random perturbations of heteroclinic attractors estimates are derived for the mean recurrence time of orbits in the neighborhood of an attracting homoclinic orbit or heteroclinic cycle in an ordinary differential equation subject to small additive random noise the theory presented is illustrated with numerical simulations of several systems including ones invariant under symmetry groups for which such heteroclinic attractors are structurally stable the physical implications of the work presented are briefly discussed

the kahler potential of abelian higgs vortices we calculate the kahler potential for the samols metric on the moduli space of abelian higgs vortices on r2 in two different ways the first uses a scaling argument the second depends on a variant of the relationship between accessory parameters and the regularized action in liouville field theory the kahler potential on the moduli space of vortices on h2 is also derived and we are led to a geometrical reinterpretation of these vortices

characterizing strong equivalence for argumentation frameworks since argumentation is an inherently dynamic process it is of great importance to understand the effect of incorporating new information into given argumentation frameworks in this work we address this issue by analyzing equivalence between argumentation frameworks under the assumption that the frameworks in question are incomplete i e further information might be added later to both frameworks simultaneously in other words instead of the standard notion of equivalence which holds between two frameworks if they possess the same extensions we require here that frameworks f and g are also equivalent when conjoined with any further framework h due to the nonmonotonicity of argumentation semantics this concept is different to but obviously implies the standard notion of equivalence we thus call our new notion strong equivalence and study how strong equivalence can be decided with respect to the most important semantics for abstract argumentation frameworks we also consider variants of strong equivalence in which we define equivalence with respect to the sets of arguments credulously or skeptically accepted and restrict strong equivalence to augmentations h where no new arguments are raised

some inequalities for the poincare metric of plane domains in this paper the poincare or hyperbolic metric and the associated distance are investigated for a plane domain based on the detailed properties of those for the particular domain open image in new window in particular another proof of a recent result of gardiner and lakic 7 is given with explicit constant this and some other constants in this paper involve particular values of complete elliptic integrals and related special functions a concrete estimate for the hyperbolic distance near a boundary point is also given from which refinements of littlewood s theorem are derived

destabilization by noise of transverse perturbations to heteroclinic cycles a simple model and an example from dynamo theory we show that transverse perturbations from structurally stable heteroclinic cycles can be destabilized by surprisingly small amounts of noise even when each individual fixed point of the cycle is stable to transverse modes a condition that favours this process is that the linearization of the dynamics in the transverse direction be characterized by a non normal matrix the phenomenon is illustrated by a simple two dimensional switching model and by a simulation of a convectively driven dynamo

a nonterminating 8 φ 7 summation for the root system c r using multiple q integrals and a determinant evaluation we establish a nonterminating 8 7 summation for the root system cr we also give some important specializations explicitly

double centralizing theorems for the alternating groups let v n be the n fold tensor product of a vector space v following i schur we consider the action of the symmetric group sn on v n by permuting coordinates in the super z2 graded case v v0 v1 a sign is added these actions give rise to the corresponding schur algebras s sn v here s sn v is compared with s an v the schur algebra corresponding to the alternating subgroup an sn while in the classical signless case these two schur algebras are the same for n large enough it is proved that in the super case where dim v0 dim v1 s an v is isomorphic to the cross product algebra s an v s sn v z2

hyperbolic 2 spheres with conical singularities accessory parameters and kahler metrics on ℳ _ 0 we show that the real valued function s on the moduli space m 0 n of pointed rational curves defined as the critical value of the liouville action functional on a hyperbolic 2 sphere with n 3 conical singularities of arbitrary orders 1 n generates accessory parameters of the associated fuchsian differential equation as their common antiderivative we introduce a family of kahler metrics on m 0 n parameterized by the set of orders a explicitly relate accessory parameters to these metrics and prove that the functions s are their kahler potentials

