minimal models are proposed to compute the full Coulomb branch index of $(A_{1},A_{2N})$ ArgyresDouglas theories on the same space. Morever, Mtheory construction of these theories suggests direct connection to the refined ChernSimons theory. The connection is made precise by showing how the modular transformation matrices of refined ChernSimons theory are related to the proposed generalized ones for minimal models and the identification of Coulomb branch indices with the partition function of the refined ChernSimons theory.
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In this paper, we establish Bocher theorems for fractional superharmonic functions, and present a unified proof for both superharmonic and fractional superharmonic functions. Based on these Bocher type theorems, we develop some maximum principles for both superharmonic and fractional superharmonic functions on punctured balls.
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In this paper, we study a certain ArtinSchreier family of elliptic curves over the function field $\mathbb{F}_q(t)$. We prove an asymptotic estimate on the size of the special value of their $L$function in terms of the degree of their conductor; loosely speaking, we show that the special values are "asymptotically as large as possible". We also provide an explicit expression for the $L$function of the elliptic curves in the family. The proof of the main result uses this expression and a detailed study of the distribution of some character sums related to Kloosterman sums. Via the BSD conjecture, the main result translates into an analogue of the BrauerSiegel theorem for these elliptic curves.
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We prove that the $\ell$adic Chern classes of canonical extensions of automorphic vector bundles, over toroidal compactifications of Shimura varieties of Hodge type over $\bar{ \mathbb{Q}}_p$, descend to classes in the $\ell$adic cohomology of the minimal compactifications. These are invariant under the Galois group of the $p$adic field above which the variety and the bundle are defined.
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This classification is found by analyzing the action of a normal subgroup of $B_3$ as hyperbolic isometries. This paper gives an example of an unfaithful specialization of the Burau representation on $B_4$ that is faithful when restricted to $B_3$, as well as examples of unfaithful specializations of $B_3$.
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It is well known that for gradient systems in Euclidean space or on a Riemannian manifold, the energy decreases monotonically along solutions. In this letter we derive and analyse functionally fitted energydiminishing methods to preserve this key property of gradient systems. It is proved that the novel methods are unconditionally energydiminishing and can achieve damping for very stiff gradient systems. We also show that the methods can be of arbitrarily high order and discuss their implementations. A numerical test is reported to illustrate the efficiency of the new methods in comparison with three existing numerical methods in the literature.
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In this paper we are interested to prove the existence and concentration of ground state solution for the following class of problems $$ \Delta u+V(x)u=A(\epsilon x)f(u), \quad x \in \R^{N}, \eqno{(P)_{\epsilon}} $$ where $N \geq 2$, $\epsilon>0$, $A:\R^{N}\rightarrow\R$ is a continuous function that satisfies $$ 0<\inf_{x\in\R^{N}}A(x)\leq\lim_{x\rightarrow+\infty}A(x)<\sup_{x\in\R^{N}}A(x)=A(0),\eqno{(A)} $$ $f:\R\rightarrow\R$ is a continuous function having critical growth, $V:\R^{N}\rightarrow\R$ is a continuous and $\Z^{N}$periodic function with $0\notin\sigma(\Delta+V)$. By using variational methods, we prove the existence of solution for $\epsilon$ small enough. After that, we show that the maximum points of the solutions concentrate around of a maximum point of $A$.
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Every study we could find on what automation will do to jobs, in one chart
0125 MIT Technology 2090 
The aim of this article is to enlarge the list of examples of nonautonomous basins of attraction from our previous paper and at the same time explore some other properties that they satisfy. For instance, we show the existence of countably many disjoint Short $\mathbb{C}^k$'s in $\mathbb{C}^k.$ We also construct a Short $\mathbb{C}^k$ which is not Runge and exhibit yet another example whose boundary has Hausdorff dimension $2k.$
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We propose a efficient method to calculate "the minimal annihilating polynomials" for all the unit vectors, of square matrix over the integers or the rational numbers. The minimal annihilating polynomials are useful for improvement of efficiency in wide variety of algorithms in exact linear algebra. We propose an efficient algorithm for calculating the minimal annihilating polynomials for all the unit vectors via pseudo annihilating polynomials with the key idea of binary splitting technique. Efficiency of the proposed algorithm is shown by arithmetic time complexity analysis.
