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A social media post from Anders G da Silva, who accused Apple of deleting movies he had purchased from iTunes, went viral earlier this month. There is more to that story, of course. In a statement to CNET, Apple explained that da Silva had purchased movies while living in Australia, with his iTunes region set to "Australia." Then he moved to Canada, and found that the movies were no longer available for download  due, no doubt, to licensing restrictions, including restrictions on Apple itself. While his local copies of the movies were not deleted, they were deleted from his cloud library. Apple said the company had shared a workaround with da Silva to make it easier for him to download his movies again. Public Knowledge posted a story Tuesday to weigh in on the subject, especially since today is International Day Against DRM. From the post: To that rare breed of person who carefully reads terms of service and keeps multiple, meticulous backups of important files, da Silva should have
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At the 70th Emmy Awards, broadcast TV was almost shut out as Netflix and HBO battled each other. The Hollywood Reporter: This year, longtime Emmy nominations leader HBO was outnominated by Netflix. Netflix then won the most Emmys on the main telecast, with seven noms to HBO's six. But earlier, HBO won one more award than Netflix at the Creative Arts Awards ceremonies, 17 to 16. So by the time the curtain came down on the 70th Emmy Awards, technically  and sort of poetically  Netflix and HBO had fought to a draw. Almost all of the major content providers left with several wins to celebrate. [...] All in all, it was a terrible night for broadcast networks  even as NBC aired the show and two stars of the network, Saturday Night Live's Michael Che and Colin Jost, hosted. SNL won the variety sketch award for the second year in a row, and ABC's The Oscars won for best direction of a variety show (that award's winner, Glenn Weiss, stole the night with his onstage marriage proposal), b
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Accelerated Mobile Pages, or AMP, has been a controversial project since its debut. Critics say AMP is a Googlespecific project and it is creating a walledgarden, which would only serve Google's best interests. On its part, Google has insisted that AMP's mission is to benefit the open web, and that many who contribute to AMP are nonGooglers. On Tuesday, Google announced that it would be giving up some control of how the code behind AMP is managed. A report adds: It plans to move the AMP Project to a "new governance model," which is to say that decisions about the code will be made by a committee that includes nonGooglers. Until now, final decisions about AMP's code have been made by Malte Ubl, the tech lead for the AMP Project at Google. A model with a single person in charge is not actually all that rare in open source. That person is often cheekily referred to as the BDFL, or "benevolent dictator for life." Ubl's been that person for AMP, but, he writes, "we've found that it does
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Security researchers have found evidence that a piece of malware peddled as "lawful intercept" software to government agencies has been deployed against victims located in 45 countries, a number that far outweighs the number of known operators, meaning that some of them are conducting illegal crossborder surveillance. The findings come from a report published by Citizen Lab, a digital rights watchdog at the University of Toronto's Munk School of Global Affairs. ZDNet: The malware, known as Pegasus (or Trident), was created by Israeli cybersecurity firm NSO Group and has been around for at least three years  when it was first detailed in a report over the summer of 2016. The malware can operate on both Android and iOS devices, albeit it's been mostly spotted in campaigns targeting iPhone users primarily. On infected devices, Pegasus is a powerful spyware that can do many things, such as record conversations, steal private messages, exfiltrate photos, and much much more. Citizen Lab'
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Google has released a Chrome OS 69 update that introduces a range of new features. From a report: Most notably, there's now support for running Linux apps. You'll need a supported machine (a handful of machines from Acer, ASUS, HP, Lenovo, Samsung and Google itself). Still, this could be more than a little helpful if you want to run a conventional desktop app or command line terminal without switching to another PC or a virtual environment. The new software also adds the longinthemaking Night Light mode to ease your eyes at the end of the day. Voice dictation is now available in any text field, and there's a fresh Files interface that can access Play files and Team Drives.
