Solidot 公告
请在发布文章时用HTML代码加上至少一条新闻来源的链接；原创性消息，可加入相关信息（如涉及公司的网址）的链接。有任何问题，邮件至：he.fang#zhiding.cn
ken：feigaobox@gmail.com
注意：收到邮件乱码的用户请修改客户端的默认字体编码，从"简体中文（GB2312）"修改为"Unicode（UTF8）"。
投 票
信息流

HTC has officially launched its newest flagship smartphone today, the U11. While it has competitive specifications for a flagship smartphone of 2017, such as a 5.5inch, Quad HD display, and Snapdragon 835 processor with 4GB RAM, it has some unique features of its own. HTC is introducing a new way to interact with the U11 by letting you squeeze the sides of the device to perform different functions. The Verge reports: This new feature is called "Edge Sense," and it can be configured to do a variety of tasks with either short or long squeezes. You can set a short squeeze to open the camera and then take a picture when the camera app is open. A long squeeze can be configured to launch the Google voice assistant or toggle the flashlight on and off. In addition to Edge Sense, the U11 has a similar design to the U Ultra from earlier this year. That means it's metal and glass  a departure from the allaluminum unibody designs of past HTC phones  with curved panels that blend into the met
收起

Apple has just been granted patents for two of the biggest features expected from the iPhone 8: an edgetoedge display, and a Touch ID button embedded into the screen. 9to5Mac reports: The edgetoedge display patent has the rather mundane heading "Reducing the border area of a device." It describes how a mostlyflat display can have a curved border area allowing it to wrap around the sides of the device: [...] "This relates to methods and systems for reducing the border areas of an electronic device so as to maximize the display/interactive touch areas of the device. In particular, a flexible substrate can be used to fabricate the display panel and/or the touch sensor panel (referred to collectively herein as a 'circuit panel') of a mobile electronic device so that the edges of the display panel and/or the touch sensor panel can be bent. Bending the edges can reduce the width (or length) of the panel, which in turn can allow the overall device to be narrower without reducing the disp
收起

Twelve readers share a Reuters report: Many countries are pinning their hopes on China and India to lead efforts to slow climate change amid a growing sense of resignation that U.S. President Donald Trump will either withdraw from a global pact or stay and play a minimal role. Delegates at the May 818 negotiations in Bonn on a detailed "rule book" for the 2015 Paris Agreement, the first U.N. talks since Trump took office, say there is less foreboding than when Washington last broke with global climate efforts in 2001. Trump doubts global warming has a human cause and says he will decide on a campaign threat to "cancel" the Paris Agreement, the first to bind all nations to set goals to curb emissions, after a group of Seven summit in Italy on May 2627. "The time when one big player could affect the whole game is past," said Ronald Jumeau, climate ambassador for the Seychelles. "There would be a void without the U.S., but China and India seem to be increasing their effort." Big emitter
收起

Ford is planning a major round of layoffs that will cut up to 20,000 jobs around the world, according to reports published Monday. From a report: Ford plans to shrink its salaried workforce in North America and Asia by about 10 percent as it works to boost profits and its sliding stock price, a source familiar with the plan told Reuters. A person briefed on the plan said Ford plans to offer generous early retirement incentives to reduce its salaried headcount by Oct. 1, but does not plan cuts to its hourly workforce or its production. The move could put the U.S. automaker on a collision course with President Donald Trump, who has made boosting auto employment a top priority. Ford has about 30,000 salaried workers in the United States. The cuts are part of a previously announced plan to slash costs by $3 billion, the person said, as U.S. new vehicles auto sales have shown signs of decline after seven years of consecutive growth since the end of the Great Recession.
收起

An anonymous reader writes: European privacy regulators from as number of countries has made a coordinated action against Facebook for violating data protection laws. The French CNIL has sanctioned Facebook with a 150,000 EUR fine, and the regulator from Netherlands is considering a similar action. Regulators are concerned with new privacy policies of Facebook, lack of transparency, cookie handling and tracking Facebook users on thirdparty sites  all without user knowledge or control. Such coordinated move is unprecedented in the history of European data protection regulators.
收起

