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Dev Bootcamp, the original "coding bootcamp," is shutting down, the company announced on Wednesday. The company's last cohort of students, who begin the program next week, will graduate in December and receive job search help before the school permanently shuts down. From a report: Why it matters: Early coding bootcamps like Dev Bootcamp launched a boom in alternative education for programing skills, with some of the school's own alumni going on to found their own successful programs, like App Academy. Ultimately, the coding bootcamp craze highlighted not only the need to rethink computer science and programming education in traditional colleges, but also the increasing demand for workers with these technical skills.
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We consider entire solutions $u$ to the minimal surface equation in $R^N$, with $ N\ge8,$ and we prove the following sharp result : if $N7$ partial derivatives $ \frac{\partial u }{\partial {x_j}}$ are bounded on one side (not necessarily the same), then $u$ is necessarily an affine function.
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In this paper we prove a lower semicontinuity result of Reshetnyak type for a class of functionals which appear in models for smallstrain elastoplasticity coupled with damage. To do so we characterise the limit of measures $\alpha_k\,\mathrm{E}u_k$ with respect to the weak convergence $\alpha_k\rightharpoonup \alpha$ in $W^{1,n}(\Omega)$ and the weak$^*$ convergence $u_k\stackrel{*}\rightharpoonup u$ in $BD(\Omega)$, $\mathrm{E}$ denoting the symmetrised gradient. A concentration compactness argument shows that the limit has the form $\alpha\,\mathrm{E}u+\eta$, with $\eta$ supported on an at most countable set.
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Around 1988, Floer introduced two important theories: instanton Floer homology as invariants of 3manifolds and Lagrangian Floer homology as invariants of pairs of Lagrangians in symplectic manifolds. Soon after that, Atiyah conjectured that the two theories should be related to each other and Lagrangian Floer homology of certain Lagrangians in the moduli space of flat connections on Riemann surfaces should recover instanton Floer homology. However, the space of flat connections on a Riemann surface is singular and the first step to address this conjecture is to make sense of Lagrangian Floer homology on this space. In this note, we formulate a possible approach to resolve this issue. A strategy to construct the desired isomorphism in the AtiyahFloer conjecture is also sketched. We also use the language of A inftycategories to state generalizations of the AtiyahFloer conjecture.
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We introduce a new family of algebras, called Serreformal algebras. They are IwanagaGorenstein algebras for which applying any power of the Serre functor on any indecomposable projective module, the result remains a stalk complex. Typical examples are given by (higher) hereditary algebras and selfinjective algebras; it turns out that other interesting algebras such as (higher) canonical algebras are also Serreformal. Starting from a Serreformal algebra, we consider a series of algebras  called the replicated algebras  given by certain subquotients of its repetitive algebra. We calculate the selfinjective dimension and dominant dimension of all such replicated algebras and determine which of them are minimal AuslanderGorenstein, i.e. when the two dimensions are finite and equal to each other. In particular, we show that there exist infinitely many minimal AuslanderGorenstien algebras in such a series if, and only if, the Serreformal algebra is twisted fractionally CalabiYau.
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Consider a sequence of AG codes evaluating at a set of evaluation points $P_1,\dots,P_n$ the functions having only poles at a defining point $Q$, with the sequence of codes satisfying the isometrydual condition (i.e. containing at the same time primal and their dual codes). We prove a necessary condition under which, after taking out a number of evaluation points (i.e. puncturing), the resulting AG codes can still satisfy the isometrydual property. The condition has to do with the socalled maximum sparse ideals of the Weierstrass semigroup of $Q$.
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We give a formal account of B\'enabou's theorem for peudoadjunctions in the context of Graycategories. We prove that to give a pseudoadjunction $F \dashv U: A \to X$ with unit $\eta$ in a Graycategory K is precisely to give an absolute left (Kan) pseudoextension $U$ of $1_X$ along $F$ witnessed by $\eta$.
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This paper considers an uplink multiuser multipleinputmultipleoutput (MUMIMO) system with onebit analogtodigital converters (ADCs), in which $K$ users with a single transmit antenna communicate with one base station (BS) with $N_{\rm r}$ receive antennas. In this system, a novel MUMIMO detection method, named weighted minimum distance (wMD) decoding, was recently proposed by introducing an equivalent coding problem. Despite of its attractive performance, the wMD decoding has the two limitations to be used in practice: i) the harddecision outputs can degrade the performance of a channel code; ii) the computational complexity grows exponentially with the $K$. To address those problems, we first present a softoutput wMD decoding that efficiently computes soft metrics (i.e., loglikelihood ratios) from onebit quantized observations. We then construct a lowcomplexity (softoutput) wMD decoding by introducing {\em hierarchical code partitioning}. This method can be regarded as a
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In this paper we combine a survey of the most important topological properties of kinematic maps that appear in robotics, with the exposition of some basic results regarding the topological complexity of a map. In particular, we discuss mechanical devices that consist of rigid parts connected by joints and show how the geometry of the joints determines the forward kinematic map that relates the configuration of joints with the pose of the endeffector of the device. We explain how to compute the dimension of the joint space and describe topological obstructions for a kinematic map to be a fibration or to admit a continuous section. In the second part of the paper we define the complexity of a continuous map and show how the concept can be viewed as a measure of the difficulty to find a robust manipulation plan for a given mechanical device. We also derive some basic estimates for the complexity and relate it to the degree of instability of a manipulation plan.
