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

In a digital communication system, information is sent from one place to another over a noisy communication channel using binary symbols (bits). Original information is encoded by adding redundant bits, which are then used by lowdensity paritycheck (LDPC) codes to detect and correct errors that may have been introduced during transmission. Error correction capability of an LDPC code is severely degraded due to harmful structures such as small cycles in its bipartite graph representation known as Tanner graph (TG). We introduce an integer programming formulation to generate a TG for a given smallest cycle length. We propose a branchandcut algorithm for its solution and investigate structural properties of the problem to derive valid inequalities and variable fixing rules. We introduce a heuristic to obtain feasible solutions of the problem. Our computational experiments show that our algorithm can generate LDPC codes without small cycles in acceptable amount of time for practicall
收起

Photoacoustic tomography is a hybrid imaging technique that combines high optical tissue contrast with high ultrasound resolution. Direct reconstruction methods such as filtered backprojection, time reversal and least squares suffer from curved line artefacts and blurring, especially in case of limited angles or strong noise. In recent years, there has been great interest in regularised iterative methods. These methods employ prior knowledge on the image to provide higher quality reconstructions. However, easy comparisons between regularisers and their properties are limited, since many tomography implementations heavily rely on the specific regulariser chosen. To overcome this bottleneck, we present a modular reconstruction framework for photoacoustic tomography. It enables easy comparisons between regularisers with different properties, e.g. nonlinear, higherorder or directional. We solve the underlying minimisation problem with an efficient firstorder primaldual algorithm. Conver
收起

Korpelainen, Lozin, and Razgon conjectured that a hereditary property of graphs which is wellquasiordered by the induced subgraph order and defined by only finitely many minimal forbidden induced subgraphs is labelled wellquasiordered, a notion stronger than that of $n$wellquasiorder introduced by Pouzet in the 1970s. We present a counterexample to this conjecture. In fact, we exhibit a hereditary property of graphs which is wellquasiordered by the induced subgraph order and defined by finitely many minimal forbidden induced subgraphs yet is not $2$wellquasiordered. This counterexample is based on the widdershins spiral, which has received some study in the area of permutation patterns.
收起

We consider in this work a system of two stochastic differential equations named the perturbed compositional gradient flow. By introducing a separation of fast and slow scales of the two equations, we show that the limit of the slow motion is given by an averaged ordinary differential equation. We then demonstrate that the deviation of the slow motion from the averaged equation, after proper rescaling, converges to a stochastic process with Gaussian inputs. This indicates that the slow motion can be approximated in the weak sense by a standard perturbed gradient flow or the continuoustime stochastic gradient descent algorithm that solves the optimization problem for a composition of two functions. As an application, the perturbed compositional gradient flow corresponds to the diffusion limit of the Stochastic Composite Gradient Descent (SCGD) algorithm for minimizing a composition of two expectedvalue functions in the optimization literatures. For the strongly convex case, such an an
收起

BPS coherent states closely resemble semiclassical states and they have gravity dual descriptions in terms of semiclassical geometries. The half BPS coherent states have been well studied, however less is known about quarter BPS coherent states. Here we provide a construction of quarter BPS coherent states. They are coherent states built with two matrix fields, generalizing the half BPS case. These states are both the eigenstates of annihilation operators and in the kernel of dilatation operator. Another useful labeling of quarter BPS states is by representations of Brauer algebras and their projection onto a subalgebra $\mathbb{C}[S_n\times S_m]$. Here, the SchurWeyl duality for the Walled Brauer algebra plays an important role in organizing the operators. One interesting subclass of these Brauer states are labeled by representations involving two Young tableaux. We obtain the overlap between quarter BPS Brauer states and quarter BPS coherent states, where the Schur polynomials are u
收起

In this paper, we prove convergence in distribution of Langevin processes in the overdamped asymptotics. The proof relies on the classical perturbed test function (or corrector) method, which is used both to show tightness in path space, and to identify the extracted limit with a martingale problem. The result holds assuming the continuity of the gradient of the potential energy, and a mild control of the initial kinetic energy.
收起

DPcoloring of a simple graph is a generalization of list coloring, and also a generalization of signed coloring of signed graphs. It is known that for each $k \in \{3, 4, 5, 6\}$, every planar graph without $C_k$ is 4choosable. Furthermore, Jin, Kang, and Steffen \cite{JKS} showed that for each $k \in \{3, 4, 5, 6\}$, every signed planar graph without $C_k$ is signed 4choosable. In this paper, we show that for each $k \in \{3, 4, 5, 6\}$, every planar graph without $C_k$ is 4DPcolorable, which is an extension of the above results.
收起

