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We provide an explicit classification of the following four families of surfaces in any homogeneous 3manifold with 4dimensional isometry group: isoparametric surfaces, surfaces with constant principal curvatures, homogeneous surfaces, and surfaces with constant mean curvature and vanishing AbreschRosenberg differential.
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Generalizing a result of Masuti and the second author, we describe inverse limits of Macaulay's inverse systems for CohenMacaulay factor algebras of formal power series or polynomial rings over an infinite field. On the way we find a strictness result for filtrations defined by regular sequences. It generalizes both a lemma of Uli Walther and the Rees isomorphism.
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Probabilistic shaping (PS) is a promising technique to approach the Shannon limit using typical constellation schemes. However, the impact of PS on the chain of signal processing algorithms of a coherent receiver still needs further investigation. In this work we study the interplay of PS and phase recovery using the blind phase search (BPS) algorithm, which is currently a defacto standard in optical communications systems. We first investigate a supervised phase search (SPS) algorithm as a theoretical upper bound on the BPS performance, assuming perfect decisions. It is shown that PS influences the SPS algorithm, but its impact can be alleviated by moderate noiserejection window sizes. On the other hand, BPS is affected by PS even for long windows because of correlated erroneous decisions in the phase recovery scheme. The simulation results also showed, for investigated constellations, that the capacitymaximizing shaping is near to the worstcase situation for BPS, causing potentia
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This paper introduces a general class of hierarchical nonparametric prior distributions. The random probability measures are constructed by a hierarchy of generalized species sampling processes with possibly nondiffuse base measures. The proposed framework provides a general probabilistic foundation for hierarchical random measures with either atomic or mixed base measures and allows for studying their properties, such as the distribution of the marginal and total number of clusters. We show that hierarchical species sampling models have a Chinese Restaurants Franchise representation and can be used as prior distributions to undertake Bayesian nonparametric inference. We provide a method to sample from the posterior distribution together with some numerical illustrations. Our class of priors includes some new hierarchical mixture priors such as the hierarchical Gnedin measures, and other wellknown prior distributions such as the hierarchical PitmanYor and the hierarchical normalized
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Yahoo has been ordered by a federal judge to face much of a lawsuit in the United States claiming that the personal information of all 3 billion users was compromised in a series of data breaches. From a report: In a decision on Friday night, U.S. District Judge Lucy Koh in San Jose, California rejected a bid by Verizon Communications, which bought Yahoo's Internet business last June, to dismiss many claims, including for negligence and breach of contract. Koh dismissed some other claims. She had previously denied Yahoo's bid to dismiss some unfair competition claims. [...] The plaintiffs amended their complaint after Yahoo last October revealed that the 2013 breach affected all 3 billion users, tripling its earlier estimate. Koh said the amended complaint highlighted the importance of security in the plaintiffs' decision to use Yahoo. 'Plaintiffs' allegations are sufficient to show that they would have behaved differently had defendants disclosed the security weaknesses of the Yahoo M
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Zack Whittaker, writing for ZDNet: For about twelve hours earlier this month, encrypted email service Tutanota seemed to fall off the face of the internet for Comcast customers. Starting in the afternoon on March 1, people weren't sure if the site was offline or if it had been attacked. Reddit threads speculated about the outage. Some said that Comcast was actively blocking the site, while others dismissed the claims altogether. Several tweets alerted the Hanover, Germanybased encrypted messaging provider to the alleged blockade, which showed a "connection timed out" message to Comcast users. It was as if to hundreds of Comcast customers, Tutanota didn't exist. But as soon as users switched to another nonComcast internet connection, the site appeared as normal. "To us, this came as a total surprise," said Matthias Pfau, cofounder of Tutanota, in an email. "It was quite a shock as such an outage shows the immense power [internet providers] are having over our Internet when they can b
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After lagging behind other countries for years, commercial drones in the U.S. are expected to begin limited package deliveries within months, according to federal regulators and industry officials. [Editor's note: the link may be paywalled; an alternative source was not immediately available] From a report: The momentum partly stems from steppedup White House pressure, prompting closer cooperation between the government and companies such as Amazon.com seeking authorizations for such fledgling businesses. The upshot, according to these officials, is newfound confidence by both sides that domestic packagedelivery services finally appear on the verge of taking off. Earlier promises of progress turned out to be premature. The green light could be delayed again if proponents can't overcome nagging security concerns on the part of local or national lawenforcement agencies. Proposed projects also may end up stymied if Federal Aviation Administration managers don't find creative ways aroun
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It is by now wellknown that small adversarial perturbations can induce classification errors in deep neural networks (DNNs). In this paper, we make the case that sparse representations of the input data are a crucial tool for combating such attacks. For linear classifiers, we show that a sparsifying front end is provably effective against $\ell_{\infty}$bounded attacks, reducing output distortion due to the attack by a factor of roughly $K / N$ where $N$ is the data dimension and $K$ is the sparsity level. We then extend this concept to DNNs, showing that a "locally linear" model can be used to develop a theoretical foundation for crafting attacks and defenses. Experimental results for the MNIST dataset show the efficacy of the proposed sparsifying front end.
