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

An anonymous reader quotes BleepingComputer: Members of the open source community are working on a new securityfocused project for the Linux kernel. Named Linux Kernel Runtime Guard (LKRG), this is a loadable kernel module that will perform runtime integrity checking of the Linux kernel. Its purpose is to detect exploitation attempts for known security vulnerabilities against the Linux kernel and attempt to block attacks. LKRG will also detect privilege escalation for running processes, and kill the running process before the exploit code runs. Since the project is in such early development, current versions of LKRG will only report kernel integrity violations via kernel messages, but a full exploit mitigation system will be deployed as the system matures... While LKRG will remain an open source project, LKRG maintainers also have plans for an LKRG Pro version that will include distrospecific LKRG builds and support for the detection of specific exploits, such as container escapes.
收起

Japan has launched the world's smallest satellitecarrying rocket. Longtime Slashdot reader hey! writes: Last week Japan Aerospace Exploration Agency (JAXA) successfully placed a threekilogram cubesat into an 180 x 1,500 kilometer orbit at 31 degrees inclination to the equator. The payload was launched on a modified sounding rocket, called the SS5205. The assembled rocket weighed a mere 2600 kilograms [2.87 tons] on the launchpad, making the SS5205 the smallest vehicle ever to put an object into orbit. Note that the difference in the SS520's modest orbital capacity of four kilograms and its ability to launch 140 kilograms to 1000 kilometers on a suborbital flight. That shows how much more difficult it is to put an object into orbit than it is to merely send it into space.
收起

An anonymous reader writes: Flat earther "Mad" Mike Hughes, who also bills himself as "the last great daredevil," promised Super Bowlsized ratings for an event Saturday where he'd blast himself nearly half a mile into the sky on a homemade rocket. "We had 20 cameras on site today, ready for a full segment," explained the videoondemand site Noize TV on their Facebook page. One newspaper described it as also being "an event which he hopes will get people to investigate the ideology which holds the earth is flat." But judging from online reactions, the event was just another disappointment. Noize TV's Facebook post titled "The Launch!!! Finally" shows a picture of Mike standing beside his rocket  but it's followed by a commenters saying things like "There was no launch. I doubt there will be," and the official Noize TV account saying "We thought he would press that button... He did not. And won't be doing so we are pretty certain." And this morning Noize TV posted that "we will no l
收起

theodp writes: On Tuesday, it was announced that Alaska Airlines will make a new Code.org series of six short videos starring Microsoft's Bill Gates on How Computers Work available as inflight entertainment. "Because students and adults alike can learn from these videos," wrote Code.org CEO Hadi Partovi, "we are pleased to announce Khan Academy and Alaska Airlines will make them available beyond Code.org classrooms." The original submission notes that Gates (and the Bill and Melinda Gates Foundation) have contributed millions to both educational groups, but Alaska Airlines calls the videos "entertaining and approachable," and says they'll start appearing on their flights in April. But the videos are also available online, and besides Gates also feature appearances by former Apple designer May Li Khoe and Nat Brown, one of the creators of Microsoft's Xbox gaming system.
收起

The Finnish Broadcasting Corporation reports: Simo Karppinen, Unit Head at the Finnish Transport and Safety Agency Trafi, says it plans to roll out an app that will function as a free digital driving license by the end of summer. The agency said it expects many Finns to take up the use of the digital driving license as soon as it is released. The digital license has been in use by a test group who report successfully using the app where proof of identity is required, such as picking up postal packages. Other uses for the digital license include informing the owner of license renewal dates... The digital driving license will not record the location of its user or serve as a tracking device. Slashdot reader Kiuas writes that it's being used as a supplement for traditional card licenses rather than a replacement, because "Current Finnish law mandates that all driver's licenses are handed out in a physical form. So everyone will still get a physical driver's license, but those who wish t
收起

The Factor Daily site has a look at work to increase the diversity of opensource contributors in India. "Over past two months, we interviewed at least two dozen people from within and outside the open source community to identify a set of women open source contributors from India. While the list is not conclusive by any measure, it’s a good starting point in identifying the women who are quietly shaping the future of open source from this part of the world and how they dealt with gender biases."
收起