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Speaking at the Goldman Sachs Communicopia conference last week, TakeTwo CEO Strauss Zelnick says the rise of streaming gaming was an inevitability that was just waiting on the technology to power it at scale. While Zelnick acknowledged that the streaming game servers "have to be pretty close to where the consumer is" to address latency issues, he said there are a few largescale companies "that have hyperscale data centers all around the world," and that infrastructure will be able to address that last remaining hurdle in a few years time. A report adds: Zelnick's comments come a few months after Ubisoft CEO Yves Guillemot suggested that streaming games will completely replace consoles after one more generation. Guillemot suggested that changeover would cause a revolution in the gaming market, which will explode in size and accessibility thanks to cheap, streamingcapable boxes delivering bigbudget hits. Zelnick agreed that streaming will increase the size of the highend, bigbudge
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An anonymous reader shares a report: Over on the EEVblog, someone noticed an interesting chip that's been apparently flying under our radar for a while. This is an ARM processor capable of running Linux. It's handsolderable in a TQFP package, has a builtin Mali GPU, support for a touch panel, and has support for 512MB of DDR3. If you do it right, this will get you into the territory of a BeagleBone or a Raspberry Pi Zero, on a board that's whatever form factor you can imagine. Here's the best part: you can get this part for $1 USD in largeish quantities. A cursory glance at the usual online retailers tells me you can get this part in quantity one for under $3. This is interesting, to say the least. The chip in question, the Allwinner A13, is a 1GHz ARM CortexA8 processor. While it's not much, it is a chip that can run Linux in a handsolderable package. There is no HDMI support, you'll need to add some more chips (that are probably in a BGA package), but, hey, it's only a dollar. I
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Google built a prototype of a censored search engine for China that links users' searches to their personal phone numbers, thus making it easier for the Chinese government to monitor people's queries, The Intercept can reveal. The search engine, codenamed Dragonfly, was designed for Android devices, and would remove content deemed sensitive by China's ruling Communist Party regime, such as information about political dissidents, free speech, democracy, human rights, and peaceful protest. Don't be evil.
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"Ireland's government has fully recovered more than [$16 billion] in disputed taxes and interest from Apple, which it will hold in an escrow fund pending its appeal against a European Union tax ruling," reports The Guardian. From the report: The European commission ruled in August 2016 that Apple had received unfair tax incentives from the Irish government. Both Apple and Dublin are appealing against the original ruling, saying the iPhone maker's tax treatment was in line with Irish and EU law. Ireland's finance ministry, which began collecting the back taxes in a series of payments in May, estimated last year the total amount could have reached  [$17.5 billion] including EU interest. In the end the amount was [$15.2 billion] in back taxes plus [$1.4 billion] interest. For its part, the commission said it would scrap its lawsuit against Ireland, which it initiated last year because of delays in recovering the money. "In light of the full payment by Apple of the illegal state aid it h
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We present a theoretical analysis of the average performance of OMP for sparse approximation. For signals, that are generated from a dictionary with $K$ atoms and coherence $\mu$ and coefficients corresponding to a geometric sequence with parameter~$\alpha$, we show that OMP is successful with high probability as long as the sparsity level $S$ scales as $S\mu^2 \log K \lesssim 1\alpha $. This improves by an order of magnitude over worst case results and shows that OMP and its famous competitor Basis Pursuit outperform each other depending on the setting.
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We prove a weak invariance principle in the Skorohod $\mathcal{J}_{1}% $topology for ergodic sums of locally (but not necessarily uniformly) Lipschitz continuous observables in the domain of attraction of a nonGaussian stable law under the action of a GibbsMarkov map, using the classical approach via finitedimensional marginals and $\mathcal{J}_{1}$tightness.
