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To unsubscribe, e-mail To: math@arXiv.org, Subject: cancel ------------------------------------------------------------------------------ received from Mon 30 Apr 12 20:00:00 GMT to Tue 1 May 12 20:00:00 GMT ------------------------------------------------------------------------------ \\ arXiv:1205.0023 Date: Mon, 30 Apr 2012 20:09:11 GMT (41kb) Title: Uniform Convergence and Rate Adaptive Estimation of a Convex Function Authors: Xiao Wang and Jinglai Shen Categories: math.ST stat.TH \\ This paper addresses the problem of estimating a convex regression function under both the sup-norm risk and the pointwise risk using B-splines. The presence of the convex constraint complicates various issues in asymptotic analysis, particularly uniform convergence analysis. To overcome this difficulty, we establish the uniform Lipschitz property of optimal spline coefficients in the $\ell_\infty$-norm by exploiting piecewise linear and polyhedral theory. Based upon this property, it is shown that this estimator attains optimal rates of convergence on the entire interval of interest over the H\"older class under both the risks. In addition, adaptive estimates are constructed under both the sup-norm risk and the pointwise risk when the exponent of the H\"older class is between one and two. These estimates achieve a maximal risk within a constant factor of the minimax risk over the H\"older class. \\ ( http://arxiv.org/abs/1205.0023 , 41kb) ------------------------------------------------------------------------------ \\ arXiv:1205.0025 Date: Mon, 30 Apr 2012 20:12:17 GMT (17kb) Title: Toric Deligne-Mumford stacks and the better behaved version of the GKZ hypergeometric system Authors: R. Paul Horja Categories: math.AG hep-th Comments: LaTex, 19 pages; submitted as a contribution to the volume "Strings, Gauge Fields, and the Geometry Behind - The Legacy of Maximilian Kreuzer" MSC-class: 13N10, 14D23, 14M25 \\ We generalize the combinatorial description of the orbifold (Chen--Ruan) cohomology and of the Grothendieck ring of a Deligne--Mumford toric stack and its associated stacky fan in a lattice $N$ in the presence of a deformation parameter $\beta \in N \otimes {\mathbb C}.$ As an application, we construct a topological mirror symmetry map that produces a complete system of $\Gamma$--series solutions to the better behaved version of the GKZ hypergeometric system for $\beta \in N \otimes {\mathbb C}.$ \\ ( http://arxiv.org/abs/1205.0025 , 17kb) ------------------------------------------------------------------------------ \\ arXiv:1205.0034 Date: Mon, 30 Apr 2012 21:30:47 GMT (17kb) Title: C-sortable words as green mutation sequences Authors: Yu Qiu Categories: math.CO math.RT Comments: 15 pages, 2 figures and 1 table \\ Let Q be an acyclic quiver and s be a sequence s with elements in the vertex set Q_0. We describe a sequence of simple (backward) tilting in the bounded derived category D(Q), starting from the standard heart H_Q=modkQ and ending at the heart H_s in D(Q). Then we interpret Keller's green mutation via King-Qiu's Ext-quiver of hearts, which provides a proof of Keller's theorem, that s is a green mutation sequence if and only if every heart in the simple tilting sequence is greater than or equal to H_Q[-1]; it is maximal if and only if H_s=Q[-1]. Further, fix a Coxeter element c in the Coxeter group W_Q of Q, which is admissible with respect to the orientation of Q. We show that the sequence induced by a c-sortable word w is a green mutation sequence. As a consequence, we obtain a bijection between the set of c-sortable words and finite torsion class in H_Q, which was first proved by Thomas and was also obtained by Amiot-Iyama-Reiten-Todorov. As byproducts, the interpretations of inversions, descents and cover reflections of a c-sortable word w, and thus noncrossing partitions, as well as the wide subcategories associated to H_w, are given in terms of non-green vertices. \\ ( http://arxiv.org/abs/1205.0034 , 17kb) ------------------------------------------------------------------------------ \\ arXiv:1205.0037 Date: Mon, 30 Apr 2012 21:40:15 GMT (8kb) Title: On Mordell-Tornheim sums and multiple zeta values Authors: David M. Bradley and Xia Zhou Categories: math.NT Comments: 8 pages AMSLaTeX MSC-class: 11M41, 11M06 Journal-ref: Ann. Sci. Math. Qu\'ebec, Vol. 34, No. 1, 2010, pp. 15--23. [MR 2744193] (2011k:11118) \\ We prove that any Mordell-Tornheim sum with positive integer arguments can be expressed as a rational linear combination of multiple zeta values of the same weight and depth. By a result of Tsumura, it follows that any Mordell-Tornheim sum with weight and depth of opposite parity can be expressed as a rational linear combination of products of multiple zeta values of lower depth. \\ ( http://arxiv.org/abs/1205.0037 , 8kb) ------------------------------------------------------------------------------ \\ arXiv:1205.0045 Date: Mon, 30 Apr 2012 22:30:29 GMT (44kb,D) Title: Computing power series expansions of modular forms Authors: John Voight and John Willis Categories: math.NT Comments: 26 pages, 5 figures \\ We exhibit a method to numerically compute power series expansions of modular forms on a cocompact Fuchsian group, using the explicit computation a fundamental domain and linear algebra. \\ ( http://arxiv.org/abs/1205.0045 , 44kb) ------------------------------------------------------------------------------ \\ arXiv:1205.0048 Date: Mon, 30 Apr 2012 22:53:45 GMT (18kb) Title: On the dynamic programming principle for uniformly nondegenerate stochastic differential games in domains Authors: N.V. Krylov Categories: math.OC Comments: 21 pages MSC-class: 35B65, 35J60, 49N70, 91A05 \\ We prove the dynamic programming principe for uniformly nondegenerate stochastic differential games in the framework of time-homogeneous diffusion processes considered up to the first exit time from a domain. The zeroth-order "coefficient" and the "free" term are only assumed to be measurable. In contrast with previous results established for constant stopping times we allow arbitrary stopping times and randomized ones as well. The main assumption, which will be removed in a subsequent article, is that there exists a sufficiently regular solution of the Isaacs equation. \\ ( http://arxiv.org/abs/1205.0048 , 18kb) ------------------------------------------------------------------------------ \\ arXiv:1205.0049 Date: Mon, 30 Apr 2012 22:59:00 GMT (1034kb) Title: Obtaining genus 2 Heegaard splittings from Dehn surgery Authors: Kenneth L Baker, Cameron Gordon, and John Luecke Categories: math.GT Comments: 127 pages, 81 figures MSC-class: 57M27 \\ Let K' be a hyperbolic knot in S^3 and suppose that some Dehn surgery on K' with distance at least 3 from the meridian yields a 3-manifold M of Heegaard genus 2. We show that if M does not contain an embedded Dyck's surface (the closed non-orientable surface of Euler characteristic -1), then the knot dual to the surgery is either 0-bridge or 1-bridge with respect to a genus 2 Heegaard splitting of M. In the case M does contain an embedded Dyck's surface, we obtain similar results. As a corollary, if M does not contain an incompressible genus 2 surface, then the tunnel number of K' is at most 2. \\ ( http://arxiv.org/abs/1205.0049 , 1034kb) ------------------------------------------------------------------------------ \\ arXiv:1205.0050 Date: Mon, 30 Apr 2012 23:03:26 GMT (20kb) Title: On the dynamic programming principle for uniformly nondegenerate stochastic differential games in domains and the Isaacs equations Authors: N.V. Krylov Categories: math.OC Comments: 24 pages MSC-class: 35B65, 35J60, 49N70, 91A05 \\ We prove the dynamic programming principe for uniformly nondegenerate stochastic differential games in the framework of time-homogeneous diffusion processes considered up to the first exit time from a domain. In contrast with previous results established for constant stopping times we allow arbitrary stopping times and randomized ones as well. There is no assumption about solvability of the the Isaacs equation in any sense (classical or viscosity). The zeroth-order "coefficient" and the "free" term are only assumed to be measurable in the space variable. We also prove that value functions are uniquely determined by the functions defining the corresponding Isaacs equations and thus stochastic games with the same Isaacs equation have the same value functions. \\ ( http://arxiv.org/abs/1205.0050 , 20kb) ------------------------------------------------------------------------------ \\ arXiv:1205.0053 Date: Mon, 30 Apr 2012 23:08:15 GMT (63kb) Title: Lagrangian fibrations on blowups of toric varieties and mirror symmetry for hypersurfaces Authors: Mohammed Abouzaid, Denis Auroux, Ludmil Katzarkov Categories: math.SG math.AG Comments: 58 pages \\ We consider mirror symmetry for (essentially arbitrary) hypersurfaces in (possibly noncompact) toric varieties from the perspective of the Strominger-Yau-Zaslow (SYZ) conjecture. Given a hypersurface $H$ in a toric variety $V$ we construct a Landau-Ginzburg model which is SYZ mirror to the blowup of $V\times\C$ along $H\times 0$, under a positivity assumption. This construction also yields SYZ mirrors to affine conic bundles, as well as a Landau-Ginzburg model which can be naturally viewed as a mirror to $H$. The main applications concern affine hypersurfaces of general type, for which our results provide a geometric basis for various mirror symmetry statements that appear in the recent literature. We also obtain analogous results for complete intersections. \\ ( http://arxiv.org/abs/1205.0053 , 63kb) ------------------------------------------------------------------------------ \\ arXiv:1205.0056 Date: Mon, 30 Apr 2012 23:49:21 GMT (54kb) Title: Geodesics in the space of K\"ahler cone metrics Authors: Simone Calama, Kai Zheng Categories: math.AP math.DG Comments: 59 pages \\ In this paper, we prove the existence and uniqueness of the weak cone geodesics in the space of K\"ahler cone metrics by solving the singular, homogeneous complex Monge-Amp\`{e}re equation. As an application, we prove the metric space structure of the appropriate subspace of the space of K\"ahler cone metrics. \\ ( http://arxiv.org/abs/1205.0056 , 54kb) ------------------------------------------------------------------------------ \\ arXiv:1205.0061 Date: Tue, 1 May 2012 00:37:59 GMT (12kb) Title: Singularities and nonhyperbolic manifolds do not coincide Authors: Nandor Simanyi Categories: math.DS math-ph math.MP Comments: 11 pages MSC-class: 37D50, 34D05 \\ We consider the billiard flow of elastically colliding hard disks on the flat 2-torus and prove that no singularity manifold can locally coincide with a manifold describing future non-hyperbolicity of the trajectories. As a corollary, we obtain the ergodicity (actually the Bernoulli mixing property) of all such systems. \\ ( http://arxiv.org/abs/1205.0061 , 12kb) ------------------------------------------------------------------------------ \\ arXiv:1205.0062 Date: Tue, 1 May 2012 00:59:26 GMT (19kb) Title: Lexicographic Shellability of Partial Involutions Authors: Mahir Bilen Can, Tim Twelbeck Categories: math.CO math.AG \\ In this manuscript we study inclusion posets of Borel orbit closures on (symmetric) matrices. In particular, we show that the Bruhat poset of partial involutions is a lexicographiically shellable poset. Also, studying the embeddings of symmetric groups and involutions into rooks and partial involutions, respectively, we find