p torsion monodromy representations of elliptic curves over geometric function fields given a complex quasiprojective curve b and a nonisotrivial familye of elliptic curves over b the p torsione p yields a monodromy representation e p 1 b gl2 fp we prove that if e p e0 p thene ande 0 are isogenous provided p is larger than a constant depending only on the gonality of b this can be viewed as a function eld analog of the frey mazur conjecture which states that an elliptic curve over q is determined up to isogeny by its p torsion galois representation for p 17 the proof relies on hyperbolic geometry and is therefore only applicable in characteristic 0

lagrangians of physics and the game of fisher information transfer the lagrangians of physics arise out of a mathematical game between a smart measurer and nature personified by a demon each contestant wants to maximize his level of fisher information i the game is zero sum by conservation of information in the closed system the payoff of the game introduces a variational principle extreme physical information epi which fixes both the lagrangian and the physical constant of each scenario the epi approach provides an understanding of the relationship between measurement and physical law epi also defines a prescription for constructing lagrangians the prior knowledge required for this purpose is a rule of symmetry or conservation that implies a unitary transformation for which i remains invariant as an example when applied to the smart measurement of the space time coordinate of a particle the symmetry used is that between position time space and momentum energy space then the unitary transformation is the fourier one and epi derives the following the equivalence of energy momentum and mass the constancy of planck s parameter h and the lagrangian that implies both the klein gordon equation and the dirac equation of quantum mechanics

uniform bounds for weil petersson curvatures we find bounds for weil petersson holomorphic sectional curvature and the weil petersson curvature operator in several regimes that do not depend on the topology of the underlying surface among other results we show that the minimal weil petersson holomorphic sectional curvature of a sufficiently thick hyperbolic surface is comparable to 1 independently of the genus this provides a counterexample to some suggestions that the weil petersson metric becomes asymptotically flat as the genus g goes to infinity in some loci in teichmuller space adopting a different perspective on curvature we also show that the minimal most negative eigenvalue of the curvature operator at any point in the teichmuller space teich sg of a closed surface sg of genus g is uniformly bounded away from zero restricting to a thick part of teich sg we show that the minimal eigenvalue is uniformly bounded below by an explicit constant which does not depend on the topology of the surface but only on the given bound on injectivity radius

rigorous properties and uncertainty like relationships on product complexity measures application to atomic systems most of research on complexities and the corresponding conclusions have been obtained by numerically quantifying their values and little attention has been paid to their theoretical properties and the exact meaning within an statistical framework valid for any arbitrary n dimensional distribution in the present work different product complexities constructed as a product of two relevant information quantities associated to the concepts of uncertainty and localization are investigated different results on product complexities such as rigorous bounds uncertainty like inequalities relationships among themselves and also statistical interpretations are given for the sake of completeness some of these analytical results on product complexities are numerically checked for the one particle densities of atomic systems in both conjugated spaces

stable systolic inequalities and cohomology products multiplicative relations in the cohomology ring of a manifold impose constraints upon its stable systoles given a compact riemannian manifold x g its real homology h x is naturally endowed with the stable norm briefly if h hk x then the stable norm of h is the infimum of the riemannian k volumes of real cycles representing h the stable k systole is the minimum of the stable norm over nonzero elements in the lattice of integral classes in hk x relying on results from the geometry of numbers due to w banaszczyk and extending work by m gromov and j hebda we prove metric independent inequalities for products of stable systoles where the product can be as long as the real cup length of x 2003 wiley periodicals inc

eigenvalue spread criteria in the particle swarm optimization algorithm for solving of constraint parametric problems this paper presents an alternative and efficient method for solving a class of constraint parametric optimization problems using particle swarm optimization algorithm pso in this paper for the first time pso is used for solving convex parametric programming but pso must be adaptive for doing it so for obtaining particles velocities adaptation weight and velocity boundaries in the updating of velocities are calculated in the recursive form computational complexity of the pso algorithm is decreased based on uniformity of population of particles the uniformity of which is obtained using eigenvalue spread of covariance of population two simple examples are provided for showing the efficiency of the proposed method for solving these examples eigenvalue spread criteria applied in the pso algorithm decrease 78 of computations

