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Modeling via fractional partial differential equations or a L\'evy process has been an active area of research and has many applications. However, the lack of efficient numerical computation methods for general nonlocal operators impedes people from adopting such modeling tools. We proposed an efficient solver for the convectiondiffusion equation whose operator is the infinitesimal generator of a L\'evy process based on $\mathcal{H}$matrix technique. The proposed Crank Nicolson scheme is unconditionally stable and has a theoretical $\mathcal{O}(h^2+\Delta t^2)$ convergence rate. The $\mathcal{H}$matrix technique has theoretical $\mathcal{O}(N)$ space and computational complexity compared to $\mathcal{O}(N^2)$ and $\mathcal{O}(N^3)$ respectively for the direct method. Numerical experiments demonstrate the efficiency of the new algorithm.
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The cost and memoryefficient numerical simulation of coupled volumebased multiphysics problems like flow, transport, wave propagation and others remains a challenging task with finite element method (FEM) approaches. Goaloriented space and time adaptive methods derived from the dual weighted residual (DWR) method appear to be a shiny key technology to generate optimal spacetime meshes to minimise costs. Current implementations for challenging problems of numerical screening tools including the DWR technology broadly suffer in their extensibility to other problems, in high memory consumption or in missing system solver technologies. This work contributes to the efficient embedding of DWR spacetime adaptive methods into numerical screening tools for challenging problems of physically relevance with a new approach of flexible data structures and algorithms on them, a modularised and complete implementation as well as illustrative examples to show the performance and efficiency.
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The dynamics of the fourbody problem have attracted increasing attention in recent years. In this paper, we extend the basic equilateral fourbody problem by introducing the effect of radiation pressure, PoyntingRobertson drag, and solar wind drag. In our setup, three primaries lay at the vertices of an equilateral triangle and move in circular orbits around their common center of mass. Here, one of the primaries is a radiating body and the fourth body (whose mass is negligible) does not affect the motion of the primaries. We show that the existence and the number of equilibrium points of the problem depend on the mass parameters and radiation factor. Consequently, the allowed regions of motion, the regions of the basins of convergence for the equilibrium points, and the basin entropy will also depend on these parameters. The present dynamical model is analyzed for three combinations of mass for the primaries: equal masses, two equal masses, different masses. As the main results, we
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We study the superlinear oscillator equation $\ddot{x}+ \lvert x \rvert^{\alpha1}x = p(t)$ for $\alpha\geq 3$, where $p$ is a quasiperiodic forcing with no Diophantine condition on the frequencies and show that typically the set of initial values leading to solutions $x$ such that $\lim_{t\to\infty} (\lvert x(t) \rvert + \lvert \dot{x}(t) \rvert) = \infty$ has Lebesgue measure zero, provided the starting energy $\lvert x(t_0) \rvert + \lvert \dot{x}(t_0) \rvert$ is sufficiently large.
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We prove existence of all possible biaxisymmetric nearhorizon geometries of 5dimensional minimal supergravity. These solutions possess the crosssectional horizon topology $S^3$, $S^1\times S^2$, or $L(p,q)$ and come with prescribed electric charge, two angular momenta, and a dipole charge (in the ring case). Moreover, we establish uniqueness of these solutions up to an isometry of the symmetric space $G_{2(2)}/SO(4)$.
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We prove existence and uniqueness of solutions to FokkerPlanck equations associated to Markov operators multiplicatively perturbed by degenerate timeinhomogeneous coefficients. Precise conditions on the timeinhomogeneous coefficients are given. In particular, we do not necessarily require the coefficients to be neither globally bounded nor bounded away from zero. The approach is based on constructing random timechanges and studying related martingale problems for Markov processes with values in locally compact, complete and separable metric spaces.
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We characterise the existentially closed models of the theory of exponential fields. We find the amalgamation bases and characterise the types over them. We define a notion of independence and show that independent systems of higher dimension can also be amalgamated. Using these results we position the category of existentially closed exponential fields in the stability hierarchy as NSOP$_1$ but TP$_2$.