"Free/libre and 100% community backed version of XenServer," promises a new Kickstarter page, adding that "Our first prototype (and proof of concept) is already functional." Currently, XenServer is a turnkey virtualization platform, distributed as a distribution (based on CentOS). It comes with a feature rich toolstack, called XAPI. The vast majority of XenServer code is Open Source. But since XenServer 7.3, Citrix removed a lot of features from it. The goal of XCPng is to make a fully community backed version of XenServer, without any feature restrictions. We also aim to create a real ecosystem, not depending on one company only. Simple equation: the more we are, the healthier is the environment. The campaign reached its fundraising goal within a few hours, reports longtime Slashdot reader NoOnesMessiah, and within three days they'd already raised four times the needed amount and began unlocking their stretch goals.
收起

wiredmikey quotes SecurityWeek: Researchers have discovered more than 130 malware samples designed to exploit the recently disclosed Spectre and Meltdown CPU vulnerabilities. While a majority of the samples appear to be in the testing phase, we could soon start seeing attacks... On Wednesday, antivirus testing firm AVTEST told SecurityWeek that it has obtained 139 samples from various sources, including researchers, testers and antivirus companies... Fortinet, which also analyzed many of the samples, confirmed that a majority of them were based on available proof of concept code. Andreas Marx, CEO of AVTEST, believes different groups are working on the PoC exploits to determine if they can be used for some purpose. "Most likely, malicious purposes at some point," he said.
收起

An anonymous reader quotes a report from The New York Times (Warning: source may be paywalled; alternative source): Two types of bacteria commonly found in the gut work together to fuel the growth of colon tumors, researchers reported on Thursday. Their study, published in the journal Science, describes what may be a hidden cause of colon cancer, the third most common cancer in the United States. The research also adds to growing evidence that gut bacteria modify the body's immune system in unexpected and sometimes deadly ways. The findings suggest that certain preventive strategies may be effective in the future, like looking for the bacteria in the colons of people getting colonoscopies. If the microbes are present, the patients might warrant more frequent screening; eventually people at high risk for colon cancer may be vaccinated against at least one of the bacterial strains. Two types of bacteria, Bacteroides fragilis and a strain of E. coli, can pierce a mucus shield that lines t
收起

A function from configuration space to moduli space of surface may induce a homomorphism between their fundamental groups which are braid groups and mapping class groups of surface, respectively. This map $\phi: B_k \rightarrow \Gamma_{g,b}$ is induced by 3fold branched covering over a disk with some branch points. In this thesis we give a concrete description of this map and show that it is injective by BirmanHilden theory. This gives us a new interesting nongeometric embedding of braid group into mapping class group. On the other hand, we show that the map on the level of classifying spaces of groups is compatible with the action of little 2cube operad so that it induces a trivial homomorphim between stable homology group of braid groups and that of mapping class groups(Harer conjecture). We also show how the lift $\tilde{\beta_i}$ acts on the fundamental group of the surface and through this we prove that $\tilde{\beta_i}$ equals the product of two inverse Dehn twists.
收起

The Kaczmarz and GaussSeidel methods both solve a linear system $\bf{X}\bf{\beta} = \bf{y}$ by iteratively refining the solution estimate. Recent interest in these methods has been sparked by a proof of Strohmer and Vershynin which shows the randomized Kaczmarz method converges linearly in expectation to the solution. Lewis and Leventhal then proved a similar result for the randomized GaussSeidel algorithm. However, the behavior of both methods depends heavily on whether the system is under or overdetermined, and whether it is consistent or not. Here we provide a unified theory of both methods, their variants for these different settings, and draw connections between both approaches. In doing so, we also provide a proof that an extended version of randomized GaussSeidel converges linearly to the least norm solution in the underdetermined case (where the usual randomized Gauss Seidel fails to converge). We detail analytically and empirically the convergence properties of both methods
收起

