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We study robust PCA for the fully observed setting, which is about separating a low rank matrix $\boldsymbol{L}$ and a sparse matrix $\boldsymbol{S}$ from their sum $\boldsymbol{D}=\boldsymbol{L}+\boldsymbol{S}$. In this paper, a new algorithm, termed accelerated alternating projections, is introduced for robust PCA which accelerates existing alternating projections proposed in [Netrapalli, Praneeth, et al., 2014]. Let $\boldsymbol{L}_k$ and $\boldsymbol{S}_k$ be the current estimates of the low rank matrix and the sparse matrix, respectively. The algorithm achieves significant acceleration by first projecting $\boldsymbol{D}\boldsymbol{S}_k$ onto a low dimensional subspace before obtaining the new estimate of $\boldsymbol{L}$ via truncated SVD. Exact recovery guarantee has been established which shows linear convergence of the proposed algorithm. Empirical performance evaluations establish the advantage of our algorithm over other stateoftheart algorithms for robust PCA.
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In this paper we present aposteriori KAM results for existence of $d$dimensional isotropic invariant tori for $n$DOF Hamiltonian systems with additional $nd$ independent first integrals in involution. We carry out a covariant formulation that does not require the use of actionangle variables nor symplectic reduction techniques. The main advantage is that we overcome the curse of dimensionality avoiding the practical shortcomings produced by the use of reduced coordinates, which may cause difficulties and underperformance when quantifying the hypotheses of the KAM theorem in such reduced coordinates. The results include ordinary and (generalized) isoenergetic KAM theorems. The approach is suitable to perform numerical computations and computer assisted proofs.
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We characterize even measures $\mu=wdx+\mu_s$ on the real line with finite entropy integral $\int_{R} \frac{\log w(t)}{1+t^2}dt>\infty$ in terms of $2\times 2$ Hamiltonian generated by $\mu$ in the sense of inverse spectral theory. As a corollary, we obtain criterion for spectral measure of Krein string to have converging logarithmic integral.
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This paper provides a simple method to extract the zeros of some weight two Eisenstein series of level $N$ where $N=2,3,5$ and $7$. We show that $\tilde{E}_N$ is integral over the polynomial ring $M(Sl_2(\mathbb{Z}))=\bigoplus_{k\ge 0}M_k(Sl_2(\mathbb{Z}))$ for these values of $N$; and thus the zeros of $\tilde{E}_N$ are `controlled' by those of $E_4$ and $E_6$ in the fundamental domain of $\Gamma_0(N)$.
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The SturmLiouville operator with singular potentials on the lasso graph is considered. We suppose that the potential is known a priori on the boundary edge, and recover the potential on the loop from a part of the spectrum and some additional data. We prove the uniqueness theorem and provide a constructive algorithm for the solution of this partial inverse problem.
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We study the dispersion of a point set, a notion closely related to the discrepancy. Given a real $r\in (0,1)$ and an integer $d\geq 2$, let $N(r,d)$ denote the minimum number of points inside the $d$dimensional unit cube $[0,1]^d$ such that they intersect every axisaligned box inside $[0,1]^d$ of volume greater than $r$. We prove an upper bound on $N(r,d)$, matching a lower bound of Aistleitner et al. up to a multiplicative constant depending only on $r$. This fully determines the rate of growth of $N(r,d)$ if $r\in(0,1)$ is fixed.
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We investigate a descent on simple graphs, starting with the complete graph on $n$ vertices and ending up with the cycle graph by removing one edge after another. We obtain quantitative results showing that graphs with small diameter must have some eigenvalues of large algebraic degree.
