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Great reporting by TechCrunch’s Josh Constine: Desperate for data on its competitors, Facebook has been secretly paying people to install a “Facebook Research” VPN that lets the company suck in all of a user’s phone and web activity, similar to Facebook’s Onavo Protect app that Apple banned in June and that was removed in August. Facebook sidesteps the App Store and rewards teenagers and adults to download the Research app and give it root access in what may be a violation of Apple policy so the social network can decrypt and analyze their phone activity, a TechCrunch investigation confirms. Facebook admitted to TechCrunch it was running the Research program to gather data on usage habits, and it has no plans to stop. Since 2016, Facebook has been paying users ages 13 to 35 up to $20 per month plus referral fees to sell their privacy by installing the iOS or Android “Facebook Research” app. Facebook even asked users to screenshot their Amazon order history page. The program is ad
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Firefox 65.0 is out. The release notes list a few new features, including: "Enhanced tracking protection: Simplified content blocking settings give users standard, strict, and custom options to control online trackers. A redesigned content blocking section in the site information panel (viewed by expanding the small “i” icon in the address bar) shows what Firefox detects and blocks on each website you visit."
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Astronomers have spotted a small first-of-its-kind object in the Kuiper Bel
01-29 MIT Technology 7448 -
An anonymous reader shares a report: It seems the stuff of fantasy. Giant ships sail the seas burning fuel that has been extracted from water using energy provided by the winds, waves and tides. A dramatic but implausible notion, surely. Yet this grand green vision could soon be realised thanks to a remarkable technological transformation that is now under way in Orkney. Perched 10 miles beyond the northern edge of the British mainland, this archipelago of around 20 populated islands -- as well as a smattering of uninhabited reefs and islets -- has become the centre of a revolution in the way electricity is generated. Orkney was once utterly dependent on power that was produced by burning coal and gas on the Scottish mainland and then transmitted through an undersea cable. Today the islands are so festooned with wind turbines, they cannot find enough uses for the emission-free power they create on their own. Community-owned wind turbines generate power for local villages; islanders d
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China may be slowing iPhone sales worldwide, but Chinese people are driving Apple's App Store business. From a report: China accounted for nearly 50 percent of all app downloads in 2018, pushing the global downloads count to reach a record 194 billion, according to research firm App Annie. China, which is the world's largest smartphone market, also accounted for nearly 40 percent of worldwide consumer spend in apps in 2018, App Annie said in its yearly "State of Mobile" report. (Note: Google Play Store is not available in China.) Global consumer spend in apps reached $101 billion last year, up 75 percent since 2016. And 74 percent of all money spent on apps last year came from games. The battle between Silicon Valley companies and Chinese tech giants generated more than half of total consumer spend in the top 300 parent companies in 2018, the report said. The top company for global consumer spend was China's Tencent, which owns stake in several startups, companies, and games -- includi
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A federal appeals court denied the FCC's request to postpone oral arguments in a court battle over the agency's decision to repeal its net neutrality rules. The FCC had asked for the hearing to be postponed since the commission's workforce has largely been furloughed due to the partial government shutdown. The hearing remains set for February 1. The Hill reports: After the FCC repealed the rules requiring internet service providers to treat all web traffic equally in December of 2017, a coalition of consumer groups and state attorneys general sued to reverse the move, arguing that the agency failed to justify it. The FCC asked the three-judge panel from the D.C. Circuit Court of Appeals to delay oral arguments out of "an abundance of caution" due to its lapse of funding. Net neutrality groups opposed the motion, arguing that there is an urgent need to settle the legal questions surrounding the FCC's order.
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We investigate various block preconditioners for a low-order Raviart-Thomas discretization of the mixed Poisson problem on adaptive quadrilateral meshes. In addition to standard diagonal and Schur complement preconditioners, we present a dedicated AMG solver for saddle point problems (SPAMG). A key element is a stabilized prolongation operator that couples the flux and scalar components. Our numerical experiments in 2D and 3D show that the SPAMG preconditioner displays nearly mesh-independent iteration counts for adaptive meshes and heterogeneous coefficients.