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Consider a totally irregular measure $\mu$ in $\mathbb{R}^{n+1}$, that is, the upper density $\limsup_{r\to0}\frac{\mu(B(x,r))}{(2r)^n}$ is positive $\mu$a.e.\ in $\mathbb{R}^{n+1}$, and the lower density $\liminf_{r\to0}\frac{\mu(B(x,r))}{(2r)^n}$ vanishes $\mu$a.e. in $\mathbb{R}^{n+1}$. We show that if $T_\mu f(x)=\int K(x,y)\,d\mu(y)$ is an operator whose kernel $K(\cdot,\cdot)$ is the gradient of the fundamental solution for a uniformly elliptic operator in divergence form associated with a matrix with H\"older continuous coefficients, then $T_\mu$ is not bounded in $L^2(\mu)$. This extends a celebrated result proved previously by Eiderman, Nazarov and Volberg for the $n$dimensional Riesz transform.
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In this article we show that the threedimensional sphere admits {transitive} expansive flows in the sense of Komuro with hyperbolic equilibrium points. The result is based on a construction that allows us to see the geodesic flow of a hyperbolic threepunctured twodimensional sphere as the flow of a smooth vector field on the threedimensional sphere.
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We propose hybrid methods for localization in wireless sensor networks fusing noisy range measurements with angular information (extracted from video). Compared with conventional methods that rely on a single sensed variable, this may pave the way for improved localization accuracy and robustness. We address both the singlesource and network (i.e., cooperative multiplesource) localization paradigms, solving them via optimization of a convex surrogate. The formulations for hybrid localization are unified in the sense that we propose a single nonlinear leastsquares cost function, fusing both angular and range measurements. We then relax the problem to obtain an estimate of the optimal positions. This contrasts with other hybrid approaches that alternate the execution of localization algorithms for each type of measurement separately, to progressively refine the position estimates. Singlesource localization uses a semidefinite relaxation to obtain a oneshot matrix solution from which
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Let $\Lambda\left(n\right)$ be the Von Mangoldt function, let \[ r_{G}\left(n\right)=\underset{{\scriptstyle m_{1}+m_{2}=n}}{\sum_{m_{1},m_{2}\leq n}}\Lambda\left(m_{1}\right)\Lambda\left(m_{2}\right), \] \[ r_{PT}\left(N,h\right)=\sum_{n=0}^{N}\Lambda\left(n\right)\Lambda\left(n+h\right),\,h\in\mathbb{N} \] be the counting function of the Goldbach numbers and the counting function of the prime tuples, respectively. Let $N>2$ be an integer. We will find the explicit formulae for the averages of $r_{G}\left(n\right)$ and $r_{PT}\left(N,h\right)$ in terms of elementary functions, the incomplete Beta function $B_{z}\left(a,b\right)$, series over $\rho$ that, with or without subscript, runs over the nontrivial zeros of the Riemann Zeta function and the Dilogarithm function. We will also prove the explicit formulae in an asymptotic form and a truncated formula for the average of $r_{G}\left(n\right)$. Some observation about these formulae and the average with Ces\`aro weight \[ \frac{1}
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We study the ergodic control problem for a class of jump diffusions in $\mathbb{R}^d$, which are controlled through the drift with bounded controls. The Levy measure is finite, but has no particular structure; it can be anisotropic and singular. Moreover, there is no blanket ergodicity assumption for the controlled process. Unstable behavior is `discouraged' by the running cost which satisfies a mild coercive hypothesis (i.e., is nearmonotone). We first study the problem in its weak formulation as an optimization problem on the space of infinitesimal ergodic occupation measures, and derive the HamiltonJacobiBellman equation under minimal assumptions on the parameters, including verification of optimality results, using only analytical arguments. We also examine the regularity of invariant measures. Then, we address the jump diffusion model, and obtain a complete characterization of optimality.
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We use the Whittaker vectors and the Drinfeld Casimir element to show that eigenfunctions of the difference Toda Hamiltonian can be expressed via fermionic formulas. Motivated by the combinatorics of the fermionic formulas we use the representation theory of the quantum groups to prove a number of identities for the coefficients of the eigenfunctions.