Environments and closures are two of the main ingredients of evaluation in lambdacalculus. A closure is a pair consisting of a lambdaterm and an environment, whereas an environment is a list of lambdaterms assigned to free variables. In this paper we investigate some dynamic aspects of evaluation in lambdacalculus considering the quantitative, combinatorial properties of environments and closures. Focusing on two classes of environments and closures, namely the socalled plain and closed ones, we consider the problem of their asymptotic counting and effective random generation. We provide an asymptotic approximation of the number of both plain environments and closures of size $n$. Using the associated generating functions, we construct effective samplers for both classes of combinatorial structures. Finally, we discuss the related problem of asymptotic counting and random generation of closed environemnts and closures.
收起

A general greedy approach to construct coverings of compact metric spaces by metric balls is given and analyzed. The analysis is a continuous version of Chvatal's analysis of the greedy algorithm for the weighted set cover problem. The approach is demonstrated in an exemplary manner to construct efficient coverings of the ndimensional sphere and ndimensional Euclidean space to give short and transparent proofs of several best known bounds obtained from deterministic constructions in the literature on sphere coverings.
收起

In the 1970s, Feigenbaum, and independently, Coullet and Tresser, discovered an interesting phenomenon in physics called period doubling that showed how a sequence of dynamical systems with stable dynamics can converge to one with chaotic dynamics. In this paper we study analogous phenomena for the tangent family $\{T_t(z)=i t\tan z\}_{\pi/2\leq t\leq \pi}$ restricted to the real and imaginary axes. Because tangent maps have no critical points but have an essential singularity at infinity and two asymptotic values, the phenomena are related but different. We find single instances of "period doubling", "period quadrupling" and "period splitting". Then we prove there is a general pattern of "period merging" where two attracting cycles of period $2^n$ "merge" into one attracting cycle of period $2^{n+1}$ and "cycle doubling" where an attracting cycle of period $2^{n+1}$ "becomes" two attracting cycles of the same period. We adapt the renormalization techniques used to study period doublin
收起

We introduce and discuss L\'evytype cylindrical martingale problems on separable reflexive Banach spaces. Our main observations are the following: Cylindrical martingale problems have a onetoone relation to weak solutions of stochastic partial differential equations. Moreover, wellposed problems possess the strong Markov property and a CameronMartinGirsanovtype formula holds. As applications, we derive existence and uniqueness results.
收起

We study ordered configuration spaces of compact manifolds with boundary. We show that for a large class of such manifolds, the real homotopy type of the configuration spaces only depends on the real homotopy type of the pair consisting of the manifold and its boundary. We moreover describe explicit real models of these configuration spaces using three different approaches. We do this by adapting previous constructions for configuration spaces of closed manifolds which relied on Kontsevich's proof of the formality of the little disks operads. We also prove that our models are compatible with the richer structure of configuration spaces, respectively a module over the SwissCheese operad, a module over the associative algebra of configurations in a collar around the boundary of the manifold, and a module over the little disks operad.
收起

We study the structure and enumeration of the final two 2x4 permutation classes, completing a research program that has spanned almost two decades. For both classes, careful structural analysis produces a complicated functional equation. One of these equations is solved with the guessandcheck paradigm, while the other is solved with kernel methodlike techniques and Gr\"obner basis calculations.
收起

Building upon the recent work in communication efficient classical secret sharing schemes of Bitar and El Rouayheb, we study communication efficient quantum secret sharing schemes. In the standard model of quantum secret sharing, typically one is interested in minimal authorized sets for the reconstruction of the secret. In such a setting, reconstruction requires the communication of all the shares of the corresponding authorized set. If we allow for nonminimal authorized sets, then we can trade off the size of the authorized sets with the amount of communication required for reconstruction. Based on the staircase codes proposed by Bitar and El Rouayheb, we propose a class of quantum threshold secret sharing schemes that are also communication efficient. In the standard model of quantum secret sharing, sharing a qudit using a $((k,2k1))$ threshold scheme requires $k$ qudits to be communicated to reconstruct the secret. In the proposed schemes, we can recover the secret by communicati
收起