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For a cyclic covering map $(\Sigma,K) \to (\Sigma',K')$ between two pairs of a 3-manifold and a knot each, we describe the fundamental group $\pi_1(\Sigma \setminus K)$ in terms of $\pi_1(\Sigma' \setminus K')$. As a consequence, we give an alternative proof for the fact that certain knots in $S^3$ cannot be represented as the preimage of any knot in a lens space, which is related to free periods of knots. In our proofs, the subgroup of a group $G$ generated by the commutators and the $p$th power of each element of $G$ plays a key role.
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In this paper, we extend the fractional Sobolev spaces with variable exponents $W^{s,p(x,y)}$ to include the general fractional case $W^{K,p(x,y)}$, where $p$ is a variable exponent, $s\in (0,1)$ and $K$ is a suitable kernel. We are concerned with some qualitative properties of the space $W^{K,p(x,y)}$ (completeness, reflexivity, separability and density). Moreover, we prove a continuous embedding theorem of these spaces into variable exponent Lebesgue spaces. As an application we establish the existence and uniqueness of a solution for a nonlocal problem involving the nonlocal integrodifferential operator of elliptic type.
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We obtain the ground state magnetization of the Heisenberg and XXZ spin chains in a magnetic field $h$ as a series in $\sqrt{h_c-h}$, where $h_c$ is the smallest field for which the ground state is fully polarized. All the coefficients of the series can be computed in closed form through a recurrence formula that involves only algebraic manipulations. The radius of convergence of the series in the full range $0<h\leq h_c$ is studied numerically. To that end we express the free energy at mean magnetization per site $-1/2\leq \langle \sigma^z_i\rangle\leq 1/2$ as a series in $1/2-\langle \sigma^z_i\rangle$ whose coefficients can be similarly recursively computed in closed form. This series converges for all $0\leq \langle \sigma^z_i\rangle\leq 1/2$. The recurrence is nothing but the Bethe equations when their roots are written as a double series in their corresponding Bethe number and in $1/2-\langle \sigma^z_i\rangle$. It can also be used to derive the corrections in finite size, tha
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We study properly immersed ancient solutions of the codimension one mean curvature flow in $n$-dimensional Euclidean space, and classify the convex hulls of the subsets of space reached by any such flow. In particular, it follows that any compact convex ancient mean curvature flow can only have a slab, a halfspace or all of space as the closure of its set of reach. The proof proceeds via a bi-halfspace theorem (also known as a wedge theorem) for ancient solutions derived from a parabolic Omori-Yau maximum principle for ancient mean curvature flows.
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Let $X$ be a ball quasi-Banach function space and $H_X(\mathbb{R}^n)$ the associated Hardy-type space. In this article, the authors establish the characterizations of $H_X(\mathbb{R}^n)$ via the Littlewood-Paley $g$-functions and $g_\lambda^\ast$-functions. Moreover, the authors obtain the boundedness of Calder\'on-Zygmund operators on $H_X(\mathbb{R}^n)$. For the local Hardy-type space $h_X(\mathbb{R}^n)$, the authors also obtain the boundedness of $S^0_{1,0}(\mathbb{R}^n)$ pseudo-differential operators on $h_X(\mathbb{R}^n)$ via first establishing the atomic characterization of $h_X(\mathbb{R}^n)$. Furthermore, the characterizations of $h_X(\mathbb{R}^n)$ by means of local molecules and local Littlewood-Paley functions are also given. The results obtained in this article have a wide range of generality and can be applied to the classical Hardy space, the weighted Hardy space, the Herz-Hardy space, the Lorentz-Hardy space, the Morrey-Hardy space, the variable Hardy space, the Orlicz-s
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[L. Gavruta, Frames for Operators, Appl. comput. Harmon. Anal. 32(2012), 139-144] introduced a special kind of frames, named $K$-frames, where $K$ is an operator, in Hilbert spaces, is significant in frame theory and has many applications. In this paper, first of all, we have introduced the notion of approximative $K$-atomic decomposition in Banach spaces. We gave two characterizations regarding the existence of approximative $K$-atomic decompositions in Banach spaces. Also some results on the existence of approximative $K$-atomic decompositions are obtained. We discuss several methods to construct approximative $K$-atomic decomposition for Banach Spaces. Further, approximative $\mathcal{X}_d$-frame and approximative $\mathcal{X}_d$-Bessel sequence are introduced and studied. Two necessary conditions are given under which an approximative $\mathcal{X}_d$-Bessel sequence and approximative $\mathcal{X}_d$-frame give rise to a bounded operator with respect to which there is an approximati
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We consider a class of max-AR(1) sequences connected with the Kendall convolution. For a large class of step size distributions we prove that the one dimensional distributions of the Kendall random walk with any unit step distribution, are regularly varying. The finite dimensional distributions for Kendall convolutions are given. We prove convergence of a continuous time stochastic process constructed from the Kendall random walk in the finite dimensional distributions sense using regularly varying functions.