Security updates have been issued by Arch Linux (libplist), Debian (mysqlconnectorjava), Fedora (jasper, kdelibs, lxterminal, menucache, pcmanfm, and postgresql), openSUSE (qemu), Slackware (freetype and kdelibs), SUSE (ghostscriptlibrary, libtirpc, and mariadb), and Ubuntu (ghostscript, kernel, linux, linuxraspi2, linuxhwe, openjdk7, qemu, shadow, and thunderbird).
收起

Four years ago, as the country was wrestling with a federalbudget crisis, conservative news outlets turned their attention, once again, to the topic of wasteful government spending. That March, a reporter with CNS News, a Web site devoted to countering “liberal bias” in the media, came across what seemed to be the quintessential example of such waste—a National Science Foundation grant to Yale University for a study of duck penises. Within days, the story had made its way to Fox News. “It’s part of President Obama’s stimulus plan, and it’s just one example of the kind of spending decisions that have added up to massive debt and deficits,” Shannon Bream told viewers. The following week, Sean Hannity piled on. “Don’t we really need to know about duck genitalia, Tucker Carlson?” he asked. To which Carlson responded, with a smirk, “I know more than I want to know already!” The controversy, dubbed Duckpenisgate by Mother Jones, roared back to life some months later, when Senator Tom Coburn
收起

An anonymous reader shares a CNBC report: Chinese state media on Wednesday criticized the United States for hindering efforts to stop global cyber threats in the wake of the WannaCry ransomware attack that has infected more than 300,000 computers worldwide in recent days. The U.S. National Security Agency (NSA) should shoulder some blame for the attack, which targets vulnerabilities in Microsoft systems and has infected some 30,000 Chinese organisations as of Saturday, the China Daily said. "Concerted efforts to tackle cyber crimes have been hindered by the actions of the United States," it said, adding that Washington had "no credible evidence" to support bans on Chinese tech firms in the United States following the attack. The malware attack, which began on Friday and has been linked by some researchers to previous hits by a North Koreanrun hacking operation, leveraged a tool built by the NSA that leaked online in April, Microsoft says.
收起

An anonymous reader quotes a report from NBC News: Army whistleblower Chelsea Manning is set to walk out of prison Wednesday  but she won't be entirely free. Manning's 35year sentence for leaking an enormous trove of military intelligence records was commuted by President Barack Obama in January. But Manning is still appealing her conviction in a case that could take years, and the government has yet to respond to the appeal. And all the while, Private First Class Manning, 29, will remain an active duty soldier in the U.S. Army. She won't be paid a salary, and it's highly unlikely that she will be called to serve. But being placed on voluntary excess leave rather than discharged, says one of her attorneys, makes her vulnerable to new military punishment or charges if she steps out of line. Such an offense could be anything from getting into a fistfight to revealing previously unreleased classified information. Manning could even get into trouble with the military for speaking and wr
收起

Let $U$ be an affine smooth curve defined over an algebraically closed field of positive characteristic. The Abhyankar Conjecture (proved by Raynaud and Harbater in 1994) describes the set of finite quotients of Grothendieck's \'etale fundamental group of $U$. In this paper, we consider a purely inseparable analogue of this problem, formulated in terms of Nori's profinite fundamental group scheme, and give a partial answer to it.
收起

This paper deals with the parameter estimation problem of the SingleInputSingleOutput (SISO) switched Hammerstein system. Suppose that the switching law is arbitrary but can be observed online. All subsystems are parameterized and the Recursive Least Squares (RLS) algorithm is applied to estimate their parameters. To overcome the difficulty caused by coupling of data from different subsystems, the concept "intrinsic switch" is introduced. Two cases are considered: i) The input is taken to be a sequence of independent identically distributed (i.i.d.) random variables when identification is the only purpose; ii) A diminishingly excited signal is superimposed on the control when the adaptive control law is given. The strong consistency of the estimates in both cases is established and a simulation example is given to verify the theoretical analysis.
收起

