adv

solidot此次改版内容包括服务器更新、编程语言、网站后台管理的优化、页面和操作流程的优化等。

信息流

  •  

    Ask Slashdot: How Dead Is Java?

    02-03 Slashdot 3272

    This week HackerRank reported Java is now only the second most popular programming language, finally dropping behind JavaScript in the year 2018. Now long-time Slashdot reader shanen asks about the rumors that Java is dead -- or is it? Can you convince me that Java isn't as dead as it seems? It's just playing dead and will spring to life? This week one Java news site argued that Java-based Minecraft has in fact "spawned a new generation of Java developers," citing an interview with Red Hat's JBoss Middleware CTO. (And he adds that "It's still the dominant programming language in the enterprise, so whether you're building enterprise clients, services or something in between, Java likely features in there somewhere.") Yet the original submission drew some interesting comments: "The licensing scheme for Java kills it..." "Java programs still are 'the alien on your desktop'. They suck in many ways. Users have learned to avoid them and install 'real programs' instead..." But what do Sl

    发表评论 查看更多 翻译此文

    收起

  • The FBI confiscated six drones in Atlanta for flying too close to the football stadium where the Super Bowl will be played Sunday, Reuters reports: Drone flight was prohibited on Saturday and from 10 a.m. until 5:30 p.m. EST on Sunday for one nautical mile (2 km) around the Mercedes-Benz Stadium and up to an altitude of 1,000 feet (305 meters), the Federal Aviation Administration said. The FAA will establish temporary flight restriction that prohibits drones within a 30-nautical-mile radius of the stadium and up to 17,999 feet in altitude from 5:30 p.m. to 11:59 p.m. EST on Sunday, the agency said. .. Drones "are a big concern," said Nick Annan, Homeland Security Investigations special agent in charge. "There are a few other things that are in place to mitigate drones," he added without elaborating. Operators who send drones into restricted areas around the Mercedes-Benz Stadium could face more than $20,000 in civil penalties and criminal prosecution, according to the FAA. Drone pil

    发表评论 查看更多 翻译此文

    收起

  • AdaCore Joins the RISC-V Foundation to Provide C and Ada Compilation Support

    发表评论 查看更多 翻译此文

    收起

  • An anonymous reader quotes TechCrunch: In September of last year, Elon Musk promised to make fixing service times a priority. On an earnings call, he outlined two ways they're working on it: more spare parts at service centers, and giving Tesla cars the ability to automatically get the process started by calling a tow truck as soon as it detects an issue. Said Elon on the call: The next thing we want to add is if a car detects something wrong -- like a flat tire or a drive unit failure -- that before the car has even come to a halt, there's a tow truck and service loaner on the way. False alarm? Don't want a tow truck to show up? You'll be able to cancel it through the in-dash display. Musk didn't provide a time frame for when this feature would become available.

    发表评论 查看更多 翻译此文

    收起

  • Blackmailers use false copyright claims to shut down victims' YouTube accounts

    发表评论 查看更多 翻译此文

    收起

  • No, we don’t know if Bill Murray’s involved—but his character’s son is.

    发表评论 查看更多 翻译此文

    收起

  • Long-time Slashdot reader darkwing_bmf writes: In an exclusive interview with Popular Mechanics, SpaceX founder Elon Musk explains why stainless steel is the best material to build rocket ships, beating carbon fiber in cost, durability and even weight. "As far as we know, this marks the first time the material has been used in spacecraft construction since some early, ill-fated attempts during the Atlas program in the late 1950s," reports Popular Mechanics. "It took me quite a bit of effort to convince the team to go in this direction..." Musk tells them. But among the other benefits "It has a high melting point. Much higher than aluminum, and although carbon fiber doesn't melt, the resin gets destroyed at a certain temperature... But steel, you can do 1500, 1600 degrees Fahrenheit."

    发表评论 查看更多 翻译此文

    收起

  • More than a year after Facebook commercially launched Express Wi-Fi in five markets, it is ready to bring the connectivity service to the sixth: Ghana. From a report: In partnership with telecom operator Vodafone Ghana, Facebook today launched Express Wi-Fi, part of Internet.org initiative, in the suburban communities of the Western African nation. The service, available locally in Nima, James Town, Kanda, Pig Farm, and Abossey Okine in the capital city Accra, will aim to offer "carrier-grade Wi-Fi" to people living in some remote communities that lack fiber optic cables. Ever since India booted Free Basics in early 2016, Facebook has seemingly grown cautious about its connectivity efforts. The company has stopped updating the social media page and press page of Internet.org. Last year, we learned that Facebook had quietly pulled Internet.org from a handful of emerging markets. In recent months, however, it has quietly expanded Internet.org to two new markets -- Morocco (in North Afr

    发表评论 查看更多 翻译此文

    收起

  • QuadrigaCX survivors try to hack encrypted laptop in hopes of accessing cold wallet.