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For a random walk on the integer lattice $\mathbb{Z}$ that is attracted to a strictly stable process with index $\alpha\in (1, 2)$ we obtain the asymptotic form of the transition probability for the walk killed when it hits a finite set. The asymptotic forms obtained are valid uniformly in a natural range of the space and time variables. The situation is relatively simple when the limit stable process has jumps in both positive and negative directions; in the other case when the jumps are one sided rather interesting matters are involved and detailed analyses are necessitated.
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The aim of this thesis is to advance the theory behind quantum information processing tasks, by deriving fundamental limits on bipartite quantum interactions and dynamics, which corresponds to an underlying Hamiltonian that governs the physical transformation of a two-body open quantum system. The goal is to determine entangling abilities of such arbitrary bipartite quantum interactions. Doing so provides fundamental limitations on information processing tasks, including entanglement distillation and secret key generation, over a bipartite quantum network. We also discuss limitations on the entropy change and its rate for dynamics of an open quantum system weakly interacting with the bath. We introduce a measure of non-unitarity to characterize the deviation of a doubly stochastic quantum process from a noiseless evolution. Next, we introduce information processing tasks for secure read-out of digital information encoded in read-only memory devices against adversaries of varying capabi
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A cyclic quadrilateral is called a Brahmagupta quadrilateral if its four sides, the two diagonals and the area are all given by integers. In this paper we consider the hitherto unsolved problem of finding two Brahmagupta quadrilaterals with equal perimeters and equal areas. We obtain two parametric solutions of the problem -- the first solution generates examples in which each quadrilateral has two equal sides while the second solution gives quadrilaterals all of whose sides are unequal. We also show how more parametric solutions of the problem may be obtained.
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In this paper we study Cauchy problem for thermoelastic plate equations with friction or structural damping in $\mathbb{R}^n$, $n\geq1$, where the heat conduction is modeled by Fourier's law. We explain some qualitative properties of solutions influenced by different damping mechanisms. We show which damping in the model has a dominant influence on smoothing effect, energy estimates, $L^p-L^q$ estimates not necessary on the conjugate line, and on diffusion phenomena. Moreover, we derive asymptotic profiles of solutions in a framework of weighted $L^1$ data. In particular, sharp decay estimates for lower bound and upper bound of solutions in the $\dot{H}^s$ norm ($s\geq0$) are shown.
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In this paper we present some characterizations for quasi-arithmetic operator means (among them the arithmetic and harmonic means) on the positive definite cone of the full algebra of Hilbert space operators, and also for the Kubo-Ando geometric mean on the positive definite cone of a general non-commutative $C^*$-algebra.
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We review the theory of Co-Gorenstein algebras, which was introduced by Beligiannis in the article "The Homological Theory of Contravariantly Finite Subcategories: Gorenstein Categories, Auslander-Buchweitz Contexts and (Co-)Stabilization". We show a connection between Co-Gorenstein algebras and the Nakayama and Generalized Nakayama conjecture.
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Given a closed Riemannian manifold $(N^{n+1},g)$, $n+1 \geq 3$ we prove the compactness of the space of singular, minimal hypersurfaces in $N$ whose volumes are uniformly bounded from above and the $p$-th Jacobi eigenvalue $\lambda_p$'s are uniformly bounded from below. This generalizes the results of Sharp and Ambrozio-Carlotto-Sharp in higher dimensions.
