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This paper contributes to the mean dimension theory of dynamical systems. We introduce a new concept called mean dimension with potential and develop a variational principle for it. This is a mean dimension analogue of the theory of topological pressure. We consider a minimax problem for the sum of rate distortion dimension and the integral of a potential function. We prove that the minimax value is equal to the mean dimension with potential for a dynamical system having the marker property. The basic idea of the proof is a dynamicalization of geometric measure theory.
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We develop a variational principle between mean dimension theory and rate distortion theory. We consider a minimax problem about the rate distortion dimension with respect to two variables (metrics and measures). We prove that the minimax value is equal to the mean dimension for a dynamical system with the marker property. The proof exhibits a new combination of ergodic theory, rate distortion theory and geometric measure theory. Along the way of the proof, we also show that if a dynamical system has the marker property then it has a metric for which the upper metric mean dimension is equal to the mean dimension.
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The early Android Q leaked build we have obtained was built just this week with the February 2019 security patches, and it’s uptodate with Google’s AOSP internal master. That means it has a ton of new Android platform features that you won’t find anywhere publicly, but there are no Google Pixel software customizations nor are there preinstalled Google Play apps or services so I don’t have any new information to share on those fronts. Still, there’s a lot to digest here, so we’ve flashed the build on the Pixel 3 XL to find out what’s new—both on the surfacelevel and underthehood. This article will focus on all the surfacelevel changes we’ve found in Android Q. There’s a lot of good stuff in here, most notably a complete redesign of the permissions user interface, as well as even stricter limitations on what applications can do, such as only granting certain permissions while the application in question is in use. There’s also a systemwide dark mode, hints of a DeXli
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The incompressible NavierStokes (NS) equation is known to govern the hydrodynamic limit of essentially any fluid and its rich nonlinear structure has critical implications in both mathematics and physics. The employability of the methods of Riemannian geometry to the study of hydrodynamical flows has been previously explored from a purely mathematical perspective. In this work, we propose a bulk metric in $(p+2)$dimensions with the construction being such that the induced metric is flat on a timelike $r = r_c$ (constant) slice. We then show that the equations of {\it parallel transport} for an appropriately defined bulk velocity vector field along its own direction on this manifold when projected onto the flat timelike hypersurface requires the satisfaction of the incompressible NS equation in $(p+1)$dimensions. Additionally, the incompressibility condition of the fluid arises from a vanishing expansion parameter $\theta$, which is known to govern the convergence (or divergence) of
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We study the eigenvalues of the Kohn Laplacian on a closed embedded strictly pseudoconvex CR manifold as functionals on the set of positive oriented contact forms $\mathcal{P}_+$. We show that the functionals are continuous with respect to a natural topology on $\mathcal{P}_+$. Using a simple adaptation of the standard KatoRellich perturbation theory, we prove that the functionals are (onesided) differentiable along 1parameter analytic deformations. We use this differentiability to define the notion of critical contact forms, in a generalized sense, for the functionals. We give a necessary (also sufficient in some situations) condition for a contact form to be critical. Finally, we present explicit examples of critical contact form on both homogeneous and nonhomogeneous CR manifolds.
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CERN wants to build a particle collider that’s four times bigger than the
0116 MIT Technology 13103 
We’re excited to announce that map and addressrelated searches on DuckDuckGo for mobile and desktop are now powered by Apple’s MapKit JS framework, giving you a valuable combination of mapping and privacy. As one of the first global companies using Apple MapKit JS, we can now offer users improved address searches, additional visual features, enhanced satellite imagery, and continually updated maps already in use on billions of Apple devices worldwide. With this updated integration, Apple Maps are now available both embedded within our private search results for relevant queries, as well as available from the “Maps” tab on any search result page. I’m sure Apple users in San Francisco will be very happy with this news. For me, this means there’s no way I’ll be using DuckDuckGo’s location search and other mapping functions – Apple Maps is entirely unusable in The Netherlands, with severely outdated and faulty maps that are outright da
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An advisory from Harry Sintonen describes several vulnerabilities in the scp clients shipped with OpenSSH, PuTTY, and others. "Many scp clients fail to verify if the objects returned by the scp server match those it asked for. This issue dates back to 1983 and rcp, on which scp is based. A separate flaw in the client allows the target directory attributes to be changed arbitrarily. Finally, two vulnerabilities in clients may allow server to spoof the client output." The outcome is that a hostile (or compromised) server can overwrite arbitrary files on the client side. There do not yet appear to be patches available to address these problems.