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The seller's riskindifference price evaluation is studied. We propose a dynamic riskindifference pricing criteria derived from a fullydynamic family of risk measures on the $L_p$spaces for $p\in [1,\infty]$. The concept of fullydynamic risk measures extends the one of dynamic risk measures by adding the actual possibility of changing the risk perspectives over time. The family is then characterised by a double time index. Our framework fits well the study of both short and long term investments. In this dynamic framework we analyse whether the riskindifference pricing criterion actually provides a proper convex price system, for which timeconsistency is guaranteed. It turns out that the analysis is quite delicate and necessitates an adequate setting. This entails the use of capacities and an extension of the whole price system to the Banach spaces derived by the capacity seminorms. Furthermore, we consider the relationship of the fullydynamic riskindifference price with nogoo
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We show existence of a unique solution and a comparison theorem for a onedimensional backward stochastic differential equation with jumps that emerge from a L\'evy process. The considered generators obey a timedependent extended monotonicity condition in the yvariable and have linear timedependent growth. Within this setting, the results generalize those of Royer (2006), Yin and Mao (2008) and, in the $L^2$case with linear growth, those of Kruse and Popier (2016). Moreover, we introduce an approximation technique: Given a BSDE driven by Brownian motion and Poisson random measure, we consider BSDEs where the Poisson random measure admits only jumps of size larger than $1/n$. We show convergence of their solutions to those of the original BSDE, as $n \to \infty.$ The proofs only rely on It\^o's formula and the BihariLaSalle inequality and do not use Girsanov transforms.
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The Lowest Landau Level (LLL) equation emerges as an accurate approximation for a class of dynamical regimes of BoseEinstein Condensates (BEC) in twodimensional isotropic harmonic traps in the limit of weak interactions. Building on recent developments in the field of spatially confined extended Hamiltonian systems, we find a fully nonlinear solution of this equation representing periodically modulated precession of a single vortex. Motions of this type have been previously seen in numerical simulations and experiments at moderately weak coupling. Our work provides the first controlled analytic prediction for trajectories of a single vortex, suggests new targets for experiments, and opens up the prospect of finding analytic multivortex solutions.
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Recovery of population size history from sequence data and testing of hypotheses about features of population size history are important problems in population genetics. Inference commonly relies on a coalescentbased model linking the population size history to genealogies. We consider the problem of recovering the true population size history from two possible alternatives on the basis of coalescent time data. We give exact expressions for the probability of selecting the correct alternative in a variety of biologically interesting cases as a function of the separation between the alternative size histories, the number of genealogies and loci sampled, and the sampling times. The results are applied to human population history. As coalescent times are inferred from sequence data rather than directly observed, the inferential limits we give can be viewed as optimistic.
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The first part of this article gives error bounds for approximations of Markov kernels under FosterLyapunov conditions. The basic idea is that when both the approximating kernel and the original kernel satisfy a FosterLyapunov condition, the longtime dynamics of the two chains  as well as the invariant measures, when they exist  will be close in a weighted total variation norm, provided that the approximation is sufficiently accurate. The required accuracy depends in part on the Lyapunov function, with more stable chains being more tolerant of approximation error. We are motivated by the recent growth in proposals for scaling Markov chain Monte Carlo algorithms to large datasets by defining an approximating kernel that is faster to sample from. Many of these proposals use only a small subset of the data points to construct the transition kernel, and we consider an application to this class of approximating kernel. We also consider applications to distribution approximations in G
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Accommodating MachinetoMachine applications and their requirements is one of the challenges on the way from LTE towards 5G networks. The envisioned high density of devices, alongside with their sporadic and synchronized transmission patterns, might create signaling storms and overload in the current LTE network. Here, we address the notorious random access (RA) challenge, namely, scalability of the radio link connection establishment protocol in LTE networks. We revisit the binary countdown technique for contention resolution (BCCR), and apply it to the LTE RA procedure. We analytically investigate the performance gains and tradeoffs of applying BCCR in LTE. We further simulatively compare BCCR RA with the stateoftheart RA techniques, and demonstrate its advantages in terms of delay and throughput.