This document seeks to prove there are infinitely many primes whose difference is 2, referred to as twin prime pairs. This proof's methodology involves constructing a function that approximates the number of positive integers, less than a known twin prime pair, which can be mapped to a twin prime pair greater than the known one by multiplication. This function is shown to be unbounded and less than the true count of integers it seeks to approximate for the majority of twin prime pairs. Additionally, it is shown there must be infinitely many integers that map a twin prime pair to one larger than itself without the use of the previously mentioned approximation.
收起

A projective manifold $M$ is algebraically hyperbolic if there exists a positive constant $A$ such that the degree of any curve of genus $g$ on $M$ is bounded from above by $A(g1)$. A classical result is that Kobayashi hyperbolicity implies algebraic hyperbolicity. It is known that Kobayashi hyperbolic manifolds have finite automorphism groups. Here we prove that, more generally, algebraically hyperbolic projective manifolds have finite automorphism groups.
收起

This summary of the doctoral thesis is created to emphasize the close connection of the proposed spectral analysis method with the Discrete Fourier Transform (DFT), the most extensively studied and frequently used approach in the history of signal processing. It is shown that in a typical application case, where uniform data readings are transformed to the same number of uniformly spaced frequencies, the results of the classical DFT and proposed approach coincide. The difference in performance appears when the length of the DFT is selected to be greater than the length of the data. The DFT solves the unknown data problem by padding readings with zeros up to the length of the DFT, while the proposed Extended DFT (EDFT) deals with this situation in a different way, it uses the Fourier integral transform as a target and optimizes the transform basis in the extended frequency range without putting such restrictions on the time domain. Consequently, the Inverse DFT (IDFT) applied to the res
收起

We extend earlier numerical and analytical considerations of the conformally invariant wave equation on a Schwarzschild background from the case of spherically symmetric solutions, discussed in Class. Quantum Grav. 34, 045005 (2017), to the case of general, nonsymmetric solutions. A key element of our approach is the modern standard representation of spacelike infinity as a cylinder. With a decomposition into spherical harmonics, we reduce the fourdimensional wave equation to a family of twodimensional equations. These equations can be used to study the behaviour at the cylinder, where the solutions turn out to have logarithmic singularities at infinitely many orders. We derive regularity conditions that may be imposed on the initial data, in order to avoid the first singular terms. We then demonstrate that the fully pseudospectral time evolution scheme can be applied to this problem leading to a highly accurate numerical reconstruction of the nonsymmetric solutions. We are particula
收起

We establish exact recovery for the Least Unsquared Deviations (LUD) algorithm of \"{O}zyesil and Singer. More precisely, we show that for sufficiently many cameras with given corrupted pairwise directions, where both camera locations and pairwise directions are generated by a special probabilistic model, the LUD algorithm exactly recovers the camera locations with high probability. A similar exact recovery guarantee was established for the ShapeFit algorithm by Hand, Lee and Voroninski. Comparing the two results, we conclude that in theory LUD can tolerate more corruption than ShapeFit.
收起

We introduce a class of distributed control policies for networks of discretetime linear systems with polytopic additive disturbances. The objective is to restrict the networklevel state and controls to userspecified polyhedral sets for all times. This problem arises in many safetycritical applications. We consider two problems. First, given a communication graph characterizing the structure of the information flow in the network, we find the optimal distributed control policy by solving a single linear program. Second, we find the sparsest communication graph required for the existence of a distributed invarianceinducing control policy. Illustrative examples, including one on platooning, are presented.
收起

We construct a fixed parameter algorithm parameterized by d and k that takes as an input a graph G' obtained from a ddegenerate graph G by complementing on at most k arbitrary subsets of the vertex set of G and outputs a graph H such that G and H agree on all but f(d,k) vertices. Our work is motivated by the first order model checking in graph classes that are first order interpretable in classes of sparse graphs. We derive as a corollary that if G_0 is a graph class with bounded expansion, then the first order model checking is fixed parameter tractable in the class of all graphs that can obtained from a graph G from G_0 by complementing on at most k arbitrary subsets of the vertex set of G; this implies an earlier result that the first order model checking is fixed parameter tractable in graph classes interpretable in classes of graphs with bounded maximum degree.
收起

We say that an exact equivalence between the derived categories of two algebraic varieties is tiltingtype if it is constructed by using tilting bundles. The aim of this article is to understand the behavior of tiltingtype equivalences for crepant resolutions under deformations. As an application of the method that we establish in this article, we study the derived equivalence for stratified Mukai flops and stratified Atiyah flops in terms of tilting bundles.
收起