new $EL$-labelings on permutations as well as on involutions. \\ ( http://arxiv.org/abs/1205.0062 , 19kb) ------------------------------------------------------------------------------ \\ arXiv:1205.0064 Date: Tue, 1 May 2012 01:05:17 GMT (11kb) Title: On incompactness for chromatic number of graphs Authors: Saharon Shelah Categories: math.LO math.CO Report-no: Shelah [Sh:1006] \\ We deal with incompactness. Assume the existence of non-reflecting stationary set of cofinality kappa . We prove that one can define a graph G whose chromatic number is > kappa, while the chromatic number of every subgraph G' subseteq G,|G'| < |G| is <= kappa . The main case is kappa = aleph_0. \\ ( http://arxiv.org/abs/1205.0064 , 11kb) ------------------------------------------------------------------------------ \\ arXiv:1205.0065 Date: Tue, 1 May 2012 01:15:32 GMT (877kb,D) Title: A Tale of Two Arc Lengths: Metric notions for curves in surfaces in equiaffine space Authors: Jeanne Clelland, Edward Estrada, Molly May, Jonah Miller, Sean Peneyra, Michael Schmidt Categories: math.DG Comments: 14 pages, 7 figures MSC-class: 53 \\ In Euclidean geometry, all metric notions (arc length for curves, the first fundamental form for surfaces, etc.) are derived from the Euclidean inner product on tangent vectors, and this inner product is preserved by the full symmetry group of Euclidean space (translations, rotations, and reflections). In equiaffine geometry, there is no invariant notion of inner product on tangent vectors that is preserved by the full equiaffine symmetry group. Nevertheless, it is possible to define an invariant notion of arc length for nondegenerate curves, and an invariant first fundamental form for nondegenerate surfaces in equiaffine space. This leads to two possible notions of arc length for a curve contained in a surface, and these two arc length functions do not necessarily agree. In this paper we will derive necessary and sufficient conditions under which the two arc length functions do agree, and illustrate with examples. \\ ( http://arxiv.org/abs/1205.0065 , 877kb) ------------------------------------------------------------------------------ \\ arXiv:1205.0071 Date: Tue, 1 May 2012 01:47:42 GMT (10kb) Title: Bonnet pairs of surfaces in Minkowski space Authors: Robert Salom Categories: math.DG \\ In this note we consider the problem of local classification of Bonnet pairs of surfaces in 3-dimensional Minkowski space. We use split quaternions in a way similar to the use of quaternions in, arXiv:dg-ga/9610006, for the solution in Euclidean 3-Space. \\ ( http://arxiv.org/abs/1205.0071 , 10kb) ------------------------------------------------------------------------------ \\ arXiv:1205.0074 Date: Tue, 1 May 2012 02:17:40 GMT (14kb) Title: Skew monoidales, skew warpings and quantum categories Authors: Stephen Lack and Ross Street Categories: math.CT math.QA \\ Kornel Szlach\'anyi recently used the term skew-monoidal category for a particular laxified version of monoidal category. He showed that bialgebroids $H$ with base ring $R$ could be characterized in terms of skew-monoidal structures on the category of one-sided $R$-modules for which the lax unit was $R$ itself. We define skew monoidales (or skew pseudo-monoids) in any monoidal bicategory $\mathscr M$. These are skew-monoidal categories when $\mathscr M$ is $\mathrm{Cat}$. Our main results are presented at the level of monoidal bicategories. However, a consequence is that quantum categories in the sense of Day-Street with base comonoid $C$ in a suitably complete braided monoidal category $\mathscr V$ are precisely skew monoidales in $\mathrm{Comod} (\mathscr V)$ with unit coming from the counit of $C$. Quantum groupoids are those skew monoidales with invertible associativity constraint. In fact, we provide some very general results connecting opmonoidal monads and skew monoidales. We use a lax version of the concept of warping defined recently by Booker-Street to modify monoidal structures. \\ ( http://arxiv.org/abs/1205.0074 , 14kb) ------------------------------------------------------------------------------ \\ arXiv:1205.0077 Date: Tue, 1 May 2012 02:58:23 GMT (13kb) Title: A Note on the Analyticity of Density of States Authors: M. Kaminaga, M. Krishna, S. Nakamura Categories: math-ph math.MP MSC-class: 82B44, 47B39, 47B80 \\ We consider the $d$-dimensional Anderson model, and we prove the density of states is locally analytic if the single site potential distribution is locally analytic and the disorder is large. We employ the random walk expansion of resolvents and a simple complex function theory trick. In particular, we discuss the uniform distribution case, and we obtain a sharper result using more precise computations. The method can be also applied to prove the analyticity of the correlation functions. \\ ( http://arxiv.org/abs/1205.0077 , 13kb) ------------------------------------------------------------------------------ \\ arXiv:1205.0080 Date: Tue, 1 May 2012 03:59:20 GMT (3429kb) Title: The Polygons of Albrecht D\"urer -1525 Authors: Gordon Hughes Categories: math.HO MSC-class: 01A40, 97A40 \\ The early Renaissance artist Albrecht D\"urer published a book on geometry a few years before he died. This was intended to be a guide for young craftsmen and artists giving them both practical and mathematical tools for their trade. In the second part of that book, Durer gives compass and straightedge constructions for the 'regular' polygons from the triangle to the 16-gon. We will examine each of these constructions using the original 1525 text and diagrams along with a translation. Then we will use Mathematica to carry out the constructions which are only approximate, in order to compare them with the regular case. In Appendix A, we discuss D\"urer's approximate trisection method for angles, which is surprisingly accurate. Appendix B outlines what is known currently about compass and straightedge constructions and includes two elegant 19th century constructions. \\ ( http://arxiv.org/abs/1205.0080 , 3429kb) ------------------------------------------------------------------------------ \\ arXiv:1205.0085 Date: Tue, 1 May 2012 04:41:09 GMT (198kb,D) Title: Spectrum Leasing via Cooperation for Enhanced Physical-Layer Secrecy Authors: Keonkook Lee, Chan-Byoung Chae, and Joonhyuk Kang Categories: cs.IT math.IT Comments: 12 pages, 6 figures, Part of this work was presented at the ICC 2011 \\ Spectrum leasing via cooperation refers to the possibility of primary users leasing a portion of the spectral resources to secondary users in exchange for cooperation. In the presence of an eavesdropper, this correspondence proposes a novel application of this concept in which the secondary cooperation aims at improving secrecy of the primary network by creating more interference to the eavesdropper than to the primary receiver. To generate the interference in a positive way, this work studies an optimal design of a beamformer at the secondary transmitter with multiple antennas that maximizes a secrecy rate of the primary network while satisfying a required rate for the secondary network. Moreover, we investigate two scenarios depending upon the operation of the eavesdropper: i) the eavesdropper treats the interference by the secondary transmission as an additive noise (single-user decoding) and ii) the eavesdropper tries to decode and remove the secondary signal (joint decoding). Numerical results confirm that, for a wide range of required secondary rate constraints, the proposed spectrum-leasing strategy increases the secrecy rate of the primary network compared to the case of no spectrum leasing. \\ ( http://arxiv.org/abs/1205.0085 , 198kb) ------------------------------------------------------------------------------ \\ arXiv:1205.0087 Date: Tue, 1 May 2012 04:48:16 GMT (71kb,D) Title: Odd-order Cayley graphs with commutator subgroup of order pq are hamiltonian Authors: Dave Witte Morris Categories: math.CO Comments: 32 pages MSC-class: 05C25, 05C45 \\ We show that if G is a nontrivial, finite group of odd order, whose commutator subgroup [G,G] is cyclic of order p^m q^n, where p and q are prime, then every connected Cayley graph on G has a hamiltonian cycle. \\ ( http://arxiv.org/abs/1205.0087 , 71kb) ------------------------------------------------------------------------------ \\ arXiv:1205.0089 Date: Tue, 1 May 2012 05:09:09 GMT (34kb) Title: Dense nuclear Fr\'echet ideals in $C^\star$-algebras Authors: Larry B. Schweitzer Categories: math.OA math.FA Comments: 55 pages MSC-class: 46H20, 46H10 \\ We show that a $C^\star$-algebra $B$ contains a dense Fr\'echet two-sided ideal $A$ satisfying seminorm inequalities $\| a_1 a_2 \|_n \leq \min \bigl\{\, \|a_1\|_n \|a_2\|_B,\, \|a_1\|_B \|a_2\|_n \, \bigr\}$, $a_1, a_2 \in A$, $n \in \N$, with $A$ a nuclear locally convex space, if and only if the primitive ideal space Prim$(B)$ of $B$ is discrete and countable, and $B/I$ is finite dimensional for each $I \in $ Prim$(B)$. Here $\{\| \cdot \|_n \}_{n=0}^\infty$ denotes a family of increasing norms topologizing $A$. In the forward direction, we show the existence of such an ideal in a Banach algebra $B$ implies that $B$ is completely continuous, and then apply results of I. Kaplansky to obtain our conclusion. We do not require that $B$ be a $C^\star$-algebra until proving the reverse direction, when we construct nuclear dense ideals by defining a set of matrix-valued Schwartz functions on the countable discrete space Prim$(B)$. The cases of nilpotent radical, semigroup, and reduced involutive Banach algebras are considered. \\ ( http://arxiv.org/abs/1205.0089 , 34kb) ------------------------------------------------------------------------------ \\ arXiv:1205.0090 Date: Tue, 1 May 2012 05:16:56 GMT (315kb,D) Title: Error term improvements for van der Corput transforms Authors: Joseph Vandehey Categories: math.NT Comments: 72 pages, 10 figures MSC-class: Primary: 11L03, 11L07 \\ We improve the error term in the van der Corput transform for exponential sums \sum_{a \le n \le b} g(n) exp(2\pi i f(n)). For many functions g and f, we can extract the next term in the asymptotic, showing that previous results, such as those of Karatsuba and Korolev, are sharp. Of particular note, the methods of this paper avoid the use of the truncated Poisson formula, and thus can be applied to much longer intervals [a,b] with far better results. We provide a detailed analysis of the error term in the case g(x)=1 and f(x)=(x/3)^{3/2}. \\ ( http://arxiv.org/abs/1205.0090 , 315kb) ------------------------------------------------------------------------------ \\ arXiv:1205.0092 Date: Tue, 1 May 2012 05:25:01 GMT (19kb) Title: Stationary distributions for a class of generalized Fleming-Viot processes Authors: Kenji Handa Categories: math.PR Comments: 21 pages MSC-class: Primary 60J75, secondary 60G57 \\ We identify stationary distributions of generalized Fleming-Viot processes with jump mechanisms specified by certain beta laws together with a parameter measure. Each of these distributions is obtained from normalized stable random measures after a suitable biased transformation followed by mixing by the law of a Dirichlet random measure with the same parameter measure. The calculations are based primarily on the well-known relationship to measure-valued branching processes with immigration. \\ ( http://arxiv.org/abs/1205.0092 , 19kb) ------------------------------------------------------------------------------ \\ arXiv:1205.0094 Date: Tue, 1 May 2012 05:31:53 GMT (37kb) Title: Spectral