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Based on the method by [K\"uc95], we give a procedure to list up all complete intersection Calabi--Yau manifolds with respect to direct sums of irreducible homogeneous vector bundles on Grassmannians for each dimension. In particular, we give a classification of such Calabi--Yau 3-folds and determine their topological invariants. We also give alternative descriptions for some of them.
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In this article, we summarize combinatorial description of complete intersection Calabi-Yau threefolds in Hibi toric varieties. Such Calabi-Yau threefolds have at worst conifold singularities, and are often smoothable to non-singular Calabi-Yau threefolds. We focus on such non-singular Calabi-Yau threefolds of Picard number one, and illustrate the calculation of topological invariants, using new motivating examples.
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Inspired by recent work of P.-L. Lions on conditional optimal control, we introduce a problem of optimal stopping under bounded rationality: the objective is the expected payoff at the time of stopping, conditioned on another event. For instance, an agent may care only about states where she is still alive at the time of stopping, or a company may condition on not being bankrupt. We observe that conditional optimization is time-inconsistent due to the dynamic change of the conditioning probability and develop an equilibrium approach in the spirit of R. H. Strotz' work for sophisticated agents in discrete time. Equilibria are found to be essentially unique in the case of a finite time horizon whereas an infinite horizon gives rise to non-uniqueness and other interesting phenomena. We also introduce a theory which generalizes the classical Snell envelope approach for optimal stopping by considering a pair of processes with Snell-type properties.
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We present a self contained tour of the Conley index and some applications. The starting point is the fundamental theorem of dynamical systems, passing through the necessary topological background, with a short stop at the basic properties of the Conley index, and arriving at the construction of connection matrices with a panoramic view of the applications: detect heteroclinic orbits arising in delay differential equations, and partial differential equations of parabolic type. The ride will be filled with examples and pictures.
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This paper describes connected components of the strata of holomorphic abelian differentials on marked Riemann surfaces with prescribed degrees of zeros. Unlike the case for unmarked Riemann surfaces, we find there can be many connected components, distinguished by roots of the cotangent bundle of the surface. In the course of our investigation we also characterize the images of the fundamental groups of strata inside of the mapping class group. The main techniques of proof are mod r winding numbers and a mapping class group-theoretic analogue of the Euclidean algorithm.
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The Helmholtz-Hodge decomposition (HHD) is applied to the construction of Lyapunov functions. It is shown that if a stability condition is satisfied, such a decomposition can be chosen so that its potential function is a Lyapunov function. In connection with the Lyapunov function, vector fields with strictly orthogonal HHD are analyzed. It is shown that they are a generalization of gradient vector fields and have similar properties. Finally, to examine the limitations of the proposed method, planar vector fields are analyzed.
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We derive two general transformations for certain basic hypergeometric series from the recurrence formulae for the partial numerators and denominators of two $q$-continued fractions previously investigated by the authors. By then specializing certain free parameters in these transformations, and employing various identities of Rogers-Ramanujan type, we derive \emph{$m$-versions} of these identities. Some of the identities thus found are new, and some have been derived previously by other authors, using different methods. By applying certain transformations due to Watson, Heine and Ramanujan, we derive still more examples of such $m$-versions of Rogers-Ramanujan-type identities.
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In the fight against vector-borne arboviruses, an important strategy of control of epidemic consists in controlling the population of vector, \textit{Aedes} mosquitoes in this case. Among possible actions, two techniques consist in releasing mosquitoes to reduce the size of the population (Sterile Insect Technique) or in replacing the wild population by a population carrying a bacteria, called \textit{Wolbachia}, blocking the transmission of viruses from mosquitoes to human. This paper is concerned with the question of optimizing the release protocol for these two strategies with the aim of getting as close as possible to the objectives. Starting from a mathematical model describing the dynamics of the population, we include the control function and introduce the cost functional for both \textit{population replacement} and \textit{Sterile Insect Technique} problems. Next, we establish some properties of the optimal control and illustrate them with some numerical simulations.