We prove a decomposition formula of logarithmic GromovWitten invariants in a degeneration setting. A oneparameter log smooth family X>B with singular fibre over b_0 \in B yields a family M(X/B,\beta) > B of moduli stacks of stable logarithmic maps. We give a virtual decomposition of the fibre of this family over b_0 in terms of rigid tropical curves. This generalizes one aspect of known results in the case that the fibre X_{b_0} is a normal crossings union of two divisors. We exhibit our formulas in explicit examples.
收起

Motivated by the recent interest in formal methodsbased control of multiagent systems, we adopt to a bottomup approach. Each agent is subject to a local signal temporal logic task that may depend on other agents behavior. These dependencies pose control challenges since some of the tasks may be opposed to each other. We first develop a local continuous feedback control law and identify conditions under which this control law guarantees satisfaction of the local tasks. If these conditions do not hold, we propose to use the developed control law in combination with an online detection & repair scheme, expressed as a local hybrid system. After detection of a critical event, a twostage procedure is initiated to resolve the problem. The theoretical results are illustrated in simulations.
收起

Let A be the jacobian variety of a hyperelliptic curve defined over a number field k. We provide a decomposition formula for the Faltings height of A and for the N\'eronTate height of krational points on A. We formulate a question of Bogomolov type on the space of principally polarized abelian varieties of dimension g.
收起

We investigate the universal cover of a Lie group that is not necessarily connected. Its existence as a Lie group is governed by a Taylor cocycle, an obstruction in 3cohomology. Alternatively, a Lie group can be thought of as a Lie 2group, and there is a natural notion of universal cover in this context. The splitness of this universal cover is also governed by an obstruction in 3cohomology, a Sinh cocycle. We give explicit formulas for both obstructions and show that they are inverse of each other.
收起

We introduce a category of dual pairs of finite locally free algebras over a ring. This gives an efficient way to represent finite locally free commutative group schemes. We give a number of algorithms to compute with dual pairs of algebras, and we apply our results to Galois representations on finite Abelian groups.
收起

Let $G$ be a simple graph of $n$ vertices. We consider the problem $\mathrm{IS}^i_\ell$ of deciding whether there exists an induced subtree with exactly $i \leq n$ vertices and $\ell$ leaves in $G$. We also study the associated optimization problem, that consists in computing the maximal number of leaves, denoted by $L_G(i)$, realized by an induced subtree with $i$ vertices, for $2\le i \le n$. We compute the values of the map $L_G$ for some classical families of graphs and in particular for the $d$dimensional hypercubic graphs $Q_d, d\leq 6$. Then we prove that the $\mathrm{IS}^i_\ell$ problem is in general NPcomplete. We also describe a nontrivial branch and bound algorithm that computes the function $L_G$ for any simple graph $G$. In the special case where $G$ is a tree, we provide a $\mathcal{O}(n^3\delta)$ time and $\mathcal{0}(n^2)$ space algorithm, where $\delta$ is the maximum degree of $G$. Finally, we exhibit a bijection between the set of discrete derivative of the sequenc
收起

When sales of a product are affected by randomness in demand, etailers use dynamic pricing strategies to maximize their profits. In this article the pricing problem is formulated as a continuoustime stochastic optimal control problem, where the optimal policy can be found by solving the associated HamiltonJacobiBellman (HJB) equation. We propose a new approach to modelling the randomness in the dynamics of sales based on diffusion processes. The model assumes a continuum approximation to the stock levels of the retailer, which should scale much better to largeinventory problems than the existing models in the revenue management literature, which are based on Poisson processes. We present closedform solutions to the HJB equation when there is no randomness in the system. It turns out that the deterministic pricing policy is nearoptimal for systems with demand uncertainty. Numerical errors in calculating the optimal pricing policy may in fact result in lower profit on average than
收起

Lubiw showed that several variants of Graph Isomorphism are NPcomplete, where the solutions are required to satisfy certain additional constraints [SICOMP 10, 1981]. One of these, called Isomorphism With Restrictions, is to decide for two given graphs $X_1=(V,E_1)$ and $X_2=(V,E_2)$ and a subset $R\subseteq V\times V$ of forbidden pairs whether there is an isomorphism $\pi$ from $X_1$ to $X_2$ such that $\pi(i)\neq j$ for all $(i,j)\in R$. We prove that this problem and several of its generalizations are in fact in FPT:  The problem of deciding whether there is an isomorphism between two graphs that moves k vertices and satisfies Lubiwstyle constraints is in FPT, with k and the size of $R$ as parameters. The problem remains in FPT if a CNF of such constraints is allowed. It follows that the problem to decide whether there is an isomorphism that moves exactly k vertices is in FPT. This solves a question left open in our article on exact weight automorphisms [STACS 2017].  When the w
收起

