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Let $G$ be a finite simple graph on $n$ vertices and $J_G$ denote the corresponding binomial edge ideal in the polynomial ring $S = K[x_1, \ldots, x_n, y_1, \ldots, y_n].$ In this article, we compute the Hilbert series of binomial edge ideal of decomposable graphs in terms of Hilbert series of its indecomposable subgraphs. Also, we compute the Hilbert series of binomial edge ideal of join of two graphs and as a consequence we obtain the Hilbert series of complete $k$partite graph, fan graph, multifan graph and wheel graph.
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Corning just announced its most durable glass yet: Gorilla Glass 6. "The company says that the glass will survive up to 15 drops from a one meter height and can be 'up to two times better' than Gorilla Glass 5," reports The Verge. From the report: As phones get slimmer and have ever sleeker glass displays, reports have appeared that the slimness may actually cancel out the improvements in new iterations of Gorilla Glass, since thinner glass is weaker glass, even if it's become stronger. Still Corning argues that sleek edgetoedge displays have actually led to stronger smartphones. Sometimes, in smartphones of previous years, the bezel would crack first, then leading to a weakness in the glass. There's also a tradeoff between drop resistance and scratch resistance, which Corning has admitted to in the past. Corning says that Gorilla Glass 6 will have the same amount of scratch resistance as previous generations. So although the company claims the new generation of Gorilla Glass is "bet
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British Airways said on Wednesday that its operations at London's Heathrow, Europe's biggest airport, were disrupted because of an issue with a supplier's IT systems. From a report: "We are working with our supplier to resolve the matter and are sorry for the disruption to our customers' travel plans," the company said in a statement. Further reading: The Telegraph, which reports that several flights have been delayed or cancelled because of the IT failure.
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We prove the existence of a unique global weak solution to the full bosonic string heat flow from closed Riemannian surfaces to an arbitrary target under smallness conditions on the twoform and the scalar potential. The solution is smooth with the exception of finitely many singular points. Finally, we discuss the convergence of the heat flow and obtain a new existence result for critical points of the full bosonic string action.
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Here, we introduce a priceformation model where a large number of small players can store and trade electricity. Our model is a constrained meanfield game (MFG) where the price is a Lagrange multiplier for the supply vs. demand balance condition. We establish the existence of a unique solution using a fixedpoint argument. In particular, we show that the price is welldefined and it is a Lipschitz function of time. Then, we study linearquadratic models that can be solved explicitly and compare our model with real data.
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In the run up to the release of Fallout, the new movie in the Mission Impossible franchise, Paramount studio rereleased the entire Mission Impossible series on 4K Bluray last month. The new discs aren't only a huge upgrade for cinephiles  they're also a fascinating glimpse at how studios can revive older films for the 4K/HDR era. Engadget: "In terms of any retransfers or remastering that we are doing for our HDR releases, we will go back to the highest resolution source available," Kirsten Pielstick, manager of Paramount's digital mastering group, said in an interview. In the case of Mission Impossible 1 and 2, that involved scanning the original 35mm negatives in 4K/16bit. As you'd expect, the studio tries to get the original artists involved with any remasters, especially with something like HDR, which allows for higher brightness and more nuanced black levels. Pielstick worked with the director of photography (DP) for the first Mission Impossible film, Stephen H. Burum, to mak
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Mumford defined a rational pullback for Weil divisors on normal surfaces, which is linear, respects effectivity, and satisfies the projection formula. In higher dimensions, the existence of small resolutions of singularities precludes such general results. We single out a higherdimensional situation that resembles the surface case and show for it that a rational pullback for Weil divisors exists, which is also linear, respects effectivity, and satisfies the projection formula.
