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Josh Aas, the executive director of Internet Security Research Group (ISRG) writing for Let's Encrypt: Let's Encrypt, a free, automated, and open certificate authority has reached a milestone: we've now issued more than 100,000,000 certificates. This number reflects at least a few things: First, it illustrates the strong demand for our services. We'd like to thank all of the sysadmins, web developers, and everyone else managing servers for prioritizing protecting your visitors with HTTPS. Second, it illustrates our ability to scale. I'm incredibly proud of the work our engineering teams have done to make this volume of issuance possible. I'm also very grateful to our operational partners, including IdenTrust, Akamai, and Sumo Logic. Third, it illustrates the power of automated certificate management. If getting and managing certificates from Let's Encrypt always required manual steps there is simply no way we'd be able to serve as many sites as we do. The total number of certificates w
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In this article M\"untz spaces $M_{\Lambda ,C}$ of continuous functions supplied with the absolute maximum norm are considered. An approximation of functions in M\"untz spaces $M_{\Lambda ,C}$ of continuous functions by Fourier series is studied. An existence of Schauder bases in M\"untz spaces $M_{\Lambda ,C}$ is investigated.
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Nicole Perlroth, and David Sanger, writing for The New York Times: Twice in the past month, National Security Agency cyberweapons stolen from its arsenal have been turned against two very different partners of the United States  Britain and Ukraine. The N.S.A. has kept quiet, not acknowledging its role in developing the weapons (alternative source). White House officials have deflected many questions, and responded to others by arguing that the focus should be on the attackers themselves, not the manufacturer of their weapons. But the silence is wearing thin for victims of the assaults, as a series of escalating attacks using N.S.A. cyberweapons have hit hospitals, a nuclear site and American businesses. Now there is growing concern that United States intelligence agencies have rushed to create digital weapons that they cannot keep safe from adversaries or disable once they fall into the wrong hands. On Wednesday, the calls for the agency to address its role in the latest attacks gre
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Security updates have been issued by Arch Linux (apache and libnl), CentOS (mercurial), Debian (drupal7), Fedora (cares), Oracle (freeradius and kernel), Scientific Linux (kernel), SUSE (php53 and xen), and Ubuntu (kernel, linux, linuxaws, linuxgke, linuxraspi2, linuxsnapdragon, linux, linuxraspi2, linuxltstrusty, and linuxltsxenial).
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Free groups have many applications in Algebraic Topology. In this paper I specifically study the finitely generated free groups by using the covering spaces and fundamental groups. By the Van Kampen's theorem, we have a famous fact that the fundamental group of a wedge sum of circles is a free group. Therefore, to study free groups, we could try to figure out the covering spaces of the wedge sum of circles. And in the appendix B, I prove the NielsenSchreier theorem which I will use this to study finitely index subgroups of a finitely generated free group.
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In this paper, we provide a generalized version of the Voiculescu theorem for normal operators by showing that, in a von Neumann algebra with separable predual and a faithful normal semifinite tracial weight $\tau$, a normal operator is an arbitrarily small $(\max\{\\cdot\, \Vert\cdot\Vert_{2}\})$norm perturbation of a diagonal operator. Furthermore, in a countably decomposable, properly infinite von Neumann algebra with a faithful normal semifinite tracial weight, we prove that each selfadjoint operator can be diagonalized modulo norm ideals satisfying a natural condition.
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J.H.C. Whitehead's second freegroup algorithm determines whether or not two given elements of a free group lie in the same orbit of the automorphism group of the free group. The algorithm involves certain connected graphs, and Whitehead used threemanifold models to prove their connectedness; later, Rapaport and Higgins & Lyndon gave grouptheoretic proofs. Combined work of Gersten, Stallings, and Hoare showed that the threemanifold models may be viewed as graphs. We give the direct translation of Whitehead's topological argument into the language of graph theory.
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We make plausible the existence of counterexamples to the Riemann hypothesis located in the neighbourhood of unusually large peaks of $\vert \zeta \vert$. The main ingredient in our argument is an identity which links the zeros of a function $f$ defined on the interval $[a,a]$ and the values of its derivatives of odd order at $\pm a$.
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We propose a new class of asymptotic preserving schemes to solve kinetic equations with monokinetic singular limit. The main idea to deal with the singularity is to transform the equations by appropriate scalings in velocity. In particular, we study two biologically related kinetic systems. We derive the scaling factors and prove that the rescaled solution does not have a singular limit, under appropriate spatial nonoscillatory assumptions, which can be verified numerically by a newly developed asymptotic preserving scheme. We set up a few numerical experiments to demonstrate the accuracy, stability, efficiency and asymptotic preserving property of the schemes.