We give explicit numerical estimates for the generalized Chebyshev functions. Explicit results of this kind are useful for estimating of computational complexity of algorithms which generates special primes. Such primes are needed to construct an elliptic curve over prime field using complex multiplication method.
收起

We show that nonflatness of a morphism f of complexanalytic spaces with a locally irreducible target Y of dimension n manifests in the existence of vertical components in the nfold fibred power of the pullback of f to the desingularization of Y. An algebraic analogue follows: Let R be a locally (analytically) irreducible finite type complexalgebra and an integral domain of Krull dimension n, and let S be a regular ndimensional algebra of finite type over R (but not necessarily a finite Rmodule), such that the induced morphism of spectra is dominant. Then a finite type Ralgebra A is Rflat if and only if the tensor product of S with the nfold tensor power of A over R is a torsionfree Rmodule.
收起

The polynomial Fre\u{\i}manRuzsa conjecture is a fundamental open question in additive combinatorics. However, over the integers (or more generally $\mathbb{R}^d$ or $\mathbb{Z}^d$) the optimal formulation has not been fully pinned down. The conjecture states that a set of small doubling is controlled by a very structured set, with polynomial dependence of parameters. The ambiguity concerns the class of structured sets needed. A natural formulation in terms of generalized arithmetic progressions was recently disproved by Lovett and Regev. A more permissive alternative is in terms of \emph{convex progressions}; this avoids the obstruction, but uses is a significantly larger class of objects, yielding a weaker statement. Here we give another formulation of PFR in terms of Euclidean ellipsiods (and some variations). We show it is in fact equivalent to the convex progression version; i.e. that the full range of convex progressions is not needed. The key ingredient is a strong result from
收起

In this paper we present and expand upon procedures for obtaining large d digit prime number to an arbitrary probability. We use a layered approach. The first step is to limit the pool of random number to exclude numbers that are obviously composite. We first remove any number ending in 1,3,7 or 9. We then exclude numbers whose digital root is not 3, 6, or 9. This sharply reduces the probability of the random number being composite. We then use the Prime Number Theorem to find the probability that the selected number n is prime and use primality tests to increase the probability to an arbitrarily high degree that n is prime. We apply primality tests including Euler's test based on Fermat Little theorem and the MillerRabin test. We computed these conditional probabilities and implemented it using the GNU GMP library.
收起

This paper introduces Schurconstant equilibrium distribution models of dimension n for arithmetic nonnegative random variables. Such a model is defined through the (several orders) equilibrium distributions of a univariate survival function. First, the bivariate case is considered and analyzed in depth, stressing the main characteristics of the Poisson case. The analysis is then extended to the multivariate case. Several properties are derived, including the implicit correlation and the distribution of the sum.
收起

We prove weighted uniform estimates for the resolvent of the Laplace operator in Schatten spaces, on nontrapping asymptotically conic manifolds of dimension $n\ge 3$, generalizing a result of Frank and Sabin, obtained in the Euclidean setting. As an application of these estimates we establish LiebThirring type bounds for eigenvalues of Schr\"odinger operators with complex potentials on nontrapping asymptotically conic manifolds, extending those of Frank, Frank and Sabin, and Frank and Simon proven in the Euclidean setting. In particular, our results are valid for the metric Schr\"odinger operator in the Euclidean space, with a metric being a sufficiently small compactly supported perturbation of the Euclidean one. To the best of our knowledge, these are the first LiebThirring type bounds for nonselfadjoint elliptic operators, with principal part having variable coefficients.
收起

In this work, we study a family of wireless channel simulation models called geometrybased stochastic channel models (GBSCMs). Compared to more complex raytracing simulation models, GBSCMs do not require an extensive characterization of the propagation environment to provide wireless channel realizations with adequate spatial and temporal statistics. The tradeoff they achieve between the quality of the simulated channels and the computational complexity makes them popular in standardization bodies. Using the generic formulation of the GBSCMs, we identify a matrix structure that can be used to improve the performance of their implementations. Furthermore, this matrix structure allows us to analyze the spatial covariance of the channel realizations. We provide a way to efficiently compute the spatial covariance matrix in most implementations of GBSCMs. In accordance to widesense stationary and uncorrelated scattering hypotheses, this covariance is static in frequency and does not evo
收起