a new nonlinear neural network for solving a class of constrained parametric optimization problems the paper deals with convex parametric programming problems in this paper convex parametric programming transform to a neural network model and then we solve neural network model with one of numerical methods finally simple numerical examples are provided for the sake of illustration

behavior of geodesic length functions on teichmuller space let t be the teichmuller space of marked genus g n punctured riemann surfaces with its bordification t the augmented teichmuller space of marked riemann surfaces with nodes abi77 ber74 pro vided with the wp metric t is a complete cat 0 metric space dw03 wol03 yam04 an invariant of a marked hyperbolic struc ture is the lengthof the geodesic in a free homotopy class a basic feature of teichmuller theory is the interplay of two dimensional hyperbolic geometry weil petersson wp geometry and the behavior of geodesic length functions our goal is to develop the understanding of the intrinsic local wp geometry through a study of the gradient and hessian of geodesic length functions considerations include ex pansions for the wp pairing of gradients expansions for the hessian and covariant derivative comparability models for the wp metric as well as the behavior of wp geodesics including a description of the alexandrov tangent cone at the augmentation approximations and applications for geodesics close to the augmentation are developed an application for fixed points of group actions is described bound ing configurations and functions on the hyperbolic plane is basic to our approach considerations include analyzing the orbit of a dis crete group of isometries and bounding sums of the inverse square exponential distance

maximum entropy and lacunary stieltjes moment problem the lacunary stieltjes moment problem in the framework of the maximum entropy approach is considered a proof for the existence conditions of the solution is provided

the existence conditions for maximum entropy distributions having prescribed the first three moments the criteria for existence of maximum entropy distributions having prescribed the first three moments in a semi infinite range are given some relationships between moments and lagrange multipliers are also presented

fisher based thermodynamics its legendre transform and concavity properties it is shown that the legendre transform structure of thermodynamics can be replicated without any change if one replaces the entropy s by fisher s information measure i also the important thermodynamic property of concavity is shown to be obeyed by i by this use of the fisher information measure we develop a thermodynamics that seems to be able to treat equilibrium and nonequilibrium situations in a manner entirely similar to the conventional one

seshadri constants and periods of polarized abelian varieties the purpose of this paper is to study the seshadri constants of abelian varieties consider a polarized abelian variety a l of dimension g over the field of complex numbers one can associate to a l a real number e a l its seshadri constant which in effect measures how much of the positivity of l can be concentrated at any given point of a the number e a l can be defined as the rate of growth in k of the number of jets that one can specify in the linear series oa kl alternatively one considers the blow up f x blx x x of x at a point x with exceptional divisor e x over x and defines e a l def sup e r f l ee is nef

differential escort transformations and the monotonicity of the lmc renyi complexity measure abstract escort distributions have been shown to be very useful in a great variety of fields ranging from information theory nonextensive statistical mechanics till coding theory chaos and multifractals in this work we give the notion and the properties of a novel type of escort density the differential escort densities which have various advantages with respect to the standard ones we highlight the behavior of the differential shannon renyi and tsallis entropies of these distributions then we illustrate their utility to prove the monotonicity property of the lmc renyi complexity measure and to study the behavior of general distributions in the two extreme cases of minimal and very high lmc renyi complexity finally this transformation allows us to obtain the tsallis q exponential densities as the differential escort transformation of the exponential density

characterization of jacobian varieties in terms of soliton equations pour dans le demi espace superieur de siegel h g soit x c g z g z g la variete abelienne principalement polarisee correspondante et soit z z m e z gexp 2 i t mz i t m m la fonction theta de riemann pour x les deux conditions a et b pour x sont equivalentes a 1 il existe des vecteurs a 1 a 2 a 3 c g a 1 0 et une forme quadratique q t i j 1 3 q ij t i t j q ij c tel que pour c g t t exp q t t 1 a 1 t 2 a 2 t 3 a 3 donne une solution a l equation de kadomtsev petviashvili sous la forme d hirota d 1 4 3d 2 2 4d 1 d 3 0 2 le diviseur de x est irreductible b x est isomorphe a la variete jacobienne d une courbe lisse complete de genre g sur c