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This work is about a slowfast data assimilation system when only slow components are observable. First, we obtain its low dimensional reduction via an invariant slow manifold. Second, we prove that the low dimensional filter on the slow manifold approximates the original filter in a suitable metric. Finally, we illustrate this approximate filter numerically in an example.
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Let $M$ be the circle or a compact interval, and let $\alpha=k+\tau\ge2$ be a real number such that $k=\lfloor \alpha\rfloor$. We write $\mathrm{Diff}_+^{\alpha}(M)$ for the group of $C^k$ diffeomorphisms of $M$ whose $k^{th}$ derivatives are H\"older continuous with exponent $\tau$. We prove that there exists a finitely generated subgroup $G_\alpha$ of $\mathrm{Diff}_+^{\alpha}(M)$ with the property that $G_\alpha$ admits no injective homomorphisms into $\mathrm{Diff}_+^{\beta}(M)$ whenever $\beta>\alpha$. We can further require the same property for all finite index subgroups of $G_\alpha$, and also for $[G_\alpha,G_\alpha]$, the latter of which is a countable simple group. This implies the existence of a continuum of isomorphism types of finitely generated subgroups (and countable simple subgroups) of $\mathrm{Diff}_+^{\alpha}(M)$ which admit no injective homomorphisms into $\mathrm{Diff}_+^{\beta}(M)$. We give some applications to smoothability of codimension one foliations and
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This paper derives the Feynman rules for the diagrammatic perturbation expansion of the effective action around an arbitrary solvable problem. The perturbation expansion around a Gaussian theory is well known and composed of oneline irreducible diagrams only. For the expansions around an arbitrary, nonGaussian problem, we show that a more general class of irreducible diagrams remains in addition to a second set of diagrams that has no analogue in the Gaussian case. The effective action is central to field theory, in particular to the study of phase transitions, symmetry breaking, effective equations of motion, and renormalization. We exemplify the method on the Ising model, where the effective action amounts to the Gibbs free energy, recovering the ThoulessAndersonPalmer meanfield theory in a fully diagrammatic derivation. Higher order corrections follow with only minimal effort compared to existing techniques. Our results show further that the Plefka expansion and the hightemper
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Let $B_{H}(t), t\geq [0,T], T\in(0,\infty)$ be the standard Multifractional Brownian Motion(mBm), in this contribution we are concerned with the exact asymptotics of \begin{eqnarray*} \mathbb{P}\left\{\sup_{t\in[0,T]}B_{H}(t)>u\right\} \end{eqnarray*} as $u\rightarrow\infty$. Mainly depended on the structures of $H(t)$, the results under several important cases are investigated.
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The aim of this paper is to establish uniqueness properties of solutions of the Helmholtz and Laplace equations. In particular, we show that if two solutions of such equations on a domain of R d agree on two intersecting d  1dimensional submanifolds in generic position, then they agree everywhere.
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Timelimited functions and bandlimited functions play a fundamental role in signal and image processing. But by the uncertainty principles, a signal cannot be simultaneously time and bandlimited. A natural assumption is thus that a signal is almost time and almost bandlimited. The aim of this paper is to prove that the set of almost time and almost bandlimited signals is not excluded from the uncertainty principles. The transforms under consideration are integral operators with bounded kernels for which there is a Parseval Theorem. Then we define the wavelet multipliers for this class of operators, and study their boundedness and Schatten class properties. We show that the wavelet multiplier is unitary equivalent to a scalar multiple of the phase space restriction operator. Moreover we prove that a signal which is almost time and almost bandlimited can be approximated by its projection on the span of the first eigenfunctions of the phase space restriction operator, corresponding to the
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We propose randomization tests of whether forecast 1 outperforms forecast 2 across a class of scoring functions. This hypothesis is of applied interest: While the prediction context often prescribes a certain class of scoring functions, it is typically hard to motivate a specific choice on statistical or substantive grounds. We investigate the asymptotic behavior of the test statistics under mild conditions, avoiding the need to assume particular dynamic properties of forecasts and realizations. Properties of onesided tests depend on a onesided variant of Anderson's inequality, which we state as a conjecture of independent interest. Simulation experiments and data examples indicate that the tests have good size and power properties in practically relevant situations.