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Let $R$ be a finite ring. The commuting probability of $R$, denoted by $\Pr(R)$, is the probability that any two randomly chosen elements of $R$ commute. $R$ is called an $n$centralizer ring if it has $n$ distinct centralizers. In this paper, we compute $\Pr(R)$ for some $n$centralizer finite rings.
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Introducing nonorthogonal multiple access (NOMA) transmission to an unmanned aerial vehicle (UAV) based communication network is a promising solution to enhance its spectral efficiency. However, for realistic deployment of such a network, identifying a practical user feedback scheme for NOMA is essential. In this paper, considering two practical feedback schemes we introduce NOMA transmission to UAVs acting as aerial base stations (BS) to provide coverage at a large stadium. In particular, a UAVBS generates directional beams, and multiple users are served simultaneously within the same beam employing NOMA transmission. Each user is considered to have a target rate based on its quality of service (QoS) requirements. In order to relieve the burden of tracking and feeding back full channel state information, we consider two limited feedback schemes as practical alternatives: 1) user distance, and 2) user angle with respect to beamforming direction under different user region geometries.
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In this paper, two kinds of occurrence mechanism on the phenomenon of concentration and the formation of delta shock waves are analyzed and identified in the flux approximation limit of Riemann solutions to the extended Chaplygin gas equations with Coulomblike friction, whose special case can also be seen as the model of the magnetogasdynamics with Coulomblike friction. Firstly, by introducing a transformation, the Riemann problem for the extended Chaplygin gas equations with Coulomblike friction is solved completely. Secondly, we rigorously show that, as the pressure vanishes, any twoshock Riemann solution to the nonhomogeneous extended Chaplygin gas equations tends to a {\delta}shock solution to the corresponding nonhomogeneous transportation equations, and the intermediate density between the two shocks tends to a weighted {\delta}measure that forms the {\delta}shock; any tworarefactionwave Riemann solution to the nonhomogeneous extended Chaplygin gas equations tends to a t
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In this paper we develop a general theory of compressed sensing for analog signals, in close similarity to prior results for vectors in finite dimensional spaces that are sparse in a given orthonormal basis. The signals are modeled by functions in a reproducing kernel Hilbert space. Sparsity is defined as the minimal number of terms in expansions based on the kernel functions. Minimizing this number is under certain conditions equivalent to minimizing an atomic norm, the predual of the supremum norm for functions in the Hilbert space. The norm minimizer is shown to exist based on a compactness argument. Recovery based on minimizing the atomic norm is robust and stable, so it provides controllable accuracy for recovery when the signal is only approximately sparse and the measurement is corrupted by noise. As applications of the theory, we include results on the recovery of sparse bandlimited functions and functions that have a sparse inverse shorttime Fourier transform.
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We derive a representation formula for harmonic polynomials and Laurent polynomials in terms of densities of the doublelayer potential on bounded piecewise smooth and simply connected domains. From this result, we obtain a method for the numerical computation of conformal maps that applies to both exterior and interior regions. We present analysis and numerical experiments supporting the accuracy and broad applicability of the method.