on the period matrix of a riemann surface of large genus with an appendix by j h conway and n j a sloane riemann showed that a period matrix of a compact riemann surface of genusg 1 satisfies certain relations we give a further simple combinatorial property related to the length of the shortest non zero lattice vector satisfied by such a period matrix see 1 13 in particular it is shown that for large genus the entire locus of jacobians lies in a very small neighborhood of the boundary of the space of principally polarized abelian varieties

stieltjes moment problem via fractional moments stieltjes moment problem is considered to recover a probability density function from the knowledge of its infinite sequence of ordinary moments the approximate density is obtained through maximum entropy technique under the constraint of few fractional moments the latter are numerically obtained from the infinite sequence of ordinary moments and are chosen in such a way as to convey the maximum information content carried by the ordinary moments as a consequence a model with few parameters is obtained and intrinsic numerical instability is avoided it is proved that the approximate density is useful for calculating expected values and some other interesting probabilistic quantities

random construction of riemann surfaces we develop a new approach for the study of typical riemann surfaces with high genus the method that we use is the construction of random riemann surfaces from oriented cubic graphs this construction enables us to get a control over the global geometry properties of compact riemann surfaces we use the theory of random regular graphs to show that almost all such surfaces have large first eigenvalues and large cheeger constants moreover a closer analysis of the probability space of oriented cubic graphs shows that on a typical surface there is a large embedded hyperbolic ball

tsallis entropy maximization procedure revisited abstract the proper way of averaging is an important question with regards to tsallis thermostatistics three different procedures have been thus far employed in the pertinent literature the third one i e the tsallis mendes plastino tmp physica a 261 1998 534 normalization procedure exhibits clear advantages with respect to earlier ones in this work we advance a distinct from the tmp one way of handling the lagrange multipliers involved in the extremization process that leads to tsallis statistical operator it is seen that the new approach considerably simplifies the pertinent analysis without losing the beautiful properties of the tsallis mendes plastino formalism

minimal vectors in the second exterior power of a lattice w x in c we studied the rankin k invariants which were defined by rankin w x in r as a natural generalization of the classical hermite invariant of a lattice in the following way let l be a lattice of maximal rank in an n dimensional euclidean space e we denote by d l the minimal k determinant of k dimensional sublattices of l and put g l s k k r n d l r det l the upper bound of g l for all lattices l in e is k k denoted by g n k it is readily verified that the k dimensional sublattice spanned by a k tuple of linearly independent vectors x x in l depends only on its 1 k image x n n x in the k th exterior power h l moreover h e 1 k inherits a canonical euclidean structure from the original scalar product on e which is defined for split multivectors that is vectors which can be written as x n n x by 1 k

logarithmic growth of systole of arithmetic riemann surfaces along congruence subgroups we apply a study of orders in quaternion algebras to the differential geometry of riemann surfaces the least length of a closed geodesic on a hyperbolic surface is called its systole and denoted sys 1 p buser and p sarnak constructed riemann surfaces x whose systole behaves logarithmically in the genus g x the fuchsian groups in their examples are principal congruence subgroups of a fixed arithmetic group with rational trace field we generalize their construction to principal congruence subgroups of arbitrary arithmetic surfaces the key tool is a new trace estimate valid for an arbitrary ideal in a quaternion algebra we obtain a particularly sharp bound for a principal congruence tower of hurwitz surfaces pch namely the 4 3bound sys 1 xpch 4 log g xpch similar results are obtained for the systole of hyperbolic 3 manifolds relative to their simplicial volume

iteration of mapping classes and limits of hyperbolic 3 manifolds let mod s be an element of the mapping class group of a surface s we classify algebraic and geometric limits of sequences q i x y i 1 of quasi fuchsian hyperbolic 3 manifolds ranging in a bers slice when has infinite order with finite order restrictions there is an essential subsurface d s so that the geometric limits have homeomorphism type s d 0 typically has pseudo anosov restrictions and d has components with negative euler characteristic these components correspond to new asymptotically periodic simply degenerate ends of the geometric limit we show there is an s 1 depending on and bounded in terms of s so that q si x y i 1 converges algebraically and geometrically and we give explicit quasi isometric models for the limits