asymptotics for nonsmooth singular Green operators Authors: Gerd Grubb Categories: math.AP math.FA math.SP Comments: 38 pages, with an appendix by Helmut Abels MSC-class: 35J40, 47G30, 58C40 \\ Singular Green operators G appear typically as boundary correction terms in resolvents for elliptic boundary value problems on a domain \Omega \subset R^n, and more generally they appear in the calculus of pseudodifferential boundary problems. In particular, the boundary term in a Krein resolvent formula is a singular Green operator. It is well-known in smooth cases that when G is of negative order -t on a bounded domain, its s-numbers have the behavior (*) s_j(G) \sim c j^{-t/(n-1)} for j\to \infty, governed by the boundary dimension n-1. In some nonsmooth cases, upper estimates (**) s_j(G) \le Cj^{-t/(n-1)} are known. We show that (*) holds when G is a general selfadjoint nonnegative singular Green operator with symbol merely H\"older continuous in x. We also show (*) with t=2 for the boundary term in the Krein resolvent formula comparing the Dirichlet and a Neumann-type problem for a strongly elliptic second-order differential operator (not necessarily selfadjoint) with coefficients in W^1_p(\Omega) for some p>n. \\ ( http://arxiv.org/abs/1205.0094 , 37kb) ------------------------------------------------------------------------------ \\ arXiv:1205.0095 Date: Tue, 1 May 2012 05:33:50 GMT (25kb) Title: Dependence of Kolmogorov widths on the ambient space Authors: Timur Oikhberg and Mikhail Ostrovskii Categories: math.FA math.MG MSC-class: primary 46B20, secondary 41A46, 41A65 \\ We study the dependence of the Kolmogorov widths of a compact set on the ambient Banach space. \\ ( http://arxiv.org/abs/1205.0095 , 25kb) ------------------------------------------------------------------------------ \\ arXiv:1205.0097 Date: Tue, 1 May 2012 06:13:02 GMT (11kb) Title: Eichler Cohomology of Generalized Modular Forms of Real Weights Authors: Wissam Raji Categories: math.NT Comments: Accepted in Proceedings of the American Mathematical Society MSC-class: 11F11, 11F20 \\ In this paper, we prove the Eichler cohomology theorem of weakly parabolic generalized modular forms of real weights on subgroups of finite index in the full modular group. We explicitly establish the isomorphism for large weights by constructing the map from the space of cusp forms to the cohomology group. \\ ( http://arxiv.org/abs/1205.0097 , 11kb) ------------------------------------------------------------------------------ \\ arXiv:1205.0101 Date: Tue, 1 May 2012 07:23:19 GMT (25kb) Title: Tensors, monads and actions Authors: Gavin J. Seal Categories: math.CT MSC-class: 18C20, 18D10, 18D35 \\ We exhibit sufficient conditions for a monoidal monad T on a monoidal category C to induce a monoidal structure on the Eilenberg--Moore category C^T that classifies bimorphisms. The category of actions in C^T is then shown to be monadic over the base category C. \\ ( http://arxiv.org/abs/1205.0101 , 25kb) ------------------------------------------------------------------------------ \\ arXiv:1205.0102 Date: Tue, 1 May 2012 07:24:38 GMT (8kb) Title: The p-Domination Number of Complete Multipartite Graphs Authors: You Lu, Jun-Ming Xu Categories: math.CO Comments: 9 pages MSC-class: 05C69 \\ Let $G=(V,E)$ be a graph and $p$ a positive integer. A subset $S\subseteq V$ is called a $p$-dominating set of $G$ if every vertex not in $S$ has at least $p$ neighbors in $S$. The $p$-domination number is the minimum cardinality of a $p$-dominating set in $G$. In this paper, we establish an exact formula of the $p$-domination number of all complete multipartite graphs for arbitrary positive integer $p$. \\ ( http://arxiv.org/abs/1205.0102 , 8kb) ------------------------------------------------------------------------------ \\ arXiv:1205.0107 Date: Tue, 1 May 2012 08:13:30 GMT (12kb) Title: Areas of triangles and Beck's theorem in planes over finite fields Authors: Alex Iosevich, Misha Rudnev and Yujia Zhai Categories: math.CO math.CA math.NT MSC-class: 52C10 \\ It is shown that any subset $E$ of a plane over a finite field $\F_q$, of cardinality $|E|>q$ determines not less than $\frac{q-1}{2}$ distinct areas of triangles, moreover once can find such triangles sharing a common base. It is also shown that if $|E|\geq 64q\log_2 q$, then there are more than $\frac{q}{2}$ distinct areas of triangles sharing a common vertex. The result follows from a finite field version of the Beck theorem for large subsets of $\F_q^2$ that we prove. If $|E|\geq 64q\log_2 q$, there exists a point $z\in E$, such that there are at least $\frac{q}{4}$ straight lines incident to $z$, each supporting the number of points of $E$ other than $z$ in the interval between $\frac{|E|}{2q}$ and $\frac{2|E|}{q}.$ This is proved by combining combinatorial and Fourier analytic techniques. We also discuss higher-dimensional implications of these results in light of recent developments. \\ ( http://arxiv.org/abs/1205.0107 , 12kb) ------------------------------------------------------------------------------ \\ arXiv:1205.0111 Date: Tue, 1 May 2012 08:48:13 GMT (6kb) Title: Alternatives for optimization in systems and control: convex and non-convex approaches Authors: Emile Simon Categories: math.OC cs.SY Comments: 4 pages, extended abstract, for the 20th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2012) MSC-class: 90C30, 93B51 \\ In this presentation, we will develop a short overview of main trends of optimization in systems and control, and from there outline some new perspectives emerging today. More specifically, we will focus on the current situation, where it is clear that convex and Linear Matrix Inequality (LMI) methods have become the most common option. However, because of its vast success, the convex approach is often the only direction considered, despite the underlying problem is non-convex and that other optimization methods specifically equipped to handle such problems should have been used instead. We will present key points on this topic, and as a side result we will propose a method to produce a virtually infinite number of papers. \\ ( http://arxiv.org/abs/1205.0111 , 6kb) ------------------------------------------------------------------------------ \\ arXiv:1205.0119 Date: Tue, 1 May 2012 09:02:55 GMT (24kb) Title: On a class of tensor product representations for the orthosymplectic superalgebra Authors: Kevin Coulembier Categories: math.RT math-ph math.MP MSC-class: 17B10 \\ We introduce the spinor representations for osp(m|2n). These generalize the spinors for so(m) and the symplectic spinors for sp(2n) and correspond to representations of the supergroup with supergroup pair (Spin(m) x Mp(2n),osp(m|2n)). We prove that these spinor spaces are uniquely characterized as the completely pointed osp(m|2n)-modules. Then the tensor product of this representation with irreducible finite dimensional osp(m|2n)-modules is studied. Therefore we derive a criterion for complete reducibility of tensor product representations. We calculate the decomposition into irreducible osp(m|2n)-representations of the tensor product of the super spinor space with an extensive class of such representations and also obtain cases where the tensor product is not completely reducible. \\ ( http://arxiv.org/abs/1205.0119 , 24kb) ------------------------------------------------------------------------------ \\ arXiv:1205.0121 Date: Tue, 1 May 2012 09:08:06 GMT (21kb) Title: Approximation Bounds for Sparse Principal Component Analysis Authors: Alexandre d'Aspremont, Francis Bach, Laurent El Ghaoui Categories: math.OC MSC-class: 62H25, 90C22, 90C27 \\ We produce approximation bounds on a semidefinite programming relaxation for sparse principal component analysis. These bounds control approximation ratios for tractable statistics in hypothesis testing problems where data points are sampled from Gaussian models with a single sparse leading component. \\ ( http://arxiv.org/abs/1205.0121 , 21kb) ------------------------------------------------------------------------------ \\ arXiv:1205.0129 Date: Tue, 1 May 2012 10:39:13 GMT (13kb) Title: Norms inequalities for square functions in some Morrey's subspaces Authors: Feuto Justin Categories: math.CA Comments: 13 pages MSC-class: 43A15, 42B20, 42B25, 42B35 \\ We prove that the intrinsic square function and the intrinsic Littlewood-Paley $g^{\ast}_{\lambda}$-function as defined by Wilson, are bounded in a family of weight subspace of Morrey space. The corresponding commutators generated by bounded mean oscillation functions are also considered. \\ ( http://arxiv.org/abs/1205.0129 , 13kb) ------------------------------------------------------------------------------ \\ arXiv:1205.0136 Date: Tue, 1 May 2012 11:18:55 GMT (25kb) Title: Explicit presentations of nonspecial line bundles and secant spaces Authors: Seonja Kim Categories: math.AG MSC-class: 14C20, 14E25, 14H30, 16E05 \\ A line bundle L on a smooth curve X is nonspecial if and only if L admits a presentation L=K_X -D +E for some effective divisors D and E>0 on X with gcd (D, E)=0 and h^0 (X, O_X (D))=1. In this work, we define a minimal presentation of L which is minimal with respect to the degree of E among the presentations. If L=K_X -D +E with degE>2 is a minimal, then L is very ample and any q-points of X with q 1, we describe the singular locus of the compactification of the moduli space R_{g,l} of curves of genus g paired with an l-torsion point in their Jacobian. Generalizing previous work for l=2, we describe the sublocus of noncanonical singularities for any l. For l<5, and for l=6, this allows us to provide a lifting result on pluricanonical forms playing an essential role in the computation of the Kodaira dimension of R_{g,l}: every pluricanonical form on the smooth locus of the moduli space extends to a desingularisation of the compactified moduli space. \\ ( http://arxiv.org/abs/1205.0201 , 56kb) ------------------------------------------------------------------------------ \\ arXiv:1205.0202 Date: Tue, 1 May 2012 16:06:21 GMT (127kb) Title: 3-manifold groups Authors: Matthias Aschenbrenner, Stefan Friedl and Henry Wilton Categories: math.GT Comments: 107 pages, 6 coloured diagrams, coloured printing recommended. Comments are very welcome \\ We summarize properties of 3-manifold groups, with a particular focus on the consequences of the recent results of Ian Agol, Jeremy Kahn, Vladimir Markovic and Dani Wise. \\ ( http://arxiv.org/abs/1205.0202 , 127kb) ------------------------------------------------------------------------------ \\ arXiv:1205.0204 Date: Tue, 1 May 2012 16:13:53 GMT (8kb,D) Title: Global isochronous Hamiltonian centers Authors: Gaetano Zampieri Categories: math.DS nlin.SI MSC-class: Primary: 37J45, Secondary: 34C25 \\ The aim of the present paper is to show a simple family of nonlinear analytic functions $g: R\to R$ such that the origin is a global isochronous center for the scalar equation $\ddot x=-g(x)$. \\ ( http://arxiv.org/abs/1205.0204 , 8kb) ------------------------------------------------------------------------------ \\ arXiv:1205.0208 Date: Tue, 1 May 2012 16:39:57 GMT (7kb) Title: On uniform continuous dependence of solution of Cauchy problem on a parameter Authors: V. Ya. Derr Categories: math.CA \\ Suppose that an $n$-dimensional Cauchy problem \frac{dx}{dt}=f(t,x,\mu) (t \in I, \mu \in M), x(t_0)=x^0 satisfies the conditions that guarantee existence, uniqueness and continuous dependence of solution x(t,t_0,\mu) on parameter \mu in an open set M. We show that if one