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We consider dynamical systems $T: X \to X$ that are extensions of a factor $S: Y \to Y$ through a projection $\pi: X \to Y$ with shrinking fibers, i.e. such that $T$ is uniformly continuous along fibers $\pi^{1}(y)$ and the diameter of iterate images of fibers $T^n(\pi^{1}(y))$ uniformly go to zero as $n \to \infty$. We prove that every $S$invariant measure has a unique $T$invariant lift, and prove that many properties of the original measure lift: ergodicity, weak and strong mixing, decay of correlations and statistical properties (possibly with weakening in the rates).The basic tool is a variation of the Wasserstein distance, obtained by constraining the optimal transportation paradigm to displacements along the fibers. We extend to a general setting classical arguments, enabling to translate potentials and observables back and forth between $X$ and $Y$.
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The problem of sequential probability forecasting is considered in the most general setting: a model set C is given, and it is required to predict as well as possible if any of the measures (environments) in C is chosen to generate the data. No assumptions whatsoever are made on the model class C, in particular, no independence or mixing assumptions; C may not be measurable; there may be no predictor whose loss is sublinear, etc. It is shown that the cumulative loss of any possible predictor can be matched by that of a Bayesian predictor whose prior is discrete and is concentrated on C, up to an additive term of order $\log n$, where $n$ is the time step. The bound holds for every $n$ and every measure in C. This is the first nonasymptotic result of this kind. In addition, a nonmatching lower bound is established: it goes to infinity with $n$ but may do so arbitrarily slow.
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Given two endomorphisms $\tau_1,\tau_2$ of $\mathbb{C}^m$ with $m \ge 2n$ and a general $n$dimensional subspace $\mathcal{V} \subset \mathbb{C}^m$, we provide eigenspace conditions under which $\tau_1(v_1)=\tau_2(v_2)$ for $v_1,v_2 \in \mathcal{V}$ can only be true if $v_1=v_2$. As a special case, we recover the result of Unnikrishnan et al. in which $\tau_1,\tau_2$ are permutations composed with coordinate projections.
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In electricity markets with a dualpricing scheme for balancing energy, controllable production units typically participate in the balancing market as "active" actors by offering regulating energy to the system, while renewable stochastic units are treated as "passive" participants that create imbalances and are subject to less competitive prices. Against this background, we propose an innovative market framework whereby the participant in the balancing market is allowed to act as an active agent (i.e., a provider of regulating energy) in some trading intervals and as a passive agent (i.e., a user of regulating energy) in some others. To illustrate and evaluate the proposed market framework, we consider the case of a virtual power plant (VPP) that trades in a twosettlement electricity market composed of a dayahead and a dualprice balancing market. We formulate the optimal market offering problem of the VPP as a threestage stochastic program, where uncertainty is in the dayahead el
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In the developing theory of infinitedimensional quantum channels the relevance of the energyconstrained diamond norms was recently corroborated both from physical and informationtheoretic points of view. In this paper we study necessary and sufficient conditions for differentiability with respect to these norms of the strongly continuous semigroups of quantum channels (quantum dynamical semigroups). We show that these conditions can be expressed in terms of the generator of the semigroup. We also analyze conditions for representation of a strongly continuous semigroup of quantum channels as an exponential series converging w.r.t. the energyconstrained diamond norm. Examples of semigroups having such a representation are presented.
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We construct a nontrivial type of 1step exceptional BannaiIto polynomials which satisfy discrete orthogonality by using a generalized Darboux transformation. In this generalization, the Darboux transformed BannaiIto operator is directly obtained through an intertwining relation. Moreover, the seed solution, which consists of a gauge factor and a polynomial part, plays an important role in the construction of these 1step exceptional BannaiIto polynomials. And we show that there are 8 classes of gauge factors. We also provide the eigenfunctions of the corresponding multiplestep exceptional BannaiIto operator which can be expressed as a 3 x 3 determinant.