Let $f$ be a function from a metric space $Y$ to a separable metric space $X$. If $f$ has the Baire property, then it is continuous apart a 1st category set. In 1935, Kuratowski asked whether the separability requirement could be lifted. A full scale attack on the problem took place in the late seventies and early eighties. What was not known then, and what remains virtually unknown today, is the fact that the first impressive attempt to solve the Kuratowski problem, due to Kinjiro Kunugi and based on a theorem of Lusin and Novikov, took place already in 1936. Lusin's remarkable 1934 Comptes Rendus note soon forgotten, remained unnoticed to this day. We analyze both papers and bring the results to full light.
收起

Capacitated fixedcharge network flows are used to model a variety of problems in telecommunication, facility location, production planning and supply chain management. In this paper, we investigate capacitated path substructures and derive strong and easytocompute \emph{path cover and path pack inequalities}. These inequalities are based on an explicit characterization of the submodular inequalities through a fast computation of parametric minimum cuts on a path, and they generalize the wellknown flow cover and flow pack inequalities for the singlenode relaxations of fixedcharge flow models. We provide necessary and sufficient facet conditions. Computational results demonstrate the effectiveness of the inequalities when used as cuts in a branchandcut algorithm.
收起

Nonorthogonal multiple access (NOMA) is one of the key techniques to address the high spectral efficiency and massive connectivity requirements for the fifth generation (5G) wireless system. To efficiently realize NOMA, we propose a joint design framework combining the polar coding and the NOMA transmission, which deeply mines the generalized polarization effect among the users. In this polar coded NOMA (PCNOMA) framework, the original NOMA channel is decomposed into multiple bit polarized channels by using a threestage channel transform, that is, user$\to$signal$\to$bit partitions. Specifically, for the firststage channel transform, we design two schemes, namely sequential user partition (SUP) and parallel user partition (PUP). For the SUP, a joint successive cancellation detecting and decoding scheme is developed, and a search algorithm is proposed to schedule the NOMA detecting order which improves the system performance by enhanced polarization among the user synthesized channe
收起

We describe new convex valid inequalities for $p$order conic mixedinteger optimization, which includes the important second order conic mixedinteger optimization as a special case. The inequalities are based on the polymatroid inequalities over binary variables for the diagonal case. We prove that the proposed inequalities completely describe the convex hull of a single conic constraint over binary variables and unbounded continuous variables. We then generalize and strengthen the inequalities using other constraints of the optimization problem. Computational experiments for second order conic mixedinteger optimization indicate that the new inequalities strengthen the convex relaxations substantially for the diagonal case as well as the general (nondiagonal) case and lead to significant performance improvements.
收起

Functional data analysis on nonlinear manifolds has drawn recent interest. We propose an intrinsic principal component analysis for smooth Riemannian manifoldvalued functional data and study its asymptotic properties. The proposed Riemannian functional principal component analysis (RFPCA) is carried out by first mapping the manifoldvalued data through Riemannian logarithm maps to tangent spaces around the timevarying Fr\'echet mean function, and then performing a classical multivariate functional principal component analysis on the linear tangent spaces. Representations of the Riemannian manifoldvalued functions and the eigenfunctions on the original manifold are then obtained by mapping back with exponential maps. The tangentspace approximation through functional principal component analysis is shown to be wellbehaved in terms of controlling the residual variation if the Riemannian manifold has nonnegative curvature. We derive uniform convergence rates for the model components,
收起

We present here a set of lecture notes on exact fluctuation relations. We prove the Jarzynski equality and the Crooks fluctuation theorem, two paradigmatic examples of classical fluctuation relations. Finally we consider their quantum versions, and analyze analogies and differences with the classical case.
收起