We show that, for each integer n, there exist infinitely many pairs of nframed knots representing homeomorphic but nondiffeomorphic (Stein) 4manifolds, which are the simplest possible exotic 4manifolds regarding handlebody structures. To produce these examples, we introduce a new description of cork twists and utilize satellite maps. As an application, we produce knots with the same 0surgery which are not concordant for any orientations, disproving the AkbulutKirby conjecture given in 1978.
收起

In this paper we present a Boltzmanntype kinetic approach to the modelling of road traffic, which includes control strategies at the level of microscopic binary interactions aimed at the mitigation of speeddependent road risk factors. Such a description is meant to mimic a system of driverassist vehicles, which by responding locally to the actions of their drivers can impact on the largescale traffic dynamics, including those related to the collective road risk and safety.
收起

For a global field, local field, or finite field $k$ with infinite Galois group, we show that there can not exist a functor from the MorelVoevodsky $\mathbb{A}^1$homotopy category of schemes over $k$ to a genuine Galois equivariant homotopy category satisfying a list of hypotheses one might expect from a genuine equivariant category and an \'etale realization functor. For example, these hypotheses are satisfied by genuine $\mathbb{Z}/2$spaces and the $\mathbb{R}$realization functor constructed by MorelVoevodsky. This result does not contradict the existence of \'etale realization functors to (pro)spaces, (pro)spectra or complexes of modules with actions of the absolute Galois group when the endomorphisms of the unit is not enriched in a certain sense. It does restrict enrichments to representation rings of Galois groups.
收起

For all positive integers $\ell$, we prove nontrivial bounds for the $\ell$torsion in the class group of $K$, which hold for almost all number fields $K$ in certain families of cyclic extensions of arbitrarily large degree. In particular, such bounds hold for almost all cyclic degree$p$extensions of $F$, where $F$ is an arbitrary number field and $p$ is any prime for which $F$ and the $p$th cyclotomic field are linearly disjoint. Along the way, we prove precise asymptotic counting results for the fields of bounded discriminant in our families with prescribed splitting behavior at finitely many primes.
收起

The largest order $n(d,k)$ of a graph of maximum degree $d$ and diameter $k$ cannot exceed the Moore bound, which has the form $M(d,k)=d^k  O(d^{k1})$ for $d\to\infty$ and any fixed $k$. Known results in finite geometries on generalised $(k+1)$gons imply, for $k=2,3,5$, the existence of an infinite sequence of values of $d$ such that $n(d,k)=d^k  o(d^k)$. This shows that for $k=2,3,5$ the Moore bound can be asymptotically approached in the sense that $n(d,k)/M(d,k)\to 1$ as $d\to\infty$; moreover, no such result is known for any other value of $k\ge 2$. The corresponding graphs are, however, far from vertextransitive, and there appears to be no obvious way to extend them to vertextransitive graphs giving the same type of asymptotic result. The second and the third author (2012) proved by a direct construction that the Moore bound for diameter $k=2$ can be asymptotically approached by Cayley graphs. Subsequently, the first and the third author (2015) showed that the same construct
收起

We use Fuchsian Reduction to study the behavior near the singularity of a class of solutions of Einstein's vacuum equations. These solutions admit two commuting spacelike Killing fields like the Gowdy spacetimes, but their twist does not vanish. The spacetimes are also polarized in the sense that one of the `gravitational degrees of freedom' is turned off. Examining an analytic family of solutions with the maximum number of arbitrary functions, we find that they are all asymptotically velocityterm dominated as one approaches the singularity.
收起

We investigate the risk of overestimating the performance gain when applying neural network based receivers in systems with pseudo random bit sequences or with limited memory depths, resulting in repeated short patterns. We show that with such sequences, a large artificial gain can be obtained which comes from pattern prediction rather than predicting or compensating the studied channel/phenomena.
收起

A polynomial assignment for a continuous action of a compact torus $T$ on a topological space $X$ assigns to each $p\in X$ a polynomial function on the Lie algebra of the isotropy group at $p$ in such a way that a certain compatibility condition is satisfied. The space ${\mathcal{A}}_T(X)$ of all polynomial assignments has a natural structure of an algebra over the polynomial ring of ${\rm Lie}(T)$. It is an equivariant homotopy invariant, canonically related to the equivariant cohomology algebra. In this paper we prove various properties of ${\mathcal{A}}_T(X)$ such as Borel localization, a ChangSkjelbred lemma, and a GoreskyKottwitzMacPherson presentation. In the special case of Hamiltonian torus actions on symplectic manifolds we prove a surjectivity criterion for the assignment equivariant Kirwan map corresponding to a circle in $T$. We then obtain a TolmanWeitsman type presentation of the kernel of this map.
收起