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In this paper, we propose a new SVRGstyle acceleated stochastic algorithm for solving a family of nonconvex optimization problems whose objective consists of a sum of $n$ smooth functions and a nonsmooth convex function. Our major goal is to improve the convergence of SVRGstyle stochastic algorithms to stationary points under a setting with a large condition number $c$  the ratio between the smoothness constant and the negative curvature constant. The proposed algorithm achieves the best known gradient complexity when $c\geq \Omega(n)$, which was achieved previously by a SAGAstyle accelerated stochastic algorithm. Compared with the SAGAstyle accelerated stochastic algorithm, the proposed algorithm is more practical due to its low memory cost that is inherited from previous SVRGstyle algorithms. Compared with previous studies on SVRGstyle stochastic algorithms, our theory provides much stronger results in terms of (i) reduced gradient complexity under a large condition number;
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Amazon is planning to release at least 8 new voicecontrolled hardware devices before the end of the year, according to CNBC. "The devices include, among others, a microwave oven, an amplifier, a receiver, a subwoofer, and an incar gadget, people familiar with the matter said," reports CNBC. "All of the devices will be Alexaenabled, meaning they can easily connect to the voice assistant. Some of the devices will also have Alexa built in." From the report: Amazon is expected to reveal some of these devices at an event later this month, according to an internal document describing the plans. The new devices reflect Amazon's ambition to make its Alexa voice technology ubiquitous by focusing on areas where people spend most of their time  at home and in the car. Alexa was initially considered a geeky experiment at Amazon. Now it is now one of the most popular voice assistants, leading the growth of the burgeoning smart speaker market, which is expected to be worth $30 billion by 2024,
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C64 OS has one goal. Make a Commodore 64 feel fast and useful in today's modern world. It's a very high bar. The C64 was introduced in 1982 and has an 8bit, 1MHz, 6510 CPU with just 64 kilobytes of directly addressable memory. It has a screen resolution of 320x200 pixels, and a fixed palette of 16 colors. But, it is an incredibly versatile machine. And it enjoys an active userbase and a great variety of modern hardware expansions. The C64 has had many operating systems written for it, So why write another? Some of these projects were designed to be experimental, or to demonstrate a point, rather than to solve a problem or to make using the C64 better. Others had good intentions but pushed the machine in ways it wasn't designed for, compromising on speed and usability in the pursuit of features available on more powerful computers. The aim of C64 OS is to work with the limitations of the Commodore 64 and enable it to become useful. It never ceases to amaze me how much
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Paul Alcorn reporting for Tom's Hardware: AMD listed the Ryzen 7 2800H and the Ryzen 5 2600H on its website. These new processors bring the inherent goodness of the Raven Ridge architecture, found in the Ryzen 5 2400G and the Ryzen 3 2200G, to gaming notebooks. As such, these processors come with AMD's Zen compute cores paired with the Vega graphics architecture, and they are also AMD's first processors to support DDR43200 as a base specification. Both new models feature a similar design as their desktop counterparts, albeit with slightly redesigned in frequencies to adjust for the flimsy cooling in mobile form factors and battery life limitations. That's reflected in the processors' reduced 45W TDP (thermal design power), which is much lower than the 65W TDP found on the desktop parts. AMD does give vendors some wiggle room with a configurable TDP (cTDP) range that spans between 35W and 45W. The Ryzen 7 2800H is analogous to the 2400G, but it comes with a 3.3 GHz base and 3.8 GHz boo
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We give an elementary proof to the asymptotic expansion formula of RochonZhang for the unique complete K\"ahlerEinstein metric of ChengYau, Kobayashi, TianYau and Bando on quasiprojective manifolds. The main tools are the solution formula for second order ODE's with constant coefficients and spectral theory for Laplacian operator on a closed manifold.
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Two separate reports are saying Apple's yettobereleased AirPower charger is facing overheating issues. The product, designed to simultaneously charge an iPhone, Apple Watch, and AirPods, was announced more than a year ago at Apple's 2017 iPhone event. Apple has yet to provide any additional information on AirPower, even during its iPhone event last week. The company even appears to have wiped all mention of it from its website. CNBC reports: Tech writer Sonny Dickson, who has a track record of accurately reporting on Apple, said over the weekend that Apple has struggled with heat management, which affects accuracy and charging speed. Dickson thinks it's unlikely Apple will make its endofyear release deadline. Daring Fireball's John Gruber said something similar. Gruber said the charging pad, which uses a multicoil design, is "getting too hot  way too hot." "There are engineers who looked at AirPower's design and said it could never work, thermally. ... I think they've either ha
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Complex autonomous control systems are subjected to sensor failures, cyberattacks, sensor noise, communication channel failures, etc. that introduce errors in the measurements. The corrupted information, if used for making decisions, can lead to degraded performance. We develop a framework for using adversarial deep reinforcement learning to design observer strategies that are robust to adversarial errors in information channels. We further show through simulation studies that the learned observation strategies perform remarkably well when the adversary's injected errors are bounded in some sense. We use neural network as function approximator in our studies with the understanding that any other suitable function approximating class can be used within our framework.