    发表评论 查看更多 翻译此文

    收起

  • An AI-enhanced tool that suggests code snippets for Python developers in real time just raised $17 million in VC funding to expand its R&D team "with a focus on accelerating developer productivity." An anonymous reader quotes VentureBeat: "Our mission is to bring the latest advancements in AI and machine learning (ML) to make writing code fluid, effortless, and more enjoyable," explained [founder Adam] Smith. "Developers using Kite can focus their productive energy toward solving the next big technical challenges, instead of searching the web for code examples illustrating mundane and frequently repeated code patterns...." Instead of relying on the cloud to run its AI engine, Kite now runs locally on a user's computer, letting developers use it offline and without having to upload any code. (Kite still trains its machine learning models with thousands of publicly available code sources from highly rated developers.) Furthermore, running locally allows Kite to fully operate with

    发表评论 查看更多 翻译此文

    收起

  •  

    Dotfile madness

    02-03 Hacker News 3200

    Dotfile madness

    发表评论 查看更多 翻译此文

    收起

  • A catalog of wealth-creation mechanisms (2009)

    发表评论 查看更多 翻译此文

    收起

  • Einsum Is All You Need – Einstein Summation in Deep Learning (2018)

    发表评论 查看更多 翻译此文

    收起

  • We give two explicit sets of generators of the group of invertible regular functions over QQ on the modular curve Y1(N). The first set of generators is the most surprising. It is essentially the set of defining equations of Y1(k) for k<=N/2 when all these modular curves are simultaneously embedded into the affine plane, and this proves a conjecture of Maarten Derickx and Mark van Hoeij. This set of generators is an elliptic divisibility sequence in the sense that it satisfies the same recurrence relation as the elliptic division polynomials. The second set of generators is explicit in terms of classical analytic functions known as Siegel functions. This is both a generalization and a converse of a result of Yifan Yang. Our proof consists of two parts. First, we relate our two sets of generators. Second, we use q-expansions and Gauss' lemma for power series to prove that our functions generate the full group of modular functions. This second part shows how a proof of Kubert and Lang

    发表评论 查看更多 翻译此文

    收起

  •  

    CSS-In-JS and Static Rendering

    02-02 Hacker News 3231

    CSS-In-JS and Static Rendering

    发表评论 查看更多 翻译此文

    收起

  • We discuss the extent to which solutions to one-phase free boundary problems can be characterized according to their topological complexity. Our questions are motivated by fundamental work of Luis Caffarelli on free boundaries and by striking results of T. Colding and W. Minicozzi concerning finitely connected, embedded, minimal surfaces. We review our earlier work on the simplest case, one-phase free boundaries in the plane in which the positive phase is simply connected. We also prove a new, purely topological, effective removable singularities theorem for free boundaries. At the same time, we formulate some open problems concerning the multiply connected case and make connections with the theory of minimal surfaces and semilinear variational problems.

    发表评论 查看更多 翻译此文

    收起

  • This week’s most thought-provoking papers from the Physics arXiv.

    发表评论 查看更多 翻译此文

    收起

  • Bests human professional gamers in the complex strategy game StarCraft II

    发表评论 查看更多 翻译此文

    收起

  • Ben McGrath writes about how New Jersey’s successful challenge to a law that restricted legal sports gambling to Nevada is likely to affect interest in this year’s Super Bowl, which will be played on Sunday.

    发表评论 查看更多 翻译此文

    收起

  • Model shows how black hole plasma jets form: may reveal event horizon details.

    发表评论 查看更多 翻译此文

    收起

  • Anti-elementarity is a strong way of ensuring that a class of structures , in a given first-order language, is not closed under elementary equivalence with respect to any infinitary language of the form $\mathscr{L}_{\infty\lambda}$. We prove that many naturally defined classes are anti-elementary, including the following: $\bullet$ the class of all lattices of finitely generated convex $\ell$-subgroups of members of any class of $\ell$-groups containing all Archimedean $\ell$-groups; $\bullet$ the class of all semilattices of finitely generated $\ell$-ideals of members of any nontrivial quasivariety of $\ell$-groups; $\bullet$ the class of all Stone duals of spectra of MV-algebras-this yields a negative solution for the MV-spectrum Problem; $\bullet$ the class of all semilattices of finitely generated two-sided ideals of rings; $\bullet$ the class of all semilattices of finitely generated submodules of modules; $\bullet$ the class of all monoids encoding the nonstable K$_0$-theory of

    发表评论 查看更多 翻译此文

    收起

  • A key theorem formulated in the context of functional Mellin transforms generalizes the important relationship $\exp\mathrm{tr} M=\det\exp M$. Along with the involution symmetry of the zeta function, the theorem suggests a strategy for tackling the Riemann hypothesis.

    发表评论 查看更多 翻译此文

    收起

  • Potential functions can be used as generating potentials of relevant geometric structures for a Riemannian manifold such as the Riemannian metric and affine connections. We study wether this procedure can also be applied to tensors of rank four and find a negative answer. We study this from the perspective of solving the inverse problem and also from an intrinsic point of view.

    发表评论 查看更多 翻译此文

    收起

  • From the archives: NASA's three worst disasters are clustered at the end of January.

    发表评论 查看更多 翻译此文

    收起

  • This paper deals with singularities of genus 2 curves on a general (d_1,d_2)-polarized abelian surface (S,L). In analogy with Chen's results concerning rational curves on K3 surfaces [Ch1,Ch2], it is natural to ask whether all such curves are nodal. We prove that this holds true if and only if d_2 is not divisible by 4. In the cases where d_2 is a multiple of 4, we exhibit genus 2 curves in |L| that have a triple, 4-tuple or 6-tuple point. We show that these are the only possible types of unnodal singularities of a genus 2 curve in |L|. Furthermore, with no assumption on d_1 and d_2, we prove the existence of at least a nodal curve in |L|. As a corollary, we obtain nonemptiness of all Severi varieties on general abelian surfaces and hence generalize [KLM, Thm 1.1] to nonprimitive polarizations.

    发表评论 查看更多 翻译此文

    收起

  • DIA Study: Invisibility Cloaking Theory and Experiments

    发表评论 查看更多 翻译此文

    收起

  • We introduce formal deformation theory of module homomorphisms. To study this we introduce a deformation cohomology of module homomorphisms.