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In this paper we provide a means to approximate Dirac operators with magnetic fields supported on links in $\mathbb{S}^3$ (and $\mathbb{R}^3$) by Dirac operators with smooth magnetic fields. We then proceed to prove that under certain assumptions, the spectral flow of paths along these operators is the same in both the smooth and the singular case. We recently characterized the spectral flow of such paths in the singular case. This allows us to show the existence of new smooth, compactly supported magnetic fields in $\mathbb{R}^3$ for which the associated Dirac operator has a nontrivial kernel. Using Clifford analysis, we also obtain criteria on the magnetic link for the nonexistence of zero modes.
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We show that there is a polynomialtime algorithm with approximation guarantee $\frac{3}{2}+\epsilon$ for the $s$$t$path TSP, for any fixed $\epsilon>0$. It is well known that Wolsey's analysis of Christofides' algorithm also works for the $s$$t$path TSP with its natural LP relaxation except for the narrow cuts (in which the LP solution has value less than two). A fixed optimum tour has either a single edge in a narrow cut (then call the edge and the cut lonely) or at least three (then call the cut busy). Our algorithm "guesses" (by dynamic programming) lonely cuts and edges. Then we partition the instance into smaller instances and strengthen the LP, requiring value at least three for busy cuts. By setting up a $k$stage recursive dynamic program, we can compute a spanning tree $(V,S)$ and an LP solution $y$ such that $(\frac{1}{2}+O(2^{k}))y$ is in the $T$join polyhedron, where $T$ is the set of vertices whose degree in $S$ has the wrong parity.
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Let $k \geq 3$ be an integer, $h_{k}(G)$ be the number of vertices of degree at least $2k$ in a graph $G$, and $\ell_{k}(G)$ be the number of vertices of degree at most $2k2$ in $G$. Dirac and Erd\H{o}s proved in 1963 that if $h_{k}(G)  \ell_{k}(G) \geq k^{2} + 2k  4$, then $G$ contains $k$ vertexdisjoint cycles. For each $k\geq 2$, they also showed an infinite sequence of graphs $G_k(n)$ with $h_{k}(G_k(n))  \ell_{k}(G_k(n)) = 2k1$ such that $G_k(n)$ does not have $k$ disjoint cycles. Recently, the authors proved that, for $k \geq 2$, a bound of $3k$ is sufficient to guarantee the existence of $k$ disjoint cycles and presented for every $k$ a graph $G_0(k)$ with $h_{k}(G_0(k))  \ell_{k}(G_0(k))=3k1$ and no $k$ disjoint cycles. The goal of this paper is to refine and sharpen this result: We show that the DiracErd\H{o}s construction is optimal in the sense that for every $k \geq 2$, there are only finitely many graphs $G$ with $h_{k}(G)  \ell_{k}(G) \geq 2k$ but no $k$ disjoin
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Following Roos, we say that a local ring $R$ is good if all finitely generated $R$modules have rational Poincar\'e series over $R$, sharing a common denominator. Rings with the BackelinRoos property and generalised Golod rings are good due to results of Levin and Avramov respectively. If $R$ is a Gorensten ring such that $R/ soc(R)$ is a Golod ring, then the ring $R$ is shown to have the BackelinRoos property. We show that fibre products of local algebras over a field with the BackelinRoos property also have the same property. We identify a certain quotient $C$ of the Koszul complex of a Gorenstein local ring $R$ such that $R$ has the BackelinRoos property whenever $C$ is a Golod algebra. It is proved that for a Gorenstein ring $R$, the ring $R$ is generalised Golod if and only if $R/ soc(R)$ is so. We show that fibre products of local rings, connected sums of Gorenstein local rings are generalised Golod if and only if constituent rings are so. We provide a uniform argument to sho
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Let $L \subset \mathbb{R} \times J^1(M)$ be a spin, exact Lagrangian cobordism in the symplectization of the 1jet space of a smooth manifold $M$. Assume that $L$ has cylindrical Legendrian ends $\Lambda_\pm \subset J^1(M)$. It is well known that the Legendrian contact homology of $\Lambda_\pm$ can be defined with integer coefficients, via a signed count of pseudoholomorphic disks in the cotangent bundle of $M$. We prove that this count can be lifted to a signed count of pseudoholomorphic disks in $\mathbb{R} \times J^1(M)$, and then we use this to prove that $L$ induces a morphism between the $\mathbb{Z}$valued DGA:s of the ends, in a functorial way. These results have been indicated in several papers before, our aim is to give rigorous proofs of these facts. The proofs are built on the technique of orienting the moduli spaces of pseudoholomorphic disks using capping operators at the Reeb chords. We give an expression for how the DGA:s change if we change the capping operators.