additionally requires that family \{f(t,x,\cdot)\}_{(t,x)} is equicontinuous, then the dependence of solution x(t,t_0,\mu) on parameter \mu \in M is uniformly continuous. An analogous result for a linear n \times n-dimensional Cauchy problem \frac{dX}{dt}=A(t,\mu)X+\Phi(t,\mu) (t \in I, \mu \in M), X(t_0,\mu)=X^0(\mu) is valid under the assumption that the integrals \int_I\|A(t,\mu_1)-A(t,\mu_2)\|dt and \int_I \|\Phi(t,\mu_1)-\Phi(t,\mu_2)\|dt can be made smaller than any given constant (uniformly with respect to \mu_1, \mu_2 \in M) provided that \|\mu_1-\mu_2\| is sufficiently small. \\ ( http://arxiv.org/abs/1205.0208 , 7kb) ------------------------------------------------------------------------------ \\ arXiv:1205.0213 Date: Tue, 1 May 2012 16:47:13 GMT (28kb,D) Title: Convex dwell-time characterizations for uncertain linear impulsive systems Authors: Corentin Briat and Alexandre Seuret Categories: math.OC cs.SY math.CA math.DS \\ New sufficient conditions for the characterization of dwell-times for linear impulsive systems are proposed and are shown to coincide with continuous decrease conditions of a certain class of looped-functionals, a recently introduced type of functionals suitable for the analysis of hybrid systems. This approach allows to consider Lyapunov functions that evolve non-monotonically along the flow of the system in a new way, enlarging then the admissible class of systems which may be analyzed. As a byproduct, due to the particular structure of the obtained conditions, the method is easily extendable to uncertain systems by exploiting some convexity properties. Several examples illustrate the approach. \\ ( http://arxiv.org/abs/1205.0213 , 28kb) ------------------------------------------------------------------------------ \\ arXiv:1205.0215 Date: Tue, 1 May 2012 16:58:50 GMT (17kb) Title: Homological eigenvalues of mapping classes and torsion homology growth for fibered 3--manifolds Authors: Thomas Koberda Categories: math.GR math.GT Comments: This is essentially part one of the author's thesis \\ Let S be an orientable surface with negative Euler characteristic, let \psi\in\Mod(S) be a mapping class of S, and let T_{\psi} be the mapping torus of \psi. We study the action of lifts of \psi on the homology of finite covers of S via the torsion homology growth of towers of finite covers of T_{\psi}. We show that \psi admits a lift to a finite cover with a homological eigenvalue of length greater than one if and only if the mapping torus T_{\psi} admits a finite cover X and a certain tower of abelian covers which have exponential torsion homology growth. We show that the existence of such a lift of \psi is intrinsic to T_{\psi}, in the sense that it does not depend on the particular fibration used to present T_{\psi}. \\ ( http://arxiv.org/abs/1205.0215 , 17kb) ------------------------------------------------------------------------------ \\ arXiv:1205.0216 Date: Tue, 1 May 2012 17:08:42 GMT (6kb) Title: On Lusternik-Schnirelmann Category of Connected Sums Authors: Robert Newton Categories: math.AT MSC-class: 55M02, 57M02 \\ In this paper we estimate the Lusternik-Schnirelmann category of the connected sum of two manifolds through their categories. We achieve a more general result regarding the category of a quotient space X/A where A is a suitable subspace of X. \\ ( http://arxiv.org/abs/1205.0216 , 6kb) ------------------------------------------------------------------------------ \\ arXiv:1205.0228 Date: Tue, 1 May 2012 18:34:50 GMT (22kb) Title: Some properties of H\"older surfaces in the Heisenberg group Authors: Enrico Le Donne, Roger Z\"ust Categories: math.MG math.DG math.GT Comments: 18 pages, 1 figure MSC-class: 53C17, 49Q15, 28A75, 26A16 \\ It is a folk conjecture that for alpha > 1/2 there is no alpha-Hoelder surface in the subRiemannian Heisenberg group. Namely, it is expected that there is no embedding from an open subset of R^2 into the Heisenberg group that is Hoelder continuous of order strictly greater than 1/2. The Heisenberg group here is equipped with its Carnot-Caratheodory distance. We show that, in the case that such a surface exists, it cannot be of essential bounded variation and it intersects some vertical line in at least a topological Cantor set. \\ ( http://arxiv.org/abs/1205.0228 , 22kb) ------------------------------------------------------------------------------ \\ arXiv:1205.0231 Date: Mon, 30 Apr 2012 11:59:43 GMT (16kb) Title: Triangles on planar Jordan $C^1$-curves Authors: Jean-Claude Hausmann Categories: math.MG Comments: 11 pages, 2 fugures MSC-class: 00A55, 51M104, 55N10 \\ We prove that a Jordan $\calc^1$-curve in the plane contains any non-flat triangle up to translation and homothety with positive ratio. This is false if the curve is not $C^1$. The proof uses a bit configuration spaces, differential and algebraic topology as well as the Schoenflies theorem. \\ ( http://arxiv.org/abs/1205.0231 , 16kb) ------------------------------------------------------------------------------ \\ arXiv:1205.0236 Date: Tue, 1 May 2012 19:20:18 GMT (14kb) Title: The theory of Hahn meromorphic functions, a holomorphic Fredholm theorem and its applications Authors: J\"orn M\"uller and Alexander Strohmaier Categories: math.CA Comments: 17 pages \\ We introduce a class of functions near zero on the logarithmic cover of the complex plane that have convergent expansions into generalized power series. These power series are general enough to cover cases where non-integer powers of z and also terms containing log(z) can appear. We show that under natural assumptions some important theorems from complex analysis carry over to the class of these functions. In particular it is possible to define a field of functions that generalize meromorphic functions and one can formulate an analytic Fredholm theorem in this class. We show that this modified analytic Fredholm theorem can be used in spectral theory to prove convergent expansions of the resolvent for Bessel type operators. \\ ( http://arxiv.org/abs/1205.0236 , 14kb) ------------------------------------------------------------------------------ \\ arXiv:1205.0237 Date: Tue, 1 May 2012 19:25:05 GMT (18kb) Title: Rational cubic fourfolds containing a plane with nontrivial Clifford invariant Authors: Asher Auel, Marcello Bernardara, Michele Bolognesi, and Anthony V\'arilly-Alvarado Categories: math.AG Comments: 10 pages, comments welcome MSC-class: 11E20, 11E88, 14C30, 14F05, 14E08, 14F22, 14J28, 15A66 \\ We isolate a general class of smooth rational cubic fourfolds containing a plane whose associated quadric surface bundle does not have a rational section. Equivalently, the Brauer class of the even Clifford algebra over the discriminant cover--a K3 surface of degree 2--associated to the quadric bundle, is nontrivial. These fourfolds provide nontrivial examples verifying Kuznetsov's conjecture on the rationality of cubic fourfolds containing a plane. \\ ( http://arxiv.org/abs/1205.0237 , 18kb) ------------------------------------------------------------------------------ \\ arXiv:1205.0240 Date: Tue, 1 May 2012 19:45:04 GMT (39kb) Title: Variation of Hodge structure for generalized complex manifolds Authors: David Baraglia Categories: math.DG math.SG Comments: 38 pages MSC-class: 53D18, 32G20 \\ A generalized complex manifold which satisfies the $\partial \overline{\partial}$-lemma admits a Hodge decomposition in twisted cohomology. Using a Courant algebroid theoretic approach we study the behavior of the Hodge decomposition in smooth and holomorphic families of generalized complex manifolds. In particular we define period maps, prove a Griffiths transversality theorem and show that for holomorphic families the period maps are holomorphic. Further results on the Hodge decomposition for various special cases including the generalized K\"ahler case are obtained. \\ ( http://arxiv.org/abs/1205.0240 , 39kb) ------------------------------------------------------------------------------ \\ arXiv:1205.0241 Date: Tue, 1 May 2012 19:51:49 GMT (22kb) Title: Counterfactual Graphical Models for Mediation Analysis via Path-Specific Effects Authors: Ilya Shpitser Categories: math.ST stat.TH Comments: Submitted to the 2012 Rumelhart Prize Special Issue of Cognitive Science honoring Judea Pearl \\ Potential outcome counterfactuals represent variation in the outcome of interest after a hypothetical treatment or intervention is performed. Causal graphical models are a concise, intuitive way of representing causal assumptions, including independence constraints among such counterfactuals. Much of modern causal inference is concerned with expressing cause effect relationships of interest in counterfactual form, showing how the resulting counterfactuals can be identified (that is expressed in terms of available data, using domain-specific causal assumptions), and subsequently estimated using statistical methods. In this paper we will use causal graphical models to analyze the identification problem of the so-called \emph{path-specific effects}, that is effects of treatment on outcome along certain specified causal paths. Such effects arise in mediation analysis settings where it's important to distinguish direct and indirect effects of treatment. We review existing results on path-specific effects in the fully observable, static treatment setting, and extend them to settings with time-varying treatments, and latent variables. \\ ( http://arxiv.org/abs/1205.0241 , 22kb) %-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%- ------------------------------------------------------------------------------ \\ arXiv:1204.2372 (*cross-listing*) Date: Wed, 11 Apr 2012 08:26:48 GMT (27kb) Date (revised v2): Mon, 30 Apr 2012 08:24:33 GMT (27kb) Title: Quantum geometric phase in Majorana's stellar representation: Mapping onto a many-body Aharonov-Bohm phase Authors: Patrick Bruno Categories: quant-ph cond-mat.quant-gas cond-mat.str-el math-ph math.MP Comments: 4 pages, 1 figure; v2: small modifications in response to a Referee's recommendations + corrections of typos in some equations. In press at PRL \\ The (Berry-Aharonov-Anandan) geometric phase acquired during a cyclic quantum evolution of finite-dimensional quantum systems is studied. It is shown that a pure quantum state in a (2J+1)-dimensional Hilbert space (or, equivalently, of a spin-J system) can be mapped onto the partition function of a gas of independent Dirac strings moving on a sphere and subject to the Coulomb repulsion of 2J fixed test charges (the Majorana stars) characterizing the quantum state. The geometric phase may be viewed as the Aharonov-Bohm phase acquired by the Majorana stars as they move through the gas of Dirac strings. Expressions for the geometric connection and curvature, for the metric tensor, as well as for the multipole moments (dipole, quadrupole, etc.), are given in terms of the Majorana stars. Finally, the geometric formulation of the quantum dynamics is presented and its application to systems with exotic ordering such as spin nematics is outlined. \\ ( http://arxiv.org/abs/1204.2372 , 27kb) ------------------------------------------------------------------------------ \\ arXiv:1204.6495 (*cross-listing*) Date: Sun, 29 Apr 2012 16:39:49 GMT (80kb,D) Title: Shape invariance in phase space Authors: Constantin Rasinariu Categories: quant-ph hep-th math-ph math.MP Comments: 21 pages, 2 figures \\ This paper is a pedagogical introduction into the deformation quantization formalism with emphasis on the supersymmetric quantum mechanics and shape