defeasible reasoning with variable degrees of justification the question addressed in this paper is how the degree of justification of a belief is determined a conclusion may be supported by several different arguments the arguments typically being defeasible and there may also be arguments of varying strengths for defeaters for some of the supporting arguments what is sought is a way of computing the on sum degree of justification of a conclusion in terms of the degrees of justification of all relevant premises and the strengths of all relevant reasons i have in the past defended various principles pertaining to this problem in this paper i reaffirm some of those principles but propose a significantly different final analysis specifically i endorse the weakest link principle for the computation of argument strengths according to this principle the degree of justification an argument confers on its conclusion in the absence of other relevant arguments is the minimum of the degrees of justification of its premises and the strengths of the reasons employed in the argument i reaffirm my earlier rejection of the accrual of reasons according to which two arguments for a conclusion can result in a higher degree of justification than either argument by itself this paper diverges from my earlier theory mainly in its treatment of defeaters first it argues that defeaters that are too weak to defeat an inference outright may still diminish the strength of the conclusion second in the past i have also denied that multiple defeaters can result in the defeat of an argument that is not defeated by any of the defeaters individually in this paper i urge that there are compelling examples that support a limited version of this collaborative defeat the need to accommodate diminishers and collaborative defeat has important consequences for the computation of degrees of justification the paper proposes a characterization of degrees of justification that captures the various principles endorsed and constructs an algorithm for computing them

a defeasible reasoning model of inductive concept learning from examples and communication this paper introduces a logical model of inductive generalization and specifically of the machine learning task of inductive concept learning icl we argue that some inductive processes like icl can be seen as a form of defeasible reasoning we define a consequence relation characterizing which hypotheses can be induced from given sets of examples and study its properties showing they correspond to a rather well behaved non monotonic logic we will also show that with the addition of a preference relation on inductive theories we can characterize the inductive bias of icl algorithms the second part of the paper shows how this logical characterization of inductive generalization can be integrated with another form of non monotonic reasoning argumentation to define a model of multiagent icl this integration allows two or more agents to learn in a consistent way both from induction and from arguments used in the communication between them we show that the inductive theories achieved by multiagent induction plus argumentation are sound i e they are precisely the same as the inductive theories built by a single agent with all data

twice punctured hyperbolic sphere with a conical singularity and generalized elliptic integral we describe in terms of generalized elliptic integrals the hyperbolic metric of the twice punctured sphere with one conical singularity of prescribed order we also give several monotonicity properties of the metric and a couple of applications

turan type inequalities for generalized complete elliptic integrals in this paper our aim is to establish some turan type inequalities for gaussian hypergeometric functions and for generalized complete elliptic integrals these results complete the earlier result of p turan proved for legendre polynomials moreover we show that there is a close connection between a turan type inequality and a sharp lower bound for the generalized complete elliptic integral of the first kind at the end of this paper we prove a recent conjecture of t sugawa and m vuorinen related to estimates of the hyperbolic distance of the twice punctured plane

metrics with conical singularities on the sphere and sharp extensions of the theorems of landau and schottky an explicit formula for the generalized hyperbolic metric on the thrice punctured sphere mathbb p backslash z 1 z 2 z 3 with singularities of order j 1 at zj is obtained in all possible cases 1 2 3 2 the existence and uniqueness of such a metric was proved long time ago by picard j reine angew math 130 243 258 1905 and heins nagoya math j 21 1 60 1962 while explicit formulas for the cases 1 2 1 were given earlier by agard ann acad sci fenn ser a i 413 1968 and recently by anderson et al math z to appear doi 10 1007 s00209 009 0560 5 we also establish precise and explicit lower bounds for the generalized hyperbolic metric this extends work of hempel j lond math soc ii ser 20 435 445 1979 and minda complex var 8 129 144 1987 as applications sharp versions of landau and schottky type theorems for meromorphic functions are obtained

local conformal structure of liouville quantum gravity liouville conformal field theory lcft is an essential building block of polyakov s formulation of non critical string theory moreover scaling limits of statistical mechanics models on planar maps are believed by physicists to be described by lcft a rigorous probabilistic formulation of lcft based on a path integral formulation was recently given by the present authors and f david in cite dkrv in the present work we prove the validity of the conformal ward identities and the belavin polyakov zamolodchikov bpz differential equations of order 2 for the correlation functions of lcft this initiates the program started in the seminal work of belavin polyakov zamolodchikov cite bpz in a probabilistic setup for a non trivial conformal field theory we also prove several celebrated results on lcft in particular an explicit formula for the 4 point correlation functions with insertion of a second order degenerate field leading to a rigorous proof of a non trivial functional relation on the 3 point structure constants derived earlier in the physics literature by teschner cite tesc the proofs are based on exact identities which rely on the underlying gaussian structure of lcft combined with estimates from the theory of critical gaussian multiplicative chaos and a careful analysis of singular integrals beurling transforms and generalizations as a by product we give bounds on the correlation functions when two points collide making rigorous certain predictions from physics on the so called operator product expansion of lcft