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With the rapid growth of quantum technologies, knowing the fundamental characteristics of quantum systems and protocols is essential for their effective implementation. A particular communication setting that has received increased focus is related to quantum key distribution and distributed quantum computation. In this setting, a quantum channel connects a sender to a receiver, and their goal is to distill either a secret key or entanglement, along with the help of arbitrary local operations and classical communication (LOCC). In this work, we establish a general theory of energyconstrained, LOCCassisted private and quantum capacities of quantum channels, which are the maximum rates at which an LOCCassisted quantum channel can reliably establish secret key or entanglement, respectively, subject to an energy constraint on the channel input states. We prove that the energyconstrained squashed entanglement of a channel is an upper bound on these capacities. We also explicitly prove t
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Let $G$ be a group. A subset $D$ of $G$ is a determining set of $G$, if every automorphism of $G$ is uniquely determined by its action on $D$. The determining number of $G$, denoted by $\alpha(G)$, is the cardinality of a smallest determining set. A generating set of $G$ is a subset such that every element of $G$ can be expressed as the combination, under the group operation, of finitely many elements of the subset and their inverses. The cardinality of a smallest generating set of $G$, denoted by $\gamma(G)$, is called the generating number of $G$. A group $G$ is called a DEGgroup if $\alpha(G)=\gamma(G)$. The main results of this article are as follows. Finite groups with determining number $0$ or $1$ are classified; Finite simple groups and finite nilpotent groups are proved to be DEGgroups; A finite group is a normal subgroup of a DEGgroup and there is an injective mapping from the set all finite groups to the set of finite DEGgroups; Nilpotent groups of order $n$ which have th
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We propose a natural discretisation scheme for classical projective minimal surfaces. We follow the classical geometric characterisation and classification of projective minimal surfaces and introduce at each step canonical discrete models of the associated geometric notions and objects. Thus, we introduce discrete analogues of classical Lie quadrics and their envelopes and classify discrete projective minimal surfaces according to the cardinality of the class of envelopes. This leads to discrete versions of GodeauxRozet, Demoulin and Tzitzeica surfaces. The latter class of surfaces requires the introduction of certain discrete line congruences which may also be employed in the classification of discrete projective minimal surfaces. The classification scheme is based on the notion of discrete surfaces which are in asymptotic correspondence. In this context, we set down a discrete analogue of a classical theorem which states that an envelope (of the Lie quadrics) of a surface is in asy
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In this paper, we consider the soliton cellular automaton introduced in [Takahashi 1990] with a random initial configuration. We give multiple constructions of a Young diagram describing various statistics of the system in terms of familiar objects like birthanddeath chains and GaltonWatson forests. Using these ideas, we establish limit theorems showing that if the first $n$ boxes are occupied independently with probability $p\in(0,1)$, then the number of solitons is of order $n$ for all $p$, and the length of the longest soliton is of order $\log n$ for $p<1/2$, order $\sqrt{n}$ for $p=1/2$, and order $n$ for $p>1/2$. Additionally, we uncover a condensation phenomenon in the supercritical regime: For each fixed $j\geq 1$, the top $j$ soliton lengths have the same order as the longest for $p\leq 1/2$, whereas all but the longest have order at most $\log n$ for $p>1/2$. As an application, we obtain scaling limits for the lengths of the $k^{\text{th}}$ longest increasing and
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In this paper we develop an adaptive dual free Stochastic Dual Coordinate Ascent (adfSDCA) algorithm for regularized empirical risk minimization problems. This is motivated by the recent work on dual free SDCA of ShalevShwartz (2016). The novelty of our approach is that the coordinates to update at each iteration are selected nonuniformly from an adaptive probability distribution, and this extends the previously mentioned work which only allowed for a uniform selection of "dual" coordinates from a fixed probability distribution. We describe an efficient iterative procedure for generating the nonuniform samples, where the scheme selects the coordinate with the greatest potential to decrease the suboptimality of the current iterate. We also propose a heuristic variant of adfSDCA that is more aggressive than the standard approach. Furthermore, in order to utilize multicore machines we consider a minibatch adfSDCA algorithm and develop complexity results that guarantee the algorithm'
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In this paper, we define finitely additive, probability and modular functions over semiringlike structures. We investigate finitely additive functions with the help of complemented elements of a semiring. We also generalize some classical results in probability theory such as the Law of Total Probability, Bayes' Theorem, the Equality of Parallel Systems, and Poincar\'{e}'s InclusionExclusion Theorem. While we prove that modular functions over a couple of known semirings are almost constant, we show it is possible to define many different modular functions over some semirings such as bottleneck algebras and the semiring $(Id(D), + ,\cdot)$, where $D$ is a Dedekind domain.