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Hackers account for 90% of of ecommerce sites' global login traffic, according to a report by cyber security firm Shape Security. They reportedly use programs to apply stolen data acquired on the dark web  all in an effort to login to websites and grab something of value like cash, airline points, or merchandise. Quartz reports: These attacks are successful as often as 3% of the time, and the costs quickly add up for businesses, Shape says. This type of fraud costs the ecommerce sector about $6 billion a year, while the consumer banking industry loses out on about $1.7 billion annually. The hotel and airline businesses are also major targets  the theft of loyalty points is a thing  costing a combined $700 million every year. The process starts when hackers break into databases and steal login information. Some of the best known "data spills" took place at Equifax and Yahoo, but they happen fairly regularly  there were 51 reported breaches last year, compromising 2.3 billion c
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The purpose of this article is to develop techniques for estimating basis log canonical thresholds on logarithmic surfaces. To that end, we develop new local intersection estimates that imply log canonicity. Our main motivation and application is to show the existence of KahlerEinstein edge metrics on all but finitely many families of asymptotically log del Pezzo surfaces, partially confirming a conjecture of two of us. In an appendix we show that the basis log canonical threshold of FujitaOdaka coincides with the greatest lower Ricci bound invariant of Tian.
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Security updates have been issued by Debian (ant, gpac, linux4.9, linuxlatest4.9, taglib, vlc, and znc), Fedora (ceph), Red Hat (fluentd and qemukvmrhev), Slackware (httpd), and SUSE (e2fsprogs, glibc, libgcrypt, mercurial, openssh, perl, rubygemsprockets, shadow, and wireshark).
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In this paper, we are concerned with the long time behavior of the piecewise smooth solutions to the generalized Riemann problem governed by the compressible isothermal Euler equations in two and three dimensions. Nonexistence result is established for the fanshaped wave structure solution, including two shocks and one contact discontinuity and which is a perturbation of plane waves. Therefore, unlike the onedimensional case, the multidimensional plane shocks are not stable globally. What is more, the sharp lifespan estimate is established which is the same as the lifespan estimate for the nonlinear wave equations in both two and three space dimensions.
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In this paper we study the property of normality of a number in base 2. A simple rule that associates a vector to a number is presented and the property of normality is stated for the vector associated to the number. The problem of testing a number for normality is shown to be equivalent to the test of geometrical properties of the associated vector. The paper provides a general approach for normality testing and then applies the proposed methodology to the study of particular numbers. The main result of the paper is to prove that an infinite class of numbers is normal in base 2. As a further result we prove that the irrational number $\sqrt{2}$ is normal in base 2.
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We define the notion of braided Coxeter category, which is informally a tensor category carrying compatible, commuting actions of a generalised braid group B_W and Artin's braid groups B_n on the tensor powers of its objects. The data which defines the action of B_W bears a formal similarity to the associativity constraints in a monoidal category, but is related to the coherence of a family of fiber functors. We show that the quantum Weyl group operators of a quantised KacMoody algebra U_h(g), together with the universal Rmatrices of its Levi subalgebras, give rise to a braided Coxeter structure on integrable, category Omodules for U_h(g). By relying on the 2categorical extension of EtingofKazhdan quantisation obtained in arXiv:1610.09744, we then prove that this structure can be transferred to integrable, category Orepresentations of g. These results are used in arXiv:1512.03041 to give a monodromic description of the quantum Weyl group operators of U_h(g) which extends the one
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This paper introduces a new member of the family of Variational Autoencoders (VAE) that constrains the rate of information transferred by the latent layer. The latent layer is interpreted as a communication channel, the information rate of which is bound by imposing a preset signaltonoise ratio. The new constraint subsumes the mutual information between the input and latent variables, combining naturally with the likelihood objective of the observed data as used in a conventional VAE. The resulting BoundedInformationRate Variational Autoencoder (BIRVAE) provides a meaningful latent representation with an information resolution that can be specified directly in bits by the system designer. The rate constraint can be used to prevent overtraining, and the method naturally facilitates quantisation of the latent variables at the set rate. Our experiments confirm that the BIRVAE has a meaningful latent representation and that its performance is at least as good as stateoftheart com
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The active bijection for oriented matroids (and real hyperplane arrangements, and graphs, as particular cases) is introduced and investigated by the authors in a series of papers. Given any oriented matroid defined on a linearly ordered ground set, we exhibit one particularit\'e of its bases, which we call its active basis, with remarkable properties. It preserves activities (for oriented matroids in the sense of Las Vergnas, for matroid bases in the sense of Tutte), as well as some active partitions of the ground set associated with oriented matroids and matroid bases. It yields a canonical bijection between classes of reorientations and bases [...]. It also yields a refined bijection between all reorientations and subsets of the ground set. Those bijections are related to various Tutte polynomial expressions [...]. They contain various noticeable bijections involving orientations/signatures/reorientations and spanning trees/simplices/bases of a graph/real hyperplane arrangement/orien
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In this paper, we introduce a new algorithm to deal with the stalling effect in the LMS algorithm used in adaptive filters. We modify the update rule of the tap weight vectors by adding noise, generated by a noise generator. The properties of the proposed method are investigated by two novel theorems. As it is shown, the resulting algorithm, called Added Noise LMS (ANLMS), improves the resistance capability of the conventional LMS algorithm against the stalling effect. The probability of update with additive white Gaussian noise is calculated in the paper. Convergence of the proposed method is investigated and it is proved that the rate of convergence of the introduced method is equal to that of LMS algorithm in the expected value sense, provided that the distribution of the added noise is uniform. Finally, it is shown that the order of complexity of the proposed algorithm is linear as the conventional LMS algorithm.