pseudospectra of linear operators if a matrix or linear operator a is far from normal its eigenvalues or more generally its spectrum may have little to do with its behavior as measured by quantities such as an or exp ta more may be learned by examining the sets in the complex plane known as the pseudospectra of a defined by level curves of the norm of the resolvent zi a 1 five years ago the author published a paper that presented computed pseudospectra of thirteen highly nonnormal matrices arising in various applications since that time analogous computations have been carried out for differential and integral operators this paper a companion to the earlier one presents ten examples each chosen to illustrate one or more mathematical or physical principles

stochastic analysis of subcritical amplification of magnetic energy in a turbulent dynamo we present and analyze a simpli ed stochastic dynamo model which is designed to assess the in2uence of additive and multiplicative noises non normality of dynamo equation and nonlinearity of the e4ect and turbulent di4usivity on the generation of a large scale magnetic eld in the subcritical case our model incorporates random 2uctuations in the parameter and additive noise arising from the small scale 2uctuations of magnetic and turbulent velocity elds we show that the noise e4ects along with non normality can lead to the stochastic ampli cation of the magnetic eld even in the subcritical case the criteria for the stochastic instability during the early kinematic stage are established and the critical value for the intensity of multiplicative noise due to 2uctuations is found we obtain numerical solutions of nonlinear stochastic differential equations and nd the series of phase transitions induced by random 2uctuations in the parameter c

prescribing curvature on open surfaces in this article we study the problem sometimes called the berger nirenberg problem of prescribing the curvature on a riemann surface that is on an oriented surface equipped with a conformal class of riemannian metrics

new combinatorial interpretations of ramanujan s partition congruences mod 5 7 and 11 soit p n le nombre de partitions non restreintes de n on donne de nouvelles interpretations combinatoires des congruences p 5n 4 p 7n 5 et p 11n 6 0 mod 5 7 et 11 respectivement

noise and slow fast dynamics in a three wave resonance problem recent research on the dynamics of certain fluid dynamical instabilities shows that when there is a slow invariant manifold subject to fast timescale instability the dynamics are extremely sensitive to noise the behaviour of such systems can be described in terms of a one dimensional map and previous work has shown how the effect of noise can be modelled by a simple adjustment to the map here we undertake an in depth investigation of a particular set of equations using the methods of stochastic integration we confirm the prediction of the earlier studies that the noise becomes important when mu log epsilon o 1 where mu is the small timescale ratio and epsilon is the noise level in addition we present detailed information about the statistics of the solution when the noise is a dominant effect the analytical results show excellent agreement with numerical simulations

a de giorgi nash type theorem for time fractional diffusion equations we study the regularity of weak solutions to linear time fractional diffusion equations in divergence form of arbitrary time order alpha in 0 1 the coefficients are merely assumed to be bounded and measurable and they satisfy a uniform parabolicity condition our main result is a de giorgi nash type theorem which gives an interior holder estimate for bounded weak solutions in terms of the data and the l infty bound of the solution the proof relies on new a priori estimates for time fractional problems and uses de giorgi s technique and the method of non local growth lemmas which has been introduced recently in the context of nonlocal elliptic equations involving operators like the fractional laplacian

liouville theory and uniformization of four punctured sphere a few years ago zamolodchikov and zamolodchikov proposed an expression for the four point classical liouville action in terms of the three point actions and the classical conformal block nucl phys b 477 577 1996 in this paper we develop a method of calculating the uniformizing map and the uniformizing group from the classical liouville action on n punctured sphere and discuss the consequences of zamolodchikovs conjecture for an explicit construction of the uniformizing map and the uniformizing group for the sphere with four punctures

moduli spaces of weighted pointed stable curves abstract a weighted pointed curve consists of a nodal curve and a sequence of marked smooth points each assigned a number between zero and one a subset of the marked points may coincide if the sum of the corresponding weights is no greater than one we construct moduli spaces for these objects using methods of the log minimal model program and describe the induced birational morphisms between moduli spaces as the weights are varied in the genus zero case we explain the connection to geometric invariant theory quotients of points in the projective line and to compactifications of moduli spaces studied by kapranov keel and losev manin

some inequalities for the q beta and the q gamma functions via some q integral inequalities some new inequalities for the q gamma the q beta and the q analogue of the psi functions are established via some q integral inequalities