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A new program at DARPA is aimed at creating a machine learning system that can sift through the innumerable events and pieces of media generated every day and identify any threads of connection or narrative in them. It's called KAIROS: Knowledgedirected Artificial Intelligence Reasoning Over Schemas. From a report: "Schema" in this case has a very specific meaning. It's the idea of a basic process humans use to understand the world around them by creating little stories of interlinked events. For instance when you buy something at a store, you know that you generally walk into the store, select an item, bring it to the cashier, who scans it, then you pay in some way, and then leave the store. This "buying something" process is a schema we all recognize, and could of course have schemas within it (selecting a product; payment process) or be part of another schema (gift giving; home cooking). Although these are easily imagined inside our heads, they're surprisingly difficult to define
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Dealmaster: Take $20 off an Xbox One Wireless Controller for your Xbox or P
0109 Ars Technica 13075 
Emerging research on digital hoarding  a reluctance to get rid of the digital clutter we accumulate through our work and personal lives  suggests that it can make us feel just as stressed and overwhelmed as physical clutter. From a report: Not to mention the cybersecurity problems it can cause for individuals and businesses and the way it makes finding that one email you need sometimes seem impossible. The term digital hoarding was first used in 2015 in a paper about a man in the Netherlands who took several thousand digital photos each day and spent hours processing them. "He never used or looked at the pictures he had saved, but was convinced that they would be of use in the future," wrote the authors. In a study published earlier this year Neave and his colleagues asked 45 people about how they deal with emails, photos, and other files. The reasons people gave for hanging on to their digital effects varied  including pure laziness, thinking something might come in handy, anx
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Google has removed 85 Android apps from the official Play Store that security researchers from Trend Micro deemed to contain a common strain of adware. "The 85 apps had been downloaded over nine million times, and one app, in particular, named 'Easy Universal TV Remote,' was downloaded over five million times," reports ZDNet. From the report: While the apps were uploaded on the Play Store from different developer accounts and were signed by different digital certificates, they exhibited similar behaviors and shared the same code, researchers said in a report published today. But besides similarities in their source code, the apps were also visually identical, and were all of the same types, being either games or apps that let users play videos or control their TVs remotely. The first time users ran any of the apps, they would proceed to show fullscreen ads in different steps, asking and reasking users to press various buttons to continue. If the user was persistent and stayed with the
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Ryne Hager, writing for AndroidPolice: Late last year, Google decided it was time to crack down on apps requesting SMS and call log permissions. Ostensibly, exceptions would be granted for categories including backups and automation, but as of now, there are still gaps which cover legitimate use cases. While some popular apps like Tasker have successfully secured exemptions, others like Cerberus have not. Instead, they've decided to strip out those permissions or risk facing the wrath of Google's upcoming January 9th banhammer, killing associated functionality and disappointing millions of longtime users to adhere to the Play Store's new policy. The Play Console support page for the applicable set of permissions notifies developers that they can submit what is effectively an application for an exemption, categories for which are listed on the same page. (And that list of exceptions has grown since the original announcement.) Nonetheless, a further set of prohibitions are also includ
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Let $\xi : \Omega \times \mathbb{R}^n \to \mathbb{R}$ be zero mean, meansquare continuous, stationary, isotropic Gaussian random field with covariance function $r(x) = \mathbb{E}[\xi(0)\xi(x)]$ and let $G : \mathbb{R} \to \mathbb{R}$ such that $G$ is square integrable with respect to the standard Gaussian measure and is of Hermite rank $d$. The BreuerMajor theorem in it's continuous setting gives that, if $r \in L^d(\mathbb{R}^n)$ and $r(x) \to 0$ as $x \to \infty$, then the finite dimensional distributions of $Z_s(t) = \frac{1}{(2s)^{n/2}} \int_{[st^{1/n},st^{1/n}]^n} \Big[G(\xi(x))  \mathbb{E}[G(\xi(x))]\Big]dx$ converge to that of a scaled Brownian motion as $s \to \infty$. Here we give a proof for the case when $\xi : \Omega \times \mathbb{R}^n \to \mathbb{R}^m$ is a random vector field. We also give conditions for the functional convergence in $C([0,\infty))$ of $Z_s$ to hold along with expression for the asymptotic variance of the second chaos component in the Wiener chaos