    发表评论 查看更多 翻译此文

    收起

  • Building Consistent Transactions with Inconsistent Replication (2015) [pdf]

    发表评论 查看更多 翻译此文

    收起

  • Skeptical judges question FCC's justification of net neutrality repeal.

    发表评论 查看更多 翻译此文

    收起

  • Fuglede's conjecture in $\mathbb{Z}_{p}^{d}$, $p$ a prime, says that a subset $E$ tiles $\mathbb{Z}_{p}^{d}$ by translation if and only if $E$ is spectral, meaning any complex-valued function $f$ on $E$ can be written as a linear combination of characters orthogonal with respect to $E$. We disprove Fuglede's conjecture in $\mathbb{Z}_p^4$ for all odd primes $p$, by using log-Hadamard matrices to exhibit spectral sets of size $2p$ which do not tile, extending the result of Aten et al. that the conjecture fails in $\mathbb{Z}_p^4$ for primes $p \equiv 3 \pmod 4$ and in $\mathbb{Z}_p^5$ for all odd primes $p$. We also prove the conjecture in $\mathbb{Z}_2^4$, resolving all cases of four-dimensional vector spaces over prime fields. We give an example showing that our simple proof method does not extend to higher dimensions. However, we include a link to a computer program which the authors have used to verify that, nevertheless, the conjecture holds in $\mathbb{Z}_2^5$ and $\mathbb{Z}_2^6$

    发表评论 查看更多 翻译此文

    收起

  •  

    Bastion Fort

    02-02 Hacker News 3030

    Bastion Fort

    发表评论 查看更多 翻译此文

    收起

  • Let $U_1,U_2,\ldots$ be random points sampled uniformly and independently from the $d$-dimensional upper half-sphere. We show that, as $n\to\infty$, the $f$-vector of the $(d+1)$-dimensional convex cone $C_n$ generated by $U_1,\ldots,U_n$ weakly converges to a certain limiting random vector, without any normalization. We also show convergence of all moments of the $f$-vector of $C_n$ and identify the limiting constants for the expectations. We prove that the expected Grassmann angles of $C_n$ can be expressed through the expected $f$-vector. This yields convergence of expected Grassmann angles and conic intrinsic volumes and answers thereby a question of B\'ar\'any, Hug, Reitzner and Schneider [Random points in halfspheres, Rand. Struct. Alg., 2017]. Our approach is based on the observation that the random cone $C_n$ weakly converges, after a suitable rescaling, to a random cone whose intersection with the tangent hyperplane of the half-sphere at its north pole is the convex hull of th

    发表评论 查看更多 翻译此文

    收起

  • Singular boundary value problems (SBVPs) arise in various fields of Mathematics, Engineering and Physics such as boundary layer theory, gas dynamics, nuclear physics, nonlinear optics, etc. The present monograph is devoted to systems of SBVPs for ordinary differential equations (ODEs). It presents existence theory for a variety of problems having unbounded nonlinearities in regions where their solutions are searched for. The main focus is to establish the existence of positive solutions. The results are based on regularization and sequential procedure. First chapter of this monograph describe the motivation for the study of SBVPs. It also include some available results from functional analysis and fixed point theory. The following chapters contain results from author's PhD thesis, National University of Sciences and Technology, Islamabad, Pakistan. These results provide the existence of positive solutions for a variety of systems of SBVPs having singularity with respect to independent

    发表评论 查看更多 翻译此文

    收起

  • Consider the minimization of a nonconvex differentiable function over a polyhedron. A popular primal-dual first-order method for this problem is to perform a gradient projection iteration for the augmented Lagrangian function and then update the dual multiplier vector using the constraint residual. However, numerical examples show that this approach can exhibit "oscillation" and may not converge. In this paper, we propose a proximal alternating direction method of multipliers for the multi-block version of this problem. A distinctive feature of this method is the introduction of a "smoothed" (i.e., exponentially weighted) sequence of primal iterates, and the inclusion, at each iteration, to the augmented Lagrangian function a quadratic proximal term centered at the current smoothed primal iterate. The resulting proximal augmented Lagrangian function is inexactly minimized (via a gradient projection step) at each iteration while the dual multiplier vector is updated using the residual o

    发表评论 查看更多 翻译此文

    收起

  • It is known that the following five counting problems lead to the same integer sequence~$f_t(n)$: the number of nonequivalent compact Huffman codes of length~$n$ over an alphabet of $t$ letters, the number of `nonequivalent' canonical rooted $t$-ary trees (level-greedy trees) with $n$~leaves, the number of `proper' words, the number of bounded degree sequences, and the number of ways of writing $1= \frac{1}{t^{x_1}}+ \dots + \frac{1}{t^{x_n}}$ with integers $0 \leq x_1 \leq x_2 \leq \dots \leq x_n$. In this work, we show that one can compute this sequence for \textbf{all} $n<N$ with essentially one power series division. In total we need at most $N^{1+\varepsilon}$ additions and multiplications of integers of $cN$ bits, $c<1$, or $N^{2+\varepsilon}$ bit operations, respectively. This improves an earlier bound by Even and Lempel who needed $O(N^3)$ operations in the integer ring or $O(N^4)$ bit operations, respectively.