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We introduce a new version of expansiveness for flows. Let $M$ be a compact Riemannian manifold without boundary and $X$ be a $C^1$ vector field on $M$ that generates a flow $\varphi_t$ on $M$. We call $X$ {\it rescaling expansive} on a compact invariant set $\Lambda$ of $X$ if for any $\epsilon>0$ there is $\delta>0$ such that, for any $x,y\in \Lambda$ and any time reparametrization $\theta:\mathbb{R}\to \mathbb{R}$, if $d(\varphi_t(x), \varphi_{\theta(t)}(y)\le \delta\X(\varphi_t(x))\$ for all $t\in \mathbb R$, then $\varphi_{\theta(t)}(y)\in \varphi_{[\epsilon, \epsilon]}(\varphi_t(x))$ for all $t\in \mathbb R$. We prove that every multisingular hyperbolic set (singular hyperbolic set in particular) is rescaling expansive and a converse holds generically.
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In this work we establish a sampling theorem for functions in Besov spaces on spaces of homogeneous type as defined in [HY] in the spirit of their recent counterpart for R d established by JamingMalinnikova in [JM]. The main tool is the wavelet decomposition presented by DengHan in [DH].
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This paper considers the exact recovery of $k$sparse signals in the noiseless setting and support recovery in the noisy case when some prior information on the support of the signals is available. This prior support consists of two parts. One part is a subset of the true support and another part is outside of the true support. For $k$sparse signals $\mathbf{x}$ with the prior support which is composed of $g$ true indices and $b$ wrong indices, we show that if the restricted isometry constant (RIC) $\delta_{k+b+1}$ of the sensing matrix $\mathbf{A}$ satisfies \begin{eqnarray*} \delta_{k+b+1}<\frac{1}{\sqrt{kg+1}}, \end{eqnarray*} then orthogonal matching pursuit (OMP) algorithm can perfectly recover the signals $\mathbf{x}$ from $\mathbf{y}=\mathbf{Ax}$ in $kg$ iterations. Moreover, we show the above sufficient condition on the RIC is sharp. In the noisy case, we achieve the exact recovery of the remainder support (the part of the true support outside of the prior support) for th
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We consider the accelerated propagation of solutions to equations with a nonlocal linear dispersion on the real line and monostable nonlinearities (both local or nonlocal), in the case when either of the dispersion kernel or the initial condition has regularly heavy tails at both $\pm\infty$, perhaps different. We show that, in such case, the propagation to the right direction is fully determined by the right tails of either the kernel or the initial condition. We describe both cases of integrable and monotone initial conditions which may give different orders of the acceleration. Our approach is based, in particular, on the extension of the theory of subexponential distributions, which we introduced early in arXiv:1704.05829 [math.PR].
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Previous work showed that all Bernoulli shifts over a free group are orbitequivalent. This result is strengthened here by replacing Bernoulli shifts with the wider class of properly ergodic countable state Markov chains over a free group. A list of related open problems is provided.
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This article gives an affirmative solution to the problem whether the ergodic Ces\'aro averages generated by a positive DunfordSchwartz operator in a noncommutative space $L^p(\mathcal M,\tau)$, $1\leq p<\infty$, converge almost uniformly (in Egorov's sense). This problem goes back to the original paper of Yeadon, published in 1977, where bilaterally almost uniform convergence of these averages was established for $p=1$.
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We establish that, in an appropriate limit, qubits of communication should be regarded as composite resources, decomposing cleanly into independent correlation and transmission components. Because qubits of communication can establish ebits of entanglement, qubits are more powerful resources than ebits. We identify a new communications resource, the zerobit, which is precisely half the gap between them; replacing classical bits by zerobits makes teleportation asymptotically reversible. The decomposition of a qubit into an ebit and two zerobits has wideranging consequences including applications to state merging, the quantum channel capacity, entanglement distillation, quantum identification and remote state preparation. The source of these results is the theory of approximate quantum error correction. The action of a quantum channel is reversible if and only if no information is leaked to the environment, a characterization that is useful even in approximate form. However, differen
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"Every once in awhile a revolutionary product comes along that changes everything," said cofounder and former Apple CEO Steve Jobs, as he kickstarted the iPhone keynote. Ten years ago, thousands of people around the world listened to him in a mock turtleneck talk about a phone. They liked it so much that they decided to wait outside Apple stores for hours on end to buy one. Little did anyone know the phone  called the iPhone  would go on to revolutionize, in the truest sense of the word, the smartphone industry as we know it. From an Economist article: No product in recent history has changed people's lives more. Without the iPhone, ridehailing, photosharing, instant messaging and other essentials of modern life would be less widespread. Shorn of cumulative sales of 1.2bn devices and revenues of $1trn, Apple would not hold the crown of the world's largest listed company. Thousands of software developers would be poorer, too: the apps they have written for the smartphone make the
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It is proved that replica symmetry is not broken in the transverse and longitudinal random field Ising model. In this model, the variance of spin overlap of any component vanishes in any dimension almost everywhere in the coupling constant space in the infinite volume limit. The weak FortuinKasteleynGinibre property in this model and the GhirlandaGuerra identities in artificial equivalent models in a path integral representation based on the LieTrotter formula enable us to extend Chatterjee's proof for the random field Ising model to the quantum model.