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We investigate the problem of covert and secret key generation over a discrete memoryless channel model with one way public discussion and in presence of an active warden who can arbitrarily vary its channel and tamper with the main channel when an information symbol is sent. In this scenario, we develop an adaptive protocol that is required to conceal not only the key but also whether a protocol is being implemented. Based on the adversary's actions, this protocol generates a key whose size depends on the adversary's actions. Moreover, for a passive adversary and for some models that we identify, we show that covert secret key generation is possible and characterize the covert secret key capacity in special cases; in particular, the covert secret key capacity is sometimes equal to the covert capacity of the channel, so that secrecy comes ``for free.
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Deep neural networks have become stateoftheart technology for a wide range of practical machine learning tasks such as image classification, handwritten digit recognition, speech recognition, or game intelligence. This paper develops the fundamental limits of learning in deep neural networks by characterizing what is possible if no constraints on the learning algorithm and the amount of training data are imposed. Concretely, we consider informationtheoretically optimal approximation through deep neural networks with the guiding theme being a relation between the complexity of the function (class) to be approximated and the complexity of the approximating network in terms of connectivity and memory requirements for storing the network topology and the associated quantized weights. The theory we develop educes remarkable universality properties of deep networks. Specifically, deep networks are optimal approximants for vastly different function classes such as affine systems and Gabor
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The first main result of this article is to prove the convergence of Lott's delocalized eta invariant holds for all invertible operators. Our second main result is to construct a pairing between delocalized cyclic cocycles of the group algebra of the fundamental group of a manifold and Ktheoretic higher rho invariants of the manifold, when the fundamental group is hyperbolic. As an application, under the assumption of hyperbolicity of the fundamental group, we compute the delocalized part of the ConnesChern character of AtiyahPatodiSinger type Ktheoretic higher indices, for example, the higher index of a spin manifold with boundary where the boundary carries a positive scalar curvature metric. Our explicit formula for this delocalized ConnesChern character is expressed in terms of our pairing of delocalized cyclic cocycles and higher rho invariants on the boundary of manifold.
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This paper presents a finite difference quasiNewton method for the minimization of noisy functions. The method takes advantage of the scalability and power of BFGS updating, and employs an adaptive procedure for choosing the differencing interval $h$ based on the noise estimation techniques of Hamming (2012) and Mor\'e and Wild (2011). This noise estimation procedure and the selection of $h$ are inexpensive but not always accurate, and to prevent failures the algorithm incorporates a recovery mechanism that takes appropriate action in the case when the line search procedure is unable to produce an acceptable point. A novel convergence analysis is presented that considers the effect of a noisy line search procedure. Numerical experiments comparing the method to a function interpolating trust region method are presented.
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The class ${\sf IV}_2$ of $2$nondegenerate constant Levi rank $1$ hypersurfaces $M^5 \subset \mathbb{C}^3$ is governed by Pocchiola's two primary invariants $W_0$ and $J_0$. Their vanishing characterizes equivalence of such a hypersurface $M^5$ to the tube $M_{\sf LC}^5$ over the real light cone in $\mathbb{R}^3$. When either $W_0 \not\equiv 0$ or $J_0 \not\equiv 0$, by normalization of certain two group parameters ${\sf c}$ and ${\sf e}$, an invariant coframe can be built on $M^5$, showing that the dimension of the CR automorphism group drops from $10$ to $5$. This paper constructs an explicit $\{e\}$structure in case $W_0$ and $J_0$ do not necessarily vanish. Furthermore, Pocchiola's calculations hidden on a computer now appear in details, especially the determination of a secondary invariant $R$, expressed in terms of the first jet of $W_0$. All other secondary invariants of the $\{e\}$structure are also expressed explicitly in terms of $W_0$ and $J_0$.