We categorify a coideal subalgebra of the quantum group of $\mathfrak{sl}_{2r+1}$ by introducing a $2$category \`a la KhovanovLaudaRouquier, and show that selfdual indecomposable $1$morphisms categorify the canonical basis of this algebra. This allows us to define a categorical action of this coideal algebra on the categories of modules over cohomology rings of partial flag varieties and on the BGG category $\mathcal{O}$ of type B/C.
收起

This paper considers convex sample approximations of chanceconstrained optimization problems, in which the chance constraints are replaced by sets of sampled constraints. We show that, if a subset of sampled constraints are discarded, then the use of a randomized sample selection strategy allows tight bounds to be derived on the probability that the solution of the sample approximation is feasible for the original chance constraints. These confidence bounds are shown to be tighter than the bounds that apply if constraints are discarded according to optimal or greedy discarding strategies. We further show that the same confidence bounds apply to solutions that are obtained from a two stage process in which a sample approximation of a chanceconstrained problem is solved, then an empirical measure of the violation probability of the solution is obtained by counting the number of violations of an additional set of sampled constraints. We use this result to design a repetitive scenario ap
收起

An anonymous reader quotes a report from Ars Technica: On Wednesday, the beleaguered credit reporting agency Equifax launched a new service to protect people from the risks of identity theft that the company vastly magnified with a breach of over 145 million people's credit records last year. The service, called Lock & Alert, is fronted by a mobile application and a Web application. It is intended to allow individuals to control access to their credit report on demand. "Lock & Alert allows You to lock and unlock your EIS credit report ('Equifax credit report')," the services' terms of service agreement states. "Locking or unlocking your Equifax credit report usually takes less than a minute." Except when it doesn't. As Tara Siegel Bernard and Ron Lieber of the New York Times reported, the new service  which is different from a "freeze" in some ways that are not clear from a legal and regulatory standpoint  has not been working for some (and possibly all) mobile app users. T
收起

This paper considers the problem of testing if a sequence of means $(\mu_t)_{t =1,\ldots ,n }$ of a nonstationary time series $(X_t)_{t =1,\ldots ,n }$ is stable in the sense that the difference of the means $\mu_1$ and $\mu_t$ between the initial time $t=1$ and any other time is smaller than a given level, that is $  \mu_1  \mu_t  \leq c $ for all $t =1,\ldots ,n $. A test for hypotheses of this type is developed using a biascorrected monotone rearranged local linear estimator and asymptotic normality of the corresponding test statistic is established. As the asymptotic variance depends on the location and order of the critical roots of the equation $ \mu_1  \mu_t  = c$ a new bootstrap procedure is proposed to obtain critical values and its consistency is established. As a consequence we are able to quantitatively describe relevant deviations of a nonstationary sequence from its initial value. The results are illustrated by means of a simulation study and by analyzing data exa
收起

A countable discrete group $G$ is said to be ChoquetDeny if it has a trivial Poisson boundary for every generating probability measure. We show that a finitely generated group $G$ is ChoquetDeny if and only if it is virtually nilpotent. Moreover, when $G$ is not virtually nilpotent, then the Poisson boundary is nontrivial for a generating measure that is symmetric and has finite entropy. For general countable discrete groups, we show that $G$ is ChoquetDeny if and only if none of its quotients have the infinite conjugacy class property.
收起

In this paper we present a necessary conditions, that simple close geodesics on regular tetrahedra in the 3dimensional hyperbolic space must satisfy. Furthermore, we explicitly describe three classes of simple closed geodesics on regular tetrahedra in the hyperbolic 3space. These are socalled 2homogeneous, 3homogeneous and (3,2)homogeneous geodesics. Up to a rigid motion of a tetrahedron there exists a unique geodesic in each class.
收起

We consider a networked control system (NCS) consisting of two plants, a global plant and a local plant, and two controllers, a global controller and a local controller. The global (resp. local) plant follows discretetime stochastically switched linear dynamics with a continuous global (resp. local) state and a discrete global (resp. local) mode. We assume that the state and mode of the global plant are observed by both controllers while the state and mode of the local plant are only observed by the local controller. The local controller can inform the global controller of the local plant's state and mode through an unreliable TCPlike communication channel where successful transmissions are acknowledged. The objective of the controllers is to cooperatively minimize a modesdependent quadratic cost over a finite time horizon. Following the method developed in [1] and [2], we construct a dynamic program based on common information and a decomposition of strategies, and use it to obtain
收起