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The aim of this paper is to introduce a finite element formulation within Arbitrary Lagrangian Eulerian framework with vanishing discrete {\it Space Conservation Law} (SCL) for differential equations on time dependent domains. The novelty of the formulation is the method for temporal integration which results in preserving the SCL property and retaining the higher order accuracy at the same time. Once the time derivative is discretized (based on integration or differentiation formula), the common approach for terms in differential equation which do not involve temporal derivative is classified to be a kind of "time averaging" between time steps. In the spirit of classical approaches, this involves evaluating these terms in several points in time between the current and the previous time step ($[t_n,t_{n+1}]$), and then averaging them in order to provide the satisfaction of discrete SCL. Here, we fully use the polynomial in time form of mapping through which evolution of domain is reali
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We provide several new asymptotic expansions of the prime counting function $\pi(x)$. We define an {\it asymptotic continued fraction expansion} of a complexvalued function of a real or complex variable to be a possibly divergent continued fraction whose approximants provide an asymptotic expansion of the given function. We show that, for each positive integer $n$, two well known continued fraction expansions of the exponential integral function $E_n(z)$, in the regions where they diverge, correspondingly yield two asymptotic continued fraction expansions of $\pi(x)/x$. We prove this by first using Stieltjes' theory of moments to establish some general results about Stieljtes and Jacobi continued fractions and then applying the theory specifically to the probability measure on $[0,\infty)$ with density function $\frac{t^n}{n!}e^{t}$. We show generally that the "best" rational approximations of a function possessing an asymptotic Jacobi continued fraction expansion are precisely the a
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In this paper, we consider a kind of ideal quotient of an extriangulated category such that the ideal is the kernel of a functor from this extriangulated category to an abelian category. We study a condition when the functor is dense and full, in another word, the ideal quotient becomes abelian. Moreover, a new equivalent characterization of clustertilting subcategories is given by applying homological methods according to this functor. As an application, we show that in a connected 2CalabiYau triangulated category B, a functorially finite, extension closed subcategory T of B is cluster tilting if and only if B/T is an abelian category.
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A general explicit form for generating functions for approximating fractional derivatives is derived. To achieve this, an equivalent characterisation for consistency and order of approximations established on a general generating function is used to form a linear system of equations with Vandermonde matrix for the coefficients of the generating function which is in the form of power of a polynomial. This linear system is solved for the coefficients of the polynomial in the generating function. These generating functions completely characterise Gr\"unwald type approximations with shifts and order of accuracy. Incidentally, the constructed generating functions happen to be generalization of the previously known Lubich forms of generating functions without shift. As a consquence, a general explicit form for new finite difference formulas for integerorder derivatives with any order of accuracy are derived.
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We consider the KelvinVoigt model for the viscoelasticity, and prove a Carleman estimate for functions without compact supports. Then we apply the Carleman estimate to prove the Lipschitz stability in determining a spatial varying function in an external source term of KelvinVoigt model by a single measurement. Finally as a related system, we consider an isothermal compressible fluid system and apply the Carleman estimate to establish the Lipschitz stability for an inverse source problem for the compressible fluid system.
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Based on a recent $L^{6}L^{\infty}$ approach, validity of diffusive limit is established for both steady and unsteady Boltzmann equation in the presence of the classical Maxwell boundary condition for a full arrange of the accommodation coefficient $0 \leq \alpha \leq 1$. A general stretching method is developed to control bouncing trajectories for the specular reflection with $\alpha=0$ in the hydrodynamic limit, and refined estimates uniform with respect to $0 \leq \alpha\leq 1$ for the macroscopic distribution $\mathbf{P}f$ are derived.