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Distributed changepoint detection has been a fundamental problem when performing realtime monitoring using sensornetworks. We propose a distributed detection algorithm, where each sensor only exchanges CUSUM statistic with their neighbors based on the average consensus scheme, and an alarm is raised when local consensus statistic exceeds a prespecified global threshold. We provide theoretical performance bounds showing that the performance of the fully distributed scheme can match the centralized algorithms under some mild conditions. Numerical experiments demonstrate the good performance of the algorithm especially in detecting asynchronous changes.
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Distributionally robust optimization (DRO) has been introduced for solving stochastic programs where the distribution of the random parameters is unknown and must be estimated by samples from that distribution. A key element of DRO is the construction of the ambiguity set, which is a set of distributions that covers the true distribution with a high probability. Assuming that the true distribution has a probability density function, we propose a class of ambiguity sets based on confidence bands of the true density function. The use of the confidence band enables us to take the prior knowledge of the shape of the underlying density function into consideration (e.g., unimodality or monotonicity). Using the confidence band constructed by density estimation techniques as the ambiguity set, we establish the convergence of the optimal value of DRO to that of the stochastic program as the sample size increases. However, the resulting DRO problem is computationally intractable, as it involves
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We propose a family of stochastic volatility models that enable direct estimation of timevarying extreme event probabilities in time series with nonlinear dependence and power law tails. The models are a white noise process with conditionally logLaplace stochastic volatility. In contrast to other, similar stochastic volatility formalisms, this process has an explicit, closedform expression for its conditional probability density function, which enables straightforward estimation of dynamically changing extreme event probabilities. The process and volatility are conditionally Paretotailed, with tail exponent given by the reciprocal of the logvolatility's mean absolute innovation. These models thus can accommodate conditional power lawtail behavior ranging from very weakly nonGaussian to Cauchylike tails. Closedform expressions for the models' conditional polynomial moments also allows for volatility modeling. We provide a straightforward, probabilistic methodofmoments estimat
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We address dissipative soliton formation in modulated PTsymmetric continuous waveguide arrays composed from waveguides with amplifying and absorbing sections, whose density gradually increases (due to decreasing waveguide separation) either towards the center of the array or towards its edges. In such a structure the level of gain/loss at which PTsymmetry gets broken depends on the direction of increase of the waveguide density. Breakup of the PTsymmetry occurs when eigenvalues of modes localized in the region, where waveguide density is largest, collide and move into complex plane. In this regime of broken symmetry the inclusion of focusing Kerrtype nonlinearity of the material and weak twophoton absorption allows to arrest the growth of amplitude of amplified modes and may lead to the appearance of stable attractors either in the center or at the edge of the waveguide array, depending on the type of array modulation. Such solitons can be stable, they acquire specific triangular
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We investigate the number of permutations that occur in random labellings of trees. This is a generalisation of the number of subpermutations occurring in a random permutation. It also generalises some recent results on the number of inversions in randomly labelled trees. We consider complete binary trees as well as random split trees a large class of random trees of logarithmic height introduced by Devroye in 1998. Split trees consist of nodes (bags) which can contain balls and are generated by a random trickle down process of balls through the nodes. For complete binary trees we show that asymptotically the cumulants of the number of occurrences of a fixed permutation in the random node labelling have explicit formulas. Our other main theorem is to show that for a random split tree, with high probability the cumulants of the number of occurrences are asymptotically an explicit parameter of the split tree. For the proof of the second theorem we show some results on the number of embed
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We are interested in the Guivarc'h inequality for admissible random walks on finitely generated relatively hyperbolic groups, endowed with a word metric. We show that for random walks with finite superexponential moment, if this inequality is an equality, then the Green distance is roughly similar to the word distance, generalizing results of Blach{\`e}re, Ha{\"i}ssinsky and Mathieu for hyperbolic groups [4]. Our main application is for relatively hyperbolic groups with respect to virtually abelian subgroups of rank at least 2. We show that for such groups, the Guivarc'h inequality with respect to a word distance and a finitely supported random walk is always strict.