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We consider finite area convex Euclidean circular sectors. We prove a variational Polyakov formula which shows how the zetaregularized determinant of the Laplacian varies with respect to the opening angle. Varying the angle corresponds to a conformal deformation in the direction of a conformal factor with a logarithmic singularity at the origin. We compute explicitly all the contributions to this formula coming from the different parts of the sector. In the process, we obtain an explicit expression for the heat kernel on an infinite area sector using CarslawSommerfeld's heat kernel. We also compute the zetaregularized determinant of rectangular domains of unit area and prove that it is uniquely maximized by the square.
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WikiLeaks has published the documentation manual for an alleged CIA tool that can track users of WiFicapable Windows devices based on the Extended Service Set (ESS) data of nearby WiFi networks. According to the tool's 42page manual, the tool's name is ELSA. Bleeping Computer has an image embedded in its report that explains how the tool works. There are six steps that summarize the ELSA operation. Bleeping Computer reports: Step 1: CIA operative configures ELSA implant (malware) based on a target's environment. This is done using a tool called the "PATCHER wizard," which generates the ELSA payload, a simple DLL file. Step 2: CIA operative deploys ELSA implant on target's WiFienabled Windows machine. Because ELSA is an implant (malware), the CIA operator will likely have to use other CIA hacking tools and exploits to place the malware on a victim's PC. Step 3: The implant begins collecting WiFi access point information based on the schedule set by the operator. Data collection c
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We extend our previous work on hypergeometric point count formulas by proving that we can express the number of points on families of Dwork hypersurfaces $$X_{\lambda}^d: \hspace{.1in} x_1^d+x_2^d+\ldots+x_d^d=d\lambda x_1x_2\cdots x_d$$ over finite fields of order $q\equiv 1\pmod d$ in terms of Greene's finite field hypergeometric functions. We prove that when $d$ is odd, the number of points can be expressed as a sum of hypergeometric functions plus $(q^{d1}1)/(q1)$ and conjecture that this is also true when $d$ is even. The proof rests on a result that equates certain Gauss sum expressions with finite field hypergeometric functions. Furthermore, we discuss the types of hypergeometric terms that appear in the point count formula and give an explicit formula for Dwork threefolds.
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There are several different modalities, e.g., surgery, chemotherapy, and radiotherapy, that are currently used to treat cancer. It is common practice to use a combination of these modalities to maximize clinical outcomes, which are often measured by a balance between maximizing tumor damage and minimizing normal tissue side effects due to treatment. However, multimodality treatment policies are mostly empirical in current practice, and are therefore subject to individual clinicians' experiences and intuition. We present a novel formulation of optimal multimodality cancer management using a finitehorizon Markov decision process approach. Specifically, at each decision epoch, the clinician chooses an optimal treatment modality based on the patient's observed state, which we define as a combination of tumor progression and normal tissue side effect. Treatment modalities are categorized as (1) Type 1, which has a high risk and high reward, but is restricted in the frequency of administr
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We study the effect of AlvisCurtis duality on the unipotent representations of $\mathrm{GL}_n(q)$ in nondefining characteristic $\ell$. We show that the permutation induced on the simple modules can be expressed in terms of a generalization of the Mullineux involution on the set of all partitions, which involves both $\ell$ and the order of $q$ modulo $\ell$.
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As companies look for ways to cut costs, Seattle's $15 minimum wage law may be hurting hourly workers instead of helping them, according to a new report. From a USA Today article: A report (PDF) from the University of Washington (UW), found that when wages increased to $13 in 2016, some companies may have responded by cutting lowwage workers' hours. The study, which was funded in part by the city of Seattle, found that workers clocked 9 percent fewer hours on average, and earned $125 less each month after the most recent increase. "If you're a lowskilled worker with one of those jobs, $125 a month is a sizable amount of money," Mark Long, a UW publicpolicy professor and an author of the report told the Seattle Times. "It can be the difference between being able to pay your rent and not being able to pay your rent."
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Samsung Electronics has agreed to open a $380 million home appliance manufacturing plant in Newberry County, South Carolina. The new plant is expected to generate 954 local jobs by 2020. CNBC reports: The South Korean firm said this year it was in talks to build a home appliances plant in the United States amid worries about protectionist policies under U.S. President Donald Trump put pressure on global companies to generate jobs in the country. "With this investment, Samsung is reaffirming its commitment to expanding its U.S. operations and deepening our connection to the American consumers, engineers and innovators," Samsung Electronics America President and CEO Tim Baxter said.
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randomErr writes: A new patent has been filed for a innovative brewing technique that incorporates a live strain of good bacteria into the brewing process. Researchers at NUS (National University of Singapore) have created a probiotic sour beer that may boost immunity and improve gut health. The bacteria Lactobacillus paracasei L26 is capable of neutralizing toxins and viruses and regulating the immune system. Chan Mei Zhi Alcine, of the Food Science and Technology Program at NUS said, "While good bacteria are often present in food that have been fermented, there are currently no beers in the market that contain probiotics. Developing sufficient counts of live probiotics in beer is a challenging feat as beers contain hop acids that prevent the growth and survival of probiotics. As a believer of achieving a healthy diet through consuming probiotics, this is a natural choice for me when I picked a topic for my finalyear project."
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