We introduce a notion of cocycleinduction for strong uniform approximate lattices in locally compact second countable groups and use it to relate (relative) Kazhdan and Haageruptype of approximate lattices to the corresponding properties of the ambient locally compact groups. Our approach applies to large classes of uniform approximate lattices (though not all of them) and is flexible enough to cover the $L^p$versions of Property (FH) and a(FH)menability as well as quasified versions thereof a la BurgerMonod and Ozawa.
收起

We use Fuchsian Reduction to construct singular solutions of Einstein's equations which belong to the class of Gowdy spacetimes. The solutions have the maximum number of arbitrary functions. Special cases correspond to polarized, or other known solutions. The method provides precise asymptotics at the singularity, which is Kasnerlike. All of these solutions are asymptotically velocitydominated. The results account for the fact that solutions with velocity parameter uniformly greater than one are not observed numerically. They also provide a justification of formal expansions proposed by Grubi\v si\'c and Moncrief.
收起

Determining entropy rates of stochastic processes is a fundamental and difficult problem, with closedform solutions known only for specific cases. This paper pushes the stateoftheart by solving the problem for Hidden Markov Models (HMMs) and Renyi entropies. While the problem for Markov chains reduces to studying the growth of a matrix product, computations for HMMs involve \emph{products of random matrices}. As a result, this case is much harder and no explicit formulas have been known so far. We show how to circumvent this issue for Renyi entropy of integer orders, reducing the problem again to a \emph{single matrix products} where the matrix is formed from transition and emission probabilities by means of tensor product. To obtain results in the asymptotic setting, we use a novel technique for determining the growth of nonnegative matrix powers. The classical approach is the FrobeniusPerron theory, but it requires positivity assumptions; we instead work directly with the spect
收起

We consider singularly perturbed boundary value problems with a simple interior turning point whose solutions exhibit an interior layer. These problems are discretised using higher order finite elements on layeradapted piecewise equidistant meshes proposed by Sun and Stynes. We also study the streamlinediffusion finite element method (SDFEM) for such problems. For these methods error estimates uniform with respect to $\varepsilon$ are proven in the energy norm and in the stronger SDFEMnorm, respectively. Numerical experiments confirm the theoretical findings.
收起

An optimizationbased approach for the Tucker tensor approximation of parameterdependent data tensors and solutions of tensor differential equations with low Tucker rank is presented. The problem of updating the tensor decomposition is reformulated as fitting problem subject to the tangent space without relying on an orthogonality gauge condition. A discrete Euler scheme is established in an alternating least squares framework, where the quadratic subproblems reduce to trace optimization problems, that are shown to be explicitly solvable and accessible using SVD of small size. In the presence of small singular values, instability for larger ranks is reduced, since the method does not need the (pseudo) inverse of matricizations of the core tensor. Regularization of Tikhonov type can be used to compensate for the lack of uniqueness in the tangent space. The method is validated numerically and shown to be stable also for larger ranks in the case of small singular values of the core unfol
收起

We consider weighted Radon transforms RW along hyperplanes in R 3 with strictly positive weights W. We construct an example of such a transform with nontrivial kernel KerRW in the space of infinitely smooth compactly supported functions and with continuous weight. Moreover, in this example the weight W is rotation invariant. In particular, by this result we continue studies of Quinto (1983), Markoe, Quinto (1985), Boman (1993) and Goncharov, Novikov (2017). We also extend our example to the case of weighted Radon transforms along twodimensional planes in R d , d $\ge$ 3.
收起

We investigate the longtime behavior of solutions of quasilinear hyperbolic systems with transparent boundary conditions when small source terms are incorporated in the system. Even if the finitetime stability of the system is not preserved, it is shown here that an exponential convergence towards the steady state still holds with a decay rate which is proportional to the logarithm of the amplitude of the source term. The result is stated for a system with dynamical boundary conditions in order to deal with initial data that are free of any compatibility condition.
收起

J{\'o}nsson and Tarski's notion of the perfect extension of a Boolean algebra with operators has evolved into an extensive theory of canonical extensions of latticebased algebras. After reviewing this evolution we make two contributions. First it is shown that the question of whether or not a variety of algebras is closed under canonical extensions reduces to the question of whether or not it contains the canonical extension of a particular one of its free algebras. The size of the set of generators of this algebra can be made a function of a collection of varieties and is a kind of Hanf number for canonical closure. Secondly we study the complete lattice of stable subsets of a polarity structure, and show that if a class of polarities is closed under ultraproducts, then its stable set lattices generate a variety that is closed under canonical extensions. This generalises an earlier result of the author about generation of canonically closed varieties of Boolean algebras with operator
收起