invariance techniques. The simple harmonic oscillator and the Morse potential are solved as examples. \\ ( http://arxiv.org/abs/1204.6495 , 80kb) ------------------------------------------------------------------------------ \\ arXiv:1205.0020 (*cross-listing*) Date: Mon, 30 Apr 2012 20:06:26 GMT (166kb) Title: Noncommutative deformation of the Ward metric Authors: Magnus Goffeng, Olaf Lechtenfeld Categories: hep-th math-ph math.MP math.SP Comments: 14 pages, 2 figures; talk at the Workshop on Noncommutative Field Theory and Gravity, Corfu Summer Institute 2011 "School and Workshops on Elementary Particle Physics and Gravity, September 4-18, 2011, Corfu, Greece \\ The moduli-space metric in the static non-Abelian charge-two sector of the Moyal-deformed CP^1 sigma model in 1+2 dimensions is analyzed. After recalling the commutative results of Ward and Ruback and the zeta-regularized construction of the noncommutative K"ahler potential due to the second author, explicit expressions and asymptotics for it are presented and discussed in different regions of the moduli space. Along two curves in the moduli space the potential can be calculated analytically. In the region of solitons known as "ring-like", perturbation theory is used. In the region of "lump-like" solitons, both perturbation theory and the zeta-function approach are employed. While the strong noncommutativity limit is smooth and under control, the commutative limit in the two-lump region remains a semiclassical challenge. \\ ( http://arxiv.org/abs/1205.0020 , 166kb) ------------------------------------------------------------------------------ \\ arXiv:1205.0022 (*cross-listing*) Date: Mon, 30 Apr 2012 20:07:18 GMT (14kb) Title: Higher loop corrections to a Schwinger--Dyson equation Authors: Marc P. Bellon and Fidel A. Schaposnik Categories: hep-th hep-ph math-ph math.MP Comments: 12 pages, 2 imbedded TiKZ pictures \\ We consider the effects of higherloop corrections to a Schwinger--Dyson equations for propagators. This is made possible by the efficiency of the methods we developed in preceding works, still using the supersymmetric Wess--Zumino model as a laboratory. We obtain the dominant contributions of the three and four loop primitive divergences at high order in perturbation theory, without the need for their full evaluations. Our main conclusion is that the asymptotic behavior of the perturbative series of the renormalization function remains unchanged, and we conjecture that this will remain the case for all finite order corrections. \\ ( http://arxiv.org/abs/1205.0022 , 14kb) ------------------------------------------------------------------------------ \\ arXiv:1205.0027 (*cross-listing*) Date: Mon, 30 Apr 2012 20:18:47 GMT (23kb) Title: Differential geometry construction of anomalies and topological invariants in various dimensions Authors: Ignatios Antoniadis and George Savvidy Categories: hep-th math-ph math.MP Comments: 27 pages Report-no: NRCPS-HE-27-2012; CERN-PH-TH/2012-088 \\ The Lagrangian of non-Abelian tensor gauge fields describes interaction of the Yang-Mills field and massless tensor gauge bosons of increasing helicities. The model allows the existence of metric-independent densities: the exact (2n+3)-forms and their secondary characteristics, the (2n+2)-forms. We also found exact 6n-forms and the corresponding secondary (6n-1)-forms. These forms are the analogs of the Pontryagin densities: the exact 2n-forms and Chern-Simons secondary characteristics, the (2n-1)-forms. The (2n+3)- and 6n-forms are gauge invariant densities, while the (2n+2)- and (6n-1)-forms transform non-trivially under gauge transformations, that we compare with the corresponding transformations of the Chern-Simons secondary characteristics. This construction allows to identify new potential anomalies in various dimensions. \\ ( http://arxiv.org/abs/1205.0027 , 23kb) ------------------------------------------------------------------------------ \\ arXiv:1205.0047 (*cross-listing*) Date: Mon, 30 Apr 2012 22:48:37 GMT (31kb) Title: $QD$-Learning: A Collaborative Distributed Strategy for Multi-Agent Reinforcement Learning Through Consensus + Innovations Authors: Soummya Kar, Jose' M.F. Moura and H. Vincent Poor Categories: stat.ML cs.MA math.OC math.PR Comments: Submitted for journal publication, 30 pages \\ The paper considers a class of multi-agent Markov decision processes (MDPs), in which the network agents respond differently (as manifested by the instantaneous one-stage random costs) to a global controlled state and the control actions of a remote controller. The paper investigates a distributed reinforcement learning setup with no prior information on the global state transition and local agent cost statistics. Specifically, with the agents' objective consisting of minimizing a network-averaged infinite horizon discounted cost, the paper proposes a distributed version of $Q$-learning, $\mathcal{QD}$-learning, in which the network agents collaborate by means of local processing and mutual information exchange over a sparse (possibly stochastic) communication network to achieve the network goal. Under the assumption that each agent is only aware of its local online cost data and the inter-agent communication network is \emph{weakly} connected, the proposed distributed scheme is almost surely (a.s.) shown to yield asymptotically the desired value function and the optimal stationary control policy at each network agent. The analytical techniques developed in the paper to address the mixed time-scale stochastic dynamics of the \emph{consensus + innovations} form, which arise as a result of the proposed interactive distributed scheme, are of independent interest. \\ ( http://arxiv.org/abs/1205.0047 , 31kb) ------------------------------------------------------------------------------ \\ arXiv:1205.0076 (*cross-listing*) Date: Tue, 1 May 2012 02:54:21 GMT (139kb,D) Title: Robust Distributed Routing in Dynamical Networks with Cascading Failures Authors: Giacomo Como, Ketan Savla, Daron Acemoglu, Munther A. Dahleh and Emilio Frazzoli Categories: cs.SY math.DS \\ Robustness of routing policies for networks is a central problem which is gaining increased attention with a growing awareness to safeguard critical infrastructure networks against natural and man-induced disruptions. Routing under limited information and the possibility of cascades through the network adds serious challenges to this problem. This abstract considers the framework of dynamical networks introduced in our earlier work [1,2], where the network is modeled by a system of ordinary differential equations derived from mass conservation laws on directed acyclic graphs with a single origin-destination pair and a constant inflow at the origin. The rate of change of the particle density on each link of the network equals the difference between the inflow and the outflow on that link. The latter is modeled to depend on the current particle density on that link through a flow function. The novel modeling element in this paper is that every link is assumed to have finite capacity for particle density and that the flow function is modeled to be strictly increasing as density increases from zero up to the maximum density capacity, and is discontinuous at the maximum density capacity, with the flow function value being zero at that point. This feature, in particular, allows for the possibility of spill-backs in our model. In this paper, we present our results on resilience of such networks under distributed routing, towards perturbations that reduce link-wise flow functions. \\ ( http://arxiv.org/abs/1205.0076 , 139kb) ------------------------------------------------------------------------------ \\ arXiv:1205.0079 (*cross-listing*) Date: Tue, 1 May 2012 03:37:13 GMT (56kb) Title: Complexity Analysis of the Lasso Regularization Path Authors: Julien Mairal and Bin Yu Categories: stat.ML cs.LG math.OC Comments: Accepted to the 29th International Conference on Machine Learning (ICML 2012). To appear in the proceedings \\ The regularization path of the Lasso can be shown to be piecewise linear, making it possible to "follow" and explicitly compute the entire path. We analyze in this paper this popular strategy, and prove that its worst case complexity is exponential in the number of variables. We then oppose this pessimistic result to an (optimistic) approximate analysis: We show that an approximate path with at most O(1/sqrt(epsilon)) linear segments can always be obtained, where every point on the path is guaranteed to be optimal up to a relative epsilon-duality gap. We complete our theoretical analysis with a practical algorithm to compute these approximate paths. \\ ( http://arxiv.org/abs/1205.0079 , 56kb) ------------------------------------------------------------------------------ \\ arXiv:1205.0088 (*cross-listing*) Date: Tue, 1 May 2012 04:59:12 GMT (44kb,DS) Title: ProPPA: A Fast Algorithm for $\ell_1$ Minimization and Low-Rank Matrix Completion Authors: Ranch Y.Q. Lai and Pong C. Yuen Categories: cs.LG math.OC \\ We propose a Projected Proximal Point Algorithm (ProPPA) for solving a class of optimization problems. The algorithm iteratively computes the proximal point of the last estimated solution projected into an affine space which itself is parallel and approaching to the feasible set. We provide convergence analysis theoretically supporting the general algorithm, and then apply it for solving $\ell_1$-minimization problems and the matrix completion problem. These problems arise in many applications including machine learning, image and signal processing. We compare our algorithm with the existing state-of-the-art algorithms. Experimental results on solving these problems show that our algorithm is very efficient and competitive. \\ ( http://arxiv.org/abs/1205.0088 , 44kb) ------------------------------------------------------------------------------ \\ arXiv:1205.0125 (*cross-listing*) Date: Tue, 1 May 2012 10:21:51 GMT (6kb) Title: On the parameter $\mu_{21}$ of a complete bipartite graph Authors: A.M. Khachatryan, R.R. Kamalian Categories: cs.DM math.CO Comments: 5 pages, no figures \\ A proper edge $t$-coloring of a graph $G$ is a coloring of edges of $G$ with colors $1,2,...,t$ such that all colors are used, and no two adjacent edges receive the same color. The set of colors of edges incident with a vertex $x$ is called a spectrum of $x$. An arbitrary nonempty subset of consecutive integers is called an interval. Suppose that all edges of a graph $G$ are colored in the game of Alice and Bob with asymmetric distribution of roles. Alice determines the number $t$ of colors in the future proper edge coloring of $G$ and aspires to minimize the number of vertices with an interval spectrum in it. Bob colors edges of $G$ with $t$ colors and aspires to maximize that number. $\mu_{21}(G)$ is equal to the number of vertices of $G$ with an interval spectrum at the finish of the game on the supposition that both players choose their best strategies. In this paper, for arbitrary positive integers $m$ and $n$, the exact value of the parameter $\mu_{21}(K_{m,n})$ is found. \\ ( http://arxiv.org/abs/1205.0125 , 6kb) ------------------------------------------------------------------------------ \\ arXiv:1205.0128 (*cross-listing*) Date: Tue, 1 May 2012 10:38:18 GMT (10kb) Title: It was not known about simple cycles Authors: R.R. Kamalian Categories: cs.DM math.CO Comments: 7 pages, no figures \\ A proper edge $t$-coloring of a graph is a coloring of its edges with colors $1,2,...,t$ such that