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Most teens today own a smartphone and go online every day, and about a quarter of them use the internet "almost constantly," according to a 2015 report by the Pew Research Center. Now a study published this week in JAMA suggests that such frequent use of digital media by adolescents might increase their odds of developing symptoms of attention deficit hyperactivity disorder. From a report: "It's one of the first studies to look at modern digital media and ADHD risk," says psychologist Adam Leventhal, an associate professor of preventive medicine at the University of Southern California and an author of the study. When considered with previous research showing that greater social media use is associated with depression in teens, the new study suggests that "excessive digital media use doesn't seem to be great for [their] mental health," he adds. Previous research has shown that watching television or playing video games on a console put teenagers at a slightly higher risk of developing
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A geometric object of great interest in combinatorial optimization is the perfect matching polytope of a graph $G$. In any investigation concerning the perfect matching polytope, one may assume that $G$ is matching covered  that is, it is a connected graph (of order at least two) and each edge lies in some perfect matching. A graph $G$ is Birkhoffvon Neumann (BvN) if its perfect matching polytope is characterized solely by nonnegativity and degree constraints. A result of Balas (1981) implies that $G$ is BvN if and only if $G$ does not contain a pair of vertexdisjoint odd cycles $(C_1,C_2)$ such that $GV(C_1)V(C_2)$ has a perfect matching. It follows immediately that the corresponding decision problem is in coNP. However, it is not known to be in NP. The problem is in P if the input graph is planar  due to a result of Carvalho, Lucchesi and Murty (2004). These authors, along with Kothari (2018), have shown that this problem is equivalent to the seemingly unrelated problem o
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This note gives a simple formula for the unique asymptotically conical CalabiYau metrics on the canonical bundle of a flag variety known to exist by the work of R. Goto and others. This is done by generalizing the well known Calabi Ansatz to general K\"{a}hler classes. We give some examples of explicit families, in particular, a formula for the two dimensional family of asymptotically conical metrics on the canonical bundle of $F_{1,2}$.
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Convex relaxations of the AC power flow equations have attracted significant interest in the power systems research community in recent years. The following collection of video lectures provides a brief introduction to the mathematics of AC power systems, continuous nonlinear optimization, and relaxations of the power flow equations. The aim of the videos is to provide the high level ideas of convex relaxations and their applications in power system optimization, and could be used as a starting point for researchers who want to study, use or develop new convex relaxations for use in their own research. The videos do not aim to provide an indepth tutorial about specific convex relaxations, but rather focus on ideas that are common to all convex relaxations of the AC optimal power flow problem.