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The subject of this note is a challenging conjecture about Xrays of permutations which is a special case of a conjecture regarding Skolem sequences. In relation to this, Brualdi and Fritscher [Linear Algebra and its Applications, 2014] posed the following problem: Determine a bijection between extremal Skolem sets and binary Hankel Xrays of permutation matrices. We give such a bijection, along with some related observations.
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Robin Thomas asked whether for every proper minorclosed class C, there exists a polynomialtime algorithm approximating the chromatic number of graphs from C up to a constant additive error independent on the class C. We show this is not the case: unless P=NP, for every integer k>=1, there is no polynomialtime algorithm to color a K_{4k+1}minorfree graph G using at most chi(G)+k1 colors. More generally, for every k>=1 and 1<=\beta<=4/3, there is no polynomialtime algorithm to color a K_{4k+1}minorfree graph G using less than beta.chi(G)+(43beta)k colors. As far as we know, this is the first nontrivial nonapproximability result regarding the chromatic number in proper minorclosed classes. We also give somewhat weaker nonapproximability bound for K_{4k+1}minorfree graphs with no cliques of size 4. On the positive side, we present additive approximation algorithm whose error depends on the apex number of the forbidden minor, and an algorithm with additive error
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This note is mostly based on the lecture delivered at the conference "Algebraic Analysis and Representation Theory" in honor of Professor Masaki Kashiwara's 70th birthday. Its main topic is the project aimed at obtaining the Plancherel formula for the regular representation of Affine Hecke Algebras (AHA) as the limit $q\to 0$ of the integraltype formulas for DAHA inner products in the polynomial and related modules. The integrals for the latter as $\Re k>0$ (in the DAHA parameters) must be analytically continued to negative $\Re k$, which is a $q$generalization of "picking up residues" due to Arthur, Heckman, Opdam and others, which can be traced back to Hermann Weyl. We arrive at finite sums of integrals over double affine residual subtori. This is not related to the DAHA reducibility of the polynomial and similar modules; the procedure is nontrivial for any $\Re k<0$. Though such formulas can be used for the DAHA stratification when these modules become reducible for singular
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The purpose of this paper is to establish, via a martingale approach, some refinements on the asymptotic behavior of the onedimensional elephant random walk (ERW). The asymptotic behavior of the ERW mainly depends on a memory parameter $p$ which lies between zero and one. This behavior is totally different in the diffusive regime $0 \leq p <3/4$, the critical regime $p=3/4$, and the superdiffusive regime $3/4<p \leq 1$. Notwithstanding of this trichotomy, we provide some new results on the almost sure convergence and the asymptotic normality of the ERW.
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In this paper we review the wellknown fact that the only spheres admitting an almost complex structure are S^2 and S^6. The proof described here uses characteristic classes and the Bott periodicity theorem in topological Ktheory. This paper originates from the talk "Almost Complex Structures on Spheres" given by the second author at the MAM1 workshop "(Non)existence of complex structures on S^6", held in Marburg from March 27th to March 30th, 2017. It is a review paper, and as such no result is intended to be original. We tried to produce a clear, motivated and as much as possible selfcontained exposition.
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We use Richter's $2$primary proof of Gray's conjecture to give a homotopy decomposition of the fibre $\Omega^3S^{17}\{2\}$ of the $H$space squaring map on the triple loop space of the $17$sphere. This induces a splitting of the mod$2$ homotopy groups $\pi_\ast(S^{17}; \mathbb{Z}/2\mathbb{Z})$ in terms of the integral homotopy groups of the fibre of the double suspension $E^2:S^{2n1} \to \Omega^2S^{2n+1}$ and refines a result of Cohen and Selick, who gave similar decompositions for $S^5$ and $S^9$. We relate these decompositions to various Whitehead products in the homotopy groups of mod$2$ Moore spaces and Stiefel manifolds to show that the Whitehead square $[i_{2n}, i_{2n}]$ of the inclusion of the bottom cell of the Moore space $P^{2n+1}(2)$ is divisible by $2$ if and only if $2n=2, 4, 8$ or $16$.
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We introduce a new knot diagram invariant called the SelfCrossing Index (SCI). Using SCI, we provide bounds for unknotting two families of framed unknots. For one of these families, unknotting using framed Reidemeister moves is significantly harder than unknotting using regular Reidemeister moves. We also investigate the relation between SCI and Arnold's curve invariant St, as well as the relation with Hass and Nowik's invariant, which generalizes cowrithe. In particular, the change of SCI under {\Omega}3 moves depends only on the forward/backward character of the move, similar to how the change of St or cowrithe depends only on the positive/negative quality of the move.