Given a set E in a complex space and a point p in E, there is a unique smallest complexanalytic germ containing the germ of E at p, called the holomorphic closure of E at p. We study the holomorphic closure of semialgebraic arcsymmetric sets. Our main application concerns CRcontinuation of semialgebraic arcanalytic mappings: A mapping f on a realanalytic CR manifold M which is semialgebraic arcanalytic and CR on a nonempty open subset of M is CR on the whole M.
收起

We use strong complementarity to introduce dynamics and symmetries within the framework of CQM, which we also extend to infinitedimensional separable Hilbert spaces: these were longmissing features, which open the way to a wealth of new applications. The coherent treatment presented in this work also provides a variety of novel insights into the dynamics and symmetries of quantum systems: examples include the extremely simple characterisation of symmetryobservable duality, the connection of strong complementarity with the Weyl Canonical Commutation Relations, the generalisations of Feynman's clock construction, the existence of time observables and the emergence of quantum clocks. Furthermore, we show that strong complementarity is a key resource for quantum algorithms and protocols. We provide the first fully diagrammatic, theoryindependent proof of correctness for the quantum algorithm solving the Hidden Subgroup Problem, and show that strong complementarity is the feature provid
收起

Securing the physical components of a city's interdependent critical infrastructure (ICI) such as power, natural gas, and water systems is a challenging task due to their interdependence and large number of involved sensors. Using a novel integrated statespace model that captures the interdependence, a twostage cyber attack on ICI is studied in which the attacker first compromises the ICI's sensors by decoding their messages, and, subsequently, it alters the compromised sensors' data to cause state estimation errors. To thwart such attacks, the administrator of the CIs must assign protection levels to the sensors based on their importance in the state estimation process. To capture the interdependence between the attacker and the ICI administrator's actions and analyze their interactions, a Colonel Blotto game framework is proposed. The mixedstrategy Nash equilibrium of this game is derived analytically. At this equilibrium, it is shown that the administrator can strategically rando
收起

We investigate the computabilitytheoretic properties of valued fields, and in particular algebraically closed valued fields and $p$adically closed valued fields. We give an effectiveness condition, related to Hensel's lemma, on a valued field which is necessary and sufficient to extend the valuation to any algebraic extension. We show that there is a computable formally $p$adic field which does not embed into any computable $p$adic closure, but we give an effectiveness condition on the divisibility relation in the value group which is sufficient to find such an embedding. By checking that algebraically closed valued fields and $p$adically closed valued fields of infinite transcendence degree have the Mal'cev property, we show that they have computable dimension $\omega$.
收起

We consider a Boussinesq system of KdVKdV type introduced by J. Bona, M. Chen and J.C. Saut as a model for the motion of small amplitude long waves on the surface of an ideal fluid. This system of two equations can describe the propagation of waves in both directions, while the single KdV equation is limited to unidirectional waves. We are concerned here with the exact controllability of the Boussinesq system by using some boundary controls. By reducing the controllability problem to a spectral problem which is solved by using the PaleyWiener method introduced by the third author for KdV, we determine explicitly all the critical lengths for which the exact controllability fails for the linearized system, and give a complete picture of the controllability results with one or two boundary controls of Dirichlet or Neumann type. The extension of the exact controllability to the full Boussinesq system is derived in the energy space in the case of a control of Neumann type. It is obtained
收起

We study the boundary regularity for the normalised $\infty$heat equation $u_t = \Delta_{\infty}^Nu$ in arbitrary domains. Perron's Method is used for constructing solutions. We characterize regular boundary points with barrier functions, and prove an Exterior Ball result. A Petrovskylike criterion is established.
收起

This paper was inspired by four articles: surface cluster algebras studied by FominShapiroThurston \cite{fst}, the mutation theory of quivers with potentials initiated by DerksenWeymanZelevinsky \cite{dwz}, string modules associated to arcs on unpunctured surfaces by AssemBr$\ddot{u}$stleCharbonneauPlamondon \cite{acbp} and Quivers with potentials associated to triangulated surfaces, part II: Arc representations by LabardiniFragoso. \cite{lf2}. For a surface with marked points ($\Sigma,M$) LabardiniFragoso associated a quiver with potential $(Q(\tau),S(\tau))$ then for an ideal triangulation of ($\Sigma,M$) and an ideal arc LabardiniFragoso defined an arc representation of $(Q(\tau),S(\tau))$. This paper focuses on extent the definition of arc representation to a more general context by considering a tagged triangulation and a tagged arc. We associate in an explicit way a representation of the quiver with potential constructed LabardiniFragoso and prove that the Jacobian rel
收起