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The standard approach to analyzing categorical correlated time series data is to fit a generalized linear model (GLM) with past data as covariate inputs. There remain challenges to conducting inference for short time series length. By treating the historical data as covariate inputs, standard errors of estimates of GLM parameters computed using the empirical Fisher information do not fully account the autocorrelation in the data. To overcome this serious limitation, we derive the exact conditional Fisher information matrix of a general logistic autoregressive model with endogenous covariates for any series length T. Moreover, we also develop an iterative computational formula that allows for relatively easy implementation of the proposed estimator. Our simulation studies show that confidence intervals derived using the exact Fisher information matrix tend to be narrower than those utilizing the empirical Fisher information matrix while maintaining type I error rates at or below nomina
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Firefox 57 has been released. From the release notes: "Brace yourself for an allnew Firefox. It’s fast. Really fast. It’s over twice as fast as Firefox from 6 months ago, built on a completely overhauled core engine with brand new technology from our advanced research group, and graced with a clean, modern interface. Today is the first of several releases we’re calling Firefox Quantum, all designed to get to the things you love and the stuff you need faster than ever before. Experience the difference on desktops running Windows, macOS, and Linux; on Android, speed improvements are landing as well, and both Android and iOS have a new look and feel. To learn more about Firefox Quantum, visit the Mozilla Blog."
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In 2017, Duchi, Guerrini, Rinaldi and Schaeffer proposed a new combinatorial object called "fighting fish", which is counted by the same formula as more classical objects, such as twostack sortable permutations and nonseparable planar maps. In this article, we explore the bijective aspect of fighting fish by establishing a bijection to twostack sortable permutations, using a new recursive decomposition of these permutations. With our bijection, we give combinatorial explanations of several results of fighting fish previously proved previously with generating functions. Using the decomposition, we also prove the algebraicity of a generating function of twostack sortable permutations, extending a result of BousquetM\'elou (1998).
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A class of integervalued functions defined on the set of ideals of an integral domain $R$ is investigated. We show that this class of functions, which we call ideal valuations, are in onetoone correspondence with countable descending chains of finite type, stable semistar operations with largest element equal to the $e$operation. We use this class of functions to recover familiar semistar operations such as the $w$operation and to give a solution to a conjecture by Chapman and Glaz when the ring is a valuation domain.
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In this paper, we study the center and representation theory of finite $W$algebra $\mathcal{T}(\mathfrak{g},e)$ over an algebraically closed field $\mathds{k}$ of characteristic $p\gg0$. We obtain an analogy of Veldkamp's theorem on the center, and then decide the structure of the reduced center of the associated reduced $W$algebra $\mathcal{T}_\chi(\mathfrak{g},e)$ via that of the reduced enveloping algebra $U_\chi(\mathfrak{g})$. For the maximal spectrum $\text{Specm}(Z)$ of the center $Z=Z(\mathcal{T}(\mathfrak{g},e))$, we show that its Azumaya locus coincides with its smooth locus of smooth points, the former of which reflects irreducible representations of the maximal dimension for $\mathcal{T}(\mathfrak{g},e)$.
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For a Catalan state $C$ of a lattice crossing $L\left( m,n\right) $ with no returns on one side, we find its coefficient $C\left( A\right) $ in the Relative Kauffman Bracket Skein Module expansion of $L\left( m,n\right) $. We show, in particular, that $C\left( A\right) $ can be found using the plucking polynomial of a rooted tree with a delay function associated to $C$. Furthermore, for $C$ with returns on one side only, we prove that $C\left( A\right) $ is a product of Gaussian polynomials, and its coefficients form a unimodal sequence.