We discuss necessary conditions for a compact quantum group to act on the algebra of noncommutative $n$torus $\mathbb{T}_\theta^n$ in a filtration preserving way in the sense of Banica and Skalski. As a result, we construct a family of compact quantum groups $\mathbb{G}_\theta=(A_\theta^n,\Delta)$ such that for each $\theta$, $\mathbb{G}_\theta$ is the final object in the category of all compact quantum groups acting on $\mathbb{T}_\theta^n$ in a filtration preserving way. We describe in details the structure of the C*algebra $A_\theta^n$ and provide a concrete example of its representation in bounded operators. Moreover, we compute the Haar measure of $\mathbb{G}_\theta$. For $\theta=0$, the quantum group $\mathbb{G}_0$ is nothing but the classical group $\mathbb{T}^n\rtimes S_n$, where $S_n$ is the symmetric group. For general $\theta$, $\mathbb{G}_\theta$ is still an extension of the classical group $\mathbb{T}^n$ by the classical group $S_n$. It turns out that for $n=2$, the alge
收起

The quasinormal modes for black holes are the resonances for the scattering of incoming waves by black holes. Here we consider scattering of massless uncharged Dirac fields propagating in the outer region of de SitterReissnerNordstr{\"o}m black hole, which is spherically symmetric charged exact solution of the EinsteinMaxwell equations. Using the spherical symmetry of the equation and restricting to a fixed harmonic the problem is reduced to a scattering problem for the 1D massless Dirac operator on the line. The resonances for the problem are related to the resonances for a certain semiclassical Schr{\"o}dinger operator with exponentially decreasing positive potential. We give exact relation between the sets of Dirac and Schr{\"o}dinger resonances. The asymptotic distribution of the resonances is close to the lattice of pseudopoles associated to the nondegenerate maxima of the potentials. Using the techniques of quantum Birkhoff normal form we give the complete asymptotic formula
收起

For a generalized permutohedron $Q$ the enumerator $F(Q)$ of positive lattice points in interiors of maximal cones of the normal fan $\Sigma_Q$ is a quasisymmetric function. We describe this function for the class of nestohedra as a Hopf algebra morphism from a combinatorial Hopf algebra of building sets. For the class of graphassociahedra the corresponding quasisymmetric function is a new isomorphism invariant of graphs. The obtained invariant is quite natural as it is the generating function of ordered colorings of graphs and satisfies the recurrence relation with respect to deletions of vertices.
收起

Three problems about recovery of a highfrequency free term in the onedimension wave equation with homogeneous initialboundary conditions by some information about partial asymptotics of its solution have been solved. It is shoun, that the free term can be completely recovered from a specific data about incomplete (threeterms) asymptotics of the solution. Before formulation of the each problem about recovery of free term, construction and justification of the asymptotics of the solution of original initialboundary problem are given.
收起

In this paper fundamental Wigner coefficients are determined algebraically by considering the eigenvalues of certain generalized Casimir invariants. Here this method is applied in the context of both type 1 and type 2 unitary representations of the Lie superalgebra gl(mjn). Extensions to the nonunitary case are investigated. A symmetry relation between two classes of Wigner coefficients is given in terms of a ratio of dimensions.
收起

We study a class of (focusing) nonlinear Schroedingertype equations derived recently by Dumas, Lannes and Szeftel within the mathematical description of high intensity laser beams [5]. These equations incorporate the possibility of a (partial) offaxis variation of the group velocity of such laser beams through a second order partial differential operator acting in some, but not necessarily all, spatial directions. We study the wellposedness theory for such models and obtain a regularizing effect, even in the case of only partial offaxis dependence. This provides an answer to an open problem posed in [5].
收起

Moreau's seminal paper, introducing what is now called the Moreau envelope and the proximity operator (a.k.a. proximal mapping), appeared in 1965. The Moreau envelope of a given convex function provides a regularized version which has additional desirable properties such as differentiability and full domain. Fifty years ago, Attouch proposed to use the Moreau envelope for regularization. Since then, this branch of convex analysis has developed in many fruitful directions. In 1967, Bregman introduced what is nowadays the Bregman distance as a measure of discrepancy between two points generalizing the square of the Euclidean distance. Proximity operators based on the Bregman distance have become a topic of significant research as they are useful in algorithmic solution of optimization problems. More recently, in 2012, Kan and Song studied regularization aspects of the left BregmanMoreau envelope even for nonconvex functions. In this paper, we complement previous works by analyzing the l
收起