EinsteinWeyl structures on a threedimensional manifold $M$ is given by a system $E$ of PDEs on sections of a bundle over $M$. This system is invariant under the Lie pseudogroup $G$ of local diffeomorphisms on $M$. Two EinsteinWeyl structures are locally equivalent if there exists a local diffeomorphism taking one to the other. Our goal is to describe the quotient equation $E/G$ whose solutions correspond to nonequivalent EinsteinWeyl structures. The approach uses symmetries of the ManakovSantini integrable system and the action of the corresponding Lie pseudogroup.
收起

A mean field type differential game is a mathematical model of a large system of identical agents under meanfield interaction controlled by two players with opposite purposes. We study the case when the dynamics of each agent is given by ODE and the players can observe the distribution of the agents. We construct suboptimal strategies and prove the existence of the value function.
收起

We single out a class of difference families which is widely used in some constructions of Hadamard matrices and which we call GoethalsSeidel (GS) difference families. They consist of four subsets (base blocks) of a finite abelian group of order $v$, which can be used to construct Hadamard matrices via the wellknown GoethalsSeidel array. We consider the special class of these families in cyclic groups, where each base block is either symmetric or skew. We omit the wellknown case where all four blocks are symmetric. By extending previous computations by several authors, we complete the classification of GSdifference families of this type for odd $v<50$. In particular, we have constructed the first examples of so called good matrices, Gmatrices and best matrices of order 43, and good matrices and Gmatrices of order 45. We also point out some errors in one of the cited references.
收起

A conjectural formula for the $k$point generating function of GromovWitten invariants of the Riemann sphere for all genera and all degrees was proposed in \cite{DY2}. In this paper, we give a proof of this formula together with an explicit analytic (as opposed to formal) expression for the corresponding matrix resolvent. We also give a formula for the $k$point function as a sum of $(k1)!$ products of hypergeometric functions of one variable. We show that the $k$point generating function coincides with the $\epsilon\rightarrow 0$ asymptotics of the analytic $k$point function, and also compute three more asymptotics of the analytic function for $\epsilon\rightarrow \infty$, $q\rightarrow 0$, $q\rightarrow\infty$, thus defining new invariants for the Riemann sphere.
收起

We present an application of Hilbert quasipolynomials to order domains, allowing the effective check of the second orderdomain condition in a direct way. We also provide an improved algorithm for the computation of the related Hilbert quasipolynomials. This allows to identify order domain codes more easily.
收起

We introduce the notion of a holonomic Dmodule on a smooth (idealized) logarithmic scheme and show that Verdier duality can be extended to this context. In contrast to the classical case, the pushforward of a holonomic module along an open immersion is in general not holonomic. We introduce a "perverse" tstructure on the category of coherent logarithmic Dmodules which makes the dualizing functor texact on holonomic modules. This allows us to transfer some of the formalism from the classical setting and in particular show that every holonomic module on an open subscheme can be extended to a holonomic module on the whole space.
收起

Hopf solitons in the SkyrmeFaddeev system on $R^3$ typically have a complicated structure, in particular when the Hopf number Q is large. By contrast, if we work on a compact 3manifold M, and the energy functional consists only of the Skyrme term (the strongcoupling limit), then the picture simplifies. There is a topological lower bound $E\geq Q$ on the energy, and the local minima of E can look simple even for large Q. The aim here is to describe and investigate some of these solutions, when M is $S^3$, $T^3$ or $S^2 \times S^1$. In addition, we review the more elementary babySkyrme system, with M being $S^2$ or $T^2$.
收起

We introduce the notion of implicative algebra, a simple algebraic structure intended to factorize the model constructions underlying forcing and realizability (both in intuitionistic and classical logic). The salient feature of this structure is that its elements can be seen both as truth values and as (generalized) realizers, thus blurring the frontier between proofs and types. We show that each implicative algebra induces a (Setbased) tripos, using a construction that is reminiscent from the construction of a realizability tripos from a partial combinatory algebra. Relating this construction with the corresponding constructions in forcing and realizability, we conclude that the class of implicative triposes encompass all forcing triposes (both intuitionistic and classical), all classical realizability triposes (in the sense of Krivine) and all intuitionistic realizability triposes built from total combinatory algebras.
收起