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A set family $F$ is said to satisfy the $(p,q)$ property if among any $p$ sets in $F$, some $q$ have a nonempty intersection. Hadwiger and Debrunner (1957) conjectured that for any $p \geq q \geq d+1$ there exists $c=c_d(p,q)$, such that any family of compact convex sets in $\mathbb{R}^d$ that satisfies the $(p,q)$ property, can be pierced by at most $c$ points. In their celebrated $(p,q)$ theorem from 1992, Alon and Kleitman proved the conjecture but did not obtain effective bounds on $c_d(p,q)$, called `the HadwigerDebrunner numbers'. Ever since, obtaining such bounds is a major open problem in convexity theory. The best currently known asymptotic lower bound on the HadwigerDebrunner numbers in the plane is $c_2(p,q) = \Omega( \frac{p}{q}\log(\frac{p}{q}))$. In this paper we present the significantly stronger lower bound $c_2(p,q) \geq p^{1+\Omega(1/q)}$. This bound, obtained by an explicit family of lines, is tight for all families that have a bounded VCdimension. Unlike previou
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A dilator is a particularly uniform transformation $X\mapsto T_X$ of linear orders that preserves wellfoundedness. We say that $X$ is a BachmannHoward fixed point of $T$ if there is an almost order preserving collapsing function $\vartheta:T_X\rightarrow X$ (precise definition to follow). In the present paper we show that $\Pi^1_1$comprehension is equivalent to the assertion that every dilator has a wellfounded BachmannHoward fixed point. This proves a conjecture of M. Rathjen and A. Montalb\'an.
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Let $n >3$ and $ 0< k < \frac{n}{2} $ be integers. In this paper, we investigate some algebraic properties of the line graph of the graph $ {Q_n}(k,k+1) $ where $ {Q_n}(k,k+1) $ is the subgraph of the hypercube $Q_n$ which is induced by the set of vertices of weights $k$ and $k+1$. In the first step, we determine the automorphism groups of these graphs for all values of $k$. In the second step, we study Cayley properties of the line graph of these graphs. In particular, we show that for $ k>2, $ if $ 2k+1 \neq n$, then the line graph of the graph $ {Q_n}(k,k+1) $ is a vertextransitive non Cayley graph. Also, we show that the line graph of the graph $ {Q_n}(1,2) $ is a Cayley graph if and only if $ n$ is a power of a prime $p$.
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We discuss analytically and numerically the propagation and energy transmission of electromagnetic waves caused by the coupling of surface plasmon polaritons (SPPs) between two spatially separated layers of 2D materials, such as graphene, at subwavelength distances. We construct an adaptive finiteelement method to compute the ratio of energy transmitted within these waveguide structures reliably and efficiently. At its heart, the method is built upon a goaloriented a posteriori error estimation with the dualweighted residual method (DWR). Further, we derive analytic solutions of the twolayer system, compare those to (known) singlelayer configurations, and compare and validate our numerical findings by comparing numerical and analytical values for optimal spacing of the twolayer configuration. Additional aspects of our numerical treatment, such as local grid refinement, and the utilization of perfectly matched layers (PMLs) are examined in detail.
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We study the Carleson measures and the Toeplitz operators on the class of socalled small weighted Bergman spaces, introduced recently by Seip. A characterization of Carleson measures is obtained which extends Seip's results from the unit disc of $\mathbb C$ to the unit ball of $\mathbb C^n$. We use this characterization to give necessary and sufficient conditions for the boundedness and compactness of Toeplitz operators. Finally, we study the Schatten $p$ classes membership of Toeplitz operators for $1<p<\infty$.
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This paper develops a comprehensive probabilistic setup to compute approximating functions in active subspaces. Constantine et al. proposed the active subspace method in (Constantine et al., 2014) to reduce the dimension of computational problems. It can be seen as an attempt to approximate a highdimensional function of interest $f$ by a lowdimensional one. To do this, a common approach is to integrate $f$ over the inactive, i.e. nondominant, directions with a suitable conditional density function. In practice, this can be done with a finite Monte Carlo sum, making not only the resulting approximation random in the inactive variable for each fixed input from the active subspace, but also its expectation, i.e. the integral of the lowdimensional function weighted with a probability measure on the active variable. In this regard we develop a fully probabilistic framework extending results from (Constantine et al., 2014, 2016). The results are supported by a simple numerical example.