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Given a diagram for a trisection of a 4manifold $X$, we describe the homology and the intersection form of $X$ in terms of the three subgroups of $H_1(\Sigma;\mathbb{Z})$ generated by the three sets of curves and the intersection pairing on the diagram surface $\Sigma$. This includes explicit formulas for the second and third homology groups of $X$ as well an algorithm to compute the intersection form. Moreover, we show that all $(g;k,0,0)$trisections admit "algebraically trivial" diagrams.
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We study compactifications of Drinfeld halfspaces over a finite field. In particular, we construct a purely inseparable endomorphism of Drinfeld's halfspace $\Omega (V)$ over a finite field $k$ that does not extend to an endomorphism of the projective space $P (V)$. This should be compared with theorem of R\'emy, Thuillier and Werner that every $k$automorphism of $\Omega (V)$ extends to a $k$automorphism of $P (V)$. Our construction uses an inseparable analogue of the Cremona transformation. We also study foliations on Drinfeld's halfspaces. This leads to various examples of interesting varieties in positive characteristic. In particular, we show a new example of a nonliftable projective CalabiYau threefold in characteristic $2$ and we show examples of rational surfaces with klt singularities, whose cotangent bundle contains an ample line bundle.
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The issue of determining not only an adequate dose but also a dosing frequency of a drug arises frequently in Phase II clinical trials. This results in the comparison of models which have some parameters in common. Planning such studies based on Bayesian optimal designs offers robustness to our conclusions since these designs, unlike locally optimal designs, are efficient even if the parameters are misspecified. In this paper we develop approximate design theory for Bayesian $D$optimality for nonlinear regression models with common parameters and investigate the cases of common location or common location and scale parameters separately. Analytical characterisations of saturated Bayesian $D$optimal designs are derived for frequently used doseresponse models and the advantages of our results are illustrated via a numerical investigation.
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A graph $\Gamma$ labelled by a set $S$ defines a group $G(\Gamma)$ whose generators are the set of labels $S$ and whose relations are all words which can be read on closed paths of this graph. We introduce the notion of aspherical graph and prove that such a graph defines an aspherical group presentation. This result generalizes a theorem of Dominik Gruber on graphs satisfying graphical $C(6)$condition.
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Using the method for constructing binary selfdual codes with an automorphism of order square of a prime number we have classified all binary selfdual codes with length 76 having minimum distance $d=14$ and automorphism of order 9. Up to equivalence, there are six selfdual $[76, 38, 14]$ codes with an automorphism of type $9$$(8,0,4)$. All codes obtained have new values of the parameter in their weight enumerator thus more than doubling the number of known values.
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We prove that the intersection hypergraph of a family of $n$ pseudodisks with respect to another family of pseudodisks admits a proper coloring with $4$ colors and a conflictfree coloring with $O(\log n)$ colors. Along the way we prove that the respective Delaunaygraph is planar. We also prove that the intersection hypergraph of a family of $n$ regions with linear union complexity with respect to a family of pseudodisks admits a proper coloring with constant many colors and a conflictfree coloring with $O(\log n)$ colors. Our results serve as a common generalization and strengthening of many earlier results, including ones about proper and conflictfree coloring points with respect to pseudodisks, coloring regions of linear union complexity with respect to points and coloring disks with respect to disks.
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We present the geometry lying behind counting twin prime polynomials in $\mathbb{F}_q[T]$ in general. We compute cohomology and explicitly count points by means of a twisted Lefschetz trace formula applied to these parametrizing varieties for cubic twin prime polynomials. The elliptic curve $X^3 = Y(Y1)$ occurs in the geometry, and thus counting cubic twin prime polynomials involves the associated modular form. In theory, this approach can be extended to higher degree twin primes, but the computations become harder. The formula we get in degree $3$ is compatible with the HardyLittlewood heuristic on average, agrees with the prediction for $q \equiv 2 \pmod 3$ but shows anomalies for $q \equiv 1 \pmod 3$.