The goal of this thesis is to provide efficient and provably convergent numerical methods for solving partial differential equations (PDEs) coming from impulse control problems motivated by finance. Impulses, which are controlled jumps in a stochastic process, are used to model realistic features in financial problems which cannot be captured by ordinary stochastic controls. The dynamic programming equations associated with impulse control problems are HamiltonJacobiBellman quasivariational inequalities (HJBQVIs) Other than in certain special cases, the numerical schemes that come from the discretization of HJBQVIs take the form of complicated nonlinear matrix equations also known as Bellman problems. We prove that a policy iteration algorithm can be used to compute their solutions. In order to do so, we employ the theory of weakly chained diagonally dominant (w.c.d.d.) matrices. As a byproduct of our analysis, we obtain some new results regarding a particular family of Markov decis
收起

The purpose of this study is to examine in a clinical setting a novel formulation of objective functions for intensitymodulated radiotherapy (IMRT) treatment plan multicriteria optimization (MCO) that we suggested in a recent study. The proposed objective functions are extended with dynamic multileaf collimator (DMLC) delivery constraints from the literature, and a tailored interiorpoint method is described to efficiently solve the resulting optimization formulation. In a numerical planning study involving three patient cases, DMLC plans Pareto optimal to the MCO formulation with the proposed objective functions are generated. Evaluated based on predefined plan quality indices, these DMLC plans are compared to conventionally generated DMLC plans. Comparable plan quality is observed. Supported by these results, the proposed objective functions are argued to have a potential to streamline the planning process, since they are designed to overcome the methodological shortcomings associa
收起

HigsonKapsparovTrout introduced an infinite dimensional Clifford algebra of a Hilbert space, and verified Bott periodicity on K theory. In order to develop algebraic topology of maps between Hilbert spaces, in this paper we introduce an induced Hilbert Clifford algebra, and construct an induced map between K theory of the HKT Clifford algebra to the induced Clifford algebra. We also compute its K group for some concrete case.
收起

Let $C$ be a hyperelliptic curve of genus $g \geq 3$. We give a new description of the theta map for moduli spaces of rank 2 semistable vector bundles with trivial determinant. In orther to do this, we describe a fibration of (a birational model of) the moduli space, whose fibers are GIT quotients $(\mathbb{P}^1)^{2g}//\operatorname{PGL(2)}$. Then, we use recent results of Kumar to identify the restriction of the theta map to these GIT quotients with some explicit osculating projection. As a corollary of this construction, we obtain a birational equivalence between the ramification locus of the theta map and a fibration in Kummer $(g1)$varieties over $\mathbb{P}^g$.
收起

Let $(X,\mu)$ be a standard probability space. An automorphism $T$ of $(X,\mu)$ has the weak Pinsker property if for every $\varepsilon > 0$ it has a splitting into a direct product of a Bernoulli shift and an automorphism of entropy less than $\varepsilon$. This property was introduced by Thouvenot, who asked whether it holds for all ergodic automorphisms. This paper proves that it does. The proof actually gives a more general result. Firstly, it gives a relative version: any factor map from one ergodic automorphism to another can be enlarged by arbitrarily little entropy to become relatively Bernoulli. Secondly, using some facts about relative orbit equivalence, the analogous result holds for all free and ergodic measurepreserving actions of a countable amenable group. The key to this work is a new result about measure concentration. Suppose now that $\mu$ is a probability measure on a finite product space $A^n$, and endow this space with its Hamming metric. We prove that $\mu$ m
收起