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We propose a semidiscrete numerical scheme and establish wellposedness of a class of parabolic systems. Such systems naturally arise while studying the optimal control of grain boundary motions. The latter is typically described using a set of parabolic variational inequalities. We use a regularization approach to deal with the variational inequality. The resulting optimization problem is a nonsmooth, nonconvex, and nonlinear programming problem. This is a long term project where in the current work we are first analyzing systems of PDEs associated with the regularized optimal control problem. Such a system is a set of highly coupled parabolic equations, and proposes significant analytical and numerical challenges. We establish wellposedness of this system. In addition, we design a provably convergent semidiscrete (time discrete spatially continuous) numerical scheme to solve the system. We have developed several new tools during the course of this paper that can be applied to a wi
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A famous theorem of Dirac states that any graph on $n$ vertices with minimum degree at least $n/2$ has a Hamilton cycle. Such graphs are called Dirac graphs. Strengthening this result, we show the existence of rainbow Hamilton cycles in $\mu n$bounded colourings of Dirac graphs for sufficiently small $\mu >0$.
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On Friday, FCC Chairman Ajit Pai called California's net neutrality bill "illegal," saying it "poses a risk to the rest of the country." The bill recently passed California's state Assembly and now awaits the signature of Governor Jerry Brown. In response to Pai's speech, Scott Wiener, California's Senator who authored the bill, said they are "necessary and legal because Chairman Pai abdicated his responsibility to ensure an open internet." "Unlike Pai's FCC, California isn't run by the big telecom and cable companies," Wiener also said. "Pai can take whatever potshots at California he wants. The reality is that California is the world's innovation capital, and unlike the crony capitalism promoted by the Trump administration, California understands exactly what it takes to foster an open innovation economy with a level playing field." Ars Technica reports: Pai targeted the California rules in a speech at the Maine Heritage Policy Center. Pai derided what he called "nannystate Californ
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An anonymous reader quotes a report from TechCrunch: Altaba, the holding company of what Verizon left behind after its acquisition of Yahoo, said it has settled three ongoing legal cases relating to Yahoo's previously disclosed data breaches. In a Monday filing with the Securities and Exchange Commission, the former web giant turned investment company said it has agreed to end litigation for $47 million, which the company said will "mark a significant milestone" in cleaning up its remaining liabilities. The deal is subject to court approval, which attorneys for both sides asked the court to approve the deal within 45 days, according to a filing submitted Friday. One of the data breaches occurred in mid2013, where data on all of the company's three billion users was stolen. The other breach occurred a year later and resulted in 500 million accounts being stolen, including email addresses and passwords.
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We prove a version of the implicit function theorem for Lipschitz mappings $f:\mathbb{R}^{n+m}\supset A \to X$ into arbitrary metric spaces. As long as the pullback of the Hausdorff content $\mathcal{H}_{\infty}^n$ by $f$ has positive upper $n$density on a set of positive Lebesgue measure, then, there is a local diffeomorphism $G$ in $\mathbb{R}^{n+m}$ and a Lipschitz map $\pi:X\to \mathbb{R}^n$ such that $\pi\circ f\circ G^{1}$, when restricted to a certain subset of $A$ of positive measure, is a the orthogonal projection of $\mathbb{R}^{n+m}$ onto the first $n$coordinates. This may be seen as a qualitative version of a similar result of Azzam and Schul. The main tool in our proof is the metric change of variables introduced in a paper of Haj\l{}asz and Malekzadeh.
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The forwardbackward splitting algorithm is a popular operator splitting method for finding a zero of the sum of two maximal monotone operators, with one of which is cocoercive operator. In this paper, we present a new convergence analysis of a variable metric forwardbackward splitting algorithm with relaxation in real Hilbert spaces. We prove the weak convergence of this algorithm under some weak conditions on the relaxation parameters. Moreover, we allow the relaxation parameters larger than one. Consequently, we recover a variable metric proximal point algorithm. As an application, we obtain a variable metric forwardbackward splitting algorithm for solving the minimization problem of the sum of two convex functions, where one of them is differentiable with a Lipschitz continuous gradient. Furthermore, we discuss the applications of this algorithm to the fundamental of the variational inequalities problem, constrained convex minimization problem, and split feasibility problem.
