topology recognition with advice in topology recognition each node of an anonymous network has to deterministically produce an isomorphic copy of the underlying graph with all ports correctly marked this task is usually unfeasible without any a priori information such information can be provided to nodes as advice an oracle knowing the network can give a possibly different string of bits to each node and all nodes must reconstruct the network using this advice after a given number of rounds of communication during each round each node can exchange arbitrary messages with all its neighbors and perform arbitrary local computations the time of completing topology recognition is the number of rounds it takes and the size of advice is the maximum length of a string given to nodes we investigate tradeoffs between the time in which topology recognition is accomplished and the minimum size of advice that has to be given to nodes we provide upper and lower bounds on the minimum size of advice that is sufficient to perform topology recognition in a given time in the class of all graphs of size n and diameter d n for any constant 1 in most cases our bounds are asymptotically tight

renaming in an asynchronous environment this paper is concerned with the solvability of the problem of processor renaming in unreliable completely asynchronous distributed systems fischer et al prove in 8 that nontrivial consensus cannot be attained in such systems even when only a single benign processor failure is possible in contrast this paper shows that problems of processor renaming can be solved even in the presence of up to t n 2 faulty processors contradicting the widely held belief that no nontrivial problem can be solved in such a system the problems deal with renaming processors so as to reduce the size of the initial name space when only uniqueness of the new names is required we present a lower bound of n 1 on the size of the new name space and a renaming algorithm that establishes an upper bound on n t if the new names are required also to preserve the original order a tight bound of 2 n t 1 1 is obtained

the existence of non minimal solutions of the yang mills higgs equations over r 3 with arbitrary positive coupling constant this paper proves the existence of a non trivial critical point of thesu 2 yang mills higgs functional onr3 with arbitrary positive coupling constant the critical point lies in the zero monopole class but has action bounded strictly away from zero

on talker verification via orthogonal parameters the method of orthogonal parameters uses the eigenvalues and eigenvectors of the matrix of covariances of measurements made on a population of utterances from a given talker to transform measurements made on an utterance from an unknown talker the values include a subset of the principle components obtained by hotelling transformation plus other values dependent on the variances of the principle components variations of the method are given earlier work applied the method to measurements which were sets of linear prediction coefficients reflection coefficients and logarithmic areas derived from the speech waveform and suggested that highly accurate speaker verification could be achieved independent of the speech transmission system and of the text present work shows that there is serious dependence on the transmission system and that accuracies in the range 90 95 percent are typical with utterances of about 2 s duration investigation of a new distance measure based on covariances combined with study of the factors influencing distortion in telephone transmission resulted in a new method based on covariances of logarithmic spectral estimates the results of this method giving accuracies of about 95 percent were robust in the presence of transmission coloration some remaining research problems are defined

topology recognition and leader election in colored networks topology recognition and leader election are fundamental tasks in distributed computing in networks the first of them requires each node to find a labeled isomorphic copy of the network while the result of the second one consists in a single node adopting the label 1 leader with all other nodes adopting the label 0 and learning a path to the leader we consider both these problems in networks whose nodes are equipped with not necessarily distinct labels called colors and ports at each node of degree d are arbitrarily numbered 0 1 d 1 colored networks are generalizations both of labeled networks in which nodes have distinct labels and of anonymous networks in which nodes do not have labels all nodes have the same color in colored networks topology recognition and leader election are not always feasible hence we study two more general problems consider a colored network and an input i given to its nodes the aim of the problem top for this colored network and for i is to solve topology recognition in this network if this is possible under input i and to have all nodes answer unsolvable otherwise likewise the aim of the problem le is to solve leader election in this network if this is possible under input i and to have all nodes answer unsolvable otherwise we show that nodes of a network can solve problems top and le if they are given as input i an upper bound k on the number of nodes of a given color called the size of this color on the other hand we show that if the nodes are given an input that does not bound the size of any color then the answer to top and le must be unsolvable even for the class of rings under the assumption that nodes are given an upper bound k on the size of a given color we study the time of solving problems top and le in the local model in which during each round each node can exchange arbitrary messages with all its neighbors and perform arbitrary local computations we give an algorithm to solve each of these problems in arbitrary networks in time o k d d log n d where d is the diameter of the network and n is its size we also show that this time is optimal by exhibiting classes of networks in which every algorithm solving problems top or le must use time k d d log n d

topological charges in monopole theories let us consider a monopole theory with a compact simply connected gauge group and the higgs field in the adjoint representation using root theory we show that

on modelling mobility we present a model of distributed computation which is based on a fragment of the calculus relying on asynchronous point to point communication we enrich the model with the following features the explicit distribution of processes to locations the routing of messages the mobility of processes and the failure of locations and their detection our contributions are two folds at the specification level we give a synthetic and flexible formalization of the features mentioned above at the verification level we provide original methods to reason about the bisimilarity of processes

monopoles and maps from s 2 to s 2 the topology of the configuration space the configuration space for the su 2 yang mills higgs equations on 3 is shown to be homotopic to the space of smooth maps froms 2 tos 2 this configuration space indexes a family of twisted dirac operators the dirac family is used to prove that the configuration space does not retract onto any subspace on which the su 2 yang mills higgs functional is bounded