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We provide a rigorous, explicit formula for the vacuum relative entropy of a coherent state on wedge local von Neumann algebras associated with a free, neutral quantum field theory on the Minkowski spacetime of arbitrary spacetime dimension. The second derivative under a null translation turns out to be manifestly nonnegative being proportional to an energy contribution on the boundary.
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In this paper, we construct a complete ndim Riemannian manifold with positive Ricci curvature, quadratically nonnegatively curved infinity and infinite topological type. This gives a negative answer to a conjecture by Jiping Sha and Zhongmin Shen in the case of n greater than or equal to 6.
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Polynomial generalizations of all 130 of the identities in Slater's list of identities of the RogersRamanujan type are presented. Furthermore, duality relationships among many of the identities are derived. Some of the these polynomial identities were previously known but many are new. The author has implemented much of the finitization process in a Maple package which is available for free download from the author's website.
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This is a sequel to the authors' article [BKO]. We consider a hyperbolic knot $K$ in a closed 3manifold $M$ and the cotangent bundle of its complement $M \setminus K$. We equip a hyperbolic metric $h$ with $M \setminus K$ and the induced kinetic energy Hamiltonian $H_h = \frac{1}{2} p_h^2$ and Sasakian almost complex structure $J_h$ with the cotangent bundle $T^*(M \setminus K)$. We consider the conormal $\nu^*T$ of a horotorus $T$, i.e., the cusp crosssection given by a level set of the Busemann function in the cusp end and maps $u: (\Sigma, \partial \Sigma) \to (T^*(M \setminus K), \nu^*T)$ converging to a \emph{nonconstant} Hamiltonian chord of $H_h$ at each puncture of $\Sigma$, a boundarypunctured open Riemann surface of genus zero with boundary. We prove that all nonconstant Hamiltonian chords are transversal and of Morse index 0 relative to the horotorus $T$. As a consequence, we prove that $\widetilde{\mathfrak m}^k = 0$ unless $k \neq 2$ and an $A_\infty$algebra asso
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The general theory developed by Ben Yaacov for metric structures provides Fra\"iss\'e limits which are approximately ultrahomogeneous. We show here that this result can be strengthened in the case of relational metric structures. We give an extra condition that guarantees exact ultrahomogenous limits. The condition is quite general. We apply it to stochastic processes, the class of diversities, and its subclass of $L_1$ diversities.
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Peng and Zhong (Acta Math Sci {\bf37B(1)}:6978, 2017) introduced and studied a new subclass of analytic functions as follows: \begin{equation*} \Omega:=\left\{f\in \mathcal{A}:\leftzf'(z)f(z)\right<\frac{1}{2}, z\in \Delta\right\}, \end{equation*} where $\mathcal{A}$ is the class of analytic and normalized functions and $\Delta$ is the open unit disc on the complex plane. The class $\Omega$ is a subclass of the starlike univalent functions. In this paper, we obtain some new results for the class $\Omega$ and improve some results that earlier obtained by Peng and Zhong.
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We give two general transformations that allows certain quite general basic hypergeometric multisums of arbitrary depth (sums that involve an arbitrary sequence $\{g(k)\}$), to be reduced to an infinite $q$product times a single basic hypergeometric sum. Various applications are given, including summation formulae for some $q$ orthogonal polynomials, and various multisums that are expressible as infinite products.
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For an arbitrary prime number $p$, we propose an action for bosonic $p$adic strings in curved target spacetime, and show that the vacuum Einstein equations of the target are a consequence of worldsheet scaling symmetry of the quantum $p$adic strings, similar to the ordinary bosonic strings case. It turns out that certain $p$adic automorphic forms are the plane wave modes of the bosonic fields on $p$adic strings, and that the regularized normalization of these modes on the $p$adic worldsheet presents peculiar features which reduce part of the computations to familiar setups in quantum field theory, while also exhibiting some new features that make loop diagrams much simpler. Assuming a certain product relation, we also observe that the adelic spectrum of the bosonic string corresponds to the nontrivial zeros of the Riemann Zeta function.