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The classical hypergraph Ramsey number $r_k(s,n)$ is the minimum $N$ such that for every redblue coloring of the $k$tuples of $\{1,\ldots, N\}$, there are $s$ integers such that every $k$tuple among them is red, or $n$ integers such that every $k$tuple among them is blue. We survey a variety of problems and results in hypergraph Ramsey theory that have grown out of understanding the quantitative aspects of $r_k(s,n)$. Our focus is on recent developments. We also include several new results and proofs that have not been published elsewhere.
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In this paper, the influence of the fractional dimensions of the L\'evy path under the Earth's gravitational field is studied, and the phase transitions of energy and wave functions are obtained: the energy changes from discrete to continuous and wave functions change from nondegenerate to degenerate when dimension of L\'evy path becomes from integer to noninteger. By analyzing the phase transitions, we solve two popular problems. First, we find an exotic way to produce the bound states in the continuum (BICs), our approach only needs a simple potential, and does not depend on interactions between particles. Second, we address the continuity of the energy will become strong when the mass of the particle becomes small. By deeply analyze, it can provide a way to distinguish ultralight particles from others types in the Earth's gravitational field, and five popular particles are discussed. In addition, we obtain analytical expressions for the wave functions and energy in the Earth's gra
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For an element $g$ of a group $G$, an Engel sink is a subset ${\mathscr E}(g)$ such that for every $x\in G$ all sufficiently long commutators $[...[[x,g],g],\dots ,g]$ belong to ${\mathscr E}(g)$. A~finite group is nilpotent if and only if every element has a trivial Engel sink. We prove that if in a finite group $G$ every element has an Engel sink generating a subgroup of rank~$r$, then $G$ has a normal subgroup $N$ of rank bounded in terms of $r$ such that $G/N$ is nilpotent.
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This paper investigates one of the fundamental issues in cacheenabled heterogeneous networks (HetNets): how many cache instances should be deployed at different base stations, in order to provide guaranteed service in a costeffective manner. Specifically, we consider twotier HetNets with hierarchical caching, where the most popular files are cached at small cell base stations (SBSs) while the less popular ones are cached at macro base stations (MBSs). For a given network cache deployment budget, the cache sizes for MBSs and SBSs are optimized to maximize network capacity while satisfying the file transmission rate requirements. As cache sizes of MBSs and SBSs affect the traffic load distribution, intertier traffic steering is also employed for load balancing. Based on stochastic geometry analysis, the optimal cache sizes for MBSs and SBSs are obtained, which are thresholdbased with respect to cache budget in the networks constrained by SBS backhauls. Simulation results are provide
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In his seminal 1983 paper, Jim Lawrence introduced lopsided sets and featured them as asymmetric counterparts of oriented matroids, both sharing the key property of strong elimination. Moreover, symmetry of faces holds in both structures as well as in the socalled affine oriented matroids. These two fundamental properties (formulated for covectors) together lead to the natural notion of "conditional oriented matroid" (abbreviated COM). These novel structures can be characterized in terms of three cocircuits axioms, generalizing the familiar characterization for oriented matroids. We describe a binary composition scheme by which every COM can successively be erected as a certain complex of oriented matroids, in essentially the same way as a lopsided set can be glued together from its maximal hypercube faces. A realizable COM is represented by a hyperplane arrangement restricted to an open convex set. Among these are the examples formed by linear extensions of ordered sets, generalizing
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Tandem duplication in DNA is the process of inserting a copy of a segment of DNA adjacent to the original position. Motivated by applications that store data in living organisms, Jain et al. (2016) proposed the study of codes that correct tandem duplications to improve the reliability of data storage. We investigate algorithms associated with the study of these codes. Two words are said to be $\le k$confusable if there exists two sequences of tandem duplications of lengths at most $k$ such that the resulting words are equal. We demonstrate that the problem of deciding whether two words is $\le k$confusable is linear time solvable through a characterisation that can be checked efficiently for $k=3$. Combining with previous results, the decision problem is linear time solvable for $k\le 3$ and we conjecture that this problem is undecidable for $k>3$. Using insights gained from the algorithm, we construct tandemduplication codes with larger sizes as compared to the previous construc
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Inferring topological and geometrical information from data can offer an alternative perspective on machine learning problems. Methods from topological data analysis, e.g., persistent homology, enable us to obtain such information, typically in the form of summary representations of topological features. However, such topological signatures often come with an unusual structure (e.g., multisets of intervals) that is highly impractical for most machine learning techniques. While many strategies have been proposed to map these topological signatures into machine learning compatible representations, they suffer from being agnostic to the target learning task. In contrast, we propose a technique that enables us to input topological signatures to deep neural networks and learn a taskoptimal representation during training. Our approach is realized as a novel input layer with favorable theoretical properties. Classification experiments on 2D object shapes and social network graphs demonstrate
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In this article, we define a generalisation of microlocal defect measures (also known as Hmeasures) to the setting of graded nilpotent Lie groups. This requires to develop the notions of homogeneous symbols and classical pseudodifferential calculus adapted to this setting and defined via the representations of the groups. Our method relies on the study of the C *algebra of 0homogeneous symbols. Then, we compute microlocal defect measures for concentrating and oscillating sequences, which also requires to investigate the notion of oscillating sequences in graded Lie groups. Finally, we discuss compacity compactness approaches in the context of graded nilpotent Lie groups.