    发表评论 查看更多 翻译此文

    收起

  • In this paper, we examine some properties of the fixed point set of a digitally continuous function. The digital setting requires new methods that are not analogous to those of classical topological fixed point theory, and we obtain results that often differ greatly from standard results in classical topology. We introduce several measures related to fixed points for continuous self-maps on digital images, and study their properties. Perhaps the most important of these is the fixed point spectrum $F(X)$ of a digital image: that is, the set of all numbers that can appear as the number of fixed points for some continuous self-map. We give a complete computation of $F(C_n)$ where $C_n$ is the digital cycle of $n$ points. For other digital images, we show that, if $X$ has at least 4 points, then $F(X)$ always contains the numbers 0, 1, 2, 3, and the cardinality of $X$. We give several examples, including $C_n$, in which $F(X)$ does not equal $\{0,1,\dots,\#X\}$. We examine how fixed point

    发表评论 查看更多 翻译此文

    收起

  • In this paper, a modified van der Pol oscillator equation is considered which appears in several heart action models. We study its global dynamics and verify many interesting bifurcations such as a Hopf bifurcation, a heteroclinic saddle connection, and a homoclinic saddle connection. Some of these bifurcations are detected by using Conley index methods. We demonstrate how the study of connection matrices and transition matrices shows how to select interesting parameter values for simulations.

    发表评论 查看更多 翻译此文

    收起

  • This paper introduces a hierarchical interpolative decomposition butterfly-LU factorization (H-IDBF-LU) preconditioner for solving two-dimensional electric-field integral equations (EFIEs) in electromagnetic scattering problems of perfect electrically conducting objects with open surfaces. H-IDBF-LU leverages the interpolative decomposition butterfly factorization (IDBF) to compress dense blocks of the discretized EFIE operator to expedite its application; this compressed operator also serves as an approximate LU factorization of the EFIE operator leading to an efficient preconditioner in iterative solvers. Both the memory requirement and computational cost of the H-IDBF-LU solver scale as $O(N\log^2 N)$ in one iteration; the total number of iterations required for a reasonably good accuracy scales as $O(1)$ to $O(\log^2N)$ in all of our numerical tests. The efficacy and accuracy of the proposed preconditioned iterative solver are demonstrated via its application to a broad range of sc

    发表评论 查看更多 翻译此文

    收起

  • Dimension profiles were introduced in [8,11] to give a formula for the box-counting and packing dimensions of the orthogonal projections of a set $R^n$ onto almost all $m$-dimensional subspaces. However, these definitions of dimension profiles are indirect and are hard to work with. Here we firstly give alternative definitions of dimension profiles in terms of capacities of $E$ with respect to certain kernels, which lead to the box-counting and packing dimensions of projections fairly easily, including estimates on the size of the exceptional sets of subspaces where the dimension of projection is smaller the typical value. Secondly, we argue that with this approach projection results for different types of dimension may be thought of in a unified way. Thirdly, we use a Fourier transform method to obtain further inequalities on the size of the exceptional subspaces.

    发表评论 查看更多 翻译此文

    收起

  • Grin, a strange new coin that runs on a technology called MimbleWimble, has captured the blockchain world’s imagination.

    发表评论 查看更多 翻译此文

    收起

  • We investigate the behavior of Boolean dimension with respect to components and blocks. To put our results in context, we note that for Dushnik-Miller dimension, we have that if $\dim(C)\le d$ for every component $C$ of a poset $P$, then $\dim(P)\le \max\{2,d\}$; also if $\dim(B)\le d$ for every block $B$ of a poset $P$, then $\dim(P)\le d+2$. By way of constrast, local dimension is well behaved with respect to components, but not for blocks: if $\text{ldim}(C)\le d$ for every component $C$ of a poset $P$, then $\text{ldim}(P)\le d+2$; however, for every $d\ge 4$, there exists a poset $P$ with $\text{ldim}(P)=d$ and $\dim(B)\le 3$ for every block $B$ of $P$. In this paper we show that Boolean dimension behaves like Dushnik-Miller dimension with respect to both components and blocks: if $\text{bdim}(C)\le d$ for every component $C$ of $P$, then $\text{bdim}(P)\le 2+d+4\cdot2^d$; also if $\text{bdim}(B)\le d$ for every block of $P$, then $\text{bdim}(P)\le 19+d+18\cdot 2^d$.

    发表评论 查看更多 翻译此文

    收起

  • We present a framework for characterizing injectivity of classes of maps (on cosets of a linear subspace) by injectivity of classes of matrices. Using our formalism, we characterize injectivity of several classes of maps, including generalized monomial and monotonic (not necessarily continuous) maps. In fact, monotonic maps are special cases of {\em component-wise affine} maps. Further, we study compositions of maps with a matrix and other composed maps, in particular, rational functions. Our framework covers classical injectivity criteria based on mean value theorems for vector-valued maps and recent results obtained in the study of chemical reaction networks.

    发表评论 查看更多 翻译此文

    收起

  • Why researchers at the year’s biggest AI conference focused on how to keep human bias out of computer algorithms.

    发表评论 查看更多 翻译此文

    收起

  • Kontsevich and Manin gave a formula for the number $N_e$ of rational plane curves of degree $e$ through $3e-1$ points in general position in the plane. When these $3e-1$ points have coordinates in the rational numbers, the corresponding set of $N_e$ rational curves has a natural Galois-module structure. We make some extremely preliminary investigations into this Galois module structure, and relate this to the deck transformations of the generic fibre of the product of the evaluation maps on the moduli space of maps. We then study the asymptotics of the number of rational points on hypersurfaces of low degree, and use this to generalise our results by replacing the projective plane by such a hypersurface.