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Optimal control problems are inherently hard to solve as the optimization must be performed simultaneously with updating the underlying system. Starting from an initial guess, Howard's policy improvement algorithm separates the step of updating the trajectory of the dynamical system from the optimization and iterations of this should converge to the optimal control. In the discrete spacetime setting this is often the case and even rates of convergence are known. In the continuous spacetime setting of controlled diffusion the algorithm consists of solving a linear PDE followed by maximization problem. This has been shown to converge, in some situations, however no global rate of is known. The first main contribution of this paper is to establish global rate of convergence for the policy improvement algorithm and a variant, called here the gradient iteration algorithm. The second main contribution is the proof of stability of the algorithms under perturbations to both the accuracy of t
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A graph $G$ is said to be chordal if it has no induced cycles of length four or more. In a recent preprint Culbertson, Guralnik, and Stiller give a new characterization of chordal graphs in terms of sequences of what they call `edgeerasures'. In this note we show that these moves are in fact equivalent to a linear quotient ordering on $I_{\overline{G}}$, the edge ideal of the complement graph $\overline G$. Known results imply that $I_{\overline G}$ has linear quotients if and only if $G$ is chordal, and hence this recovers an algebraic proof of their characterization. We investigate higherdimensional analogues of this result, and show that in fact linear quotients for more general circuit ideals of $d$clutters can be characterized in terms of removing exposed circuits in the complement clutter. Restricting to properly exposed circuits can be characterized by a homological condition. This leads to a notion of higher dimensional chordal clutters which borrows from commutative algebra
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We recall Charles Babbage's 1819 criterion for primality, based on simultaneous congruences for binomial coefficients, and extend it to a leastprimefactor test. We also prove a partial converse of his nonprimality test, based on a single congruence. Two problems are posed. Along the way we encounter Bachet, Bernoulli, Bezout, Euler, Fermat, Kummer, Lagrange, Lucas, Vandermonde, Waring, Wilson, Wolstenholme, and several contemporary mathematicians.
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For each $p>1$ and each positive integer $m$ we give intrinsic characterizations of the restriction of the homogeneous Sobolev space $L^m_p(R)$ to an arbitrary closed subset $E$ of the real line. We show that the classical one dimensional Whitney extension operator is "universal" for the scale of $L^m_p(R)$ spaces in the following sense: for every $p\in(1,\infty]$ it provides almost optimal $L^m_p$extensions of functions defined on $E$. The operator norm of this extension operator is bounded by a constant depending only on $m$. This enables us to prove several constructive $L^m_p$extension criteria expressed in terms of $m^{th}$ order divided differences of functions.
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This is a supplement for "Pearls in graph theory"  a textbook written by Nora Hartsfield and Gerhard Ringel. We discuss bounds on Ramsey numbers, the probabilistic method, deletioncontraction formulas, the matrix theorem, chromatic polynomials, the marriage theorem and its relatives, the Rado graph, and generating functions.
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In this paper we are concerned with the analysis of heavytailed data when a portion of the extreme values is unavailable. This research was motivated by an analysis of the degree distributions in a large social network. The degree distributions of such networks tend to have power law behavior in the tails. We focus on the Hill estimator, which plays a starring role in heavytailed modeling. The Hill estimator for this data exhibited a smooth and increasing "sample path" as a function of the number of upper order statistics used in constructing the estimator. This behavior became more apparent as we artificially removed more of the upper order statistics. Building on this observation we introduce a new version of the Hill estimator. It is a function of the number of the upper order statistics used in the estimation, but also depends on the number of unavailable extreme values. We establish functional convergence of the normalized Hill estimator to a Gaussian process. An estimation proc
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Dyson's celebrated constant term conjecture ({\em J. Math. Phys.}, 3 (1962): 140156) states that the constant term in the expansion of $\prod_{1\leqq i\neq j\leqq n} (1x_i/x_j)^{a_j}$ is the multinomial coefficient $(a_1 + a_2 + \cdots + a_n)!/ (a_1! a_2! \cdots a_n!)$. The definitive proof was given by I. J. Good ({\em J. Math. Phys.}, 11 (1970) 1884). Later, Andrews extended Dyson's conjecture to a $q$analog ({\em The Theory and Application of Special Functions}, (R. Askey, ed.), New York: Academic Press, 191224, 1975.) In this paper, closed form expressions are given for the coefficients of several other terms in the Dyson product, and are proved using an extension of Good's idea. Also, conjectures for the corresponding $q$analogs are supplied. Finally, perturbed versions of the $q$Dixon summation formula are presented.