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This paper discusses differential stability of convex programming problems in Hausdorff locally convex topological vector spaces. Among other things, we obtain formulas for computing or estimating the subdifferential and the singular subdifferential of the optimal value function via suitable multiplier sets.
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In this paper we study curvature types of immersed surfaces in threedimensional (normed or) Minkowski spaces. By endowing the surface with a normal vector field, which is a transversal vector field given by the ambient Birkhoff orthogonality, we get an analogue of the Gauss map. Then we can define concepts of principal, Gaussian, and mean curvatures in terms of the eigenvalues of the differential of this map. Considering planar sections containing the normal field, we also define normal curvatures at each point of the surface, and with respect to each tangent direction. We investigate the relations between these curvature types, and several analogues of classical rigidity and global theorems are proven in this extended framework (like, e.g., Hadamardtype theorems and the Bonnet theorem). We investigate whether the normal field of a surface is the (Blaschke) affine normal, proving that this is only true for subsets of the spheres in the Euclidean subcase. Moreover, curvatures of surfa
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A parametric constrained convex optimal control problem, where the initial state is perturbed and the linear state equation contains a noise, is considered in this paper. Formulas for computing the subdifferential and the singular subdifferential of the optimal value function at a given parameter are obtained by means of some recent results on differential stability in mathematical programming. The computation procedures and illustrative examples are presented.
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Let $\mathrm{G}$ be a split reductive group, $K$ be a nonArchimedean local field, and $O$ be its ring of integers. Satake isomorphism identifies the algebra of compactly supported invariants $\mathbb{C}_c[\mathrm{G}(K)/\mathrm{G}(O))]^{\mathrm{G}(O)}$ with a complexification of the algebra of characters of finitedimensional representations $\mathcal{O}(\mathrm{G}^L(\mathbb{C}))^{\mathrm{G}^L(\mathbb{C})}$ of the Langlands dual group. In this note we report on the results of the study of analogues of such an isomorphism for finite groups. In our setup we replaced Gelfand pair $\mathrm{G}(O)\subset \mathrm{G}(K)$ by a finite pair $H\subset G$. It is convenient to rewrite the character side of the isomorphism as $\mathcal{O}(\mathrm{G}^L(\mathbb{C}))^{\mathrm{G}^L(\mathbb{C})}=\mathcal{O}((\mathrm{G}^L(\mathbb{C})\times \mathrm{G}^L(\mathbb{C}))/\mathrm{G}^L(\mathbb{C}))^{\mathrm{G}^L(\mathbb{C})}$. We replace diagonal Gelfand pair $\mathrm{G}^L(\mathbb{C})\subset \mathrm{G}^L(\mathbb{C
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In this paper we study convex caustics in Minkowski billiards. We show that for the Euclidean billiard dynamics in a planar smooth centrally symmetric and strictly convex body $K$, for every convex caustic which $K$ possesses, the "dual" billiard dynamics in which the table is the Euclidean unit disk and the geometry that governs the motion is induced by the body $K$, possesses a dual convex caustic. Such a pair of caustics is dual in a strong sense, and in particular they have the same perimeter, Lazutkin parameter (both measured with respect to the corresponding geometries), and rotation number. We show moreover that for general Minkowski billiards this phenomenon fails, and one can construct a smooth caustic in a Minkowski billiard table which possesses no dual convex caustic.
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In this paper we analyse the structure of the spaces of coefficients of eigenfunction expansions of functions in Komatsu classes on compact manifolds, continuing the research in our previous paper. We prove that such spaces of Fourier coefficients are perfect sequence spaces. As a consequence we describe the tensor structure of sequential mappings on spaces of Fourier coefficients and characterise their adjoint mappings. In particular, the considered classes include spaces of analytic and Gevrey functions, as well as spaces of ultradistributions, yielding tensor representations for linear mappings between these spaces on compact manifolds.