estimation of distribution laws and physical laws by a principle of extremized physical information abstract a new method of estimating physical probability laws is given this arises from a new form of information which in turn follows from four physically based axioms extremization of this physical information gives rise to the required probability laws as verifications of the approach the following statistical and non statistical laws of physics are derived the complex schrodinger and helmholtz wave equations relativistic quantum mechanics in the klein gordon dirac and weyl pauli formulations the boltzmann energy and maxwell boltzmann velocity distributions the lorentz transformation group of special relativity and maxwell s equations also derived are inequalities defining a class of uncertainty principles e g heisenberg s finally the einstein equations of motion but not the fields of general relativity are derived along with an equivalence d i d mc 2 between information flow rate and matter energy

a new nonlinear neural network for solving convex nonlinear programming problems this paper presents a new recurrent neural network for solving convex nonlinear programming problems the new model is simpler and more intuitive than existing models and converge very fast to exact solution of the original problem we show that this new model is asymptotically stable

on the existence and characterization of the maxent distribution under general moment inequality constraints a broad set of sufficient conditions that guarantees the existence of the maximum entropy maxent distribution consistent with specified bounds on certain generalized moments is derived most results in the literature are either focused on the minimum cross entropy distribution or apply only to distributions with a bounded volume support or address only equality constraints the results of this work hold for general moment inequality constraints for probability distributions with possibly unbounded support and the technical conditions are explicitly on the underlying generalized moment functions an analytical characterization of the maxent distribution is also derived using results from the theory of constrained optimization in infinite dimensional normed linear spaces several auxiliary results of independent interest pertaining to certain properties of convex coercive functions are also presented

special features of the relation between fisher information and schrodinger eigenvalue equation it is well known that a suggestive relation exists that links schrodinger s equation se to the information optimizing principle based on fisher s information measure the connection entails the existence of a legendre transform structure underlying the se here we show that appeal to this structure leads to a first order differential equation for the se s eigenvalues that in certain cases can be used to obtain the eigenvalues without explicitly solving the se complying with the above mentioned equation constitutes a necessary condition to be satisfied by an energy eigenvalue we show that the general solution is unique

growth of weil petersson volumes and random hyperbolic surfaces of large genus in this paper we investigate the geometric properties of random hyperbolic surfaces of large genus we describe the relationship between the behavior of lengths of simple closed geodesics on a hyperbolic surface and properties of the moduli space of such surfaces first we study the asymptotic behavior of weil petersson volume vg n of the moduli spaces of hyperbolic surfaces of genus g with n punctures as g then we discuss basic geometric properties of a random hyperbolic surface of genus g with respect to the weil petersson measure as g

possible generalization of boltzmann gibbs statistics with the use of a quantity normally scaled in multifractals a generalized form is postulated for entropy namelys q k 1 i 1 w p i q q 1 whereq characterizes the generalization andp i are the probabilities associated withw microscopic configurations w the main properties associated with this entropy are established particularly those corresponding to the microcanonical and canonical ensembles the boltzmann gibbs statistics is recovered as theq 1 limit

factoring polynomials with rational coefficients in this paper we present a polynomial time algorithm to solve the following problem given a non zero polynomial fe q x in one variable with rational coefficients find the decomposition of f into irreducible factors in q x it is well known that this is equivalent to factoring primitive polynomials fez x into irreducible factors in z x here we call f z x primitive if the greatest common divisor of its coefficients the content of f is 1 our algorithm performs well in practice cf 8 its running time measured in bit operations is o nl2 n9 log fd3

ends of hyperbolic 3 manifolds let n h3 f be a hyperbolic 3 manifold which is homeomorphic to the interior of a compact 3 manifold we prove that n is geometrically tame as a consequence we prove that f s limit set l is either the entire sphere at infinity or has measure zero we also prove that n s geodesic flow is ergodic if and only if lf is the entire sphere at infinity department of mathematics stanford university stanford california 94305 current address department of mathematics university of michigan ann arbor michigan 48109 e mail address dick canary math lsa umich edu this content downloaded from 40 77 167 14 on wed 15 jun 2016 05 36 06 utc all use subject to http about jstor org terms