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We develop a Gentzenstyle proof theory for superBelnap logics (extensions of the fourvalued DunnBelnap logic), expanding on an approach initiated by Pynko. We show that just like substructural logics may be understood prooftheoretically as logics which relax the structural rules of classical logic but keep its logical rules as well as the rules of Identity and Cut, superBelnap logics may be seen as logics which relax Identity and Cut but keep the logical rules as well as the structural rules of classical logic. A generalization of the cut elimination theorem for classical propositional logic is then proved and used to establish interpolation for various superBelnap logics. In particular, we obtain an alternative syntactic proof of a refinement of the Craig interpolation theorem for classical propositional logic discovered recently by Milne.
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We establish integral formulas and sharp twosided bounds for the Ricci curvature, mean curvature and second fundamental form on a Riemannian manifold with boundary. As applications, the Lichnerowicz estimate and Obata theorem for the first eigenvalue, as well as sharp gradient/Hessian estimates on the boundary for eigenfunctions, are presented for the Dirichlet and Neumann eigenproblems.
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This is the second part of a series of three strongly related papers in which three equivalent structures are studied:  internal categories in categories of monoids; defined in terms of pullbacks relative to a chosen class of spans  crossed modules of monoids relative to this class of spans  simplicial monoids of socalled Moore length 1 relative to this class of spans. The most important examples of monoids that are covered are small categories (treated as monoids in categories of spans) and bimonoids in symmetric monoidal categories (regarded as monoids in categories of comonoids). In this second part we define relative crossed modules of monoids and prove their equivalence with the relative categories of Part I.
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In this expository note, I showcase the relevance of Coxeter groups to quiver representations. I discuss (1) real and imaginary roots, (2) reflection functors, and (3) torsion free classes and csortable elements. The first two topics are classical, while the third is a more recent development. I show that torsion free classes in rep Q containing finitely many indecomposables correspond bijectively to csortable elements in the corresponding Weyl group. This was first established in Dynkin type by Ingalls and Thomas; it was shown in general by Amiot, Iyama, Reiten, and Todorov. The proof in this note is elementary, essentially following the argument of Ingalls and Thomas, but without the assumption that Q is Dynkin.
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In this paper, on $\mathbb{D}$ we define CowenDouglas function introduced by CowenDouglas operator $M_\phi^*$ on Hardy space $\mathcal{H}^2(\mathbb{D})$ and we give a sufficient condition for CowenDouglas function, where $\phi\in\mathcal{H}^\infty(\mathbb{D})$. Moreover, we give some applications of CowenDouglas function on chaos, such as application on the inverse chaos problem for $\phi(T)$, where $\phi$ is a CowenDouglas function and $T$ is the backward shift operator on $\mathcal{L}^2(\mathbb{N})$.
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We present a new implementation of anisotropic mean curvature flow for contour recognition. Our procedure couples the mean curvature flow of planar closed smooth curves, with an external field from a potential of pointwise charges. This coupling constrains the motion when the curve matches a picture placed as background. We include a stability criteria for our numerical approximation.
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In this paper we study the existence of continuous solutions and their constructions for a second order iterative functional equation, which involves iterate of the unknown function and a nonlinear term. Imposing Lipschitz conditions to those given functions, we prove the existence of continuous solutions on the whole $\mathbb{R}$ by applying the contraction principle. In the case without Lipschitz conditions we hardly use the contraction principle, but we construct continuous solutions on $\mathbb{R}$ recursively with a partition of $\mathbb{R}$.
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This paper develops techniques which are used to answer a number of questions in the theory of equivalence relations generated by continuous actions of abelian groups. The methods center around the construction of certain specialized hyperaperiodic elements, which produce compact subflows with useful properties. For example, we show that there is no continuous $3$coloring of the Cayley graph on $F(2^{\mathbb{Z}^2})$, the free part of the shift action of $\mathbb{Z}^2$ on $2^{\mathbb{Z}^2}$. With earlier work of the authors this computes the continuous chromatic number of $F(2^{\mathbb{Z}^2})$ to be exactly $4$. Combined with marker arguments for the positive directions, our methods allow us to analyze continuous homomorphisms into graphs, and more generally equivariant maps into subshifts of finite type. We present a general construction of a finite set of "tiles" for $2^{\mathbb{Z}^n}$ (there are $12$ for $n=2$) such that questions about the existence of continuous homomorphisms int
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We give an explicit construction of the HondaKazezMati\'c gluing maps in terms of contact handles. We use this to prove a duality result for turning a sutured manifold cobordism around, and to compute the trace in the sutured Floer TQFT. We also show that the decorated link cobordism maps on the hat version of link Floer homology defined by the first author via sutured manifold cobordisms and by the second author via elementary cobordisms agree.