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A secretive Australian startup called Zoox (an abbreviation of zooxanthellae, the algae that helps fuel coral reef growth) is working on an autonomous vehicle that is unlike any other. Theirs is allelectric and bidirectional, meaning it can cruise into a parking spot traveling one way and cruise out the other. It can make noises to communicate with pedestrians. It even has displays on the windows for passengers to interact with. Bloomberg sheds some light on this company, reporting on their ambitions to build the safest and most inventive autonomous vehicle on the road: Zoox founders Tim KentleyKlay and Jesse Levinson say everyone else involved in the race to build a selfdriving car is doing it wrong. Both founders sound quite serious as they argue that Zoox is obvious, almost inevitable. The world will eventually move to perfectly engineered robotic vehicles, so why waste time trying to incorporate selfdriving technology into yesteryear's cars? Levinson, whose father, Arthur, ran
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The 2nd Circuit denies an immediate appeal in a case that challenges how news organizations used embedded photos of Tom Brady. The Hollywood Reporter: Back in February, a New York judge caused a bit of a freakout by issuing a copyright decision regarding the embedding of a copyrighted photo of NFL superstar Tom Brady. Now comes another surprise with potentially big ramifications to the future of embedding and inline linking: The 2nd Circuit Court of Appeals has denied an interlocutory appeal. Justin Goldman is the plaintiff in the lawsuit after finding the photo of the New England Patriots quarterback he shot and uploaded to Snapchat go viral. Many news organizations embedded social media posts that took Goldman's photo in stories about whether the Boston Celtics would recruit NBA star Kevin Durant with Brady's assistance. Breitbart, Heavy, Time, Yahoo, Vox Media, Gannett Company, Herald Media, Boston Globe Media Partners and New England Sports Network were defendants in the lawsuit,
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Let $\C$ be an $(n+2)$angulated category with shift functor $\Sigma$ and $\X$ be a clustertilting subcategory of $\C$. Then we show that the quotient category $\C/\X$ is an $n$abelian category. If $\C$ has a Serre functor, then $\C/\X$ is equivalent to an $n$cluster tilting subcategory of an abelian category $\textrm{mod}(\Sigma^{1}\X)$. Moreover, we also prove that $\textrm{mod}(\Sigma^{1}\X)$ is Gorenstein of Gorenstein dimension at most $n$. As an application, we generalize recent results of JacobsenJ{\o}rgensen and KoenigZhu.
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The contributions of scalars and fermions to the null polygonal bosonic Wilson loops/gluon MHV scattering amplitudes in $\mathcal{N} = 4$ SYM are considered. We first examine the resummation of scalars at strong coupling. Then, we disentangle the form of the fermion contribution and show its strong coupling expansion. In particular, we derive the leading order with the appearance of a fermionantifermion bound state first and then effective multiple bound states thereof. This reproduces the string minimal area result and also applies to the Nekrasov instanton partition function $\mathcal{Z}$ of the $\mathcal{N}=2$ theories. Especially, in the latter case the method appears to be suitable for a systematic expansion.
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For arbitrary radial weights $w$ and $u$, we study the integration operator between the growth spaces $H_w^\infty$ and $H_u^\infty$ on the complex plane. Also, we investigate the differentiation operator on the Hardy growth spaces $H_w^p$, $0<p<\infty$, defined on the unit disk or on the complex plane. As in the case $p=\infty$, the logconvex weights $w$ play a special role in the problems under consideration.
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We study the learnability of sums of independent integer random variables given a bound on the size of the union of their supports. For $\mathcal{A} \subset \mathbf{Z}_{+}$, a sum of independent random variables with collective support $\mathcal{A}$} (called an $\mathcal{A}$sum in this paper) is a distribution $\mathbf{S} = \mathbf{X}_1 + \cdots + \mathbf{X}_N$ where the $\mathbf{X}_i$'s are mutually independent (but not necessarily identically distributed) integer random variables with $\cup_i \mathsf{supp}(\mathbf{X}_i) \subseteq \mathcal{A}.$ We give two main algorithmic results for learning such distributions: 1. For the case $ \mathcal{A}  = 3$, we give an algorithm for learning $\mathcal{A}$sums to accuracy $\epsilon$ that uses $\mathsf{poly}(1/\epsilon)$ samples and runs in time $\mathsf{poly}(1/\epsilon)$, independent of $N$ and of the elements of $\mathcal{A}$. 2. For an arbitrary constant $k \geq 4$, if $\mathcal{A} = \{ a_1,...,a_k\}$ with $0 \leq a_1 < ... < a_k$,
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An anonymous reader quotes a report from Gizmodo: Scientists' models show that sound waves seem to travel too quickly through the old, stable cores of continents, called "cratons," which extend deep into the mantle at depths around 120 to 150 kilometers (75 to 93 miles). Through observations, experiments, and modeling, one team figured that a potential way to explain the sound speed anomaly would be the presence of a lot of diamonds, a medium that allows for a faster speed of sound than other crystals. Perhaps the Earth is as much as 2 percent diamonds by volume, they found. Scientists have modeled the rock beneath continents through tomography, which you can think of as like an xray image, but using sound waves. But soundwave velocities of around 4.7 kilometers per second (about 10,513 mph) are faster than soundwave velocities in other kinds of minerals beneath the crust, according to the paper in the journal Geochemistry, Geophysics, Geosystems. The researchers realized that if th