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A sharp bound is obtained for the number of ways to express the monomial $X^n$ as a product of linear factors over $\mathbb{Z}/p^{\alpha}\mathbb{Z}$. The proof relies on an inductiononscale procedure which is used to estimate the number of solutions to a certain system of polynomial congruences. The method also applies to more general systems of polynomial congruences that satisfy a nondegeneracy hypothesis.
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Conformally variational Riemannian invariants (CVIs), such as the scalar curvature, are homogeneous scalar invariants which arise as the gradient of a Riemannian functional. We establish a wide range of stability and rigidity results involving CVIs, generalizing many such results for the scalar curvature.
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In the setting of the massive KleinGordon equation on de Sitter space, we discuss Vasy's asymptotic data at conformal infinity in terms of plane waves. In particular, we derive a shorthand formula for reconstructing solutions from their asymptotic data. Furthermore, we show that the natural Hadamard state induced from future (or past) conformal infinity coincides with the BunchDavies state.
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Let M be a compact oriented manifold such that there is a submersion from its boundary to the circle. We construct a class of magnetic fields defined over its interior which posses a complete magnetic flow. This means that charged particles inside of M under the influence of such magnetic fields become confined to its interior for all time.
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We study minimum energy problems relative to the $\alpha$Riesz kernel $xy^{\alphan}$, $\alpha\in(0,2]$, over signed Radon measures $\mu$ on $\mathbb R^n$, $n\geqslant3$, associated with a generalized condenser $(A_1,A_2)$ where $A_1$ is a relatively closed subset of a domain $D$ and $A_2=\mathbb R^n\setminus D$. We show that, though $A_2\cap{C\ell}_{\mathbb R^n}A_1$ may have nonzero capacity, this minimum energy problem is uniquely solvable (even in the presence of an external field) if we restrict ourselves to $\mu$ with $\mu^+\leqslant\xi$ where a constraint $\xi$ is properly chosen. We establish the sharpness of the sufficient conditions on the solvability thus obtained, provide descriptions of the weighted $\alpha$Riesz potentials of the solutions, single out their characteristic properties, and analyze their supports. The approach developed is mainly based on the establishment of an intimate relationship between the constrained minimum $\alpha$Riesz energy problem over sign
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In this paper we provide a new Bennequintype inequality for the RasmussenBeliakovaWehrli invariant, featuring the numerical transverse braid invariants (the $c$invariants) introduced in \[https://arxiv.org/abs/1705.03481]. From the Bennequin typeinequality, and a combinatorial bound on the value of the $c$invariants, we deduce a new computable bound on the RasmussenBeliakovaWehrli invariant.
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IBM released its new bespoke typeface IBM Plex in beta this week. The company is hoping that the new typeface would become just as iconic as Helvetica in the years to come. From a Fast Co Design story: "When I came to IBM, it was a big discussion: Why does IBM not have a bespoke typeface? Why are we still clinging on to Helvetica?" Mike Abbink, the typeface's designer and IBM's executive creative director of brand experience and design said. To uncover what the typeface should express, Abbink and his team took a deep dive into IBM's archives. They were especially interested in the company's history in the postwar years, when its designled business strategy first took shape and the legendary practitioner Paul Rand, who defined design as a system of relationships, created its famous eightbar logo. In Rand's logo, Abbink and his team saw a contrast between hard edges  the engineered, rational, and mechanical  and curves  the softer more humanistic elements. It's a reflection of th
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schwit1 shares a report from The Hill: The amendment, Section 801 of the National Defense Authorization Act (NDAA), would help Amazon establish a tight grip on the lucrative, $53 billion government acquisitions market, experts say. The provision, dubbed the "Amazon amendment" by experts, according to an article in The Intercept, would allow for the creation of an online portal that government employees could use to purchase everyday items such as office supplies or furniture. This governmentonly version of Amazon, which could potentially include a few other websites, would give participating companies direct access to the $53 billion market for government acquisitions of commercial products. "It hands an enormous amount of power over to Amazon," said Stacy Mitchell of the Institute for Local SelfReliance, a research group that advocates for local businesses. Mitchell said that the provision could allow Amazon to gain a monopoly or duopoly on the profitable world of commercial governm
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New Delhi, the Indian capital declared a pollution emergency on Thursday as toxic smog hung over the city for a third day and air quality worsened by the hour. From a report: Illegal crop burning in the farm states surrounding New Delhi, vehicle exhaust emissions in a city with limited public transport and swirling construction dust have caused the crisis, which arises every year. The problem has been compounded this year by still conditions, the weather office said. A U.S. embassy measure of tiny particulate matter PM 2.5 showed a reading of 608 at 10 a.m. when the safe limit is 25. An hour before it was 591.