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This paper deals with the stabilization of linear systems with process noise under packet drops between the sensor and the controller. Our aim is to ensure exponential convergence of the second moment of the plant state to a given bound in finite time. Motivated by considerations about the efficient use of the available resources, we adopt an eventtriggering approach to design the transmission policy. In our design, the sensor's decision to transmit or not the state to the controller is based on an online evaluation of the future satisfaction of the control objective. The resulting eventtriggering policy is hence specifically tailored to the control objective. We formally establish that the proposed eventtriggering policy meets the desired objective and quantify its efficiency by providing an upper bound on the fraction of expected number of transmissions in an infinite time interval. Simulations for scalar and vector systems illustrate the results.
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It was recently shown that an interacting Kitaev topological superconductor model is exactly solvable based on two step JordanWigner transformations together with one spin rotation. We generalize this model by including the dimerization, which is also exactly solvable. In this extended model there are two topological indices associated with the sublattice symmetry and the particlehole symmetry. We analytically determine the topological phase diagram containing seven distinct topological phases. There are two tetracritical points, at which four distinct phases touch. It is intriguing that a topological chargedensitywave state and a topological Schr\"odingercat state emerge for strong interactions. We confirm various topological phases by examining the presence of zeroenergy edge states.
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This paper develops an interference aware design for cooperative hybrid automatic repeat request (HARQ) assisted nonorthogonal multiple access (NOMA) scheme for largescale devicetodevice (D2D) networks. Specifically, interference aware rate selection and power allocation are considered to maximize long term average throughput (LTAT) and area spectral efficiency (ASE). The design framework is based on stochastic geometry that jointly accounts for the spatial interference correlation at the NOMA receivers as well as the temporal interference correlation across HARQ transmissions. It is found that ignoring the effect of the aggregate interference, or overlooking the spatial and temporal correlation in interference, highly overestimates the NOMA performance and produces misleading design insights. An interference oblivious selection for the power and/or transmission rates leads to violating the network outage constraints. To this end, the results demonstrate the effectiveness of NOMA t
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In this paper, we describe the construction of superelliptic curves with a rational point of prescribed order on their jacobians. The construction is based on Hensel's Lemma and produces for a given integer $N$ a superelliptic curve of genus linear in $N$ with a rational $N$division point on the jacobian. The method is illustrated with multiple examples.
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We study constrained percolation models on planar lattices including the $[m,4,n,4]$ lattice and the square tilings of the hyperbolic plane, satisfying certain local constraints on faces of degree 4, and investigate the existence of infinite clusters. The constrained percolation models on these lattices are closely related to Ising models and XOR Ising models on regular tilings of the Euclidean plane or the hyperbolic plane. In particular, we obtain a complete picture of the number of infinite "$+$" and "$$" clusters of the ferromagnetic Ising model with the free boundary condition on a vertextransitive triangular tiling of the hyperbolic plane with all the possible values of coupling constants. Our results show that for the Ising model on a vertextransitive triangular tiling of the hyperbolic plane, it is possible that its random cluster representation has no infinite open clusters, while the Ising model has infinitely many infinite "$+$"clusters and infinitely many infinite "$$"
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We study representations of the braid groups from braiding gapped boundaries of DijkgraafWitten theories and their twisted generalizations, which are (twisted) quantum doubled topological orders in two spatial dimensions. We show that the resulting braid (pure braid) representations are all monomial with respect to some specific bases, hence all such representation images of the braid groups are finite groups. We give explicit formulas for the monomial matrices and the ground state degeneracy of the Kitaev models that are Hamiltonian realizations of DijkgraafWitten theories. Our results imply that braiding gapped boundaries alone cannot provide universal gate sets for topological quantum computing with gapped boundaries.
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Whereas the usual notions of immunity  e.g., immunity, hyperimmunity, etc.  are associated with Cohen genericity, canonical immunity, as introduced by Beros, Khan and KjosHanssen, is associated instead with Mathias genericity. Specifically, every Mathias generic is canonically immune and no Cohen 2generic computes a canonically immune set.
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In this paper we consider the asymptotic distributions of functionals of the sample covariance matrix and the sample mean vector obtained under the assumption that the matrix of observations has a matrixvariate location mixture of normal distributions. The central limit theorem is derived for the product of the sample covariance matrix and the sample mean vector. Moreover, we consider the product of the inverse sample covariance matrix and the mean vector for which the central limit theorem is established as well. All results are obtained under the largedimensional asymptotic regime where the dimension $p$ and the sample size $n$ approach to infinity such that $p/n\to c\in[0 , +\infty)$ when the sample covariance matrix does not need to be invertible and $p/n\to c\in [0, 1)$ otherwise.
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We establish new bounds on character values and character ratios for finite groups $G$ of Lie type, which are considerably stronger than previously known bounds, and which are best possible in many cases. These bounds have the form $\chi(g) \le \chi(1)^{\alpha_g}$, and give rise to a variety of applications, for example to covering numbers and mixing times of random walks on such groups. In particular we deduce that, if $G$ is a classical group in dimension $n$, then, under some conditions on $G$ and $g \in G$, the mixing time of the random walk on $G$ with the conjugacy class of $g$ as a generating set is (up to a small multiplicative constant) $n/s$, where $s$ is the support of $g$.