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Kim Zetter, reporting for Motherboard: The nation's top voting machine maker has admitted in a letter to a federal lawmaker that the company installed remoteaccess software on electionmanagement systems it sold over a period of six years, raising questions about the security of those systems and the integrity of elections that were conducted with them. In a letter sent to Sen. Ron Wyden (DOR) in April and obtained recently by Motherboard, Election Systems and Software acknowledged that it had "provided pcAnywhere remote connection software ... to a small number of customers between 2000 and 2006," which was installed on the electionmanagement system ES&S sold them. The statement contradicts what the company told me and fact checkers for a story I wrote for the New York Times in February. At that time, a spokesperson said ES&S had never installed pcAnywhere on any election system it sold. "None of the employees, â¦ including longtenured employees, has any knowled
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Last week, Apple announced new MacBook Pros, including a 15inch model that supports Intel's 6core 2.9GHz i9 processor. YouTube Dave Lee managed to get his hands on this topoftheline device early and run some tests, revealing that the laptop gets severely throttled due to thermal issues. 9to5Mac reports: Dave Lee this afternoon shared a new video on the Core i9 MacBook Pro he purchased, and according to his testing, the new machine is unable to maintain even its base clock speed after just a short time doing processor intensive work like video editing. "This CPU is an unlocked, overclockable chip but all of that CPU potential is wasted inside this chassis  or more so the thermal solution that's inside here," says Lee. He goes on to share some Premiere Pro render times that suggest the new 2018 MacBook Pro with Core i9 chip underperforms compared to a 2017 model with a Core i7 chip. It took 39 minutes for the 2018 MacBook Pro to render a video that the older model was able to rend
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Control and estimation on largescale social networks often necessitate the availability of models for the interactions amongst the agents in the network. However characterizing accurate models of social interactions pose new challenges due to their inherent complexity and unpredictability. Moreover, model uncertainty on the interaction dynamics becomes more pronounced for largescale networks. For certain classes of social networks, in the meantime, the layering structure allows a compositional approach for modeling as well as control and estimation. The layering can be induced in the network, for example, due to the presence of distinct social types and other indicators, such as geography and financial ties. In this paper, we present a compositional approach to determine performance guarantees on layered networks with inherent model uncertainties induced by the network. To this end, we use a factorization approach to determine robust stability and performance of the composite network
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Google has been hit with a recordbreaking â¬4.3 billion ($5 billion) fine by EU regulators for breaking antitrust laws. The European Commission says Google has abused its Android market dominance by bundling its search engine and Chrome apps into the operating system. Google has also allegedly blocked phone makers from creating devices that run forked versions of Android, and "made payments to certain large manufacturers and mobile network operators" to exclusively bundle the Google Search app on handsets. I'm okay with bundling applications, but I'm 100% opposed to large corporations like Google blocking competing companies from running forked versions of Android  allowed through Android's licensing  and wealthy corporations basically buying dominance by sending large sums of money to in this case carriers and manufacturers that smaller companies could never afford. That being said, I do feel like the way we determine what is and is not corporate behaviour damaging to c
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BrianFagioli shares a report from BetaNews: System76 has long been a Linux computer seller, but recently, it has transitioned into a Linux computer maker. What's the difference, you ask? Well, currently, the company doesn't really make its own computers. System76's laptops, for instance, are made by other manufacturers, which it rebrands as its own. No, System76 doesn't just slap its name on other company's laptops and ship them out the door. Actually, it works closely with the manufacturers, tweaks firmware, and verifies that both Ubuntu and its Ubuntubased Pop!_OS will work well on the hardware. System76 then offers topnotch support too. In other words, the company isn't just selling a computer, but an experience too. Unfortunately, when you rely on other computer manufacturers, you don't fully control the experience. Ultimately, System76 cannot achieve its true vision without building its own laptops. And so, that is exactly what it is going to do! Yes, System76 will be building
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We show that fractional Brownian motion(fBM) defined via Volterra integral representation with Hurst parameter $H\geq\frac{1}{2}$ is a quasisurely defined Wiener functional on classical Wiener space,and we establish the large deviation principle(LDP) for such fBM with respect to $(p,r)$capacity on classical Wiener space in Malliavin's sense.