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Let $f$ be the infinitesimal generator of a oneparameter semigroup $\left\{ F_{t}\right\} _{t\ge0}$ of holomorphic selfmappings of the open unit disk $\Delta$. In this paper we study properties of the family $R$ of resolvents $(I+rf)^{1}:\Delta\to\Delta~ (r\ge0)$ in the spirit of geometric function theory. We discovered, in particular, that $R$ forms an inverse L\"owner chain of hyperbolically convex functions. Moreover, each element of $R$ satisfies the NoshiroWarschawski condition and is a starlike function of order at least $\frac12$,. This, in turn, implies that each element of $R$ is also a holomorphic generator. We mention also quasiconformal extension of an element of $R.$ Finally we study the existence of repelling fixed points of this family.
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We study a natural generalization of inverse systems of finite regular covering spaces. A limit of such a system is a fibration whose fibres are profinite topological groups. However, as shown in a previous paper (ConnerHerfortPavesic: Some anomalous examples of lifting spaces), there are many fibrations whose fibres are profinite groups, which are far from being inverse limits of coverings. We characterize profinite fibrations among a large class of fibrations and relate the profinite topology on the fundamental group of the base with the action of the fundamental group on the fibre, and develop a version of the Borel construction for fibrations whose fibres are profinite groups.
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We classify global bifurcations in generic oneparameter local families of \vfs on $S^2$ with a parabolic cycle. The classification is quite different from the classical results presented in monographs on the bifurcation theory. As a by product we prove that generic families described above are structurally stable.
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Google Drive has a pretty bad spam problem, and it seems Google doesn't care. Spammers can share files that automatically appear in your Drive, and there's no way to stop it. From a report: Google Drive's sharing system is the problem. Since it doesn't offer any sharing acceptance, all files and folders shared with your account are automatically available to you in Drive  they just show up. To make matters worse, if you only have "View" permission, you can't remove yourself from the share. It's a mess. And to make matters even worse, this is far from a new problem, but Google still hasn't done anything to fix it. Google got back to us with a statement saying that changes are coming to Drive's sharing features and they're"making it a priority." Here's the statement in full: "For the vast majority of users, the default sharing permissions in Drive work as intended. Unfortunately, this was not the case for this user and we sincerely apologize for her experience. In light of this issue
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Why is Grindr being sued by Matthew Herrick, an aspiring actor working in a restaurant in New York? "His former partner created fake profiles on the app to impersonate Herrick and then direct men to show up at Herrick's home and the restaurant where he worked asking for sex, sometimes more than a dozen times per day." But 14 police reports later, Herrick's lawsuit is now arguing that all tech companies should face greater accountability for what happens on their platforms, reports NBC News: His lawsuit alleges that the software developers who write code for Grindr have been negligent, producing an app that's defective in its design and that is "fundamentally unsafe" and "unreasonably dangerous"  echoing language that's more typically used in lawsuits about, say, a faulty kitchen appliance or a defective car part. If successful, the lawsuit could bring about a significant legal change to the risks tech companies face for what happens on their platforms, adding to growing public and p
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We investigate a parabolicelliptic system for maps $(u,v)$ from a compact Riemann surface $M$ into a Lorentzian manifold $N\times{\mathbb{R}}$ with a warped product metric. That system turns the harmonic map type equations into a parabolic system, but keeps the $v$equation as a nonlinear second order constraint along the flow. We prove a global existence result of the parabolicelliptic system by assuming either some geometric conditions on the target Lorentzian manifold or small energy of the initial maps. The result implies the existence of a Lorentzian harmonic map in a given homotopy class with fixed boundary data.
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This paper presents a nonlinear stability analysis for dcmicrogrids in both, interconnected mode and island operation with primary control. The proposed analysis is based on the fact that the dynamical model of the grid is a gradient system generated by a strongly convex function. The stability analysis is thus reduced to a series of convex optimization problems. The proposed method allows to: i) demonstrate the existence and uniqueness of the equilibrium ii) calculate this equilibrium numerically iii) give conditions for global stability using a Lyapunov function iv) estimate the attraction region. Previous works only address one of these aspects. Numeric calculations performed in cvx and simulations results in Matlab complement the analysis and demonstrate how to use this theoretical results in practical problems.