We consider the Dirichlet eigenvalue problem on a simple polytope. We use the Rellich identity to obtain an explicit formula expressing the Dirichlet eigenvalue in terms of the Neumann data on the faces of the polytope of the corresponding eigenfunction. The formula is particular simple for polytopes admitting an inscribed ball tangent to all the faces. Our result could be viewed as a generalization of similar identities for simplices recently found by Christianson [1][2].
收起

We introduce the ring of partial differential operators with constant coefficients and commensurate time lags (we use the terminology D$\Delta$ operators from now) initially defined by H. Gl\"usingL\"ur\ss en for ordinary $D\Delta$ operators and investigate its cohomological properties. Combining this ring theoretic observation with the integral representation technique developed by M. Andersson, we solve a certain type of division with bounds. In the last chapter, we prove the injectivity property of various function modules over this ring as well as spectral synthesis type theorems for $D\Delta$ equations.
收起

In this paper we combine the Parareal parallelintime method together with spatial parallelization and investigate this spacetime parallel scheme by means of solving the threedimensional incompressible NavierStokes equations. Parallelization of time stepping provides a new direction of parallelization and allows to employ additional cores to further speed up simulations after spatial parallelization has saturated. We report on numerical experiments performed on a Cray XE6, simulating a driven cavity flow with and without obstacles. Distributed memory parallelization is used in both space and time, featuring up to 2,048 cores in total. It is confirmed that the spacetimeparallel method can provide speedup beyond the saturation of the spatial parallelization.
收起

The boundaries of the hyperbolic components of odd period of the multicorns contain realanalytic arcs consisting of quasiconformally conjugate parabolic parameters. One of the main results of this paper asserts that the Hausdorff dimension of the Julia sets is a realanalytic function of the parameter along these parabolic arcs. This is achieved by constructing a complex onedimensional quasiconformal deformation space of the parabolic arcs which are contained in the dynamically defined algebraic curves $\mathrm{Per}_n(1)$ of a suitably complexified family of polynomials. As another application of this deformation step, we show that the dynamically natural parametrization of the parabolic arcs has a nonvanishing derivative at all but (possibly) finitely many points. We also look at the algebraic sets $\mathrm{Per}_n(1)$ in various families of polynomials, the nature of their singularities, and the `dynamical' behavior of these singular parameters.
收起

Let $D$ be a bounded domain $D$ in $\mathbb R^n $ with infinitely smooth boundary and $n$ is odd. We prove that if the volume cut off from the domain by a hyperplane is an algebraic function of the hyperplane, free of real singular points, then the domain is an ellipsoid. This partially answers a question of V.I. Arnold: whether odddimensional ellipsoids are the only algebraically integrable domains?
收起

We study lattices on ~A_2 buildings that preserve types, act regularly on each type of edge, and whose vertex stabilizers are cyclic. We show that several of their properties, such as their automorphism group and isomorphism class, can be determined from purely combinatorial data. As a consequence we can show that the number of such lattices (up to isomorphism) grows superexponentially with the thickness parameter q. We look in more detail at the 3295 lattices with q in {2,3,4,5}. We show that with one exception for each q these are all exotic. For the exotic examples we prove that the automorphism group of the lattice and of the building coincide, and that two lattices are quasiisometric only if they are isomorphic.
收起

We give several families of reasonably small integers $k, \ell \ge 1$ and real positive $\alpha, \beta \le 1$, such that the products $p_1\ldots p_k s$, where $p_1, \ldots, p_k \le m^\alpha$ are primes and $s \le m^\beta$ is a product of at most $\ell$ primes, represent all reduced residue classes modulo $m$. This is a relaxed version of the still open question of P. Erdos, A. M. Odlyzko and A. Sarkozy (1987), that corresponds to $k = \ell =1$ (that is, to products of two primes). In particular, we improve recent results of A. Walker (2016).
收起