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Beck's distributive laws provide sufficient conditions under which two monads can be composed, and monads arising from distributive laws have many desirable theoretical properties. Unfortunately, finding and verifying distributive laws, or establishing if one even exists, can be extremely difficult and errorprone. We develop generalpurpose techniques for showing when there can be no distributive law between two monads. Two approaches are presented. The first widely generalizes ideas from a counterexample attributed to Plotkin, yielding generalpurpose theorems that recover the previously known situations in which no distributive law can exist. Our second approach is entirely novel, encompassing new practical situations beyond our generalization of Plotkin's approach. It negatively resolves the open question of whether the list monad distributes over itself. Our approach adopts an algebraic perspective throughout, exploiting a syntactic characterization of distributive laws. This appr
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If spectrum of a Schr\"{o}dinger oparator with a nonHermitian potential contains a spectral singularity (SS), the latter requires exact matching of the parameters characterizing the potential. We provide a necessary and sufficient condition for a potential to have a SS at a given wavelength. It is shown that potentials with SS at prescribed wavelengths can be obtained by a simple and effective procedure. In particular, the developed approach allows one to obtain potentials with several SSs or with SSs of the second order and potentials obeying a given symmetry, say, PTsymmetric potentials. Also, the problem can be solved when it is required to obtain a potential obeying a given symmetry, say, $\mathcal{PT}$symmetric potential. We illustrate all opportunities with examples. We also describe splitting of the SSs of the second order, under change of the potential parameters, and discuss possibilities of experimental observation of SSs of different orders.
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We prove that the known formulae for computing the optimal number of maximally entangled pairs required for entanglementassisted quantum errorcorrecting codes (EAQECCs) over the binary field holds for codes over arbitrary finite fields as well. We also give a GilbertVarshamov bound for EAQECCs and constructions of EAQECCs coming from punctured selforthogonal linear codes which are valid for any finite field.
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We establish existence of the etainvariant as well as of the AtiyahPatodiSinger and the CheegerGromov rhoinvariants for a class of Dirac operators on an incomplete edge space. Our analysis applies in particular to the signature, the GaussBonnet and the spin Dirac operator. We derive an analogue of the AtiyahPatodiSinger index theorem for incomplete edge spaces and their noncompact infinite Galois coverings with edge singular boundary. Our arguments employ microlocal analysis of the heat kernel asymptotics on incomplete edge spaces and the classical argument of AtiyahPatodiSinger. As an application, we discuss stability results for the two rhoinvariants we have defined.
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In this paper we study the $(2+1)$dimensional DiracDunkl oscillator coupled to an external magnetic field. Our Hamiltonian is obtained from the standard Dirac oscillator coupled to an external magnetic field by changing the partial derivatives by the Dunkl derivatives. We solve the DunklKleinGordontype equations in polar coordinates in a closed form. The angular part eigenfunctions are given in terms of the JacobiDunkl polynomials and the radial functions in terms of the Laguerre functions. Also, we compute the energy spectrum of this problem and show that, in the nonrelativistic limit, it properly reduces to the Hamiltonian of the two dimensional harmonic oscillator.
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We discuss generalized partition function of 2d CFTs decorated by higher qKdV charges on thermal cylinder. We propose that in the large central charge limit qKdV charges factorize such that generalized partition function can be rewritten in terms of auxiliary noninteracting bosons. The explicit expression for the generalized free energy is readily available in terms of the boson spectrum, which can be deduced from the conventional thermal expectation values of qKdV charges. In other words, the picture of the auxiliary noninteracting bosons allows extending thermal onepoint functions to the full nonperturbative generalized partition function. We verify this conjecture for the first seven qKdV charges using recently obtained pertrubative results and find corresponding contributions to the auxiliary boson masses. We further extend these results by conjecturing the full spectrum of bosons and find an exact expression for the generalized partition function as a function of infinite towe
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The class of split matroids arises by putting conditions on the system of split hyperplanes of the matroid base polytope. It can alternatively be defined in terms of structural properties of the matroid. We use this structural description to give an excluded minor characterisation of the class.
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In this paper, sufficient conditions are given for the existence of limiting distribution of a conservative affine process on the canonical state space $\mathbb{R}_{\geqslant0}^{m}\times\mathbb{R}^{n}$, where $m,\thinspace n\in\mathbb{Z}_{\geqslant0}$ with $m+n>0$. Our main theorem extends and unifies some known results for OUtype processes on $\mathbb{R}^{n}$ and onedimensional CBI processes (with state space $\mathbb{R}_{\geqslant0}$). To prove our result, we combine analytical and probabilistic techniques; in particular, the stability theory for ODEs plays an important role.