all colors are used, and no two adjacent edges receive the same color. For any integer $n\geq 3$, all possible values of $t$ are found, for which there exists such a proper edge $t$-coloring of the simple cycle C(n), which uses for each pair of adjacent edges either consecutive colors or the first and the last ones. \\ ( http://arxiv.org/abs/1205.0128 , 10kb) ------------------------------------------------------------------------------ \\ arXiv:1205.0130 (*cross-listing*) Date: Tue, 1 May 2012 10:47:49 GMT (10kb) Title: On one-sided interval edge colorings of biregular bipartite graphs Authors: R.R. Kamalian Categories: cs.DM math.CO Comments: 6 pages, no figures \\ A proper edge $t$-coloring of a graph $G$ is a coloring of edges of $G$ with colors $1,2,...,t$ such that all colors are used, and no two adjacent edges receive the same color. The set of colors of edges incident with a vertex $x$ is called a spectrum of $x$. An arbitrary nonempty subset of consecutive integers is called an interval. We say that a proper edge $t$-coloring of a graph $G$ is interval in the vertex $x$ if the spectrum of $x$ is an interval. We say that a proper edge $t$-coloring $\varphi$ of a graph $G$ is interval on a subset $R_0$ of vertices of $G$, if for an arbitrary $x\in R_0$, $\varphi$ is interval in $x$. We say that a subset $R$ of vertices of $G$ has an $i$-property if there is a proper edge $t$-coloring of $G$ which is interval on $R$. If $G$ is a graph, and a subset $R$ of its vertices has an $i$-property, then the minimum value of $t$ for which there is a proper edge $t$-coloring of $G$ interval on $R$ is denoted by $w_R(G)$. In this paper, for some bipartite graphs, we estimate the value of this parameter in that cases when $R$ coincides with the set of all vertices of one part of the graph. \\ ( http://arxiv.org/abs/1205.0130 , 10kb) ------------------------------------------------------------------------------ \\ arXiv:1205.0131 (*cross-listing*) Date: Tue, 1 May 2012 10:52:09 GMT (10kb) Title: Estimates for the number of vertices with an interval spectrum in proper edge colorings of some graphs Authors: R.R. Kamalian Categories: cs.DM math.CO Comments: 10 pages, no figures \\ A proper edge $t$-coloring of a graph $G$ is a coloring of edges of $G$ with colors $1,2,...,t$ such that each of $t$ colors is used, and adjacent edges are colored differently. The set of colors of edges incident with a vertex $x$ of $G$ is called a spectrum of $x$. A proper edge $t$-coloring of a graph $G$ is interval for its vertex $x$ if the spectrum of $x$ is an interval of integers. A proper edge $t$-coloring of a graph $G$ is persistent-interval for its vertex $x$ if the spectrum of $x$ is an interval of integers beginning from the color 1. For graphs $G$ from some classes of graphs, we obtain estimates for the possible number of vertices for which a proper edge $t$-coloring of $G$ can be interval or persistent-interval. \\ ( http://arxiv.org/abs/1205.0131 , 10kb) ------------------------------------------------------------------------------ \\ arXiv:1205.0135 (*cross-listing*) Date: Tue, 1 May 2012 11:11:18 GMT (12kb) Title: Euclidean Pseudoduality and Boundary Conditions in Sigma Models Authors: Mustafa Sarisaman Categories: hep-th math-ph math.MP Comments: 12 pages \\ We discuss pseudoduality transformations in two dimensional conformally invariant classical sigma models, and extend our analysis to a given boundaries of world-sheet, which gives rise to an appropriate framework for the discussion of the pseudoduality between D-branes. We perform analysis using the Euclidean spacetime and show that structures on the target space can be transformed into pseudodual manifold identically. This map requires that torsions and riemann connections related to individual spaces are the same. Boundary pseudoduality imposes locality condition. \\ ( http://arxiv.org/abs/1205.0135 , 12kb) ------------------------------------------------------------------------------ \\ arXiv:1205.0139 (*cross-listing*) Date: Tue, 1 May 2012 11:30:27 GMT (142kb,D) Title: Lambda calculus combined with emergent algebras Authors: Marius Buliga Categories: cs.LO math.RA \\ I propose an enrichment of lambda-calculus which contains the formalism of emergent algebras. \\ ( http://arxiv.org/abs/1205.0139 , 142kb) ------------------------------------------------------------------------------ \\ arXiv:1205.0152 (*cross-listing*) Date: Tue, 1 May 2012 12:53:41 GMT (18kb) Title: Lorentz invariant CPT violation Authors: Masud Chaichian, Kazuo Fujikawa and Anca Tureanu Categories: hep-th hep-ph math-ph math.MP Comments: 26 pages \\ A Lorentz invariant CPT violation, which may be termed as long distance CPT violation in contrast to the familiar short distance CPT violation, has been proposed in Ref. [Chaichian et al., Phys. Lett. B 699 (2011) 177, arXiv:1103.0168 [hep-th]]. This scheme is based on a non-local interaction vertex and characterized by an infrared divergent form factor. We show that the Lorentz covariant $T^{\star}$-product is consistently defined and the energy-momentum conservation is preserved in perturbation theory if the path integral is suitably defined for this non-local theory, although unitarity is generally lost. It is illustrated that T violation is realized in the decay and formation processes. It is also argued that the equality of masses and decay widths of the particle and anti-particle is preserved if the non-local CPT violation is incorporated either directly or as perturbation by starting with the conventional CPT-even local Lagrangian. However, we also explicitly show that the present non-local scheme can induce the splitting of particle and anti-particle mass eigenvalues if one considers a more general class of Lagrangians. \\ ( http://arxiv.org/abs/1205.0152 , 18kb) ------------------------------------------------------------------------------ \\ arXiv:1205.0157 (*cross-listing*) Date: Tue, 1 May 2012 13:39:25 GMT (10kb) Title: A Secret Sharing Scheme Based on Group Presentations and the Word Problem Authors: Maggie Habeeb, Delaram Kahrobaei, Vladimir Shpilrain Categories: cs.CR math.GR Comments: 8 pages \\ A (t,n)-threshold secret sharing scheme is a method to distribute a secret among n participants in such a way that any t participants can recover the secret, but no t-1 participants can. In this paper, we propose two secret sharing schemes using non-abelian groups. One scheme is the special case where all the participants must get together to recover the secret. The other one is a (t,n)-threshold scheme that is a combination of Shamir's scheme and the group-theoretic scheme proposed in this paper. \\ ( http://arxiv.org/abs/1205.0157 , 10kb) ------------------------------------------------------------------------------ \\ arXiv:1205.0170 (*cross-listing*) Date: Mon, 30 Apr 2012 12:45:39 GMT (10kb) Title: New developments in parsing Mizar Authors: Czeslaw Bylinski and Jesse Alama Categories: cs.PL math.LO Comments: 5 pages. Accepted at Mathematical Knowledge Management 2012 Track D (Systems and Projects), Bremen, Germany, July 2012 ACM-class: D.3.4 \\ The Mizar language aims to capture mathematical vernacular by providing a rich language for mathematics. From the perspective of a user, the richness of the language is welcome because it makes writing texts more "natural". But for the developer, the richness leads to syntactic complexity, such as dealing with overloading. Recently the Mizar team has been making a fresh approach to the problem of parsing the Mizar language. One aim is to make the language accessible to users and other developers. In this paper we describe these new parsing efforts and some applications thereof, such as large-scale text refactorings, pretty-printing, HTTP parsing services, and normalizations of Mizar texts. \\ ( http://arxiv.org/abs/1205.0170 , 10kb) ------------------------------------------------------------------------------ \\ arXiv:1205.0193 (*cross-listing*) Date: Tue, 1 May 2012 15:40:33 GMT (12kb) Title: On cyclically-interval edge colorings of trees Authors: R.R. Kamalian Categories: cs.DM math.CO Comments: 9 pages, no figures \\ For an undirected, simple, finite, connected graph $G$, we denote by $V(G)$ and $E(G)$ the sets of its vertices and edges, respectively. A function $\varphi:E(G)\rightarrow\{1,2,\ldots,t\}$ is called a proper edge $t$-coloring of a graph $G$ if adjacent edges are colored differently and each of $t$ colors is used. An arbitrary nonempty subset of consecutive integers is called an interval. If $\varphi$ is a proper edge $t$-coloring of a graph $G$ and $x\in V(G)$, then $S_G(x,\varphi)$ denotes the set of colors of edges of $G$ which are incident with $x$. A proper edge $t$-coloring $\varphi$ of a graph $G$ is called a cyclically-interval $t$-coloring if for any $x\in V(G)$ at least one of the following two conditions holds: a) $S_G(x,\varphi)$ is an interval, b) $\{1,2,\ldots,t\}\setminus S_G(x,\varphi)$ is an interval. For any $t\in \mathbb{N}$, let $\mathfrak{M}_t$ be the set of graphs for which there exists a cyclically-interval $t$-coloring, and let $$\mathfrak{M}\equiv\bigcup_{t\geq1}\mathfrak{M}_t.$$ For an arbitrary tree $G$, it is proved that $G\in\mathfrak{M}$ and all possible values of $t$ are found for which $G\in\mathfrak{M}_t.$ \\ ( http://arxiv.org/abs/1205.0193 , 12kb) ------------------------------------------------------------------------------ \\ arXiv:1205.0196 (*cross-listing*) Date: Tue, 1 May 2012 15:53:11 GMT (50kb,D) Title: Constructive Renormalization of 2-dimensional Grosse-Wulkenhaar Model Authors: Zhituo Wang Categories: hep-th math-ph math.MP Comments: 13 pages. Based on the talk at the Corfu Summer Institute 2011 School and Workshops on Elementary Particle Physics and Gravity. To appear in the proceedings \\ In this talk we briefly report the recent work on the construction of the 2-dimensional Grosse-Wulkenhaar model with the method of loop vertex expansion. We treat renormalization with this new tool, adapt Nelson's argument and prove Borel summability of the perturbation series. This is the first non-commutative quantum field theory model to be built in a non-perturbative sense. \\ ( http://arxiv.org/abs/1205.0196 , 50kb) ------------------------------------------------------------------------------ \\ arXiv:1205.0200 (*cross-listing*) Date: Tue, 1 May 2012 16:04:45 GMT (75kb) Title: Local Availability of mathematics and number scaling: Effects on quantum physics Authors: Paul Benioff Categories: quant-ph gr-qc math-ph math.MP Comments: 21 pages, 2 figures, To appear in SPIE conference proceedings, Quantum information and computation X, April 26,27, 2012 \\ Local availability of mathematics and number scaling provide an approach to a coherent theory of physics and mathematics. Local availability of mathematics assigns separate mathematical universes, U_{x}, to each space time point, x. The mathematics available to an observer, O_{x}, at x is contained in U_{x}. Number scaling is based on extending the choice freedom of vector space bases in gauge theories to choice freedom of underlying number systems. Scaling arises in the description, in U_{x}, of mathematical systems in U_{y}. If a_{y} or \psi_{y} is a number or a quantum state in U_{y}, then the corresponding number or state in U_{x} is r_{y,x}a_{x} or r_{y,x}\psi_{x}. Here a_{x} and \psi_{x} are the same number and state in U_{x} as a_{y} and \psi_{y} are in U_{y}. If y=x+\hat{\mu}dx is a neighbor point of x, then the scaling factor is r_{y,x}=\exp(\vec{A}(x)\cdot\hat{\mu}dx) where \vec{A} is a vector field, assumed here to be the gradient of a scalar field. The effects of scaling and local availability of mathematics on quantum theory show that scaling has two components, external and internal. External scaling is shown above for a_{y} and \psi_{y}. Internal scaling occurs in expressions with integrals or derivatives over space or space time. An example is the replacement of the position expectation value, \int\psi^{*}(y)y\psi(y)dy, by \int_{x}r_{y,x}\psi^{*}_{x}(y_{x})y_{x}\psi_{x}(y_{x})dy_{x}. This is an integral in U_{x}. The good agreement between quantum theory and experiment shows that scaling is negligible in a space region, L, in which experiments and calculations can be done, and results compared. L includes the solar system, but the speed of light limits the size of L to a few light years. Outside of $L$, at cosmological distances, the limits on scaling are not present. \\ ( http://arxiv.org/abs/1205.0200 , 75kb) ------------------------------------------------------------------------------ \\ arXiv:1205.0222 (*cross-listing*) Date: Tue, 1 May 2012 17:27:22 GMT (1269kb,D) Title: Continuous variable methods in relativistic quantum information: Characterisation of quantum and classical correlations of scalar field modes in noninertial frames Authors: Gerardo Adesso, Sammy Ragy, Davide Girolami Categories: quant-ph gr-qc hep-th math-ph math.MP Comments: 19 pages, 3 figures. Submitted to Class. Quantum Grav. for a Focus Issue on `Relativistic Quantum Information' \\ We review a recently introduced unified approach to the analytical quantification of correlations in Gaussian states of bosonic scalar fields by means of Renyi-2 entropy. This allows us to obtain handy formulae for classical, quantum, total correlations, as well as bipartite and multipartite entanglement. We apply our techniques to the study of correlations between two modes of a scalar field as detected by observers in different statuses of motion. When one or both observers are in uniform acceleration, the quantum and classical correlations are degraded differently by the Unruh effect, depending on which mode is detected. Residual quantum correlations, in the form of quantum discord without entanglement, may survive in the limit of an infinitely accelerated observer Rob, provided they are revealed in a measurement performed by the inertial Alice. \\ ( http://arxiv.org/abs/1205.0222 , 1269kb) ------------------------------------------------------------------------------ \\ arXiv:1205.0234 (*cross-listing*) Date: Tue, 1 May 2012 19:17:03 GMT (194kb) Title: Quantum Bose and Fermi gases with large negative scattering length in the 2-body S-matrix approximation Authors: Andre LeClair, Edgar Marcelino, Andre Nicolai, and Itzhak Roditi Categories: cond-mat.quant-gas hep-th math-ph math.MP Comments: 22 pages, 8 figures \\ We study both Bose and Fermi gases at finite temperature and density in an approximation that sums an infinite number of many body processes that are reducible to 2-body scatterings. This is done for arbitrary negative scattering length, which interpolates between the ideal and unitary gas limits. In the unitary limit, we compute the first four virial coefficients within our approximation. The second virial coefficient is exact, and we extend the previously known result for fermions to bosons, and also for both bosons and fermions for the upper branch on the other side of unitarity (infinitely large positive scattering length). Assuming bosons can exist in a meta-stable state before undergoing mechanical collapse, we map out the critical temperatures for strongly coupled Bose-Einstein condensation as a function of scattering length. \\ ( http://arxiv.org/abs/1205.0234 , 194kb) %%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%% ------------------------------------------------------------------------------ \\ arXiv:math/0208216 replaced with revised version Tue, 1 May 2012 15:59:00 GMT (3kb) Title: Generalized Serre--Tate Ordinary Theory Authors: Adrian Vasiu (Binghamton University, U.S.A.) Categories: math.AG Comments: Final version 196 pages (including contents and index) to be published by International Press, Inc. All copyrights reserved to International Press, Inc. Until publication the pdf file is available at http://www.math.binghamton.edu/adrian/" The page 1 is the last version attached here MSC-class: 11G10, 11G15, 11G18, 14F20, 14F30, 14F40, 14G35, 14K10, 14K22, 14L05, 14L15, and 17B45 \\ ( http://arxiv.org/abs/math/0208216 , 3kb) ------------------------------------------------------------------------------ \\ arXiv:math/0602554 replaced with revised version Tue, 1 May 2012 14:04:09 GMT (50kb) Title: Bost-Connes type systems for function fields Authors: Beno\^it Jacob Categories: math.OA math.NT Comments: 55 pages; index of notations; v5: added erratum on the wrong result on the subtype of the type III factors \\ ( http://arxiv.org/abs/math/0602554 , 50kb) ------------------------------------------------------------------------------ \\ arXiv:0812.1625 (*cross-listing*) replaced with revised version Mon, 30 Apr 2012 23:07:02 GMT (18kb) Title: Simultaneous confidence intervals for the population cell means, for two-by-two factorial data, that utilize uncertain prior information Authors: Paul Kabaila, Khageswor Giri Categories: stat.ME math.ST stat.AP stat.TH Comments: The exposition has been improved. In particular, the introduction has been improved and some new references have been added \\ ( http://arxiv.org/abs/0812.1625 , 18kb) ------------------------------------------------------------------------------ \\ arXiv:0901.0381 replaced with revised version Tue, 1 May 2012 12:17:41 GMT (45kb) Title: The Atiyah-Patodi-Singer index theorem for Dirac operators over C*-algebras Authors: Charlotte Wahl Categories: math.DG math.KT Comments: 53 pages; some corrections and streamlining; references added MSC-class: 58J22, 58J32 \\ ( http://arxiv.org/abs/0901.0381 , 45kb) ------------------------------------------------------------------------------ \\ arXiv:0907.4642 replaced with revised version Tue, 1 May 2012 11:04:09 GMT (12kb,D) Title: A combinatorial proof of the Degree Theorem in Auter space Authors: Robert McEwen, Matthew C. B. Zaremsky Categories: math.GR Comments: Substantial changes, most prominently one new author. Results and methods unchanged, though many arguments and proofs have been improved. 8 pages, 2 figures MSC-class: 20F65, 57M07, 20F28 \\ ( http://arxiv.org/abs/0907.4642 , 12kb) ------------------------------------------------------------------------------ \\ arXiv:1004.2726 replaced with revised version Tue, 1 May 2012 10:22:14 GMT (13kb) Title: Crossover to the KPZ equation Authors: Patr\'icia Gon\c{c}alves, Milton Jara Categories: math.PR math-ph math.MP Comments: Published by Annales Henri Poincare Volume 13, Number 4 (2012), 813-826 MSC-class: 60K35 DOI: 10.1007/s00023-011-0147-7 \\ ( http://arxiv.org/abs/1004.2726 , 13kb) ------------------------------------------------------------------------------ \\ arXiv:1006.3246 replaced with revised version Tue, 1 May 2012 06:57:14 GMT (63kb,D) Title: Sparse approaches for the exact distribution of patterns in long state sequences generated by a Markov source Authors: Gr\'egory Nuel (MAP5), Jean-Guillaume Dumas (LJK) Categories: math.PR cs.SC q-bio.QM \\ ( http://arxiv.org/abs/1006.3246 , 63kb) ------------------------------------------------------------------------------ \\ arXiv:1009.3084 replaced with revised version Tue, 1 May 2012 00:41:38 GMT (56kb) Title: Resolvent at low energy III: the spectral measure Authors: Colin Guillarmou, Andrew Hassell and Adam Sikora Categories: math.AP math.SP Comments: 42 pages, 4 figures MSC-class: 35P25, 47A40, 58J50 \\ ( http://arxiv.org/abs/1009.3084 , 56kb) ------------------------------------------------------------------------------ \\ arXiv:1012.3780 replaced with revised version Tue, 1 May 2012 00:28:59 GMT (59kb) Title: Restriction and spectral multiplier theorems on asymptotically conic manifolds Authors: Colin Guillarmou, Andrew Hassell and Adam Sikora Categories: math.AP math.CA math.SP Comments: 50 pages, 1 figure MSC-class: 42B37, 58J50, 35P25 \\ ( http://arxiv.org/abs/1012.3780 , 59kb) ------------------------------------------------------------------------------ \\ arXiv:1102.4937 replaced with revised version Tue, 1 May 2012 08:17:18 GMT (66kb,D) Title: Brownian Motions on Metric Graphs Authors: Vadim Kostrykin and J\"urgen Potthoff and Robert Schrader Categories: math.PR Comments: 43 pages, 7 figures. 2nd revision of our article 1102.4937: The introduction has been modified, several references were added. This article will appear in the special issue of Journal of Mathematical Physics celebrating Elliott Lieb's 80th birthday MSC-class: 60J65, 60J45, 60H99, 58J65, 35K05, 05C99 \\ ( http://arxiv.org/abs/1102.4937 , 66kb) ------------------------------------------------------------------------------ \\ arXiv:1104.4531 replaced with revised version Tue, 1 May 2012 00:53:53 GMT (68kb) Title: Quantum ergodic restriction theorems, II: manifolds without boundary Authors: J. A. Toth and S. Zelditch Categories: math.SP Comments: 53 pages. Second in a series. The paper is self-contained; the methods and results are independent of the first article (arXiv:1005.1636), which dealt with Euclidean domains with ergodic billiards. Some clarifications and an appendix added extending the result to the semi-classical case \\ ( http://arxiv.org/abs/1104.4531 , 68kb) ------------------------------------------------------------------------------ \\ arXiv:1105.5306 replaced with revised version Tue, 1 May 2012 14:25:20 GMT (166kb) Title: On the Generalized Degrees of Freedom of the K-user Symmetric MIMO Gaussian Interference Channel Authors: Parthajit Mohapatra and Chandra R. Murthy Categories: cs.IT math.IT Comments: 52 pages, 4 figures, part of it accepted in ISIT 2011 \\ ( http://arxiv.org/abs/1105.5306 , 166kb) ------------------------------------------------------------------------------ \\ arXiv:1107.2846 replaced with revised version Tue, 1 May 2012 15:06:48 GMT (208kb,D) Title: The Reversal Ratio of a Poset Authors: Graham Brightwell and Mitchel T. Keller Categories: math.CO Comments: 10 pages, 2 figures MSC-class: 06A07 \\ ( http://arxiv.org/abs/1107.2846 , 208kb) ------------------------------------------------------------------------------ \\ arXiv:1108.3539 replaced with revised version Tue, 1 May 2012 14:27:57 GMT (21kb) Title: Elliptic curves with a given number of points over finite fields Authors: Chantal David and Ethan Smith Categories: math.NT Comments: A few minor correction have been made, most notably is the correction of some of the factors which define the function K(N) \\ ( http://arxiv.org/abs/1108.3539 , 21kb) ------------------------------------------------------------------------------ \\ arXiv:1109.1550 replaced with revised version Tue, 1 May 2012 16:16:35 GMT (27kb) Title: The Yang-Mills flow and the Atiyah-Bott formula on compact Kahler manifolds Authors: Adam Jacob Categories: math.DG Comments: 34 pages. We simplify the proof of Theorem 1. The new proof is shorter and much more direct. The main result is unchanged \\ ( http://arxiv.org/abs/1109.1550 , 27kb) ------------------------------------------------------------------------------ \\ arXiv:1110.3164 replaced with revised version Tue, 1 May 2012 12:24:45 GMT (16kb) Title: Interpreting Dirac variables in terms of the Hilbert space of gauge-invariant and Poincare-covariant states Authors: L.D