hecke algebras and cohomotopical mackey functors in this paper we define the concept of the cohomotopical mackey functor which is more general than the usual cohomological mackey functor and show that hecke algebra techniques are applicable to cohomotopical mackey functors our theory is valid for any possibly infinite discrete group some applications to topology are also given

the weil petersson metric and volumes of 3 dimensional hyperbolic convex cores we present a coarse interpretation of the weil petersson distance dwp x y between two finite area hyperbolic riemann surfaces x and y using a graph of pants decompositions introduced by hatcher and thurston the combinatorics of the pants graph reveal a connection between riemann surfaces and hyperbolic 3 manifolds conjectured by thurston the volume of the convex core of the quasi fuchsian manifold q x y with x and y in its conformal boundary is comparable to the weil petersson distance dwp x y in applications we relate the weil petersson distance to the hausdorff dimen sion of the limit set and the lowest eigenvalue of the laplacian for q x y and give a new finiteness criterion for geometric limits mathematics department university of chicago 5734 s university ave chicago il 60637 e mail address brock math uchicago edu

weil petersson volumes and intersection theory on the moduli space of curves in this paper we establish a relationship between the weil petersson volume vgin b of the moduli space mg n b of hyperbolic riemann surfaces with geodesic boundary components of lengths b bn and the intersection numbers of tauto logical classes on the moduli space mg n of stable curves as a result by using the recursive formula for vg n b obtained in 22 we derive a new proof of the virasoro constraints for a point this result is equivalent to the witten kontsevich formula 14

hyperbolic structures on 3 manifolds i deformation of acylindrical manifolds this is the first in a series of papers showing that haken manifolds have hyperbolic structures this first was published the second two have existed only in preprint form and later preprints were never completed this eprint is only an approximation to the published version which is the definitive form for part i and is provided for convenience only all references and quotations should be taken from the published version since the theorem numbering is different and not all corrections have been incorporated into the present version parts ii and iii will be made available as eprints shortly

on the q 1 2 non extensive maximum entropy distribution abstract a detailed mathematical analysis on the q 1 2 non extensive maximum entropy distribution of tsallis is undertaken the analysis is based upon the splitting of such a distribution into two orthogonal components one of the components corresponds to the minimum norm solution of the problem posed by the fulfillment of the a priori conditions on the given expectation values the remaining component takes care of the normalization constraint and is the projection of a constant onto the null space of the expectation values transformation

existence conditions and spreading properties of extreme entropy d dimensional distributions abstract the extremization of the information theoretic measures fisher information shannon entropy tsallis entropy which complementary describe the spreading of the physical states of natural systems gives rise to fundamental equations of motion and or conservation laws at times the associated extreme entropy distributions are known for some given constraints usually moments or radial expectation values in this work first we give the existence conditions of the maxent probability distributions in a d dimensional scenario where two moments not necessarily of consecutive order are known then we find general relations which involve four elements the extremized entropy the other two information theoretic measures and the variance of the extremum density in scenarios with different dimensionalities and moment constraints

extremum entrop y based heisenberg like uncertainty relations in this work we use the extremization method of various information theoretic measures fisher information shannon entropy tsallis entropy for d dimensional quantum systems which complementarily describe the spreading of the quantum states of natural systems under some given constraints usually one or two radial expectation values this variational method allows us to determine an extremum entropy distribution which is the least biased one to characterize the state among all those compatible with the known data then we use it together with the spin dependent uncertainty like relations of daubechies thakkar type as a tool to obtain relationships between the position and momentum radial expectation values of the type for d dimensional systems of n fermions with spin s the resulting uncertainty like products which take into account both spatial and spin degrees of freedom of the fermionic constituents of the system are shown to often improve the best corresponding relationships existing in the literature