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Facial recognition has to be regulated to protect the public, says AI repor
1207 MIT Technology 3870 
In this paper we present novel $ADE$ correspondences by combining an earlier induction theorem of ours with one of Arnold's observations concerning Trinities, and the McKay correspondence. We first extend Arnold's indirect link between the Trinity of symmetries of the Platonic solids $(A_3, B_3, H_3)$ and the Trinity of exceptional 4D root systems $(D_4, F_4, H_4)$ to an explicit Clifford algebraic construction linking the two ADE sets of root systems $(I_2(n), A_1\times I_2(n), A_3, B_3, H_3)$ and $(I_2(n), I_2(n)\times I_2(n), D_4, F_4, H_4)$. The latter are connected through the McKay correspondence with the ADE Lie algebras $(A_n, D_n, E_6, E_7, E_8)$. We show that there are also novel indirect as well as direct connections between these ADE root systems and the new ADE set of root systems $(I_2(n), A_1\times I_2(n), A_3, B_3, H_3)$, resulting in a web of threeway ADE correspondences between three ADE sets of root systems.
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For a domain $D \subset \mathbb C^n$, $n \ge 2$, let $F^k_D(z)=K_D(z)\lambda\big(I^k_D(z)\big)$, where $K_D(z)$ is the Bergman kernel of $D$ along the diagonal and $\lambda\big(I^k_D(z)\big)$ is the Lebesgue measure of the Kobayashi indicatrix at the point $z$. This biholomorphic invariant was introduced by B\l ocki and in this note, we study the boundary behaviour of $F^k_D(z)$ near a finite type boundary point where the boundary is smooth, pseudoconvex with the corank of its Levi form being at most $1$. We also compute its limiting behaviour near the boundary of certain other basic classes of domains.
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The classical Eulerian polynomials $A_n(t)$ are known to be gamma positive. Define the positive Eulerian polynomial $\mathsf{AExc^{+}}_n(t)$ as the polynomial obtained when we sum excedances over the alternating group. We show that $\mathsf{AExc^{+}}_n(t)$ is gamma positive iff $n \geq 5$ and $n \equiv 1$ (mod 2). When $n \geq 4$, and $n \equiv 0$ (mod 2) we show that $\mathsf{AExc^{+}}_n(t)$ can be written as a sum of two gamma positive polynomials. Similar results are shown when we consider the positive typeD and typeD Eulerian polynomials. Finally, we show gamma positivity results when we sum excedances over derangements with positive and negative sign. Our main resuls is that the polynomial obtained by summing excedance over a conjugacy class indexed by $\lambda$ is gamma positive.
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We shall generalize the notion of a Laver table to algebras which may have many generators, several fundamental operations, fundamental operations of arity higher than 2, and to algebras where only some of the operations are selfdistributive or where the operations satisfy a generalized version of selfdistributivity. These algebras mimic the algebras of rankintorank embeddings $\mathcal{E}_{\lambda}/\equiv^{\gamma}$ in the sense that composition and the notion of a critical point make sense for these sorts of algebras.
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In Kac's classification of finitedimensional Lie superalgebras, the contragredient ones can be constructed from Dynkin diagrams similar to those of the simple finitedimensional Lie algebras, but with additional types of nodes. For example, $A(n1,0) = \mathfrak{sl}(1n)$ can be constructed by adding a "gray" node to the Dynkin diagram of $A_{n1} = \mathfrak{sl}(n)$, corresponding to an odd null root. The Cartan superalgebras constitute a different class, where the simplest example is $W(n)$, the derivation algebra of the Grassmann algebra on $n$ generators. Here we present a novel construction of $W(n)$, from the same Dynkin diagram as $A(n1,0)$, but with additional generators and relations.
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We consider links that are alternating on surfaces embedded in a compact 3manifold. We show that under mild restrictions, the complement of the link decomposes into simpler pieces, generalising the polyhedral decomposition of alternating links of Menasco. We use this to prove various facts about the hyperbolic geometry of generalisations of alternating links, including weakly generalised alternating links described by the first author. We give diagrammatical properties that determine when such links are hyperbolic, find the geometry of their checkerboard surfaces, bound volume, and exclude exceptional Dehn fillings.