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At the annual meeting of the Society for Neuroscience starting November 11 in Washington D.C., two teams of scientists plan to present previously unpublished research on the unexpected interaction between human minibrains and their rat and mouse hosts. "In the new papers, according to STAT, scientists will report that the organoids survived for extended periods of time  two months in one case  and even connected to lab animals' circulatory and nervous systems, transferring blood and nerve signals between the host animal and the implanted human cells," reports Inverse. "This is an unprecedented advancement for minibrain research." From the report: That minibrains can even be grown in the lab is a huge advancement in the first place, as they have many of the same characteristics as living human brains that are in the early stages of development. Though they're not "alive" in the same sense that you and I are, they grow and are organized into different layers like our brains are. T
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An anonymous reader quotes a report from Tom's Hardware: Intel's Management Engine (ME) technology is built into almost all modern Intel CPUs. At the Embedded Linux Conference, a Google engineer named Ronald Minnich revealed that the ME is actually running its own entire MINIX OS and that Google is working on removing it. Due to MINIX's presence on every Intel system, the barebones Unixlike OS is the most widely deployed operating system in the world. Intel's ME technology is a hardwarelevel system within Intel CPUs that consists of closedsource firmware running on a dedicated microprocessor. There isn't much public knowledge of the workings of the ME, especially in its current state. It's not even clear where the hardware is physically located anymore. What's concerning Google is the complexity of the ME. Public interest in the subject piqued earlier this year when a vulnerability was discovered in Intel's Active Management Technology (AMT), but that's just a software that runs on
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Google is digging into the dark corners of the web to better secure people's accounts. From a report: For one year, Google researchers investigated the different ways hackers steal personal information and take over Google accounts. Google published its research, conducted between March 2016 and March 2017, on Thursday. Focusing exclusively on Google accounts and in partnership with the University of California, Berkeley, researchers created an automated system to scan public websites and criminal forums for stolen credentials. The group also investigated over 25,000 criminal hacking tools, which it received from undisclosed sources. Google said it is the first study taking a long term and comprehensive look at how criminals steal your data, and what tools are most popular. [...] Google researchers identified 788,000 potential victims of keylogging and 12.4 million potential victims of phishing. These types of attacks happen all the time. For example on average, the phishing tools Goog
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We explore two approaches to integration of representations from a Lie algebra to its algebraic group in positive characteristic. The first approach, a variation of a theme of Haboush, exploits exponentials. The second approach, a variation of a theme of Cline and Donkin, utilises $G$stability.
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In this paper we investigate the integrability properties of a twostate vertex model on the square lattice whose microstates at a vertex has always an odd number of incoming or outcoming arrows. This model was named odd eightvertex model by Wu and Kunz \cite{WK} to distinguish it from the well known eightvertex model possessing an even number of arrows orientations at each vertex. When the energy weights are invariant under arrows inversion we show that the integrable manifold of the odd eightvertex model coincides with that of the even eightvertex model. The form of the $\mathrm{R}$matrix for the odd eightvertex model is however not the same as that of the respective Lax operator. Altogether we find that these eightvertex models give rise to a generic sheaf of $\mathrm{R}$matrices satisfying the YangBaxter equations resembling intertwiner relations associated to equidimensional representations.