Let $F_n$ denote the $n^{th}$ term of the Fibonacci sequence. In this paper, we investigate the Diophantine equation $F_1^p+2F_2^p+\cdots+kF_{k}^p=F_{n}^q$ in the positive integers $k$ and $n$, where $p$ and $q$ are given positive integers. A complete solution is given if the exponents are included in the set $\{1,2\}$. Based on the specific cases we could solve, and a computer search with $p,q,k\le100$ we conjecture that beside the trivial solutions only $F_8=F_1+2F_2+3F_3+4F_4$, $F_4^2=F_1+2F_2+3F_3$, and $F_4^3=F_1^3+2F_2^3+3F_3^3$ satisfy the title equation.
收起

For an undirected simple graph $G$, we write $G \rightarrow (H_1, H_2)^v$ if and only if for every redblue coloring of its vertices there exists a red $H_1$ or a blue $H_2$. The generalized vertex Folkman number $F_v(H_1, H_2; H)$ is defined as the smallest integer $n$ for which there exists an $H$free graph $G$ of order $n$ such that $G \rightarrow (H_1, H_2)^v$. The generalized edge Folkman numbers $F_e(H_1, H_2; H)$ are defined similarly, when colorings of the edges are considered. We show that $F_e(K_{k+1},K_{k+1};K_{k+2}e)$ and $F_v(K_k,K_k;K_{k+1}e)$ are well defined for $k \geq 3$. We prove the nonexistence of $F_e(K_3,K_3;H)$ for some $H$, in particular for $H=B_3$, where $B_k$ is the book graph of $k$ triangular pages, and for $H=K_1+P_4$. We pose three problems on generalized Folkman numbers, including the existence question of edge Folkman numbers $F_e(K_3, K_3; B_4)$, $F_e(K_3, K_3; K_1+C_4)$ and $F_e(K_3, K_3; \overline{P_2 \cup P_3} )$. Our results lead to some genera
收起

Let $D\geq 2$, $S\subset \mathbb R^D$ be finite and let $\phi:S\to \mathbb R^D$ with $\phi$ a small distortion on $S$. We solve the Whitney extensioninterpolationalignment problem of how to understand when $\phi$ can be extended to a function $\Phi:\mathbb R^D\to \mathbb R^D$ which is a smooth small distortion on $\mathbb R^D$. Our main results are in addition to Whitney extensions, results on interpolation and alignment of data in $\mathbb R^D$ and complement those of [26].
收起

A graph is pathpairable if for any pairing of its vertices there exist edgedisjoint paths joining the vertices in each pair. We investigate the behaviour of the maximum degree in pathpairable planar graphs. We show that any $n$vertex pathpairable planar graph must contain a vertex of degree linear in $n$.
收起

We survey the problem of separation under conjugacy and malnormality of the abelian peripheral subgroups of an orientable, irreducible $3$manifold $X$. We shall focus on the relation between this problem and the existence of acylindrical splittings of $\pi_1(X)$ as an amalgamated product or HNNextension along the abelian subgroups corresponding to the JSJtori.
收起

In \cite{hien}, M. Hien introduced rapid decay homology group $\Homo^{rd}_{*}(U, (\nabla, E))$ associated to an irregular connection $(\nabla, E)$ on a smooth complex affine variety $U$, and showed that it is the dual group of the algebraic de Rham cohomology group $\Homo^*_{dR}(U,(\nabla^{\vee}, E^{\vee}))$. On the other hand, F. Pham has already introduced his version of rapid decay homology when $(\nabla, E)$ is the socalled elementary irregular connection (\cite{Sab}) in \cite{Pham}. In this report, we will state a comparison theorem of these homology groups and give an outline of its proof. This can be regarded as a homological counterpart of the result \cite{Sab} of C. Sabbah. As an application, we construct a basis of some rapid decay homologies associated to a hyperplane arrangement and hypersphere arrangement of Schl\"ofli type.
收起