We study the spectral approximation of a secondorder elliptic differential eigenvalue problem that arises from structural vibration problems using isogeometric analysis. In this paper, we generalize recent work in this direction. We present optimally blended quadrature rules for the isogeometric spectral approximation of a diffusionreaction operator with both Dirichlet and Neumann boundary conditions. The blended rules improve the accuracy and the robustness of the isogeometric approximation. In particular, the optimal blending rules minimize the dispersion error and lead to two extra orders of superconvergence in the eigenvalue error. Various numerical examples (including the Schr$\ddot{\text{o}}$dinger operator for quantum mechanics) in one and three spatial dimensions demonstrate the performance of the blended rules.
收起

We consider partial symmetric Toeplitz matrices where a positive definite completion exists. We characterize those patterns where the maximum determinant completion is itself Toeplitz. We then extend these results with positive definite replaced by positive semidefinite, and maximum determinant replaced by maximum rank. These results are used to determine the singularity degree of a family of semidefinite optimization problems.
收起

The local dynamics around a fixed point has been extensively studied for germs of one and several complex variables. In one dimension, there exist a complete picture of the trajectory of the orbits on a whole neighborhood of the fixed point. In dimensions larger or equal than two some partial results are known. In this article we analyze a case that lies in the boundary between one and several complex variables. We consider skew product maps of the form F (z, w) = ({\lambda}(z), f (z, w)). We deal with the case of parabolic skew product maps, that is when DF(0,0) = Id. Our goal is to describe the behavior of orbits around a whole neighborhood of the origin. We establish formulas for conjugacy maps in different regions of a neighborhood of the origin.
收起

Let $S$ be a closed surface of genus $g$. In this paper, we investigate the relationship between hyperbolic conestructure on $S$ and representations of the fundamental group into PSL$_2\Bbb R$. We prove that, if $S$ has genus $2$, then every representation $\rho$ with Euler number $\mathcal{E}(\rho)=\pm1$ sends a simple nonseparating curve to an elliptic element. After that, we use this result to derive that every representation with $\mathcal{E}(\rho)=\pm1$ arises as the holonomy of some hyperbolic conestructure. Finally we consider surfaces of genus greater than $2$ and we show that, under suitable condition, every representation $\rho:\pi_1 S\longrightarrow $ PSL$_2\Bbb R$ with Euler number $\mathcal{E}(\rho)=\pm\big(\chi(S)+1\big)$ arises as holonomy of a hyperbolic conestructure $\sigma$ on $S$ with a single cone point of angle $4\pi$.
收起

A binary string transmitted via a memoryless i.i.d. deletion channel is received as a subsequence of the original input. From this, one obtains a posterior distribution on the channel input, corresponding to a set of candidate supersequences weighted by the number of times the received subsequence can be embedded in them. In a previous work it is conjectured on the basis of experimental data that the entropy of the posterior is minimized and maximized by the constant and the alternating strings, respectively. In this work, we present an algorithm for counting the number of subsequence embeddings using a runlength encoding of strings. We then describe two different ways of clustering the space of supersequences and prove that their cardinality depends only on the length of the received subsequence and its Hamming weight, but not its exact form. Then, we consider supersequences that contain a single embedding of a fixed subsequence, referred to as singletons, and provide a closed form e
收起

We show directly that the fractal uncertainty principle of BourgainDyatlov [arXiv:1612.09040] implies that there exists $ \sigma > 0 $ for which the Selberg zeta function for a convex cocompact hyperbolic surface has only finitely many zeros with $ \Re s \geq \frac12  \sigma$. That eliminates advanced microlocal techniques of DyatlovZahl [arXiv:1504.06589] though we stress that these techniques are still needed for resolvent bounds and for possible generalizations to the case of nonconstant curvature.
收起

We derive explicit formulas for the resultants and discriminants of classical quasiorthogonal polynomials, as a full generalization of the results of Dilcher and Stolarsky (2005) and Gishe and Ismail (2008). We consider a certain system of Diophantine equations, originally designed by Hausdorff (1909) as a simplification of Hilbert's solution (1909) of Waring's problem, and then create the relationship to quadrature formulas and quasiHermite polynomials. We reduce these equations to the existence problem of rational points on a hyperelliptic curve associated with discriminants of quasiHermite polynomials, and thereby show a nonexistence theorem for solutions of Hausdorfftype equations.
收起