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A novel linear combination representation aided timedomain smooth signal design is proposed by continuityenhanced basis signals for the Ncontinuous orthogonal frequency division multiplexing (NCOFDM) system. Compared to the conventional NCOFDM, the proposed scheme is capable of reducing the interference and maintaining the same sidelobe suppression performance imposed with the aid of two groups of basis signals assisted by the linear combination form. Our performance results demonstrate that with a low complexity overhead, the proposed scheme is capable of improving the error performance in comparison to the conventional NCOFDM, while maintaining the same sidelobe suppression as the conventional counterpart.
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It is known that Hochschild cohomology groups are represented by crossed extensions of associative algebras. In this paper, we introduce crossed $n$fold extensions of a Lie algebra $\mathfrak{g}$ by a module $M$, for $n \geq 2$. The equivalence classes of such extensions are represented by the $(n+1)$th ChevalleyEilenberg cohomology group $H^{n+1}_{CE} (\mathfrak{g}, M).$
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We establish a duality for two factorization questions, one for general positive definite (p.d) kernels $K$, and the other for Gaussian processes, say $V$. The latter notion, for Gaussian processes is stated via Itointegration. Our approach to factorization for p.d. kernels is intuitively motivated by matrix factorizations, but in infinite dimensions, subtle measure theoretic issues must be addressed. Consider a given p.d. kernel $K$, presented as a covariance kernel for a Gaussian process $V$. We then give an explicit duality for these two seemingly different notions of factorization, for p.d. kernel $K$, vs for Gaussian process $V$. Our result is in the form of an explicit correspondence. It states that the analytic data which determine the variety of factorizations for $K$ is the exact same as that which yield factorizations for $V$. Examples and applications are included: pointprocesses, sampling schemes, constructive discretization, graphLaplacians, and boundaryvalue problems.
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The FBI has shut down the domains of 15 highprofile distributed denialofservice (DDoS) websites. "Several seizure warrants granted by a California federal judge went into effect Thursday, removing several of these 'border' or 'stresser' sites off the internet 'as part of coordinated law enforcement action taken against illegal DDoSforhire services,'" reports TechCrunch. "The orders were granted under federal seizure laws, and the domains were replaced with a federal notice." From the report: Prosecutors have charged three men, Matthew Gatrel and Juan Martinez in California and David Bukoski in Alaska, with operating the sites, according to affidavits filed in three U.S. federal courts, which were unsealed Thursday. The FBI had assistance from the U.K.'s National Crime Agency and the Dutch national police, and the Justice Department named several companies, including Cloudflare, Flashpoint and Google, for providing authorities with additional assistance. In all, several sites were
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Videos and pictures of children being subjected to sexual abuse are being openly shared on Facebook's WhatsApp on a vast scale, with the encrypted messaging service failing to curb the problem despite banning thousands of accounts every day. From a report: Without the necessary number of human moderators, the disturbing content is slipping by WhatsApp's automated systems. A report reviewed by TechCrunch from two Israeli NGOs details how thirdparty apps for discovering WhatsApp groups include "Adult" sections that offer invite links to join rings of users trading images of child exploitation. TechCrunch has reviewed materials showing many of these groups are currently active. TechCrunch's investigation shows that Facebook could do more to police WhatsApp and remove this kind of content. Even without technical solutions that would require a weakening of encryption, WhatsApp's moderators should have been able to find these groups and put a stop to them. Groups with names like "child po
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A former Microsoft intern has revealed details of a YouTube incident that has convinced some Edge browser engineers that Google added code to purposely break compatibility. In a post on Hacker News, Joshua Bakita, a former software engineering intern at Microsoft, lays out details and claims about an incident earlier this year. Microsoft has since announced the company is moving from the EdgeHTML rendering engine to the open source Chromium project for its Edge browser. Google disputes Bakita's claims, and says the YouTube blank div was merely a bug that was fixed after it was reported. "YouTube does not add code designed to defeat optimizations in other browsers, and works quickly to fix bugs when they're discovered," says a YouTube spokesperson in a statement to The Verge. "We regularly engage with other browser vendors through standards bodies, the Web Platform Tests project, the opensource Chromium project and more to improve browser interoperability." While we're unli