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We study the induced subgraph isomorphism problem on inhomogeneous random graphs with infinite variance powerlaw degrees. We provide a fast algorithm that determines for any connected graph $H$ on $k$ vertices if it exists as induced subgraph in a random graph with $n$ vertices. By exploiting the scalefree graph structure, the algorithm runs in $O(n e^{k^4})$ time, and finds for constant $k$ an instance of $H$ in linear time with high probability.
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In this paper, we propose three methods to solve the PageRank problem for the transition matrices with both row and column sparsity. Our methods reduce the PageRank problem to the convex optimization problem over the simplex. The first algorithm is based on the gradient descent in L1 norm instead of the Euclidean one. The second algorithm extends the FrankWolfe to support sparse gradient updates. The third algorithm stands for the mirror descent algorithm with a randomized projection. We proof converges rates for these methods for sparse problems as well as numerical experiments support their effectiveness.
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In this paper, we are interested on the extinction time of continuous state branching processes with competition in a L\'evy random environment. In particular we prove, under the socalled Grey's condition together with the assumption that the L\'evy random environment does not drift towards infinity, that for any starting point the process gets extinct in finite time a.s. Moreover if we replace the condition on the L\'evy random environment by a technical integrability condition on the competition mechanism, then the process also gets extinct in finite time a.s. and it comes down from infinity under the condition that the negative jumps associated to the environment are driven by a compound Poisson process. Then the logistic case in a Brownian random environment is treated. Our arguments are base on a Lampertitype representation where the driven process turns out to be a perturbed Feller diffusion by an independent spectrally positive L\'evy process. If the independent random perturb
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If there's one thing that will make even the most powerful computer feel like a 7 year old rig, it's Adobe Lightroom paired with RAW files from any highmegapixel camera. In my case, I spent over a year of spare time editing 848GB worth of 11,000+ 42megapixel RAW photos and 4K videos from my New Zealand trip and making these nine photosets. I quickly realized that my two year old iMac was not up to the challenge. In 2015 I took a stab at solving my photo storage problem with a cloudbacked 12TB Synology NAS. That setup is still running great. Now I just need to keep up with the performance requirements of having the latest camera gear with absurd file sizes. I decided it was time to upgrade to something a bit more powerful. This time I decided to build a PC and switch to Windows 10 for my heavy computing tasks. Yes, I switched to Windows. I love articles like this, because there is no one true way to build a computer for any task, and everyone has their own opinions and ideas and
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The European Commission has fined Qualcomm â¬997m for abusing its market dominance in LTE baseband chipsets. Qualcomm prevented rivals from competing in the market by making significant payments to a key customer on condition it would not buy from rivals. This is illegal under EU antitrust rules. Qualcomm sounds like an upstanding company. Of course, they are appealing the decision.
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Today we're taking a major step to simplify online privacy with the launch of fully revamped versions of our browser extension and mobile app, now with builtin tracker network blocking, smarter encryption, and, of course, private search  all designed to operate seamlessly together while you search and browse the web. Our updated app and extension are now available across all major platforms  Firefox, Safari, Chrome, iOS, and Android  so that you can easily get all the privacy essentials you need on any device with just one download. Seems like a natural extension of what DuckDuckGo is already known for. Nice work.