We study dispersive mixedorder systems of pseudodifferential operators in the setting of $L^p$Sobolev spaces. Under the weak condition of quasihyperbolicity, these operators generate a semigroup in the space of tempered distributions. However, if the basic space is a tuple of $L^p$Sobolev spaces, a strongly continuous semigroup is in many cases only generated if $p=2$ or $n=1$. The results are applied to the linear thermoelastic plate equation inertial term and with Fourier's or MaxwellCattaneo's law of heat conduction.
收起

To what extent do thermodynamic resource theories capture physically relevant constraints? Inspired by quantum computation, we define a set of elementary thermodynamic gates that only act on 2 energy levels of a system at a time. We show that this theory is well reproduced by a JaynesCummings interaction in rotating wave approximation and draw a connection to standard descriptions of thermalisation. We then prove that elementary thermal operations present tighter constraints on the allowed transformations than thermal operations. Mathematically, this illustrates the failure at finite temperature of fundamental theorems by Birkhoff and MuirheadHardyLittlewoodPolya concerning stochastic maps. Physically, this implies that stronger constraints than those imposed by singleshot quantities can be given if we tailor a thermodynamic resource theory to the relevant experimental scenario. We provide new tools to do so, including necessary and sufficient conditions for a given change of the
收起

Consider a nilpotent element e in a simple complex Lie algebra. The Springer fibre corresponding to e admits a discretization (discrete analogue) introduced by the author in 1999. In this paper we propose a conjectural description of that discretization which is more amenable to computation.
收起

We show that the parabola is of strong Khintchine type for convergence, which is the first result of its kind for curves. Moreover, Jarnik type theorems are established in both the simultaneous and the dual settings, without monotonicity on the approximation function. To achieve the above, we prove a new counting result for the number of rational points with fixed denominators lying close to the parabola, which uses Burgess's bound on short character sums.
收起

We consider a nonlinear, free boundary fluidstructure interaction model in a bounded domain. The viscous incompressible fluid interacts with a nonlinear elastic body on the common boundary via the velocity and stress matching conditions. The motion of the fluid is governed by incompressible NavierStokes equations while the displacement of elastic structure is determined by a nonlinear elastodynamic system with boundary dissipation. The boundary dissipation is inserted in the velocity matching condition. We prove the global existence of the smooth solutions for small initial data and obtain the exponential decay of the energy of this system as well.
收起

Ridge functions have recently emerged as a powerful set of ideas for subspacebased dimension reduction. In this paper we begin by drawing parallels between ridge subspaces, sufficient dimension reduction and active subspaces; contrasting between techniques rooted in statistical regression to those rooted in approximation theory. This sets the stage for our new algorithm that approximates what we call a Gaussian ridge functionthe posterior mean of a Gaussian process on a dimension reducing subspacesuitable for both regression and approximation problems. To compute this subspace we develop an iterative algorithm that optimizes over the Grassmann manifold to compute the subspace, followed by an optimization of the hyperparameters of the Gaussian process. We demonstrate the utility of the algorithm on an analytical function, where we obtain near exact ridge recovery, and a turbomachinery case study, where we compare the efficacy of our approach with four well known sufficient dimens
收起

We cope with a free boundary fluidstructure interaction model. In the model, the viscous incompressible fluid interacts with elastic body via the common boundary. The motion of the fluid is governed by NavierStokes equations while the displacement of elastic structure is described by variable coefficient wave equations. The dissipation is placed on the common boundary between fluid and elastic body. Given small initial data, the global existence of the solutions of this system is proved and the exponential decay of solutions are obtained.
收起

Entropy numbers and covering numbers of sets and operators are well known geometric notions, which found many applications in various fields of mathematics, statistics, and computer science. Their values for finitedimensional embeddings $id:\ell_p^n\to \ell_q^n$, $0<p,q\le\infty$, are known (up to multiplicative constants) since the pioneering work of Sch\"utt in 1984, with later improvements by Edmunds and Triebel, K\"uhn and Gu\'edon and Litvak. The aim of this survey is to give a selfcontained presentation of the result and an overview of the different techniques used in its proof.
收起