variation of cone metrics on riemann surfaces we discuss the variational properties of the unique conical metric of constant curvature 1 associated to a compact riemann surface together with a weighted divisor 2005 elsevier inc all rights reserved

on the merging of dung s argumentation systems in this paper the problem of deriving sensible information from a collection of argumentation systems coming from different agents is addressed the underlying argumentation theory is dung s one each argumentation system gives both a set of arguments and the way they interact i e attack or non attack according to the corresponding agent the inadequacy of the simple yet appealing method which consists in voting on the agents selected extensions calls for a new approach to this purpose a general framework for merging argumentation systems from dung s theory of argumentation is presented the objective is achieved through a three step process first each argumentation system is expanded into a partial system over the set of all arguments considered by the group of agents reflecting that some agents may easily ignore arguments pointed out by other agents as well as how such arguments interact with her own ones then merging is used on the expanded systems as a way to solve the possible conflicts between them and a set of argumentation systems which are as close as possible to the whole profile is generated finally voting is used on the selected extensions of the resulting systems so as to characterize the acceptable arguments at the group level

an improved sectional anosov closing lemma we prove that all nonwandering points of a sectional anosov flow on a compact 3 manifold can be approximated by periodic points or by points for which the omega limit set is a singularity this improves the closing lemma in morales mich math j 56 1 29 53 2008 we also describe a sectional anosov flow for which the recurrent points are not dense in the nonwandering set

comparing poincare densities however there is no formula for the poincare density pn of a general plane domain q and so one must resort to estimates many research articles have been devoted to finding and working with such estimates see for example 4 5 15 19 24 and 25 the first tool to establish such estimates is schwarz s lemma which says that every holomorphic map is a contraction with respect to the poincare metric that is ps f ldf i pd z idzl for any holomorphic map f from a riemann surface d to another riemann surface q applying this lemma

a logic based theory of deductive arguments abstract we explore a framework for argumentation based on classical logic in which an argument is a pair where the first item in the pair is a minimal consistent set of formulae that proves the second item which is a formula we provide some basic definitions for arguments and various kinds of counter arguments defeaters this leads us to the definition of canonical undercuts which we argue are the only defeaters that we need to take into account we then motivate and formalise the notion of argument trees and argument structures which provide a way of exhaustively collating arguments and counter arguments we use argument structures as the basis of our general proposal for argument aggregation there are a number of frameworks for modelling argumentation in logic they incorporate formal representation of individual arguments and techniques for comparing conflicting arguments in these frameworks if there are a number of arguments for and against a particular conclusion an aggregation function determines whether the conclusion is taken to hold we propose a generalisation of these frameworks in particular our new framework makes it possible to define aggregation functions that are sensitive to the number of arguments for or against we compare our framework with a number of other types of argument systems and finally discuss an application in reasoning with structured news reports

prescribing curvature on compact surfaces with conical singularities we study the berger nirenberg problem on surfaces with conical singularities i e we discuss conditions under which a function on a riemann surface is the gaussian curvature of some conformal metric with a prescribed set of singularities of conical types

estimation of the hyperbolic metric by using the punctured plane let rho omega denote the density of the hyperbolic metric for a domain in the extended complex plane overline mathbb c we prove the inequality rho omega z leq c rm sup rho mathbb c setminus a b z a b in partial omega quad z in omega omega subset mathbb c with c 8 27 the inequality was proved by sugawa and vuorinen with c 10 33 the proof uses monotonicity properties of the hyperbolic metric for the thrice punctured extended plane gardiner and lakic proved the inequality rho omega z leq c 1 rm sup rho overline mathbb c setminus a b c z a b c in partial omega quad z in omega with an unspecified constant c1 we show that the best constant 1 in this inequality is between 3 25 and 8 27 we also prove a related conjecture formulated by sugawa and vuorinen

transverse bifurcations of homoclinic cycles abstract homoclinic cycles exist robustly in dynamical systems with symmetry and may undergo various bifurcations not all of which have an analog in the absence of symmetry we analyze such a bifurcation the transverse bifurcation and uncover a variety of phenomena that can be distinguished representation theoretically for example exponentially flat branches of periodic solutions a typical feature of bifurcation from homoclinic cycles occur for some but not all representations of the symmetry group our study of transverse bifurcations is motivated by the problem of intermittent dynamos in rotating convection