In the $R$spread out, $d$dimensional voter model, each site $x$ of $\mathbb{Z}^d$ has state (or 'opinion') 0 or 1 and, with rate 1, updates its opinion by copying that of some site $y$ chosen uniformly at random among all sites within distance $R$ from $x$. If $d \geq 3$, the set of (extremal) stationary measures of this model is given by a family $\mu_{\alpha, R}$, where $\alpha \in [0,1]$. Configurations sampled from this measure are polynomially correlated fields of 0's and 1's in which the density of 1's is $\alpha$ and the correlation weakens as $R$ becomes larger. We study these configurations from the point of view of nearest neighbor site percolation on $\mathbb{Z}^d$, focusing on asymptotics as $R \to \infty$. In \cite{RV15}, we have shown that, if $R$ is large, there is a critical value $\alpha_c(R)$ such that there is percolation if $\alpha > \alpha_c(R)$ and no percolation if $\alpha < \alpha_c(R)$. Here we prove that, as $R \to \infty$, $\alpha_c(R)$ converges to t
收起

We investigate the optimal mass transport problem associated to the following "ballistic" cost functional on phase space $M\times M^*$, b_T(v, x):=\inf\{\langle v, \gamma (0)\rangle +\int_0^TL(\gamma (t), {\dot \gamma}(t))\, dt; \gamma \in C^1([0, T), M); \gamma(T)=x\}, where $M=\mathbb{R}^d$, $T>0$, and $L:M\times M^* \to \mathbb{R}$ is a Lagrangian that is jointly convex in both variables. Under suitable conditions on the initial and final probability measures, we use convex duality \`a la Bolza and MongeKantorovich theory to lift classical HopfLax formulae from state space to Wasserstein space. This allows us to relate optimal transport maps for the ballistic cost to those associated with the fixedend cost defined on $M\times M$ by c_T(x,y):=\inf\{\int_0^TL(\gamma(t), {\dot \gamma}(t))\, dt; \gamma\in C^1([0, T), M); \gamma(0)=x, \gamma(T)=y\}. We also point to links with the theory of mean field games.
收起

In 1996, Jackson and Martin proved that a strong ideal ramp scheme is equivalent to an orthogonal array. However, there was no good characterization of ideal ramp schemes that are not strong. Here we show the equivalence of ideal ramp schemes to a new variant of orthogonal arrays that we term augmented orthogonal arrays. We give some constructions for these new kinds of arrays, and, as a consequence, we also provide parameter situations where ideal ramp schemes exist but strong ideal ramp schemes do not exist.
收起

In this paper, we study powerefficient resource allocation for multicarrier nonorthogonal multiple access (MCNOMA) systems. The resource allocation algorithm design is formulated as a nonconvex optimization problem which jointly designs the power allocation, rate allocation, user scheduling, and successive interference cancellation (SIC) decoding policy for minimizing the total transmit power. The proposed framework takes into account the imperfection of channel state information at transmitter (CSIT) and quality of service (QoS) requirements of users. To facilitate the design of optimal SIC decoding policy on each subcarrier, we define a channeltonoise ratio outage threshold. Subsequently, the considered nonconvex optimization problem is recast as a generalized linear multiplicative programming problem, for which a globally optimal solution is obtained via employing the branchandbound approach. The optimal resource allocation policy serves as a system performance benchmark du
收起

We present an explicit construction of the moduli spaces of rank 2 stable parabolic bundles of parabolic degree 0 over the Riemann sphere, corresponding to an "optimum" open weight chamber of parabolic weights in the weight polytope. The complexity of the different moduli space' weight chambers is understood in terms of the complexity of the actions of the corresponding groups of bundle automorphisms on stable parabolic structures. For the given choices of parabolic weights, $\mathscr{N}$ consists entirely of isomorphism classes of strictly stable parabolic bundles whose underlying BirkhoffGrothendieck splitting coefficients are constant and minimal, is constructed as a quotient of a set of stable parabolic structures by a group of bundle automorphisms, and is a smooth, compact complex manifold biholomorphic to$\left(\mathbb{C}\mathbb{P}^{1}\right)^{n3}$ for even degree, and $\mathbb{C}\mathbb{P}^{n3}$ for odd degree.
收起