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Recently knapsack problems have been generalized from the integers to arbitrary finitely generated groups. The knapsack problem for a finitely generated group $G$ is the following decision problem: given a tuple $(g, g_1, \ldots, g_k)$ of elements of $G$, are there natural numbers $n_1, \ldots, n_k \in \mathbb{N}$ such that $g = g_1^{n_1} \cdots g_k^{n_k}$ holds in $G$? Myasnikov, Nikolaev, and Ushakov proved that for every (Gromov)hyperbolic group, the knapsack problem can be solved in polynomial time. In this paper, the precise complexity of the knapsack problem for hyperbolic group is determined: for every hyperbolic group $G$, the knapsack problem belongs to the complexity class $\mathsf{LogCFL}$, and it is $\mathsf{LogCFL}$complete if $G$ contains a free group of rank two. Moreover, it is shown that for every hyperbolic group $G$ and every tuple $(g, g_1, \ldots, g_k)$ of elements of $G$ the set of all $(n_1, \ldots, n_k) \in \mathbb{N}^k$ such that $g = g_1^{n_1} \cdots g_k^{n_
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Over the last few months, it became clear that the battle over PEP 572 would be consequential; its scale and vehemence was largely unprecedented in the history of Python. The announcement by Guido van Rossum that he was stepping down from his role as benevolent dictator for life (BDFL), due in part to that battle, underscored the importance of it. While the Python project charts its course in the wake of his resignation, it makes sense to catch up on where things stand with this contentious PEP now that has now been accepted for Python 3.8.
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Security updates have been issued by Arch Linux (curl, lib32curl, lib32libcurlcompat, lib32libcurlgnutls, libcurlcompat, and libcurlgnutls), Debian (blender, ffmpeg, and wordpress), Fedora (curl), Gentoo (tqdm), Oracle (kernel), Slackware (mutt), SUSE (xen), and Ubuntu (policykit1).
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We explain a new phenomenon on non compact complete Riemannian four manifolds, where d^+ image of one forms can not exhaust densely on L^2 self dual forms on each compact subset, if a certain L^2 self dual harmonic form exists. This leads to construct a new functional analytic framework on the SeibergWitten map.
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Approximately regularized minimizer of the least squares functional with a nonsmooth, convex penalty term and an indicator function is considered to be produced iteratively by some nested primaldual algorithm. The algorithm is a proximalgradient linesearch based iterative procedure and is introduced as an iterative variational regularization method. Under the consideration of that the exact solution for the linear illposed inverse problem satisfies a variational source condition (VSC), convergence of the regularized solution of the minimization problem to the exact solution, and convergence of the iteratively regularized approximate minimizer by our primaldual algorithm to the exact solution are analysed separately. It is in the emphasis of this work that the regularization parameter obeys {\em Morozov`s discrepancy principle} (MDP) in order for the stability analysis of regularized solution. Furthermore, stability analysis of the algorithm requires us to define the additional par
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In order to actually do anything, a kernel module must gain access to functions and data structures in the rest of the kernel. Enabling and controlling that access is the job of the symbolexport mechanism. While the enabling certainly happens, the control part is not quite so clear; many developers view the nearly 30,000 symbols in current kernels that are available to all modules as being far too many. The symbol namespaces patch set from Martijn Coenen doesn't reduce that number, but it does provide a mechanism that might help to impose some order on exported symbols in general.
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