    发表评论 查看更多 翻译此文

    收起

  • In this paper we improve upon in terms of S the best known effective upper bounds for the solutions of S-unit equations and decomposable form equations.

    发表评论 查看更多 翻译此文

    收起

  • Beijing has approved four new reactors after a two-year pause, according to Chinese media.

    发表评论 查看更多 翻译此文

    收起

  • We present, to the best of the authors' knowledge, all known results for the crossing numbers of specific graphs and graph families. The results are separated into various categories; specifically, results for general graph families, results for graphs arising from various graph products, and results for recursive graph constructions.

    发表评论 查看更多 翻译此文

    收起

  • For a low-mobile Poisson bipolar network and under line-of-sight/non-line-of-sight (LOS/NLOS) path-loss model, we study repetitive retransmissions (RR) and blocked incremental redundancy (B-IR). We consider spatially-coded multiple-input multiple-output (MIMO) zero-forcing beamforming (ZFBF) multiplexing system, whereby the packet success reception is determined based on the aggregate data rate across spatial dimensions of the MIMO system. Characterization of retransmission performance in this low-mobile configuration is practically important, but inherently complex due to a substantial rate correlation across retransmissions and intractability of evaluating the probability density function (pdf) of aggregate data rate. Adopting tools of stochastic geometry, we firstly characterize the rate correlation coefficient (RCC) for both schemes. Our results show that, compared to RR scheme, B-IR scheme has higher RCC while its coverage probability is substantially larger. We demonstrate that t

    发表评论 查看更多 翻译此文

    收起

  • Detecting the components common or correlated across multiple data sets is challenging due to a large number of possible correlation structures among the components. Even more challenging is to determine the precise structure of these correlations. Traditional work has focused on determining only the model order, i.e., the dimension of the correlated subspace, a number that depends on how the model-order problem is defined. Moreover, identifying the model order is often not enough to understand the relationship among the components in different data sets. We aim at solving the complete modelselection problem, i.e., determining which components are correlated across which data sets. We prove that the eigenvalues and eigenvectors of the normalized covariance matrix of the composite data vector, under certain conditions, completely characterize the underlying correlation structure. We use these results to solve the model-selection problem by employing bootstrap-based hypothesis testing.

    发表评论 查看更多 翻译此文

    收起

  • This paper studies curves on quartic K3 surfaces, or more generally K3 surfaces which are complete intersection in weighted projective spaces. A folklore conjecture concerning rational curves on K3 surfaces states that all K3 surfaces contain infinite number of irreducible rational curves. It is known that all K3 surfaces, except those contained in the countable union of hypersurfaces in the moduli space of K3 surfaces satisfy this property. In this paper we present a new approach for constructing curves on varieties which admit nice degenerations. We apply this technique to the above problem and prove that there is a Zariski open dense subset in the moduli space of quartic K3 surfaces whose members satisfy the conjecture. Various other curves of positive genus can be also constructed.

    发表评论 查看更多 翻译此文

    收起

  • We consider sentence-definable and diagram-definable subfamilies of given families of theories, calculi for these subfamilies, as well dynamics and characteristics of these subfamilies with respect to rank and degree.

    发表评论 查看更多 翻译此文

    收起

  • We initiate the study of Boolean function analysis on high-dimensional expanders. We give a random-walk based definition of high dimensional expansion, which coincides with the earlier definition in terms of two-sided link expanders. Using this definition, we describe an analogue of the Fourier expansion and the Fourier levels of the Boolean hypercube for simplicial complexes. Our analogue is a decomposition into approximate eigenspaces of random walks associated with the simplicial complexes. We then use this decomposition to extend the Friedgut-Kalai-Naor theorem to high-dimensional expanders. Our results demonstrate that a high-dimensional expander can sometimes serve as a sparse model for the Boolean slice or hypercube, and quite possibly additional results from Boolean function analysis can be carried over to this sparse model. Therefore, this model can be viewed as a derandomization of the Boolean slice, containing only $|X(k-1)|=O(n)$ points in contrast to $\binom{n}{k}$ points

    发表评论 查看更多 翻译此文

    收起

  • Given two $\left( n+1\right) \times\left( n+1\right)$-matrices $A$ and $B$ over a commutative ring, and some $k\in\left\{ 0,1,\ldots,n\right\}$, we consider the $\dbinom{n}{k}\times\dbinom{n}{k}$-matrix $W$ whose entries are $\left( k+1\right) \times\left( k+1\right)$-minors of $A$ multiplied by corresponding $\left( k+1\right) \times\left( k+1\right)$-minors of $B$. Here we require the minors to use the last row and the last column (which is why we obtain an $\dbinom{n}{k}\times\dbinom{n}{k}$-matrix, not a $\dbinom{n+1}{k+1}\times\dbinom{n+1}{k+1}$-matrix). We prove that the determinant $\det W$ is a multiple of $\det A$ if the $\left( n+1,n+1\right)$-th entry of $B$ is $0$. Furthermore, if the $\left( n+1,n+1\right)$-th entries of both $A$ and $B$ are $0$, then $\det W$ is a multiple of $\left( \det A\right) \left( \det B\right)$. This extends a previous result of Olver and the author ( arXiv:1802.02900 ).

    发表评论 查看更多 翻译此文

    收起

  • Using dual perturbation theory in a non-sun-reflexive context, we establish a correspondence between 1. a class of nonlinear abstract delay differential equations (DDEs) with unbounded linear part and an unknown taking values in an arbitrary Banach space and 2. a class of abstract weak* integral equations of convolution type involving the sun-star adjoint of a translation-like strongly continuous semigroup. For this purpose we also characterize the sun dual of the underlying state space. More generally we consider bounded linear perturbations of an arbitrary strongly continuous semigroup and we comment on some implications for the particular case of abstract DDEs.