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An anonymous reader quotes the EFF: The Electronic Frontier Foundation (EFF) and mobile security company Lookout have uncovered a new malware espionage campaign infecting thousands of people in more than 20 countries. Hundreds of gigabytes of data has been stolen, primarily through mobile devices compromised by fake secure messaging clients. The trojanized apps, including Signal and WhatsApp, function like the legitimate apps and send and receive messages normally. However, the fake apps also allow the attackers to take photos, retrieve location information, capture audio, and more. The threat, called Dark Caracal by EFF and Lookout researchers, may be a nationstate actor and appears to employ shared infrastructure which has been linked to other nationstate actors. In a new report, EFF and Lookout trace Dark Caracal to a building belonging to the Lebanese General Security Directorate in Beirut. "People in the U.S., Canada, Germany, Lebanon, and France have been hit by Dark Caracal. T
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Selftaught rocket scientist/daredevil "Mad" Mike Hughes will finally launch his homemade rocket in two weeks  despite "anonymous online haters questioning his every move." An anonymous reader quotes PhillyVoice: He's found some private land in the "ghost town" of Amboy, California  complete with a brandspankingnew road that'll enable him to get his motor home and rocket gear to the site... "It'll be a vertical launch, me strapped into the rocket with 6,000 pounds of thrust, going up about threeeighths of a mile," he said, noting it's a prologue to a major launch this Fourth of July weekend. "It's the ultimate Wile E. Coyote move." As with the scrubbed mission, this is in part an event which he hopes will get people to investigate the ideology which holds the earth is flat  despite quite a bit of evidence to the contrary. He said it would've happened back in November if international publicity hadn't prompted government bureaucrats to "cover their asses" by pointing out that
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Fluid queues are mathematical models frequently used in stochastic modelling. Their stationary distributions involve a key matrix recording the conditional probabilities of returning to an initial level from above, often known in the literature as the matrix $\Psi$. Here, we present a probabilistic interpretation of the family of algorithms known as \emph{doubling}, which are currently the most effective algorithms for computing the return probability matrix $\Psi$. To this end, we first revisit the links described in \cite{ram99, soares02} between fluid queues and QuasiBirthDeath processes; in particular, we give new probabilistic interpretations for these connections. We generalize this framework to give a probabilistic meaning for the initial step of doubling algorithms, and include also an interpretation for the iterative step of these algorithms. Our work is the first probabilistic interpretation available for doubling algorithms.
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We obtain a new bound on the number of tworich points spanned by an arrangement of low degree algebraic curves in $\mathbb{R}^4$. Specifically, we show that an arrangement of $n$ algebraic curves determines at most $C_\epsilon n^{4/3+3\epsilon}$ tworich points, provided at most $n^{2/3+2\epsilon}$ curves lie in any low degree hypersurface and at most $n^{1/3+\epsilon}$ curves lie in any low degree surface. This result follows from a structure theorem about arrangements of curves that determine many tworich points.
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We extend results of ColliotTh\'el\`ene and Raskind on the $\mathcal{K}_2$cohomology of smooth projective varieties over a separably closed field $k$ to the \'etale motivic cohomology of smooth, not necessarily projective, varieties over $k$. Some consequences are drawn, such as the degeneration of the BlochLichtenbaum spectral sequence for any field containing $k$.