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We verify some "arithmetic" predictions made by conjectures of Campana, HassettTschinkel, GreenGriffiths, Lang, and Vojta. Firstly, we prove that every dominant endomorphism of an arithmetically hyperbolic variety over an algebraically closed field of characteristic zero is in fact an automorphism of finite order, and that the automorphism group of an arithmetically hyperbolic variety is a locally finite group. To prove these two statements we use (a mild generalization of) a theorem of Amerik on dynamical systems which in turn builds on work of BellGhiocaTucker, and combine this with a classical result of BassLubotzky. Furthermore, we show that if the automorphism group of a projective variety is torsion, then it is finite. In particular, we obtain that the automorphism group of a projective arithmetically hyperbolic variety is finite, as predicted by Lang's conjectures. Next, we apply this result to verify that projective hyperkahler varieties with Picard rank at least three are
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We consider uniqueness in an inverse Schr\"odinger problem in a bounded domain in $\mathbb{R}^2$ given the DirichlettoNeumann map on part of the boundary. On the remaining boundary we impose a new type of singular boundary condition with unknown parameter. Owing to recent results on this class of boundary conditions, we discuss the necessity of an extra point condition to welldefine the data for the inverse problem. Our results are twofold. At a single frequency the inverse problem displays nonuniqueness, since an unknown boundary condition can spoil `seeing' the Schr\"odinger potential via the DirichlettoNeumann map. On the other hand, taking as input data the DirichlettoNeumann map at every frequency $\lambda\in\mathbb{R}$ for which it is welldefined yields full uniqueness of the potential and all the boundary conditions. We adapt recent methods in related twodimensional inverse problems and develop new techniques to cope with the singularity in the boundary condition.
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We prove that a link is strongly quasipositive if it admits a diagram with a single negative crossing. This answers a question of Stoimenow's in the (strong) positive. As a second main result, we give simple and complete characterizations of link diagrams with quasipositive Seifert surfaces produced by Seifert's algorithm.
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Peter Aczel has given a categorical construction for fixed points of normal functors, i.e. dilators which preserve initial segments. For a general dilator $X\mapsto T_X$ we cannot expect to obtain a wellfounded fixed point, as the order type of $T_X$ may always exceed the order type of $X$. In the present paper we show how to construct a BachmannHoward fixed point of $T$, i.e. an order $\operatorname{BH}(T)$ with an `almost' order preserving collapse $\vartheta:T_{\operatorname{BH}(T)}\rightarrow\operatorname{BH}(T)$. Building on previous work, we show that $\Pi^1_1$comprehension is equivalent to the assertion that $\operatorname{BH}(T)$ is wellfounded for any dilator $T$.
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We investigate three cases regarding asymptotic associate primes. First, assume $ (A,\mathfrak{m}) $ is an excellent CohenMacaulay (CM) nonregular local ring, and $ M = \operatorname{Syz}^A_1(L) $ for some maximal CM $ A $module $ L $ which is free on the punctured spectrum. Let $ I $ be a normal ideal. In this case, we examine when $ \mathfrak{m} \notin \operatorname{Ass}(M/I^nM) $ for all $ n \gg 0 $. We give sufficient evidence to show that this occurs rarely. Next, assume that $ (A,\mathfrak{m}) $ is excellent Gorenstein nonregular isolated singularity, and $ M $ is a CM $ A $module with $\operatorname{projdim}_A(M) = \infty $ and $ \dim(M) = \dim(A) 1 $. Let $ I $ be a normal ideal with analytic spread $ l(I) < \dim(A) $. In this case, we investigate when $\mathfrak{m} \notin \operatorname{Ass} \operatorname{Tor}^A_1(M, A/I^n)$ for all $n \gg 0$. We give sufficient evidence to show that this also occurs rarely. Finally, suppose $ A $ is a local complete intersection ring.
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This paper investigates the robust stabilisation of a class of fractionalorder nonlinear system with positive real uncertainty via fixedorder dynamic output feedback controller in terms of linear matrix inequalities (LMIs). the systematic stabilisation algorithm design for loworder controller based on direct Lyapunov approach is proposed for uncertain fractionalorder systems. In the presented algorithm the conditions containing the bilinear variables are decoupled into separate conditions without imposing equality constraints or considering an iterative search of the controller parameters. There is no any limiting constraint on state space matrices and also we assumed the most complete output feedback controller. Simulations results are given to approve the effectiveness and the straightforwardness of the proposed design.
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