    发表评论 查看更多 翻译此文

    收起

  • The presented splitting lemma extends the techniques of Gromov and Forstneri\v{c} to glue local sections of a given analytic sheaf, a key step in the proof of all Oka principles. The novelty on which the proof depends is a lifting lemma for transition maps of coherent sheaves, which yields a reduction of the proof to the work of Forstneri\v{c}. As applications we get shortcuts in the proofs of Forster and Ramspott's Oka principle for admissible pairs and of the interpolation property of sections of elliptic submersions, an extension of Gromov's results obtained by Forstneri\v{c} and Prezelj.

    发表评论 查看更多 翻译此文

    收起

  • Inspired by a PDE-ODE system of aggregation developed in the biomathematical literature, an interacting particle system representing aggregation at the level of individuals is investigated. It is proved that the empirical density of the individual converges to solution of the PDE-ODE system.

    发表评论 查看更多 翻译此文

    收起

  • Caching the content closer to the user equipments (UEs) in heterogenous cellular networks (HetNets) improves user-perceived Quality-of-Service (QoS) while lowering the operators backhaul usage/costs. Nevertheless, under the current networking strategy that promotes aggressive densification, it is unclear whether cache-enabled HetNets preserve the claimed cost-effectiveness and the potential benefits. This is due to 1) the collective cost of caching which may inevitably exceed the expensive cost of backhaul in a dense HetNet, and 2) the excessive interference which affects the signal reception irrespective of content placement. We analyze these significant, yet overlooked, issues, showing that while densification reduces backhaul load and increases spectral efficiency in cache-enabled dense networks, it simultaneously reduces cache-hit probability and increases the network cost. We then introduce a caching efficiency metric, area spectral efficiency per unit spent cost, and find it enou

    发表评论 查看更多 翻译此文

    收起

  • Let $K$ be a Henselian, non-trivially valued field with separated analytic structure. We prove the existence of definable retractions onto an arbitrary closed definable subset of $K^{n}$. Hence directly follow definable non-Archimedean versions of the extension theorems by Tietze--Urysohn and Dugundji. This generalizes our previous paper dealing with complete non-Archimedean fields with separated power series and remains true for Henselian valued fields with strictly convergent analytic structure, because every such a structure can be extended in a definitional way to a separated analytic structure. Our proof uses a variant of the one from that paper, based on canonical resolution of singularities, and a model-theoretic compactness argument.

    发表评论 查看更多 翻译此文

    收起

  • In this note, we extend work of Farkas and Rim\'anyi on applying quadric rank loci to finding divisors of small slope on the moduli space of curves by instead considering all divisorial conditions on the hypersurfaces of a fixed degree containing a projective curve. This gives rise to a large family of virtual divisors on $\overline{\mathcal{M}_g}$. We determine explicitly which of these divisors are candidate counterexamples to the Slope Conjecture. The potential counterexamples exist on $\overline{\mathcal{M}_g}$, where the set of possible values of $g\in \{1,\ldots,N\}$ has density $\Omega(\log(N)^{-0.087})$ for $N>>0$. Furthermore, no divisorial condition defined using hypersurfaces of degree greater than 2 give counterexamples to the Slope Conjecture, and every divisor in our family has slope at least $6+\frac{8}{g+1}$.

    发表评论 查看更多 翻译此文

    收起

  • We investigate the effect of surface tension on the linear Rayleigh--Taylor (RT) instability in stratified incompressible viscous fluids with or without (interface) surface tension. The existence of linear RT instability solutions with largest growth rate $\Lambda$ is proved under the instability condition (i.e., the surface tension coefficient $\vartheta$ is less than a threshold $\vartheta_{\mm{c}}$) by modified variational method of PDEs. Moreover we find a new upper bound for $\Lambda$. In particular, we observe from the upper bound that $\Lambda$ decreasingly converges to zero, as $\vartheta$ goes from zero to the threshold $\vartheta_{\mm{c}}$. The convergence behavior of $\Lambda$ mathematically verifies the classical RT instability experiment that the instability growth is limited by surface tension during the linear stage.

    发表评论 查看更多 翻译此文

    收起

  • Let $(\bf U, \bf U^\imath)$ be a quasi-split quantum symmetric pair of arbitrary Kac-Moody type, where "quasi-split" means the corresponding Satake diagram contains no black node. We give a presentation of the $\imath$quantum group $\bf U^\imath$ with explicit $\imath$Serre relations. The verification of new $\imath$Serre relations is reduced to some new q-binomial identities. Consequently, $\bf U^\imath$ is shown to admit a bar involution under suitable conditions on the parameters.

    发表评论 查看更多 翻译此文

    收起

  • Calabi observed that there is a natural correspondence between the solutions of the minimal surface equation in $\mathbb{R}^3$ with those of the maximal spacelike surface equation in $\mathbb{L}^3$. We are going to show how this correspondence can be extended to the family of $\varphi $-minimal graphs in $\mathbb{R}^3 $ when the function $\varphi$ is invariant under a two-parametric group of translations. We give also applications in the study and description of new examples.

    发表评论 查看更多 翻译此文

    收起

  • We prove that the KLR algebra associated with the cyclic quiver of length $e$ is a subquotient of the KLR algebra associated with the cyclic quiver of length $e+1$. We also give a geometric interpretation of this fact. This result has an important application in the theory of categorical representations. We prove that a category with an action of $\widetilde{\mathfrak{sl}}_{e+1}$ contains a subcategory with an action of $\widetilde{\mathfrak{sl}}_{e}$. We also give generalizations of these results to more general quivers and Lie types.