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The KantorovichRubinshtein metric is an $L^1$like metric on spaces of probability distributions that enjoys several serendipitous properties. It is complete separable if the underlying metric space of points is complete separable, and in that case it metrizes the weak topology. We introduce a variant of that construction in the realm of quasimetric spaces, and prove that it is algebraic Yonedacomplete as soon as the underlying quasimetric space of points is algebraic Yonedacomplete, and that the associated topology is the weak topology. We do this not only for probability distributions, represented as normalized continuous valuations, but also for subprobability distributions, for various hyperspaces, and in general for different brands of functionals. Those functionals model probabilistic choice, angelic and demonic nondeterministic choice, and their combinations. The mathematics needed for those results are more demanding than in the simpler case of metric spaces. To obtain ou
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This paper proves that given a doubling weight $w$ on the unit sphere $\mathbb{S}^{d1}$ of $\mathbb{R}^d$, there exists a positive constant $K_w$ such that for each positive integer $n$ and each integer $N\geq \max_{x\in \mathbb{S}^{d1}} \frac {K_w} {w(B(x, n^{1}))}$, there exists a set of $N$ distinct nodes $z_1,\cdots, z_N$ on $\mathbb{S}^{d1}$ which admits a strict Chebyshevtype cubature formula (CF) of degree $n$ for the measure $w(x) d\sigma_d(x)$, $$ \frac 1{w(\mathbb{S}^{d1})} \int_{\mathbb{S}^{d1}} f(x) w(x)\, d\sigma_d(x)=\frac 1N \sum_{j=1}^N f(z_j),\ \ \forall f\in\Pi_n^d, $$ and which, if in addition $w\in L^\infty(\mathbb{S}^{d1})$, satisfies $$\min_{1\leq i\neq j\leq N}\mathtt{d}(z_i,z_j)\geq c_{w,d} N^{\frac1{d1}}$$ for some positive constant $c_{w,d}$. Here, $d\sigma_d$ and $\mathtt{d}(\cdot, \cdot)$ denote the surface Lebesgue measure and the geodesic distance on $\mathbb{S}^{d1}$ respectively, $B(x,r)$ denotes the spherical cap with center $x\in\mathbb{S}^{
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We introduce a new geometric flow called the chord shortening flow which is the negative gradient flow for the length functional on the space of chords with end points lying on a fixed submanifold in Euclidean space. As an application, we give a simplified proof of a classical theorem of Lusternik and Schnirelmann (and a generalization by Riede and Hayashi) on the existence of multiple orthogonal geodesic chords. For a compact convex planar domain, we show that any convex chord which is not orthogonal to the boundary would shrink to a point in finite time under the flow.
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In millimeter wave (mmWave) systems, antenna architecture limitations make it difficult to apply conventional fully digital precoding techniques but call for low cost analog radiofrequency (RF) and digital baseband hybrid precoding methods. This paper investigates joint RFbaseband hybrid precoding for the downlink of multiuser multiantenna mmWave systems with a limited number of RF chains. Two performance measures, maximizing the spectral efficiency and the energy efficiency of the system, are considered. We propose a codebook based RF precoding design and obtain the channel state information via a beam sweep procedure. Via the codebook based design, the original system is transformed into a virtual multiuser downlink system with the RF chain constraint. Consequently, we are able to simplify the complicated hybrid precoding optimization problems to joint codeword selection and precoder design (JWSPD) problems. Then, we propose efficient methods to address the JWSPD problems and join
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In this article we provide a general construction when $n\ge3$ for immersed in Euclidean $(n+1)$space, complete, smooth, constant mean curvature hypersurfaces of finite topological type (in short CMC $n$hypersurfaces). More precisely our construction converts certain graphs in Euclidean $(n+1)$space to CMC $n$hypersurfaces with asymptotically Delaunay ends in two steps: First appropriate small perturbations of the given graph have their vertices replaced by round spherical regions and their edges and rays by Delaunay pieces so that a family of initial smooth hypersurfaces is constructed. One of the initial hypersurfaces is then perturbed to produce the desired CMC $n$hypersurface which depends on the given family of perturbations of the graph and a small in absolute value parameter $\underline\tau$. This construction is very general because of the abundance of graphs which satisfy the required conditions and because it does not rely on symmetry requirements. For any given $k\ge2$
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The study of conformal restriction properties in twodimensions has been initiated by Lawler, Schramm and Werner who focused on the natural and important chordal case: They characterized and constructed all random subsets of a given simply connected domain that join two marked boundary points and that satisfy the additional restriction property. The radial case (sets joining an inside point to a boundary point) has then been investigated by Wu. In the present paper, we study the third natural instance of such restriction properties, namely the "trichordal case", where one looks at random sets that join three marked boundary points. This case involves somewhat more technicalities than the other two, as the construction of this family of random sets relies on special variants of SLE$_{8/3}$ processes with a drift term in the driving function that involves hypergeometric functions. It turns out that such a random set can not be a simple curve simultaneously in the neighborhood of all thre
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We axiomatize and study the matrices of type $H\in M_N(A)$, having unitary entries, $H_{ij}\in U(A)$, and whose rows and columns are subject to orthogonality type conditions. Here $A$ can be any $C^*$algebra, for instance $A=\mathbb C$, where we obtain the usual complex Hadamard matrices, or $A=C(X)$, where we obtain the continuous families of complex Hadamard matrices. Our formalism allows the construction of a quantum permutation group $G\subset S_N^+$, whose structure and computation is discussed here.