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We revisit the phenomenon of instability of solitons in the two dimensional generalization of the Kortewegde Vries equation, the generalized ZakharovKuznetsov (ZK) equation, $u_t + \partial_{x_1} (\Delta u + u^p) = 0, (x_1,x_2) \in \mathbb R^2$. It is known that solitons are unstable in this two dimensional equation for nonlinearities $p > 3$. This was shown by Anne de Bouard in [4] generalizing the arguments of BonaSouganidisStrauss in [1] for the generalized KdV equation. In this paper, we use a different method to obtain the instability of solitons, namely, truncation and monotonicity properties. Not only does this approach simplify the proof, but it can also be useful for studying various other stability questions in the ZK equation as well as other generalizations of the KdV equation.
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We revisit the phenomenon of instability of solitons in the generalized Kortewegde Vries equation, $u_t + \partial_x(u_{xx} + u^p) = 0$. It is known that solitons are unstable for nonlinearities $p \geq 5$, with the critical power $p=5$ being the most challenging case to handle. The critical case was proved by MartelMerle in [11], where the authors crucially relied on the pointwise decay estimates of the linear KdV flow. In this paper, we show simplified approaches to obtain the instability of solitons via truncation and monotonicity, which can be also useful for other KdVtype equations.
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We consider a fractional elliptic equation in an unbounded set with both Dirichlet and fractional normal derivative datum prescribed. We prove that the domain and the solution are necessarily radially symmetric. The extension of the result in bounded nonconvex regions is also studied, as well as the radial symmetry of the solution when the set is a priori supposed to be rotationally symmetric.
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A simple scheme was proposed by Knuth to generate balanced codewords from a random binary information sequence. However, this method presents a redundancy which is twice as that of the full sets of balanced codewords, that is the minimal achievable redundancy. The gap between the Knuth's algorithm generated redundancy and the minimal one is significantly considerable and can be reduced. This paper attempts to achieve this goal through a method based on information sequence candidates. The proposed scheme is suitable for various communication systems as it generates very efficient and less redundant balanced codes.
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We present numerical reconstructions of anisotropic conductivity tensors in three dimensions, from knowledge of a finite family of power density functionals. Such a problem arises in the coupledphysics imaging modality Ultrasound Modulated Electrical Impedance Tomography for instance. We improve on the algorithms previously derived in [Bal et al, Inverse Probl Imaging (2013), pp.353375, Monard and Bal, Comm. PDE (2013), pp.11831207] for both isotropic and anisotropic cases, and we address the wellknown issue of vanishing determinants in particular. The algorithm is implemented and we provide numerical results that illustrate the improvements.
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We investigate the large $n$ asymptotics of the $n$th eigenvalue for a class of unbounded selfadjoint operators defined by infinite Jacobi matrices with discrete spectrum. In the case of the quantum Rabi model we obtain the first three terms of the asymptotics which determine the parameters of the model. This paper is based on our previous paper [5] that it completes and improves.
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Motivated by an old conjecture of P. Erd\H{o}s and V. NeumannLara, our aim is to investigate digraphs with uncountable dichromatic number and orientations of undirected graphs with uncountable chromatic number. A graph has uncountable chromatic number if its vertices cannot be covered by countably many independent sets, and a digraph has uncountable dichromatic number if its vertices cannot be covered by countably many acyclic sets. We prove that consistently there are digraphs with uncountable dichromatic number and arbitrarily large digirth; this is in surprising contrast with the undirected case: any graph with uncountable chromatic number contains a 4cycle. Next, we prove that several well known graphs (uncountable complete graphs, certain comparability graphs, and shift graphs) admit orientations with uncountable dichromatic number in ZFC. However, we show that the statement "every graph $G$ of size and chromatic number $\omega_1$ has an orientation $D$ with uncountable dichroma
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