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Both the use of very large arrays of antennas and flexible time division duplexing (TDD) designs have become prominent features of next generation 5G cellular systems. However, both enabling technologies suffer from severe interference effects, respectively known as pilot contamination and basestationtobasestation (B2B) interference. In this paper, a practical novel TDD design principle is proposed for massive multipleinput multipleoutput (MIMO) heterogeneous networks (HetNets) that leverages the inherent features of a flexible TDD design to mitigate both the beamformed interference caused by the pilot contamination effect and B2B interference. The design is based on the key observation that the transmission path chosen for training by the nonmassive MIMO base stations plays an important role in the interference behavior of the network, and the data slots need to be configured accordingly. We propose TDFLEX, a lowcomplexity heuristic solution that follows these design guideline
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Let n be an integer$>$. Let S^{n+2}_1 (respectively, S^{n+2}_2) be the (n+2)sphere embedded in the (n+4)sphere S^{n+4}. Let S^{n+2}_1 and S^{n+2}_2 intersect transversely. Suppose that the smooth submanifold, the intersection of S^{n+2}_1 and S^{n+2}_2 in S^{n+2}_i is PL homeomophic to the nsphere. Then S^{n+2}_1 and S^{n+2}_2 in S^{n+2}_i is an nknot K_i. We say that the pair (K_1,K_2) of nknots is realizable. We consider the following problem in this paper. Let A_1 and A_2 be nknots. Is the pair (A_1,A_2) of nknots realizable? We give a complete characterization.
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An efficient JacobiGalerkin spectral method for calculating eigenvalues of Riesz fractional partial differential equations with homogeneous Dirichlet boundary values is proposed in this paper. In order to retain the symmetry and positive definiteness of the discrete linear system, we introduce some properly defined Sobolev spaces and approximate the eigenvalue problem in a standard Galerkin weak formulation instead of the PetrovGalerkin one as in literature. Poincar\'{e} and inverse inequalities are proved for the proposed Galerkin formulation which finally help us establishing a sharp estimate on the algebraic system's condition number. Rigorous error estimates of the eigenvalues and eigenvectors are then readily obtained by using Babu\v{s}ka and Osborn's approximation theory on selfadjoint and positivedefinite eigenvalue problems. Numerical results are presented to demonstrate the accuracy and efficiency, and to validate the asymptotically exponential oder of convergence. Moreove
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Consider a system of $N$ parallel singleserver queues with unitexponential service time distribution and a single dispatcher where tasks arrive as a Poisson process of rate $\lambda(N)$. When a task arrives, the dispatcher assigns it to one of the servers according to the JointheShortest Queue (JSQ) policy. Eschenfeldt and Gamarnik (2015) established that in the HalfinWhitt regime where $(N\lambda(N))/\sqrt{N}\to\beta>0$ as $N\to\infty$, appropriately scaled occupancy measure of the system under the JSQ policy converges weakly on any finite time interval to a certain diffusion process as $N\to\infty$. Recently, it was further established by Braverman (2018) that the stationary occupancy measure of the system converges weakly to the steady state of the diffusion process as $N\to\infty$. In this paper we perform a detailed analysis of the steady state of the above diffusion process. Specifically, we establish precise tailasymptotics of the stationary distribution and scaling of
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The rapid development of highthroughput technologies has enabled the generation of data from biological or disease processes that span multiple layers, like genomic, proteomic or metabolomic data, and further pertain to multiple sources, like disease subtypes or experimental conditions. In this work, we propose a general statistical framework based on Gaussian graphical models for horizontal (i.e. across conditions or subtypes) and vertical (i.e. across different layers containing data on molecular compartments) integration of information in such datasets. We start with decomposing the multilayer problem into a series of twolayer problems. For each twolayer problem, we model the outcomes at a node in the lower layer as dependent on those of other nodes in that layer, as well as all nodes in the upper layer. We use a combination of neighborhood selection and grouppenalized regression to obtain sparse estimates of all model parameters. Following this, we develop a debiasing techniqu
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We consider a discretetime Markov chain $\boldsymbol{\Phi}$ on a general statespace ${\sf X}$, whose transition probabilities are parameterized by a realvalued vector $\boldsymbol{\theta}$. Under the assumption that $\boldsymbol{\Phi}$ is geometrically ergodic with corresponding stationary distribution $\pi(\boldsymbol{\theta})$, we are interested in estimating the gradient $\nabla \alpha(\boldsymbol{\theta})$ of the steadystate expectation $$\alpha(\boldsymbol{\theta}) = \pi( \boldsymbol{\theta}) f.$$ To this end, we first give sufficient conditions for the differentiability of $\alpha(\boldsymbol{\theta})$ and for the calculation of its gradient via a sequence of finite horizon expectations. We then propose two different likelihood ratio estimators and analyze their limiting behavior.