    发表评论 查看更多 翻译此文

    收起

  • Let $p$ be an odd prime with $p\equiv1\bmod 4$. Then for any odd power $q$ of $p$ and a positive integer $j$ we show that the groups $\text{Sp}_{p^j+1}(q),\text{PSp}_{p^j+1}(q)$, and their Sylow $p$-subgroups are non-$FSZ_{p^j}$.

    发表评论 查看更多 翻译此文

    收起

  • Recently, in the paper \cite{CJKM1} we suggested the two conjectures about the diameter of io-decomposable Riordan graphs of the Bell type. In this paper, we give a counterexample for the first conjecture. Then we prove that the first conjecture is true for the graphs of some particular size and propose a new conjecture. Finally, we show that the second conjecture is true for some special io-decomposable Riordan graphs.

    发表评论 查看更多 翻译此文

    收起

  • Unmanned aerial vehicles (UAVs) have recently found abundant applications in the public and civil domains. To ensure reliable control and navigation, connecting UAVs to controllers via existing cellular network infrastructure, i.e., ground base stations (GBSs), has been proposed as a promising solution. Nevertheless, it is highly challenging to characterize the communication performance of cellular-connected UAVs, due to their unique propagation conditions. This paper proposes a tractable framework for the coverage analysis of cellular-connected UAV networks, which consists of a new blockage model and an effective approach to handle general fading channels. In particular, a line-of-sight (LoS) ball model is proposed to capture the probabilistic propagation in UAV communication systems, and a tractable expression is derived for the Laplace transform of the aggregate interference with general Nakagami fading. This framework leads to a tractable expression for the coverage probability, wh

    发表评论 查看更多 翻译此文

    收起

  • Our aim is to study the existence and uniqueness of the $L^{p}$ - variational solution, with $p>1,$ of the following multivalued backward stochastic differential equation with $p$-integrable data: \[ \left\{ \begin{align*} &-dY_{t}+\partial_{y}\Psi\left( t,Y_{t}\right) dQ_{t} \ni H\left( t,Y_{t},Z_{t}\right) dQ_{t}-Z_{t}dB_{t},\;t\in\left[ 0,T\right] ,\\ &Y_{T} =\eta, \end{align*} \right. \] where $Q$ is a progresivelly measurable increasing continuous stochastic process and $\partial_{y}\Psi$ is the subdifferential of the convex lower semicontinuous function $y\mapsto\Psi(t,y)$. In the framework $p\geq2$ of Maticiuc, R\u{a}\c{s}canu from [Bernoulli, 2015], the strong solution found it there is the unique variational solution, via the uniqueness property proved in the present article.

    发表评论 查看更多 翻译此文

    收起

  • Presented is a method to compute certain classes of Hamilton-Jacobi equations that result from optimal control and trajectory generation problems with time delays. Many robotic control and trajectory problems have limited information of the operating environment a priori and must continually perform online trajectory optimization in real time after collecting measurements. The sensing and optimization can induce a significant time delay, and must be accounted for when computing the trajectory. This paper utilizes the generalized Hopf formula, which avoids the use of grids and numerical gradients that is typical of other methods for computing solutions to the Hamilton-Jacobi equation, which suffer exponential dimensional scaling. We present as an example a robot that incrementally predicts a communication channel from measurements as it travels. As part of this example, we introduce a seemingly new generalization of a non-parametric formulation of robotic communication channel estimatio

    发表评论 查看更多 翻译此文

    收起

  • Let $\text{Mod}(S_g)$ be the mapping class group of the closed orientable surface $S_g$ of genus $g\geq 2$. In this paper, we derive necessary and sufficient conditions for two finite-order mapping classes to have commuting conjugates in $\text{Mod}(S_g)$. As an application of this result, we show that any finite-order mapping class, whose corresponding orbifold is not a sphere, has a conjugate that lifts under any finite-sheeted cover of $S_g$. Furthermore, we show that any torsion element in the centralizer of an irreducible finite order mapping class is of order at most $2$. We also obtain conditions for the primitivity of a finite-order mapping class. Finally, we describe a procedure for determining the explicit hyperbolic structures that realize two-generator finite abelian groups of $\text{Mod}(S_g)$ as isometry groups.

    发表评论 查看更多 翻译此文

    收起

  • Derived equivalences of twisted K3 surfaces induce twisted Hodge isometries between them; that is, isomorphisms of their cohomologies which respect certain natural lattice structures and Hodge structures. We prove a criterion for when a given Hodge isometry arises in this way. In particular, we describe the image of the representation which associates to any autoequivalence of a twisted K3 surface its realization in cohomology: this image is a subgroup of index one or two in the group of all Hodge isometries of the twisted K3 surface. We show that both indices can occur.

    发表评论 查看更多 翻译此文

    收起

  • In this work we consider the following class of fractional $p\&q$ Laplacian problems \begin{equation*} (-\Delta)_{p}^{s}u+ (-\Delta)_{q}^{s}u + V(\varepsilon x) (|u|^{p-2}u + |u|^{q-2}u)= f(u) \mbox{ in } \mathbb{R}^{N}, \end{equation*} where $\varepsilon>0$ is a parameter, $s\in (0, 1)$, $1< p<q<\frac{N}{s}$, $(-\Delta)^{s}_{t}$, with $t\in \{p,q\}$, is the fractional $t$-Laplacian operator, $V:\mathbb{R}^{N}\rightarrow \mathbb{R}$ is a continuous potential and $f:\mathbb{R}\rightarrow \mathbb{R}$ is a $\mathcal{C}^{1}$-function with subcritical growth. Applying minimax theorems and the Ljusternik-Schnirelmann theory, we investigate the existence, multiplicity and concentration of nontrivial solutions provided that $\varepsilon$ is sufficiently small.