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Chinese hackers allegedly stole data of more than 100,000 US Navy personnel
1221 MIT Technology 13251Effective resource allocation plays a pivotal role for performance optimization in wireless networks. Unfortunately, typical resource allocation problems are mixedinteger nonlinear programming (MINLP) problems, which are NPhard in general. Machine learningbased methods recently emerge as a disruptive way to obtain nearoptimal performance for MINLP problems with affordable computational complexity. However, a key challenge is that these methods require huge amounts of training samples, which are difficult to obtain in practice. Furthermore, they suffer from severe performance deterioration when the network parameters change, which commonly happens and can be characterized as the task mismatch issue. In this paper, to address the sample complexity issue, instead of directly learning the inputoutput mapping of a particular resource allocation algorithm, we propose a Learning to Optimize framework for Resource Allocation, called LORA, that learns the pruning policy in the optimal bran
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Last night, Elon Musk unveiled his vision of a highspeed tunnel system he believes could ease congestion and revolutionize how millions of commuters get around cities. CNBC reports: Musk, who founded the Boring Co. two years ago after complaining that traffic in Los Angeles was driving him "nuts," says the demonstration tunnel cost approximately $10 million to complete. Engineers and workers have been boring the 1.14milelong tunnel underneath one of the main streets in Hawthorne, California. One end of the tunnel starts in a parking lot owned by Musk's Space X. The other end of the demonstration tunnel is in a neighborhood about a mile away in Hawthorne. Tuesday afternoon, the Boring Co. gave reporters demonstration rides through the tunnel in modified Tesla Model X SUVs, going between 40 and 50 miles per hour. Engineers have attached deployable alignment wheels to the two front wheels of the Model X. Those alignment wheels stick out to the side of the main wheels and act as a bumpe
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The extension of persistent homology to multiparameter setups is an algorithmic challenge. Since most computation tasks scale badly with the size of the input complex, an important preprocessing step consists of simplifying the input while maintaining the homological information. We present an algorithm that drastically reduces the size of an input. Our approach is an extension of the chunk algorithm for persistent homology (Bauer et al., Topological Methods in Data Analysis and Visualization III, 2014). We show that our construction produces the smallest multifiltered chain complex among all the complexes quasiisomorphic to the input, improving on the guarantees of previous work in the context of discrete Morse theory. Our algorithm also offers an immediate parallelization scheme in shared memory. Already its sequential version compares favorably with existing simplification schemes, as we show by experimental evaluation.
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In this paper the relation between the cluster integrable systems and $q$difference equations is extended beyond the Painlev\'e case. We consider the class of hyperelliptic curves when the Newton polygons contain only four boundary points. The corresponding cluster integrable Toda systems are presented, and their discrete automorphisms are identified with certain reductions of the Hirota difference equation. We also construct nonautonomous versions of these equations and find that their solutions are expressed in terms of 5d Nekrasov functions with the ChernSimons contributions, while in the autonomous case these equations are solved in terms of the Riemann thetafunctions.
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We introduce the notion of a symplectic capacity relative to a coisotropic submanifold of a symplectic manifold, and we construct two examples of such capacities through modifications of the HoferZehnder capacity. As a consequence, we obtain a nonsqueezing theorem for symplectic embeddings relative to coisotropic constraints and existence results for leafwise chords on energy surfaces.
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We provide the missing member of a family of four $q$series identities related to the modulus 36, the other members having been found by Ramanujan and Slater. We examine combinatorial implications of the identities in this family, and of some of the identities we considered in "Identities of the RamanujanSlater type related to the moduli 18 and 24," [\emph{J. Math. Anal. Appl.} \textbf{344}/2 (2008) 765777].
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