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The purpose of this work is to incorporate numerically, in a discontinuous Galerkin (DG) solver of a BoltzmannPoisson model for hot electron transport, an electronic conduction band whose values are obtained by the spherical averaging of the full band structure given by a local empirical pseudopotential method (EPM) around a local minimum of the conduction band for silicon, as a midpoint between a radial band model and an anisotropic full band, in order to provide a more accurate physical description of the electron group velocity and conduction energy band structure in a semiconductor. This gives a better quantitative description of the transport and collision phenomena that fundamentally define the behaviour of the Boltzmann  Poisson model for electron transport used in this work. The numerical values of the derivatives of this conduction energy band, needed for the description of the electron group velocity, are obtained by means of a cubic spline interpolation. The EPMBoltzmann
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The direct sampling method (DSM) has been introduced for noniterative imaging of small inhomogeneities and is known to be fast, robust, and effective for inverse scattering problems. However, to the best of our knowledge, a full analysis of the behavior of the DSM has not been provided yet. Such an analysis is proposed here within the framework of the asymptotic hypothesis in the 2D case leading to the expression of the DSM indicator function in terms of the Bessel function of order zero and the sizes, shapes and permittivities of the inhomogeneities. Thanks to this analytical expression the limitations of the DSM method when one of the inhomogeneities is smaller and/or has lower permittivity than the others is exhibited and illustrated. An improved DSM is proposed to overcome this intrinsic limitation in the case of multiple incident waves. Then we show that both the traditional and improved DSM are closely related to a normalized version of the Kirchhoff migration. The theoretical e
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Multilayered artificial neural networks are becoming a pervasive tool in a host of application fields. At the heart of this deep learning revolution are familiar concepts from applied and computational mathematics; notably, in calculus, approximation theory, optimization and linear algebra. This article provides a very brief introduction to the basic ideas that underlie deep learning from an applied mathematics perspective. Our target audience includes postgraduate and final year undergraduate students in mathematics who are keen to learn about the area. The article may also be useful for instructors in mathematics who wish to enliven their classes with references to the application of deep learning techniques. We focus on three fundamental questions: what is a deep neural network? how is a network trained? what is the stochastic gradient method? We illustrate the ideas with a short MATLAB code that sets up and trains a network. We also show the use of stateofthe art software on a la
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We develop a cut finite element method (CutFEM) for the convection problem in a so called fractured domain which is a union of manifolds of different dimensions such that a $d$ dimensional component always resides on the boundary of a $d+1$ dimensional component. This type of domain can for instance be used to model porous media with embedded fractures that may intersect. The convection problem can be formulated in a compact form suitable for analysis using natural abstract directional derivative and divergence operators. The cut finite element method is based on using a fixed background mesh that covers the domain and the manifolds are allowed to cut through a fixed background mesh in an arbitrary way. We consider a simple method based on continuous piecewise linear elements together with weak enforcement of the coupling conditions and stabilization. We prove a priori error estimates and present illustrating numerical examples.
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In this paper, the optimal power flow (OPF) problem is augmented to account for the costs associated with the loadfollowing control of a power network. Loadfollowing control costs are expressed through the linear quadratic regulator (LQR). The power network is described by a set of nonlinear differential algebraic equations (DAEs). By linearizing the DAEs around a known equilibrium, a linearized OPF that accounts for steadystate operational constraints is formulated first. This linearized OPF is then augmented by a set of linear matrix inequalities that are algebraically equivalent to the implementation of an LQR controller. The resulting formulation, termed LQROPF, is a semidefinite program which furnishes optimal steadystate setpoints and an optimal feedback law to steer the system to the new steady state with minimum loadfollowing control costs. Numerical tests demonstrate that the setpoints computed by LQROPF result in lower overall costs and frequency deviations compared to
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In 2016, Y\"uce and Torunbalc\i\ Ayd\i n \cite{YucTor} defined dual Fibonacci quaternions. In this paper, we defined the dual thirdorder Jacobsthal quaternions and dual thirdorder JacobsthalLucas quaternions. Also, we investigated the relations between the dual thirdorder Jacobsthal quaternions and thirdorder Jacobsthal numbers. Furthermore, we gave some their quadratic properties, the summations, the Binet's formulas and Cassinilike identities for these quaternions.
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Quadric hypersurfaces are wellknown to satisfy the Hasse principle. However, this is no longer true in the case of the Hasse principle for integral points, where counterexamples are known to exist in dimension 1 and 2. This work explores the frequency that such counterexamples arise in a family of affine quadric surfaces defined over the integers.
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We present a numerical algorithm for evaluating the Boltzmann collision operator with $O(N^2)$ operations based on high order discontinuous Galerkin discretizations in the velocity variable. To formulate the approach, Galerkin projection of the collision operator is written in the form of a bilinear circular convolution. An application of the discrete Fourier transform allows to rewrite the six fold convolution sum as a three fold weighted convolution sum in the frequency space. The new algorithm is implemented and tested in the spatially homogeneous case, and results in a considerable improvement in speed as compared to the direct evaluation. Simultaneous and separate evaluations of the gain and loss terms of the collision operator were considered. Less numerical error was observed in the conserved quantities with simultaneous evaluation.