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CNET reports: Mozilla launched the faster Quantum version of its Firefox browser last fall in a bid to restore the nonprofit's reach and influence. Now, the leader of that effort has been promoted to oversee all Mozilla products. Mark Mayo, formerly senior vice president of Firefox, is now Mozilla's chief product officer, CNET has learned. That means he's taking over more projects, including the Pocket tool and mobile app. Pocket lets people save websites they'd like to revisit, but Mozilla also plans to use the resulting data to help recommend interesting or useful sites to Firefox users. In addition, Mozilla has promoted Denelle Dixon, formerly head of business and legal work, to chief operations officer. She's overseen an effort to diversify Mozilla revenue sources, including through the Pocket acquisition in February 2017.
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JustAnotherOldGuy writes: It seems like we're seeing a sudden outbreak of common sense from one of the most unlikely places. Florida might become the third state  after Hawaii and Arizona  to be done with the hassle of changing their clocks twice a year. Yesterday, the Senate overwhelmingly passed the Sunshine Protection Act in under one minute, with only two dissenters. The House had already passed it 10311 last month. Now it has to be signed by Gov. Rick Scott. If Scott passes it, however, it still has to go through Congress before Florida has Daylight Savings Time all year long.
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This paper proposes a discontinuitysensitive approach to learn the solutions of parametric optimal control problems with high accuracy. Many tasks, ranging from model predictive control to reinforcement learning, may be solved by learning optimal solutions as a function of problem parameters. However, nonconvexity, discrete homotopy classes, and control switching cause discontinuity in the parametersolution mapping, thus making learning difficult for traditional continuous function approximators. A mixture of experts (MoE) model composed of a classifier and several regressors is proposed to address such an issue. The optimal trajectories of different parameters are clustered such that in each cluster the trajectories are continuous function of problem parameters. Numerical examples on benchmark problems show that training the classifier and regressors individually outperforms joint training of MoE. With suitably chosen clusters, this approach not only achieves lower prediction error
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We show, assuming a weak form of the Axiom of Choice, that the existence of a discontinuous homomorphism of the additive group of real numbers induces a selector for the Vitali equivalence relation $\mathbb{R}/\mathbb{Q}$. This shows that a nonprincipal ultrafilter on the integers is not sufficient to construct a discontinuous automorphism of the complex field, confirming a conjecture of Simon Thomas.