maximum entropy in the problem of moments the maximum entropy approach to the solution of underdetermined inverse problems is studied in detail in the context of the classical moment problem in important special cases such as the hausdorff moment problem we establish necessary and sufficient conditions for the existence of a maximum entropy solution and examine the convergence of the resulting sequence of approximations a number of explicit illustrations are presented in addition to some elementary examples we analyze the maximum entropy reconstruction of the density of states in harmonic solids and of dynamic correlation functions in quantum spin systems we also briefly indicate possible applications to the lee yang theory of ising models to the summation of divergent series and so on the general conclusion is that maximum entropy provides a valuable approximation scheme a serious competitor of traditional pade like procedures

maxentropic solution of fractional moment problems the problem of reconstructing a function from the knowledge of a few of its moments is a special case of the problem inverting an integral transform when there are finitely many data points the classical method of maximum entropy and the method of maximum entropy in the mean are well suited to attack these problems what is interesting is that when we are free to choose the data points the choice can be made to improve the quality of the reconstruction when the method of maximum entropy is used too in this note we review how to apply these methods and compare them in a couple of examples

related aspects of positivity in riemannian geometry pour une variete de riemann on etudie le lien entre le point 0 du l 2 spectre le plus proche de zero pour l extension de friedrich d un operateur semi defini symetrique et le taux exponentiel de transition d un operateur de markoff conservant la positivite

an explicit upper bound for weil petersson volumes of the moduli spaces of punctured riemann surfaces an explicit upper bound for the weil petersson volumes of punctured riemann surfaces is obtained using penner s combinatorial integration scheme from 4 it is shown that for a fixed number of punctures n and for genus g increasing

quantum error correcting codes and 4 dimensional arithmetic hyperbolic manifolds using 4 dimensional arithmetic hyperbolic manifolds we construct some new homological quantum error correcting codes they are low density parity check codes with linear rate and distance ne their rate is evaluated via euler characteristic arguments and their distance using z2 systolic geometry this construction answers a question of zemor on cayley graphs surface codes and the limits of homological coding for quantum error correction in proceedings of second international workshop on coding and cryptology iwcc lecture notes in computer science vol 5557 2009 pp 259 273 who asked whether homological codes with such parameters could exist at all

group representations and lattices this paper began as an attempt to understand the euclidean lattices that were recently constructed using the theory of elliptic curves by elkies e and shioda shl sh2 from the point of view of group representations the main idea appears in a note of thompson th2 if one makes strong irreducibility hypotheses on a rational representation v of a finite group g then the g stable euclidean lattices in v are severely restricted unfortunately these hypotheses are rarely satisfied when v is absolutely irreducible over q but there are many examples where the ring endg v is an imaginary quadratic field or a definite quaternion algebra these representations allow us to construct some of the mordell weil lattices considered by elkies and shioda as well as some interesting even unimodular lattices that do not seem to come from the theory of elliptic curves in 1 we discuss lattices and hermitian forms on y7 and in 2 4 the strong irreducibility hypotheses we wish to make in 5 we show how our hypotheses imply the existence of a finite number up to isomorphism of euclidean z g lattices l in v with endg l a maximal order in endg v we give some examples with dim v 8 in 6 and in 7 9 discuss the invariants of l such as the dual lattice and theta function the rest of the paper is devoted to examples in most g is a finite group of lie type and v is obtained as an irreducible summand of the weil representation of g some of the representation theoretic problems left open by this paper are to find all examples of pairs g v satisfying the strong irreducibility hypotheses of 2 4 and to determine the invariants shortest nonzero vector theta function thompson series of the g lattices l so effortlessly constructed inside v

estimates of weil petersson volumes via effective divisors we study the asymptotics of the weil petersson volumes of the moduli spaces of compact riemann surfaces of genus g with n punctures for fixed n as g

legendre transform structure derived from quantum theorems abstract by recourse to i the hellmann feynman theorem and ii the virial one the information optimizing principle based on fisher s information measure uncovers a legendre transform structure associated with schrodinger s equation in close analogy with the structure that lies behind the standard thermodynamical formalism the present developments provide new evidence for the information theoretical links based on fisher s measure that exist between schrodinger s equation on the one hand and thermodynamics thermostatistics on the other hand