Lantsman Categories: math-ph math.MP Comments: 17 pages, the wrong conclusion about Dirac variables is deleted \\ ( http://arxiv.org/abs/1110.3164 , 16kb) ------------------------------------------------------------------------------ \\ arXiv:1110.4019 replaced with revised version Tue, 1 May 2012 12:03:57 GMT (6kb) Title: Existence and classifiction of radial solutions of a nonlinear nonautonomous Dirichlet problem Authors: Mohamed Rouaki Categories: math.AP math.CA \\ ( http://arxiv.org/abs/1110.4019 , 6kb) ------------------------------------------------------------------------------ \\ arXiv:1110.6654 replaced with revised version Tue, 1 May 2012 00:05:21 GMT (86kb,D) Title: Pointwise Relations between Information and Estimation in Gaussian Noise Authors: Kartik Venkat, Tsachy Weissman Categories: cs.IT math.IT Comments: 31 pages, 2 figures, submitted to IEEE Transactions on Information Theory \\ ( http://arxiv.org/abs/1110.6654 , 86kb) ------------------------------------------------------------------------------ \\ arXiv:1111.3171 replaced with revised version Tue, 1 May 2012 17:38:50 GMT (30kb) Title: Explicit renaming of bound variables Authors: George Cherevichenko Categories: math.LO Comments: expanded list of references \\ ( http://arxiv.org/abs/1111.3171 , 30kb) ------------------------------------------------------------------------------ \\ arXiv:1111.6237 replaced with revised version Tue, 1 May 2012 14:43:49 GMT (143kb) Title: Fast Algorithms for Sparse Recovery with Perturbed Dictionary Authors: Xuebing Han, Hao Zhang, Gang Li Categories: cs.IT math.IT \\ ( http://arxiv.org/abs/1111.6237 , 143kb) ------------------------------------------------------------------------------ \\ arXiv:1111.7123 replaced with revised version Tue, 1 May 2012 17:10:10 GMT (18kb) Title: Multivariate truncated moments problems and maximum entropy Authors: Calin-Grigore Ambrozie Categories: math.FA MSC-class: 44A60 (Primary) 49J99 (Secondary) \\ ( http://arxiv.org/abs/1111.7123 , 18kb) ------------------------------------------------------------------------------ \\ arXiv:1111.7282 (*cross-listing*) replaced with revised version Tue, 1 May 2012 18:48:06 GMT (1007kb,D) Title: Conformal Smectics and their Many Metrics Authors: Gareth P. Alexander, Randall D. Kamien, and Ricardo A. Mosna Categories: cond-mat.soft cond-mat.stat-mech math-ph math.MP Comments: 5 pages, figures included \\ ( http://arxiv.org/abs/1111.7282 , 1007kb) ------------------------------------------------------------------------------ \\ arXiv:1112.2648 replaced with revised version Tue, 1 May 2012 13:22:59 GMT (357kb) Title: Electronic Structure of Superheavy Atoms. Revisited Authors: D. M. Gitman, A. D. Levin, I. V. Tyutin, and B. L. Voronov Categories: math-ph math.MP quant-ph Comments: 4 pages 3 figures \\ ( http://arxiv.org/abs/1112.2648 , 357kb) ------------------------------------------------------------------------------ \\ arXiv:1112.4553 replaced with revised version Tue, 1 May 2012 01:30:24 GMT (771kb,D) Title: Cooperative Algorithms for MIMO Amplify-and-Forward Relay Networks Authors: Kien T. Truong, Philippe Sartori, and Robert W. Heath Jr Categories: cs.IT math.IT Comments: submitted to IEEE Transactions on Signal Processing in December 2011, revised in April 2012 \\ ( http://arxiv.org/abs/1112.4553 , 771kb) ------------------------------------------------------------------------------ \\ arXiv:1201.1032 replaced with revised version Tue, 1 May 2012 10:56:18 GMT (169kb) Title: Memory Elements: A Paradigm Shift in Lagrangian Modeling of Electrical Circuits Authors: Dimitri Jeltsema Categories: math.DS physics.class-ph \\ ( http://arxiv.org/abs/1201.1032 , 169kb) ------------------------------------------------------------------------------ \\ arXiv:1201.2906 (*cross-listing*) replaced with revised version Tue, 1 May 2012 14:42:41 GMT (19kb) Title: Quantum polar codes for arbitrary channels Authors: Mark M. Wilde and Joseph M. Renes Categories: quant-ph cs.IT math.IT Comments: 9 pages, submission to the 2012 International Symposium on Information Theory (ISIT 2012), Boston, MA, USA; v2: minor changes and accepted for conference \\ ( http://arxiv.org/abs/1201.2906 , 19kb) ------------------------------------------------------------------------------ \\ arXiv:1201.5232 replaced with revised version Tue, 1 May 2012 16:01:47 GMT (17kb) Title: Problems and Conjectures in Matrix and Operator Inequalities Authors: K. M. R. Audenaert and F. Kittaneh Categories: math.FA Comments: 18 pages; v2: omission of first author's name rectified; v3: section 2 amended on the basis of recent results MSC-class: 15A60 \\ ( http://arxiv.org/abs/1201.5232 , 17kb) ------------------------------------------------------------------------------ \\ arXiv:1201.5497 replaced with revised version Tue, 1 May 2012 12:29:38 GMT (53kb) Title: Bosonic Loop Diagrams as Perturbative Solutions of the Classical Field Equations in $\phi^4$-Theory Authors: Felix Finster, J\"urgen Tolksdorf Categories: math-ph hep-th math.AP math.MP Comments: 37 pages, LaTeX, 6 figures, Section 3.3 expanded, Section 4.4 added (published version) \\ ( http://arxiv.org/abs/1201.5497 , 53kb) ------------------------------------------------------------------------------ \\ arXiv:1202.0518 (*cross-listing*) replaced with revised version Tue, 1 May 2012 14:34:32 GMT (16kb) Title: Explicit capacity-achieving receivers for optical communication and quantum reading Authors: Mark M. Wilde, Saikat Guha, Si-Hui Tan, and Seth Lloyd Categories: quant-ph cs.IT math.IT Comments: 7 pages, submission to the 2012 International Symposium on Information Theory (ISIT 2012), Boston, MA, USA; v2: Accepted \\ ( http://arxiv.org/abs/1202.0518 , 16kb) ------------------------------------------------------------------------------ \\ arXiv:1202.0871 replaced with revised version Tue, 1 May 2012 17:30:23 GMT (379kb,D) Title: Channel Capacity under General Nonuniform Sampling Authors: Yuxin Chen, Yonina C. Eldar, and Andrea J. Goldsmith Categories: cs.IT math.IT Comments: 5 pages, accepted to IEEE International Symposium on Information Theory (ISIT), 2012 \\ ( http://arxiv.org/abs/1202.0871 , 379kb) ------------------------------------------------------------------------------ \\ arXiv:1202.2687 replaced with revised version Tue, 1 May 2012 17:09:07 GMT (114kb,D) Title: Worst-Case Additive Noise in Wireless Networks Authors: Ilan Shomorony and A. Salman Avestimehr Categories: cs.IT math.IT \\ ( http://arxiv.org/abs/1202.2687 , 114kb) ------------------------------------------------------------------------------ \\ arXiv:1202.4539 replaced with revised version Mon, 30 Apr 2012 20:13:38 GMT (36kb) Title: On some open problems in Diophantine approximation Authors: Nikolay G. Moshchevitin Categories: math.NT Comments: Submitted to FAOM MSC-class: 11J99 \\ ( http://arxiv.org/abs/1202.4539 , 36kb) ------------------------------------------------------------------------------ \\ arXiv:1204.0139 replaced with revised version Tue, 1 May 2012 02:01:33 GMT (6kb) Title: A game generalizing Hall's theorem Authors: Landon Rabern Categories: math.CO Comments: minor edit \\ ( http://arxiv.org/abs/1204.0139 , 6kb) ------------------------------------------------------------------------------ \\ arXiv:1204.0699 replaced with revised version Tue, 1 May 2012 07:49:41 GMT (34kb,D) Title: Logarithmic structures on K-theory spectra Authors: Steffen Sagave Categories: math.AT math.KT Comments: v2: exposition improved; 29 pages MSC-class: Primary 55P43, Secondary 14F10, 55P47 \\ ( http://arxiv.org/abs/1204.0699 , 34kb) ------------------------------------------------------------------------------ \\ arXiv:1204.3248 replaced with revised version Tue, 1 May 2012 11:32:14 GMT (0kb,I) Title: Harmonic Sections of Dirac Bundles Authors: Simone Farinelli Categories: math.DG math.FA Comments: This paper has been withdrawn by the author due to a crucial error in the proof of lemma 4.2 \\ ( http://arxiv.org/abs/1204.3248 , 0kb) ------------------------------------------------------------------------------ \\ arXiv:1204.3418 replaced with revised version Tue, 1 May 2012 15:42:09 GMT (9kb) Title: An Araki-Lieb-Thirring inequality for geometrically concave and geometrically convex functions Authors: Koenraad M. R. Audenaert Categories: math.FA Comments: 11 pages; v2: Necessity proof corrected, condition added that dom(f) should contain 0 MSC-class: 15A60 \\ ( http://arxiv.org/abs/1204.3418 , 9kb) ------------------------------------------------------------------------------ \\ arXiv:1204.3867 replaced with revised version Mon, 30 Apr 2012 23:24:31 GMT (30kb) Title: Sobolev Differentiable Stochastic Flows of SDE`s with Measurable Drift and Applications Authors: Salah-Eldin A. Mohammed, Torstein Nilssen, Frank Proske Categories: math.PR Comments: 37 pages. Another application to stochastic transport equations is included (Section 3) in the paper. Therefore the title of the article and the introduction is changed. Corollary 13 is now formulated for higher order moments MSC-class: 2000: 60H10, 60H15, 34A36 \\ ( http://arxiv.org/abs/1204.3867 , 30kb) ------------------------------------------------------------------------------ \\ arXiv:1204.4921 replaced with revised version Tue, 1 May 2012 15:14:33 GMT (186kb,D) Title: Doubly periodic self-translating surfaces for the mean curvature flow Authors: Xuan Hien Nguyen Categories: math.DG Comments: corrected typos and added figures. 8 pages, 2 figures \\ ( http://arxiv.org/abs/1204.4921 , 186kb) ------------------------------------------------------------------------------ \\ arXiv:1204.6100 replaced with revised version Mon, 30 Apr 2012 23:59:18 GMT (1569kb) Title: On the Overhead of Interference Alignment: Training, Feedback, and Cooperation Authors: Omar El Ayach, Angel Lozano, and Robert W. Heath Jr Categories: cs.IT math.IT Comments: 20 pages, 9 figures, submitted to IEEE Transactions on Wireless Communications \\ ( http://arxiv.org/abs/1204.6100 , 1569kb) ------------------------------------------------------------------------------ \\ arXiv:1204.6402 replaced with revised version Tue, 1 May 2012 08:59:46 GMT (36kb) Title: On the Rayleigh-Taylor instability for incompressible viscous magnetohydrodynamic equations Authors: Fei Jiang, Song Jiang and Yanjin Wang Categories: math.GM math.AP Comments: 34 pages. arXiv admin note: substantial text overlap with arXiv:0911.4703, arXiv:0911.4098 by other authors \\ ( http://arxiv.org/abs/1204.6402 , 36kb) ------------------------------------------------------------------------------ \\ arXiv:1204.6425 replaced with revised version Tue, 1 May 2012 12:21:19 GMT (19kb) Title: The Deformation of Poincar\'e Subgroups Concerning Very Special Relativity Authors: Lei Zhang and Xun Xue Categories: math-ph math.MP Comments: 21 pages, no figures \\ ( http://arxiv.org/abs/1204.6425 , 19kb) ------------------------------------------------------------------------------ \\ arXiv:1204.6526 replaced with revised version Tue, 1 May 2012 12:43:27 GMT (18kb) Title: The Perfect Local $ Tb$ Theorem and Twisted Martingale Transforms Authors: Michael T. Lacey and Antti V. V\"ah\"akangas Categories: math.CA Comments: 12 pages v2: typos corrected in section 5 \\ ( http://arxiv.org/abs/1204.6526 , 18kb) %%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%--- For general information on the new math archive (partitioned by keyword subject classification), see http://arXiv.org/new/math.html For subscribe options to combined math archives, e-mail To: math@arXiv.org, Subject: subscribe