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The recent development of spectral method has been praised for its highorder convergence in simulating complex physical problems. The combination of embedded boundary method and spectral method becomes a mainstream way to tackle geometrically complicated problems. However, the convergence is deteriorated when embedded boundary strategies are employed. Owing to the loss of regularity, in this paper we propose a new spectral collocation method which retains the regularity of solutions to solve differential equations in the case of complex geometries. The idea is rooted in the basis functions defined in an extended domain, which leads to a useful upper bound of the Lebesgue constant with respect to the Fourier best approximation. In particular, how the stretching of the domain defining basis functions affects the convergence rate directly is detailed. Error estimates chosen in our proposed method show that the exponential decay convergence for problems with analytical solutions can be re
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The AskeyWilson polynomials are a fourparameter family of orthogonal symmetric Laurent polynomials $R_n[z]$ which are eigenfunctions of a secondorder $q$difference operator $L$, and of a secondorder difference operator in the variable $n$ with eigenvalue $z + z^{1}=2x$. Then $L$ and multiplication by $z+z^{1}$ generate the AskeyWilson (Zhedanov) algebra. A nice property of the AskeyWilson polynomials is that the variables $z$ and $n$ occur in the explicit expression in a similar and to some extent exchangeable way. This property is called duality. It returns in the nonsymmetric case and in the underlying algebraic structures: the AskeyWilson algebra and the double affine Hecke algebra (DAHA). In this paper we follow the degeneration of the AskeyWilson polynomials until two arrows down and in four diferent situations: for the orthogonal polynomials themselves, for the degenerate AskeyWilson algebras, for the nonsymmetric polynomials and for the (degenerate) DAHA and its re
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We construct a finite dimensional representation of the face type, i.e dynamical, elliptic quantum group associated with $sl_N$ on the GelfandTsetlin basis of the tensor product of the $n$vector representations. The result is described in a combinatorial way by using the partitions of $[1,n]$. We find that the change of basis matrix from the standard to the GelfandTsetlin basis is given by a specialization of the elliptic weight function obtained in the previous paper[Konno17]. Identifying the elliptic weight functions with the elliptic stable envelopes obtained by Aganagic and Okounkov, we show a correspondence of the GelfandTsetlin bases (resp. the standard bases) to the fixed point classes (resp. the stable classes) in the equivariant elliptic cohomology $E_T(X)$ of the cotangent bundle $X$ of the partial flag variety. As a result we obtain a geometric representation of the elliptic quantum group on $E_T(X)$.
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We show that evolutionary Hirota type EulerLagrange equations in (2+1) dimensions have a symplectic MongeAmp\`ere form. We consider integrable equations of this type in the sense that they admit infinitely many hydrodynamic reductions and determine Lax pairs for them. For two sevenparameter families of integrable equations converted to twocomponent form we have constructed Lagrangians, recursion operators and biHamiltonian representations. We have also presented a sixparameter family of triHamiltonian systems.
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This article deals with the stability analysis of a drilling system which is modelled as a coupled ordinary differential equation / string equation. The string is damped at the two boundaries but leading to a stable openloop system. The aim is to derive a linear matrix inequality ensuring the exponential stability with a guaranteed decayrate of this interconnected system. A strictly proper dynamic controller based on boundary measurements is proposed to accelerate the system dynamics and its effects are investigated through the stability theorem and simulations. It results in an efficient finite dimension controller which subsequently improves the system performances.
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Quantum repeater networks are a fundamental of any future quantum Internet and longdistance quantum communications. The entangled quantum nodes can communicate through several different levels of entanglement, leading to a heterogeneous, multilevel network structure. The level of entanglement between the quantum nodes determines the hop distance and the probability of the existence of an entangled link in the network. In this work we define a decentralized routing for entangled quantum networks. The proposed method allows an efficient routing to find the shortest paths in entangled quantum networks by using only local knowledge of the quantum nodes. We give bounds on the maximum value of the total number of entangled links of a path. The proposed scheme can be directly applied in practical quantum communications and quantum networking scenarios.
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We are concerned with the convexity of transonic shocks in twodimensional selfsimilar coordinates for compressible fluid flows, which not only arises in continuum physics but also is fundamental in the mathematical theory of multidimensional conservation laws. We first develop a general framework under which selfsimilar transonic shock waves, as free boundaries, are proved to be uniformly convex for potential flow and then apply this framework to the complete proof of the uniform convexity of transonic shocks in the two longstanding fundamental shock problems  the shock reflectiondiffraction problem by wedges and the PrandtlMeyer reflection problem for supersonic flows past solid ramps. To achieve this, we develop a nonlinear approach to explore the detailed nonlocal behavior of the solution on the boundary to prove the uniform convexity of the transonic shock. This approach and related techniques, developed here, will also be useful for other related nonlinear problems involvin
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In this paper we characterize groups according to the number of end vertices in the associated coprime graphs. An upper bound on the order of the group that depends on the number of end vertices is obtained. We also prove that $2$groups are the only groups whose coprime graphs have odd number of end vertices. Classifications of groups with small number of end vertices in the coprime graphs are given. One of the results shows that $\mathbb{Z}_4$ and $\mathbb{Z}_2\times \mathbb{Z}_2$ are the only groups whose coprime graph has exactly three end vertices.
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We address the problem to determine the limit of the collision of fat points in $\mathbb{P}^n. We give a description of the limit scheme in many cases, in particular in low dimension and multiplicities. The problem turns out to be closely related with interpolation theory, and as an application we exploit collisions to prove some new cases of LafaceUgaglia Conjecture.