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Convexification is a core technique in global polynomial optimization. Currently, two different approaches compete in practice and in the literature. First, general approaches rooted in nonlinear programming. They are comparitively cheap from a computational point of view, but typically do not provide good (tight) relaxations with respect to bounds for the original problem. Second, approaches based on sum-of-squares and moment relaxations. They are typically computationally expensive, but do provide tight relaxations. In this paper, we embed both kinds of approaches into a unified framework of monomial relaxations. We develop a convexification strategy that allows to trade off the quality of the bounds against computational expenses. Computational experiments show that a combination with a prototype cutting-plane algorithm gives very encouraging results.
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Radicalization is the process by which people come to adopt increasingly extreme political, social or religious ideologies. When radicalization leads to violence radical thinking becomes a threat to national security. Prevention and de-radicalization programs are part of a set of strategies used to combat violent extremism, which are collectively known as Countering Violent Extremism (CVE). Prevention programs seek to stop the radicalization process from occurring and taking hold in the first place. De-radicalization programs work with violent extremists and attempt to alter their extremist beliefs and violent behavior with the aim to reintegrate them into society. In this paper we introduce a simple compartmental model suitable to describe prevention and de-radicalization programs. The prevention initiatives are modeled by including a vaccination compartment, while the de-radicalization process is modeled by including a treatment compartment. We calculate the basic reproduction number
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We consider here the Cramer-Lundberg model based on generalized convolutions. In our model the insurance company invests at least part of its money, have employees, shareholders. The financial situation of the company after paying claims can be even better than before. We compute the ruin probability for $\alpha$-convolution case, maximal convolution and the Kendall convolution case, which is formulated in the Williamson transform terms. We also give some new results on the Kendall random walks.
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This is a short review of the two papers on the $x$-space asymptotics of the critical two-point function $G_{p_c}(x)$ for the long-range models of self-avoiding walk, percolation and the Ising model on $\mathbb{Z}^d$, defined by the translation-invariant power-law step-distribution/coupling $D(x)\propto|x|^{-d-\alpha}$ for some $\alpha>0$. Let $S_1(x)$ be the random-walk Green function generated by $D$. We have shown that $\bullet~~S_1(x)$ changes its asymptotic behavior from Newton ($\alpha>2$) to Riesz ($\alpha<2$), with log correction at $\alpha=2$; $\bullet~~G_{p_c}(x)\sim\frac{A}{p_c}S_1(x)$ as $|x|\to\infty$ in dimensions higher than (or equal to, if $\alpha=2$) the upper critical dimension $d_c$ (with sufficiently large spread-out parameter $L$). The model-dependent $A$ and $d_c$ exhibit crossover at $\alpha=2$. The keys to the proof are (i) detailed analysis on the underlying random walk to derive sharp asymptotics of $S_1$, (ii) bounds on convolutions of power functio
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We consider those simply connected isothermic surfaces for which their Hopf differential factorizes into a real function and a meromorphic quadratic differential that has a zero or pole at some point, but is nowhere zero and holomorphic otherwise. Upon restriction to a simply connected patch that does not contain the zero or pole, the Darboux and Calapso transformations yield new isothermic surfaces. We determine the limiting behaviour of these transformed patches as the zero or pole of the meromorphic quadratic differential is approached and investigate whether they are continuous around that point.