    发表评论 查看更多 翻译此文

    收起

  • Apple has now shut down Google’s ability to distribute its internal iOS apps, following a similar shutdown that was issued to Facebook earlier this week. A person familiar with the situation tells The Verge that early versions of Google Maps, Hangouts, Gmail, and other pre-release beta apps have stopped working today, alongside employee-only apps like a Gbus app for transportation and Google’s internal cafe app. “We’re working with Apple to fix a temporary disruption to some of our corporate iOS apps, which we expect will be resolved soon,” says a Google spokesperson in a statement to The Verge. Apple has not yet commented on the situation. There are two sides to this story. One the one hand, I’m glad Apple is taking measures and revoking some of these companies’ developer rights. These kinds of privacy-invading apps are a terrible idea, even if people get paid for them, and no platform should allow them. On the other hand, though, I would much rather have such tactics be w

    发表评论 查看更多 翻译此文

    收起

  • Engineers from Johns Hopkins reinvent the humble stethoscope to save lives

    发表评论 查看更多 翻译此文

    收起

  • We show that if $M$ is a sub-Riemannian manifold and $N$ is a Carnot group such that the nilpotentization of $M$ at almost every point is isomorphic to $N$, then there are subsets of $N$ of positive measure that embed into $M$ by bilipschitz maps. Furthermore, $M$ is countably $N$--rectifiable, i.e., all of $M$ except for a null set can be covered by countably many such maps.

    发表评论 查看更多 翻译此文

    收起

  • Nonnegative matrix factorization (NMF) is a linear dimensionality reduction technique for analyzing nonnegative data. A key aspect of NMF is the choice of the objective function that depends on the noise model (or statistics of the noise) assumed on the data. In many applications, the noise model is unknown and difficult to estimate. In this paper, we define a multi-objective NMF (MO-NMF) problem, where several objectives are combined within the same NMF model. We propose to use Lagrange duality to judiciously optimize for a set of weights to be used within the framework of the weighted-sum approach, that is, we minimize a single objective function which is a weighted sum of the all objective functions. We design a simple algorithm using multiplicative updates to minimize this weighted sum. We show how this can be used to find distributionally robust NMF (DR-NMF) solutions, that is, solutions that minimize the largest error among all objectives. We illustrate the effectiveness of this

    发表评论 查看更多 翻译此文

    收起

  • A nested Schur complement solver is proposed for iterative solution of linear systems arising in exponential and implicit time integration of the Maxwell equations with perfectly matched layer (PML) nonreflecting boundary conditions. These linear systems are the so-called double saddle point systems whose structure is handled by the Schur complement solver in a nested, two-level fashion. The solver is demonstrated to have a mesh-independent convergence at the outer level, whereas the inner level system is of elliptic type and thus can be treated efficiently by a variety of solvers.

    发表评论 查看更多 翻译此文

    收起

  • We introduce the $2$-nodal spherical deformation of certain singular fibers of genus $2$ fibrations, and use such deformations to construct various examples of simply connected minimal symplectic $4$-manifolds with small topology. More specifically, we construct new exotic minimal symplectic $4$-manifolds homeomorphic but not diffeomorphic to ${\mathbb{CP}}^{2}\#6({\overline{\mathbb{CP}}^{2}})$, ${\mathbb{CP}}^{2}\#7({\overline{\mathbb{CP}}^{2}})$, and $3{\mathbb{CP}}^{2}\#k({\overline{\mathbb{CP}}^{2}})$ for $k=16, 17, 18, 19$ using combinations of such deformations, symplectic blowups, and (generalized) rational blowdown surgery. We also discuss generalizing our constructions to higher genus fibrations using $g$-nodal spherical deformations of certain singular fibers of genus $g \geq 3$ fibrations.

    发表评论 查看更多 翻译此文

    收起

  • In this paper we study axially symmetric solutions of Allen-Cahn equation with finite Morse index. It is shown that there does not exist such a solution in dimensions between $4$ and $10$. In dimension $3$, we prove that these solutions have finitely many ends. Furthermore, the solution has exactly two ends if its Morse index equals $1$.

    发表评论 查看更多 翻译此文

    收起

  • We establish the rectifiability of measures satisfying a linear PDE constraint. The obtained rectifiability dimensions are optimal for many usual PDE operators, including all first-order systems and all second-order scalar operators. In particular, our general theorem provides a new proof of the rectifiability results for functions of bounded variations (BV) and functions of bounded deformation (BD). For divergence-free tensors we obtain refinements and new proofs of several known results on the rectifiability of varifolds and defect measures.

    发表评论 查看更多 翻译此文

    收起

  • Thomassen formulated the following conjecture: Every $3$-connected cubic graph has a red-blue vertex coloring such that the blue subgraph has maximum degree $1$ (that is, it consists of a matching and some isolated vertices) and the red subgraph has minimum degree at least $1$ and contains no $3$-edge path. We prove the conjecture for Generalized Petersen graphs. We indicate that a coloring with the same properties might exist for any subcubic graph. We confirm this statement for all subcubic trees.

    发表评论 查看更多 翻译此文

    收起