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We compute the number of $\mathcal{X}$variables (also called coefficients) of a cluster algebra of finite type when the underlying semifield is the universal semifield. For classical types, these numbers arise from a bijection between coefficients and quadrilaterals (with a choice of diagonal) appearing in triangulations of certain marked surfaces. We conjecture that similar results hold for cluster algebras from arbitrary marked surfaces, and obtain corollaries regarding the structure of finite type cluster algebras of geometric type.
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We show a cotorsion pair cogenerated by a class is complete under suitable conditions in an arbitrary exact category using the generalized small object argument given by Chorny. This recovers Saor\'in and \v{S}\v{t}ov\'{i}\v{c}ek's criterion of the completeness of cotorsion pairs in their efficient exact categories. Examples in the categories of chain complexes of exact categories are given.
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Suppose $H$ is a finite dimensional reproducing kernel Hilbert space of functions on $X.$ If $H$ has the complete Pick property then there is an isometric map, $\Phi,$ from $X,$ with the metric induced by $H,$ into complex hyperbolic space, $\mathbb{CH}^{n},$ with its pseudohyperbolic metric. We investigate the relationships between the geometry of $\Phi(X)$ and the function theory of $H$ and its multiplier algebra.
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We establish average consensus on graphs with dynamic topologies prescribed by evolutionary games among strategic agents. Each agent possesses a private reward function and dynamically decides whether to create new links and/or whether to delete existing ones in a selfish and decentralized fashion, as indicated by a certain randomized mechanism. This model incurs a timevarying and statedependent graph topology for which traditional consensus analysis is not applicable. We prove asymptotic average consensus almost surely and in mean square for any initial condition and graph topology. In addition, we establish exponential convergence in expectation. Our results are validated via simulation studies on random networks.
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We give a short proof that a uniform noncrossing partition of the regular $n$gon weakly converges toward Aldous's Brownian triangulation of the disk, in the sense of the Hausdorff topology. This result was first obtained by Curien & Kortchemski, using a more complicated encoding. Thanks to a result of Marchal on strong convergence of Dyck paths toward the Brownian excursion, we furthermore give an algorithm that allows to recursively construct a sequence of uniform noncrossing partitions for which the previous convergence holds almost surely. In addition, we also treat the case of uniform noncrossing pair partitions of evensided polygons.
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Let $(E,\tau)$ be a locally solid vector lattice. A filter $\mathcal{F}$ on the set $E$ is said to be converge to a vector $e\in E$ if, each zero neighborhood set $U$ containing $e$, $U$ belongs to $\mathcal{F}$. We study on the concept of this convergence and give some basic properties of it.
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Recently Hui et al. (\cite{HAP}, \cite{HAN}) studied contact CRwarped product submanifolds and also warped product pseudoslant submanifolds of a $(LCS)_n$manifold $\bar{M}$. In this paper we have studied the characterization for both these classes of warped product submanifolds. It is also shown that there do not exists any proper warped product bislant submanifold of a $(LCS)_n$manifold. Although we constructed an example of a bislant submanifold of $(LCS)_n$manifold.
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An anonymous reader quotes a report from Ars Technica: FBI Director Christopher Wray again has called for a solution to what the bureau calls the "Going Dark" problem, the idea that the prevalence of default strong encryption on digital devices makes it more difficult for law enforcement to extract data during an investigation. However, in a Wednesday speech at Boston College, Wray again did not outline any specific piece of legislation or technical solution that would provide both strong encryption and allow the government to access encrypted devices when it has a warrant. A key escrow system, with which the FBI or another entity would be able to unlock a device given a certain set of circumstances, is by definition weaker than what cryptographers would traditionally call "strong encryption." There's also the problem of how to compel device and software makers to impose such a system on their customers  similar efforts were attempted during the Clinton administration, but they faile
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Fast genome tests are diagnosing some of the sickest babies in time to save
0308 MIT Technology 1123 
A simple method of calculating the HausdorffBesicovitch dimension of the Kronecker Product based fractals is presented together with a compact R script realizing it. The proposed new formula is based on traditionally used values of the number of selfsimilar objects and the scale factor that are now calculated using appropriate values of both the initial fractal matrix and the second order resultant matrix. This method is reliable and producing dimensions equal to many already determined values of wellknown fractals.