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On a reduced analytic space $X$ we introduce the concept of a generalized cycle, which extends the notion of a formal sum of analytic subspaces to include also a form part. We then consider a suitable equivalence relation and corresponding quotient $\mathcal{B}(X)$ that we think of as an analogue of the Chow group and a refinement of de Rham cohomology. This group allows us to study both global and local intersection theoretic properties. We provide many $\mathcal{B}$analogues of classical intersection theoretic constructions: For an analytic subspace $V\subset X$ we define a $\mathcal{B}$Segre class, which is an element of $\mathcal{B}(X)$ with support in $V$. It satisfies a global King formula and, in particular, its multiplicities at each point coincide with the Segre numbers of $V$. When $V$ is cut out by a section of a vector bundle we interpret this class as a MongeAmp\`eretype product. For regular embeddings we construct a $\mathcal{B}$analogue of the Gysin morphism.
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Seeking compliance with Linux's new Code of Conduct, Intel software engineer Jarkko Sakkinen recently requested comments on a set of changes to kernel code comments which Neowin described as "replacing the Fword with 'hug'. " 80 comments quickly followed on the Linux Kernel Maintainer's List: Several contributors responded to the alterations calling them insane. One wondered if Sakkinen was just trying to make a joke, and another called it censorship and said he'd refuse to apply any sort of patches like this to the code he's in charge of... Some of the postchange comments read "Some Athlon laptops have really hugged PST tables", "If you don't see why, please stay the hug away from my code", and "Only Sun can take such nice parts and hug up the programming interface". Eventually LWN.net publisher Jonathan Corbet deflated most of the controversy by pointing out that Linux's new Code of Conduct applies to future comments but clearly indicates that it does not apply explicitly to pas
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A logistics division of DHL announced today that it will invest $300 million to modernize 60 percent of its warehouses in North America with more IoT sensors and robots. Robotic process automation and software made to reduce workflow interruptions will also play a role. VentureBeat reports: Such technology is already in operation in 85 DHL facilities, or roughly 20 percent of warehouses across North America. Funding announced today will bring emerging technology to 350 of DHL Supply Chain's 430 operating sites. The company has more than 35,000 employees in North America. Conversations are ongoing with more than 25 robotics and process automation industry leaders, DHL Supply Chain president of retail Jim Gehr said. DHL Supply Chain warehouse robots will work primarily with unitpicking operations and will be able to complete a range of tasks, from collaborative piece picking to shuttling items across a factory to following human packers.
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Internal Facebook documents seized by British lawmakers suggest that the social media giant once considered selling access to user data, according to extracts obtained by the Wall Street Journal. Back in April, Facebook CEO Mark Zuckerberg told congress unequivocally that, "We do not sell data." But these documents suggest that it was something that the company internally considered doing between 2012 and 2014, while the company struggled to generate revenue after its IPO. This just goes to show that no matter what promises a company makes, once the shareholders come knocking, they'll disregard all promises, morals, and values they claim to have.
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As of today, Fedora 27 will not be getting any more updates, including security updates. Users should be planning to upgrade more or less immediately. "Fedora 28 will continue to receive updates until 4 weeks after the release of Fedora 30. The maintenance schedule of Fedora releases is documented on the Fedora Project wiki. The Fedora Project wiki also contains instructions on how to upgrade from a previous release of Fedora to a version receiving updates."
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George H.W. Bush, the 41st president of the United States, has passed away tonight at the age of 94. As The Washington Post reports, he was "the last veteran of World War II to serve as president, he was a consummate public servant and a statesman who helped guide the nation and the world out of a fourdecade Cold War that had carried the threat of nuclear annihilation." From the report: Although Mr. Bush served as president three decades ago, his values and ethic seem centuries removed from today's acrid political culture. His currency of personal connection was the handwritten letter  not the social media blast. He had a competitive nature and considerable ambition that were not easy to discern under the sheen of his New England politesse and his earnest generosity. He was capable of running hardedge political campaigns, and took the nation to war. But his principal achievements were produced at negotiating tables. Despite his grace, Mr. Bush was an easy subject for caricature. He
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A major difference between Go 1 and Go 2 is who is going to influence the design and how decisions are made. Go 1 was a small team effort with modest outside influence; Go 2 will be much more communitydriven. After almost 10 years of exposure, we have learned a lot about the language and libraries that we didn't know in the beginning, and that was only possible through feedback from the Go community. The Go team s revealing some things about the future of the programming language.