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Assume that we observe a sample of size n composed of pdimensional signals, each signal having independent entries drawn from a scaled Poisson distribution with an unknown intensity. We are interested in estimating the sum of the n unknown intensity vectors, under the assumption that most of them coincide with a given 'background' signal. The number s of pdimensional signals different from the background signal plays the role of sparsity and the goal is to leverage this sparsity assumption in order to improve the quality of estimation as compared to the naive estimator that computes the sum of the observed signals. We first introduce the group hard thresholding estimator and analyze its mean squared error measured by the squared Euclidean norm. We establish a nonasymptotic upper bound showing that the risk is at most of the order of {\sigma}^2(sp + s^2sqrt(p)) log^3/2(np). We then establish lower bounds on the minimax risk over a properly defined class of collections of ssparse sign
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The main aim of this paper is to bridge two directions of research generalizing asymptotic density zero sets. This enables to transfer results concerning one direction to the other one. Consider a function $g\colon\omega\to [0,\infty)$ such that $\lim_{n\to\infty}g(n)=\infty$ and $\frac{n}{g(n)}$ does not converge to $0$. Then the family $\mathcal{Z}_g=\{A\subseteq\omega:\ \lim_{n\to\infty}\frac{\text{card}(A\cap n)}{g(n)}=0\}$ is an ideal called simple density ideal (or ideal associated to upper density of weight $g$). We compare this class of ideals with Erd\H{o}sUlam ideals. In particular, we show that there are $\sqsubseteq$antichains of size $\mathfrak{c}$ among Erd\H{o}sUlam ideals which are and are not simple density ideals. We characterize simple density ideals which are Erd\H{o}sUlam as those containing the classical ideal of sets of asymptotic density zero. We also characterize Erd\H{o}sUlam ideals which are simple density ideals. In the latter case we need to introduce
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We obtain sufficient criteria for endomorphisms of torsionfree nilpotent groups of finite rank to be automorphisms, by considering the induced maps on the torsionfree abelianisation and the centre. Whilst these results are known in the finitely generated case removing this assumption introduces several difficulties.
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This paper introduces a new fast algorithm for the 8point discrete cosine transform (DCT) based on the summationbyparts formula. The proposed method converts the DCT matrix into an alternative transformation matrix that can be decomposed into sparse matrices of low multiplicative complexity. The method is capable of scaled and exact DCT computation and its associated fast algorithm achieves the theoretical minimal multiplicative complexity for the 8point DCT. Depending on the nature of the input signal simplifications can be introduced and the overall complexity of the proposed algorithm can be further reduced. Several types of input signal are analyzed: arbitrary, null mean, accumulated, and null mean/accumulated signal. The proposed tool has potential application in harmonic detection, image enhancement, and feature extraction, where input signal DC level is discarded and/or the signal is required to be integrated.
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An anonymous reader quotes SiliconBeat: Santa Clara autotech firm Telenav has just announced an "incar advertising platform" for cars that connect to the internet. Telenav wants to sell the system to major auto manufacturers. And although it's probably the last thing many consumers want, vehicle owners will pay more for connectedcar services if they decline the ads. "This approach helps car makers offset costs related to connected services, such as wireless data, content, software and cloud services," a spokeswoman for Telenav said Jan. 5. "In return for accepting ads in vehicles, drivers benefit from access to connected services without subscription fees, as well as new driving experiences that come from the highlytargeted and relevant offers delivered based on information coming from the vehicle." Auto makers including Toyota, Lexus, Ford, GM and Cadillac already use the company's connectedcar products, the spokeswoman said. Telenav CEO H.P. Jin in a press release called the ad
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An anonymous reader quotes a report from The Verge: Amid vocal calls for the company to act, Twitter today offered its first explanation for why it hasn't banned President Donald Trump  without ever saying the man's name. "Elected world leaders play a critical role in that conversation because of their outsized impact on our society," the company said in a blog post. "Blocking a world leader from Twitter or removing their controversial Tweets, would hide important information people should be able to see and debate. It would also not silence that leader, but it would certainly hamper necessary discussion around their words and actions." In its blog post, Twitter reiterated its previous statement that all accounts still must follow the company's rules. The statement seemed to leave open the possibility that it might one day take action against Trump's account, or the accounts of other world leaders who might use the platform to incite violence or otherwise break its rules. "We review
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