Asymptotic approximations to the zeros of Hermite and Laguerre polynomials are given, together with methods for obtaining the coefficients in the expansions. These approximations can be used as a standalone method of computation of Gaussian quadratures for high enough degrees, with Gaussian weights computed from asymptotic approximations for the orthogonal polynomials. We provide numerical evidence showing that for degrees greater than $100$ the asymptotic methods are enough for a double precision accuracy computation ($15$$16$ digits) of the nodes and weights of the GaussHermite and GaussLaguerre quadratures.
收起

We survey the dynamics of functions in the EremenkoLyubich class, $\mathcal{B}$. Among transcendental entire functions, those in this class have properties that make their dynamics markedly accessible to study. Many authors have worked in this field, and the dynamics of class $\mathcal{B}$ functions is now particularly wellunderstood and welldeveloped. There are many striking and unexpected results. Several powerful tools and techniques have been developed to help progress this work. We consider the fundamentals of this field, review some of the most important results, techniques and ideas, and give steppingstones to deeper inquiry.
收起

In 2007, Dubouloz introduced Danielewski varieties. Such varieties generalize Danielewski surfaces and provide counterexamples to generalized Zariski cancellation problem in arbitrary dimension. In the present work we describe the automorphism group of a Danielewski variety. This result is a generalization of a description of automorphisms of Danielewski surfaces due to MakarLimanov.
收起

In dimension $d\geq 3$, a variational principle for the size of the pure point spectrum of (discrete) Schr\"odinger operators $H(\mathfrak{e},V)$ on the hypercubic lattice $\mathbb{Z}^{d}$, with dispersion relation $\mathfrak{e}$ and potential $V$, is established. The dispersion relation $\mathfrak{e}$ is assumed to be a Morse function and the potential $V(x)$ to decay faster than $x^{2(d+3)}$, but not necessarily to be of definite sign. Our estimate on the size of the purepoint spectrum yields the absence of embedded and threshold eigenvalues of $H(\mathfrak{e},V)$ for a class ot potentials of this kind. The proof of the variational principle is based on a limiting absorption principle combined with a positive commutator (Mourre) estimate, and a Virial theorem. A further observation of crucial importance for our argument is that, for any selfadjoint operator $B$ and positive number $\lambda >0$, the number of negative eigenvalues of $\lambda B$ is independent of $\lambda$.
收起

The grid Ramsey number $ G(r) $ is the smallest number $ n $ such that every edgecolouring of the grid graph $\Gamma_{n,n} := K_n \times K_n$ with $r$ colours induces a rectangle whose parallel edges receive the same colour. We show $ G(r) \leq r^{\binom{r+1}{2}}  \left( 1/4  o(1) \right) r^{\binom{r}{2}+1} $, slightly improving the currently best known upper bound due to Gy\'arf\'as.
收起

The main result of this article is a BerryEsseenlike bound, which states the convergence to the normal distribution of sums of independent, identically distributed random variables in chisquare distance, defined as the variance of the density with respect to the normal distribution. Our main assumption is that the random variables involved in the sum are independent and have polynomial density; the identical distribution hypothesis can in fact be relaxed. The method consists of taking advantage of the underlying time nonhomogeneous Markovian structure and providing a Poincar{\'e}like inequality for the nonreversible transition operator, which allows to find the optimal rate in the convergence above under matching moments assumptions.
收起

Let $G$ be a complex semisimple algebraic group. In 2006, BelkaleKumar defined a new product $odot\_0$ on thecohomology group $H^*(G/P,{\mathbb C})$ of any projective $G$homogeneousspace $G/P$.Their definition uses the notion of Levimovability for triples ofSchubert varieties in $G/P$.In this article, we introduce a family of $G$equivariant subbundlesof the tangent bundle of $G/P$ and the associated filtration of the DeRham complex of $G/P$ viewed as a manifold. As a consequence one gets a filtration of the ring $H^*(G/P,{\mathbb C})$and proves that $\odot\_0$ is the associated graded product.One of the aim of this more intrinsic construction of $\odot\_0$ isthat there is a natural notion of fundamental class$[Y]\_{\odot\_0}\in(H^*(G/P),\odot\_0)$ for any irreducible subvariety $Y$ of $G/P$.Given two Schubert classes $\sigma\_u$ and $\sigma\_v$ in$H^*(G/P)$, we define a subvariety $\Sigma\_u^v$ of $G/P$. This variety should play the role of the Richardson variety; moreprecisely, we
收起