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We explore the representation theory of Renner monoids associated to classical groups and their Hecke algebras. In Cartan type $A_n$, the Hecke algebra is a natural deformation of the rook monoid algebra, and its representation theory has been studied extensively by Solomon and Halverson, among others. It is known that the character tables are block upper triangular, i.e. $M=AY=YB$ for some matrices $A$ and $B$. We compute the $A$ and $B$ matrices in Cartan type $B_n$ by using the results of Li, Li, and Cao to pursue analogous results to those of Solomon. We then compute some type $B_n$ Hecke algebra character values by using the same $B$ matrix as in the monoid case.
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This work focuses on finding optimal locations for charging stations for oneway electric car sharing programs. The relocation of vehicles by a service staff is generally required in vehicle sharing programs in order to correct imbalances in the network. We seek to limit the need for vehicle relocation by strategically locating charging stations given estimates of traffic flow. A mixedinteger linear programming formulation is presented with a large number of potential charging station locations. A column generation approach is used which finds an optimal set of locations for the continuous relaxation of our problem. Results of a numerical experiment using real traffic and geographic information system location data show that our formulation significantly increases the balanced flow across the network, while our column generation technique was found to produce a superior solution in much shorter computation time compared to solving the original formulation with all possible station loc
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We show a method to build new examples of Lie algebras admitting LCS or LCK structures starting with a smaller dimensional Lie algebra endowed with a LCS or LCK structure respectively, and a suitable representation. We also study the existence of lattices in the associated simply connected Lie groups in order to obtain compact examples of manifolds admitting these kind of structures. Finally we show that the Lie algebra underlying of the well known OeljesklausToma solvmanifold can me reobtained using our construction.
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In this article we investigate partially truncated correlation functions (PTCF) of infinite continuous systems of classical point particles with pair interaction. We derive KirkwoodSalsburg (KS)type equations for the PTCF and write the solutions of these equations as a sum of contributions labelled by certain special graphs (forests), the connected components of which are tree graphs. We generalize the method introduced by Minlos and Pogosyan in the case of truncated correlations. These solutions make it possible to derive strong cluster properties for PTCF which were obtained earlier for lattice spin systems.
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In this article we give normal forms in a neighbourhood of a compact orbit of a Poisson Lie group action on a $b$symplectic manifold. In particular we establish cotangent models for Poisson group actions on $b$Poisson manifolds and a $b$symplectic slice theorem. We examine interesting particular instances of PoissonLie group actions on $b$symplectic manifolds. Also, we revise the notion of cotangent lift and twisted $b$cotangent lift introduced in \cite{km} and provide a generalization of the twisted $b$cotangent lift to higher dimensional torus actions. We introduce the notion of $b$Lie group and the associated $b$symplectic structures in its $b$cotangent bundle together with their reduction theory.
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We explore combinatorial formulas for deformations of highest weight characters of the odd orthogonal group $SO(2n+1)$. Our goal is to represent these deformations of characters as partition functions of statistical mechanical models  in particular, twodimensional solvable lattice models. In Cartan type $A$, Hamel and King [8] and Brubaker, Bump, and Friedberg [3] gave square ice models on a rectangular lattice which produced such a deformation. Outside of type $A$, icetype models were found using rectangular lattices with additional boundary conditions that split into two classes  those with `nested' and `nonnested bends.' Our results fill a gap in the literature, providing the first such formulas for type $B$ with nonnested bends. In type $B$, there are many known combinatorial parameterizations of highest weight representation basis vectors as catalogued by Proctor [19]. We show that some of these permit icetype models via appropriate bijections (those of Sundaram [21] and
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Despite CRISPR baby controversy, Harvard University will begin geneediting
1130 MIT Technology 3947 
Let $f(X)=X(1+aX^{q(q1)}+bX^{2(q1)})\in\Bbb F_{q^2}[X]$, where $a,b\in\Bbb F_{q^2}^*$. In a series of recent papers by several authors, sufficient conditions on $a$ and $b$ were found for $f$ to be a permutation polynomial (PP) of $\Bbb F_{q^2}$ and, in characteristic $2$, the sufficient conditions were shown to be necessary. In the present paper, we confirm that in characteristic 3, the sufficient conditions are also necessary. More precisely, we show that when $\text{char}\,\Bbb F_q=3$, $f$ is a PP of $\Bbb F_{q^2}$ if and only if $(ab)^q=a(b^{q+1}a^{q+1})$ and $1(b/a)^{q+1}$ is a square in $\Bbb F_q^*$.