inferring an optimal fisher measure abstract it is well known that a suggestive relation exists that links the schrodinger equation se to the information optimizing principle based on the fisher information measure fim we explore here an approach that will allow one to infer the optimal fim compatible with a given amount of prior information without explicitly solving first the associated se this technique is based on the virial theorem and it provides analytic solutions for the physically relevant fim that which is minimal subject to the constraints posed by the prior information

a high performance neural network for solving linear and quadratic programming problems two classes of high performance neural networks for solving linear and quadratic programming problems are given we prove that the new system converges globally to the solutions of the linear and quadratic programming problems in a neural network network parameters are usually not specified the proposed models can overcome numerical difficulty caused by neural networks with network parameters and obtain desired approximate solutions of the linear and quadratic programming problems

transplantation and jacobians of sunada isospectral riemann surfaces abstract we consider relations among the jacobians of isospectral compact riemann surfaces constructed using sunada s theorem we use a simple algebraic formulation of transplantation of holomorphic 1 forms and singular 1 cycles to obtain two main results first we obtain a geometric proof of a result of prasad and rajan that sunada isospectral riemann surfaces have isogenous jacobians second we determine a relationship weaker than isogeny that holds among the jacobians of sunada isospectral riemann surfaces when the jacobians extra structure as principally polarized abelian varieties is taken into account we also show all sunada isospectral manifolds have isomorphic real cohomology algebras finally we exhibit transplantation of cycles explicitly in a concrete example of a pair of isospectral riemann surfaces constructed by brooks and tse

the diameter of the thick part of moduli space and simultaneous whitehead moves let s be a surface of genus g with p punctures with negative euler characteristic we study the diameter of the thick part of moduli space of s equipped with the teichmuller or thurston s lipschitz metric we show that the asymptotic behaviors in both metrics are of order log g p the same result also holds for the thick part of the moduli space of metric graphs of rank n equipped with the lipschitz metric the proof involves a sorting algorithm that sorts an arbitrarily labeled tree with n labels using simultaneous whitehead moves where the number of steps is of order log n as a related combinatorial problem we also compute in the appendix of this paper the asymptotic diameter of the moduli space of pants decompositions on s in the metric of elementary moves

hopfield neural networks in large scale linear optimization problems abstract hopfield neural networks and affine scaling interior point methods are combined in a hybrid approach for solving linear optimization problems the hopfield networks perform the early stages of the optimization procedures providing enhanced feasible starting points for both primal and dual affine scaling interior point methods thus facilitating the steps towards optimality the hybrid approach is applied to a set of real world linear programming problems the results show the potential of the integrated approach indicating that the combination of neural networks and affine scaling interior point methods can be a good alternative to obtain solutions for large scale optimization problems

injectivity radius and gonality of a compact riemann surface we obtain a sharp lower bound for the volumes of purely 1 dimensional complex analytic subvarieties in a geodesic tubular neighborhood of the diagonal of the cartesian product of a compact riemann surface with itself this leads to a lower bound of the seshadri number of the canonical line bundle of the cartesian product with respect to the diagonal as a consequence we obtain an upper bound for the hyperbolic injectivity radii of compact riemann surfaces of a fixed gonality in particular we obtain the limiting behavior of the gonalities of a tower of compact riemann surfaces we also give an application of our results to an invariant related to the ample cone of the symmetric product of a riemann surface

the role of constraints within generalized nonextensive statistics the gibbs jaynes path for introducing statistical mechanics is based on the adoption of a specific entropic form sand of physically appropriate constraints for instance for the usual canonical ensemble one adopts i ii ipi 1 and iii ei eigenvalues of the hamiltonian u1 internal energy equilibrium consists in optimizing s1 with regard to pi in the presence of constraints ii and iii within the recently introduced nonextensive statistics i is generalized into sq k 1 ipiq q 1 q 1 reproduces s1 ii is maintained and iii is generalized in a manner which might involve piq in the present effort we analyze the consequences of some special choices for iii and their formal and practical implications for the various physical systems that have been studied in the literature to illustrate some mathematically relevant points we calculate the specific heat respectively associated with a nondegenerate two level system as well as with the classical and quantum harmonic oscillators