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One of the chief annoyances of Apple's closed ecosystem is the limited ability to move files to and from your device using iTunes. Utilities that open up file management have been available for ages, but generally cost money, so stingy people like me just make do with iTunes. To commemorate the iPhone 10 year anniversary, MacX is offering OSNews readers a free license to their MediaTrans tool (in exchange for your email address). It's good for moving files of various types, backup, and removing media DRM. If any OSNews readers can recommend other options for working around Apple's restrictions and managing files on their iOS devices, I'd love to read about them in the comments.
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The Fedora 26 release is out. "First, of course, we have thousands improvements from the various upstream software we integrate, including new development tools like GCC 7, Golang 1.8, and Python 3.6. We’ve added a new partitioning tool to Anaconda (the Fedora installer) — the existing workflow is great for nonexperts, but this option will be appreciated by enthusiasts and sysadmins who like to build up their storage scheme from basic building blocks. F26 also has many underthehood improvements, like better caching of user and group info and better handling of debug information. And the DNF package manager is at a new major version (2.5), bringing many new features." More details can be found in the release notes.
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Encrypted Media Extensions (EME) have been under review by the W3C Advisory Committee since last March. This report from the committee addresses comments and objections to EME. "After consideration of the issues, the Director reached a decision that the EME specification should move to W3C Recommendation. The Encrypted Media Extensions specification remains a better alternative for users than other platforms, including for reasons of security, privacy, and accessibility, by taking advantage of the Web platform. While additional work in some areas may be beneficial for the future of the Web Platform, it remains appropriate for the W3C to make the EME specification a W3C Recommendation. Formal publication of the W3C Recommendation will happen at a later date. We encourage W3C Members and the community to work in both technical and policy areas to find better solutions in this space." The Free Software Foundation's Defective by Design campaign opposes EME arguing that it infringes
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Preventing human casualties caused by car collisions is a high priority. Engineers are using the SystemVue Scenario Framework Solution for automotive frequency modulated continuous waveform (FMCW) radar system simulation to increase design fidelity and save cost during design and test.
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An anonymous reader shares a report: Hulu this morning announced it's finally adding HBO as an optional addon for subscribers, as well as HBOowned Cinemax. The premium networks will be offered to those who subscribe to Hulu's ondemand service plus those who pay for Hulu's new live TV service, including both the adsupported and commercialfree versions. As on most other streaming services, including HBO NOW, the HBO addon will cost subscribers an extra $14.99 per month. Cinemax is a more affordable upgrade at $9.99 per month. The deal's timing comes just ahead of "Game of Thrones" big summer release, which will allow Hulu the opportunity to capture some number of subscribers for this premium upgrade. Many HBO viewers only pay for the streaming service while the flagship series is airing, as they want to watch it live but no longer pay for cable TV. Now, they'll be able to watch the show live or ondemand, along with past seasons of other popular HBO series, like the "The Sopranos,"
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An edgecolored graph $G$ is \emph{conflictfree connected} if any two of its vertices are connected by a path, which contains a color used on exactly one of its edges. The \emph{conflictfree connection number} of a connected graph $G$, denoted by $cfc(G)$, is the smallest number of colors needed in order to make $G$ conflictfree connected. For a graph $G,$ let $C(G)$ be the subgraph of $G$ induced by its set of cutedges. In this paper, we first show that for a connected noncomplete graph $G$ of order $n$ such that $C(G)$ is a linear forest, if $\delta(G)\geq 2$, then $cfc(G)=2$ for $4 \leq n\leq 8 $; if $\delta(G)\geq \max\{3, \frac{n4}{5}\}$, then $cfc(G)=2$ for $n\geq 9$. Moreover, the minimum degree conditions are best possible. Next, we prove that for a connected noncomplete graph of order $n\geq 33$ such that $C(G)$ is a linear forest and $d(x)+d(y)\geq \frac{2n9}{5}$ for each pair of two nonadjacent vertices $x, y$ of $V(G)$, then $cfc(G)=2$. Moreover, the degree sum condit
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