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Projective Reed-Solomon (PRS) codes are Reed-Solomon codes of the maximum possible length q+1. The classification of deep holes --received words with maximum possible error distance-- for PRS codes is an important and difficult problem. In this paper, we use algebraic methods to explicitly construct three classes of deep holes for PRS codes. We show that these three classes completely classify all deep holes of PRS codes with redundancy at most four. Previously, the deep hole classification was only known for PRS codes with redundancy at most three in work arXiv:1612.05447
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We propose a deep-learning approach for the joint MIMO detection and channel decoding problem. Conventional MIMO receivers adopt a model-based approach for MIMO detection and channel decoding in linear or iterative manners. However, due to the complex MIMO signal model, the optimal solution to the joint MIMO detection and channel decoding problem (i.e., the maximum likelihood decoding of the transmitted codewords from the received MIMO signals) is computationally infeasible. As a practical measure, the current model-based MIMO receivers all use suboptimal MIMO decoding methods with affordable computational complexities. This work applies the latest advances in deep learning for the design of MIMO receivers. In particular, we leverage deep neural networks (DNN) with supervised training to solve the joint MIMO detection and channel decoding problem. We show that DNN can be trained to give much better decoding performance than conventional MIMO receivers do. Our simulations show that a DN
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We show that if $(K,v_1,v_2)$ is a bi-valued NIP field with $v_1$ henselian (resp. t-henselian) then $v_1$ and $v_2$ are comparable (resp. dependent). As a consequence Shelah's conjecture for NIP fields implies the henselianity conjecture for NIP fields. Furthermore, the latter conjecture is proved for any field admitting a henselian valuation with a dp-minimal residue field.
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Graph homomorphisms from the $\mathbb{Z}^d$ lattice to $\mathbb{Z}$ are functions on $\mathbb{Z}^d$ whose gradients equal one in absolute value. These functions are the height functions corresponding to proper $3$-colorings of $\mathbb{Z}^d$ and, in two dimensions, corresponding to the $6$-vertex model (square ice). We consider the uniform model, obtained by sampling uniformly such a graph homomorphism subject to boundary conditions. Our main result is that the model delocalizes in two dimensions, having no translation-invariant Gibbs measures. Additional results are obtained in higher dimensions and include the fact that every Gibbs measure which is ergodic under even translations is extremal and that these Gibbs measures are stochastically ordered.
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Denoising stationary process $(X_i)_{i \in Z}$ corrupted by additive white Gaussian noise is a classic and fundamental problem in information theory and statistical signal processing. Despite considerable progress in designing efficient denoising algorithms, for general analog sources, theoretically-founded computationally-efficient methods are yet to be found. For instance in denoising $X^n$ corrupted by noise $Z^n$ as $Y^n=X^n+Z^n$, given the full distribution of $X^n$, a minimum mean square error (MMSE) denoiser needs to compute $E[X^n|Y^n]$. However, for general sources, computing $E[X^n|Y^n]$ is computationally very challenging, if not infeasible. In this paper, starting by a Bayesian setup, where the source distribution is fully known, a novel denoising method, namely, quantized maximum a posteriori (Q-MAP) denoiser, is proposed and its asymptotic performance in the high signal to noise ratio regime is analyzed. Both for memoryless sources, and for structured first-order Markov s
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We derive exact results for the Lindblad equation for a quantum spin chain (one-dimensional quantum compass model) with dephasing noise. The system possesses doubly degenerate nonequilibrium steady states due to the presence of a conserved charge commuting with the Hamiltonian and Lindblad operators. We show that the system can be mapped to a non-Hermitian Kitaev model on a two-leg ladder, which is solvable by representing the spins in terms of Majorana fermions. This allows us to study the Liouvillian gap, the inverse of relaxation time, in detail. We find that the Liouvillian gap increases monotonically when the dissipation strength $ \gamma $ is small, while it decreases monotonically for large $ \gamma $, implying a kind of phase transition in the first decay mode. The Liouvillian gap and the transition point are obtained in closed form in the case where the spin chain is critical. We also obtain the explicit expression for the autocorrelator of the edge spin. The result implies th
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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 up-to-date 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 pre-installed 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 surface-level and under-the-hood. This article will focus on all the surface-level 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 system-wide dark mode, hints of a DeX-li
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The incompressible Navier-Stokes (NS) equation is known to govern the hydrodynamic limit of essentially any fluid and its rich non-linear 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 Kato-Rellich perturbation theory, we prove that the functionals are (one-sided) differentiable along 1-parameter 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 non-homogeneous CR manifolds.
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CERN wants to build a particle collider that’s four times bigger than the
01-16 MIT Technology 13301 -
We’re excited to announce that map and address-related 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: Knowledge-directed 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
01-09 Ars Technica 13315 -
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 long-time 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, mean-square 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 Breuer-Major 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 state-of-the-art 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 information-theoretically 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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