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This article studies a FokkerPlanck type equation of fractional diffusion with conservative drift $\partial$f/$\partial$t = $\Delta$^($\alpha$/2) f + div(Ef), where $\Delta$^($\alpha$/2) denotes the fractional Laplacian and E is a confining force field. The main interest of the present paper is that it applies to a wide variety of force fields, with a few local regularity and a polynomial growth at infinity. We first prove the existence and uniqueness of a solution in weighted Lebesgue spaces depending on E under the form of a strongly continuous semigroup. We also prove the existence and uniqueness of a stationary state, by using an appropriate splitting of the fractional Laplacian and by proving a weak and strong maximum principle. We then study the rate of convergence to equilibrium of the solution. The semigroup has a property of regularization in fractional Sobolev spaces, as well as a gain of integrability and positivity which we use to obtain polynomial or exponential convergen
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We use techniques of dyadic analysis in order to prove that, for every $0<s<\tfrac{1}{2}$, there exists a positive constant $\gamma(s)$ such that the inequality $$\left(\iint_{\mathbb{R}^2}xy^{2s1}\varphi(x)\varphi(y)dx dy\right)\left(\iint_{\mathbb{R}^2}xy^{2s1}\varphi(x)\varphi(y)^2 dx dy\right)\geq \gamma(s)$$ holds for every $\varphi$ with $\varphi_{L^2(\mathbb{R})}=1$. The second integral on the left hand side is the energy quadratic form of order $s$, which for the limit case $s=1$ gives the local form $Var\hat{\varphi}^2$ or $\int\nabla\varphi^2$. The first is a natural substitution of the position form, which on the Haar system shows the same behavior of the classical $Var\varphi^2$.
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A bipartite quantum interaction corresponds to the most general quantum interaction that can occur between two quantum systems. In this work, we determine bounds on the capacities of bipartite interactions for entanglement generation and secret key agreement. Our upper bound on the entanglement generation capacity of a bipartite quantum interaction is given by a quantity that we introduce here, called the bidirectional maxRains information. Our upper bound on the secretkeyagreement capacity of a bipartite quantum interaction is given by a related quantity introduced here also, called the bidirectional maxrelative entropy of entanglement. We also derive tighter upper bounds on the capacities of bipartite interactions obeying certain symmetries. Observing that quantum reading is a particular kind of bipartite quantum interaction, we leverage our bounds from the bidirectional setting to deliver bounds on the capacity of a task that we introduce, called private reading of a wiretap mem
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We consider BerezinToeplitz operators on compact Kahler manifolds whose symbols are characteristic functions. When the support of the characteristic function has a smooth boundary, we prove a twoterm Weyl law, the second term being proportional to the Riemannian volume of the boundary. As a consequence, we deduce the area law for the entanglement entropy of integer quantum Hall states.
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Given the same anticanonical linear system on two distinct toric varieties, we provide a derived equivalence between partial crepant resolutions of the corresponding stacky hypersurfaces. The applications include: a derived unification of toric mirror constructions, calculations of Picard lattices for linear systems of quartic surfaces, and a birational reduction of Reid's list to 81 families.
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This paper analysis the energy efficiency of an unlicensed wireless network in which retransmission is possible if the transmitted message is decoded in outage. A wireless sensor network is considered in which the sensor nodes are unlicensed users of a wireless network which transmit its data in the uplink channel used by the licensed users. Poisson point process is used to model the distributions of the nodes and the interference caused by the licensed users for the sensor nodes. After finding the optimal throughput in the presence of retransmissions, we focus on analyzing the total power consumption and energy efficiency of the network and how retransmissions, network density and outage threshold affects the energy efficiency of the network.
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In this paper, we find necessary and sufficient conditions for the boundedness of fractional maximal operator $M_{\alpha}$ on Orlicz spaces. As an application of this results we consider the boundedness of fractional maximal commutator $M_{b,\alpha}$ and nonlinear commutator of fractional maximal operator $[b,M_{\alpha}]$ on Orlicz spaces, when $b$ belongs to the Lipschitz space, by which some new characterizations of the Lipschitz spaces are given.
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