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In this paper, we first present a GearhardtPr\"uss type theorem with a sharp bound for maccretive operators. Then we give two applications: (1) give a simple proof of the result proved by Constantin et al. on relaxation enhancement induced by incompressible flows; (2) show that shear flows with a class of Weierstrass functions obey logarithmically fast dissipation timescales.
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Strong invariants of evendimensional topological insulators of independent Fermions are expressed in terms of an invertible operator on the Hilbert space over the boundary. It is given by the Cayley transform of the boundary restriction of the halfspace resolvent. This dimensional reduction is routed in new representation for the $K$theoretic exponential map. It allows to express the invariants via the reflection matrix at the Fermi energy, for the scattering setup of a wire coupled to the halfspace insulator.
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In the framework of Density Functional Theory with Strongly Correlated Electrons we consider the so called bond dissociating limit for the energy of an aggregate of atoms. We show that the multimarginals optimal transport cost with Coulombian electronelectron repulsion may correctly describe the dissociation effect. The variational limit is completely calculated in the case of N=2 electrons. The theme of fractional number of electrons appears naturally and brings into play the question of optimal partial transport cost. A plan is outlined to complete the analysis which involves the study of the relaxation of optimal transport cost with respect to the weak* convergence of measures.
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The millimeter wave (mmWave) bands and other high frequencies above 6~GHz have emerged as a central component of FifthGeneration (5G) cellular standards to deliver high data rates and ultralow latency. A key challenge in these bands is blockage from obstacles, including the human body. In addition to the reduced coverage, blockage can result in highly intermittent links where the signal quality varies significantly with motion of obstacles in the environment. The blockages have widespread consequences throughout the protocol stack including beam tracking, link adaptation, cell selection, handover and congestion control. Accurately modeling these blockage dynamics is therefore critical for the development and evaluation of potential mmWave systems. In this work, we present a novel spatial dynamic channel sounding system based on phased array transmitters and receivers operating at 60 GHz. Importantly, the sounder can measure multiple directions rapidly at high speed to provide detaile
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We study the extremal particles of the twodimensional Coulomb gas with confinement generated by a radially symmetric positive background in the determinantal case and the zeros of the corresponding random polynomials. We show that when the background is supported on the unit disk, the point process of the particles outside of the disk converges towards a universal point process, i.e. that does not depend on the background. This limiting point process may be seen as the determinantal point process governed by the Bergman kernel on the complement of the unit disk. It has an infinite number of particles and its maximum is a heavy tailed random variable. To prove this convergence we study the case where the confinement is generated by a positive background outside of the unit disk. For this model we show that the point process of the particles inside the disk converges towards the determinantal point process governed by the Bergman kernel on the unit disk. In the case where the background
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We generalize DengDu's folding argument, for the bounded derived category D(Q) of an acyclic quiver Q, to the finite dimensional derived category D(Gamma Q) of the Ginzburg algebra Gamma Q associated to Q. We show that the Fstable category of D(Gamma Q) is equivalent to the finite dimensional derived category D(Gamma\SS) of the Ginzburg algebra Gamma\SS associated to the specie \SS, which is folded from Q. Then we show that, if (Q,\SS) is of Dynkin type, the principal component Stab_0 D(Gamma\SS) of the space of the stability conditions of D(Gamma\SS) is canonically isomorphic to the principal component Stab_0^F D(Gamma Q) of the space of Fstable stability conditions of D(Gamma Q). As an application, we show that, if (Q,\SS) is of type (A_3, B_2) or (D_4, G_2), the space Stab^N D(Gamma Q) of numerical stability conditions in Stab^0 D(Gamma Q), consists of Br Gamma Q/Br Gamma\SS many connected components, each of which is isomorphic to Stab^0 D(Gamma\SS) \cong Stab^F D(Gamma Q).
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We give an overview of the general framework of forms of Bak, Tits and Wall, when restricting to vector spaces over fields, including its relationship to the classical notions of Hermitian, alternating and quadratic forms. We then prove a version of Witt's lemma in this context, showing in particular that the action of the group of isometries of a space equipped with a form is transitive on isometric subspaces.
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