new combinatorial topology bounds for renaming the upper bound in the renaming task n 1 processes start with unique input names from a large space and must choose unique output names taken from a smaller name space 0 1 k to rule out trivial solutions a protocol must be anonymous the value chosen by a process can depend on its input name and on the execution but not on the specific process id attiya et al 1990 showed that renaming has a wait free solution when k 2n several algebraic topology proofs of a lower bound stating that no such protocol exists when k

min max theory for the yang mills higgs equations in each monopole sector there exist an infinite number of finite energy solutions to the prasad sommerfield limit of the su 2 yang mills higgs equations on 3 whose energy is greater than any finite number

hyper kahler metrics and a generalization of the bogomolny equations we generalize the bogomolny equations to field equations on 3 n and describe a twistor correspondence we consider a general hyper kahler metric in dimension 4n with an action of the torustn compatible with the hyper kahler structure we prove that such a metric can be described in terms of thetn solution of the field equations coming from the twistor space of the metric

monopoles non linear σ models and two fold loop spaces in this paper we study the topology of hat m k the moduli spaces ofsu 2 monopoles associated with the yang mills higgs and bogomol nyi equations and m k non linear models from quantum field theory beautiful work of donaldson 18 19 hitchin 24 25 and taubes 37 39 40 shows that gauge equivalence classes of monopoles correspond to based rational self maps of the riemann sphere similarly the non linear models we consider here are based harmonic maps from the riemann sphere to complex projectivem space in seminal work segal 35 studied m k the space of based rational maps from the riemann sphere to complex projectivem space of a fixed degreek any element of m k is clearly an element of k2cp m the space of all based continuous maps from the riemann sphere to complex projectivem space of a fixed degreek and this assignment gives rise to the natural inclusion of m k in k2cp m segal showed that these natural inclusions are homotopy equivalences through dimensionk 2m 1 as the topology of the two fold loop space 2cp m is well understood segal s result gives a very efficient way to explicitly determine the low dimensional topology of m k thus iterated loop spaces have much to say about the topology of monopoles and non linear models

pattern recognition via observation correlations in some pattern recognition tasks multiple observations of an observation vector y y1 y2 ym are available for each object and the covariances of the yi are characteristic of the object with the assistance of a model of the generating process for y a theoretical basis for the comparison of the covariance matrices is developed measurements based on synthetic data support the theory and an application to some speaker verification is given as an example

analysis of the adiabatic limit for solitons in classical field theory we discuss the approximation of classical field theories by reduced systems of differential equations on the space of equilibria the adiabatic limit various examples in which the approximation p

integrality of the monopole number in su 2 yang mills higgs theory on ℝ3 we prove that in classical su 2 yang mills higgs theories on 3 with a higgs field in the adjoint representation an integer valued monopole number magnetic charge is canonically defined for any finite actionl1 loc2 configuration in particular the result is true for smooth configurations the monopole number is shown to decompose the configuration space into path components

duality and yang mills fields on quaternionic kahler manifolds the concept of a self dual connection on a four dimensional riemannian manifold is generalized to the 4n dimensional case of any quaternionic kahler manifold the generalized self dual connections are minima of a modified yang mills functional it is shown that our definitions give a correct framework for a mapping theory of quaternionic kahler manifolds the mapping theory is closely related to the construction of yang mills fields on such manifolds some monopole like equations are discussed

algebraic topology and concurrency we show in this article that some concepts from homotopy theory in algebraic topology are relevant for studying concurrent programs we exhibit a natural semantics of semaphore programs based on partially ordered topological spaces which are studied up to elastic deformation or homotopy giving information about important properties of the program such as deadlocks unreachables serializability essential schedules etc in fact it is not quite ordinary homotopy that has to be used but rather a directed homotopy that does not reverse the flow of time we show some of the essential differences between ordinary and directed homotopy through examples we also relate the topological view to a combinatorial view of concurrent programs closer to transition systems through the notion of a cubical set finally we apply some of these concepts to the proof of the safeness of a two phase protocol well known and used in concurrent database theory we end up with a list of problems from both a mathematical and a computer scientific point of view

tight bounds for asynchronous renaming this article presents the first tight bounds on the time complexity of shared memory renaming a fundamental problem in distributed computing in which a set of processes need to pick distinct identifiers from a small namespace we first prove an individual lower bound of k process steps for deterministic renaming into any namespace of size subexponential in k where k is the number of participants the bound is tight it draws an exponential separation between deterministic and randomized solutions and implies new tight bounds for deterministic concurrent fetch and increment counters queues and stacks the proof is based on a new reduction from renaming to another fundamental problem in distributed computing mutual exclusion we complement this individual bound with a global lower bound of k log k c on the total step complexity of renaming into a namespace of size ck for any c 1 this result applies to randomized algorithms against a strong adversary and helps derive new global lower bounds for randomized approximate counter implementations that are tight within logarithmic factors on the algorithmic side we give a protocol that transforms any sorting network into a randomized strong adaptive renaming algorithm with expected cost equal to the depth of the sorting network this gives a tight adaptive renaming algorithm with expected step complexity o log k where k is the contention in the current execution this algorithm is the first to achieve sublinear time and it is time optimal as per our randomized lower bound finally we use this renaming protocol to build monotone consistent counters with logarithmic step complexity and linearizable fetch and increment registers with polylogarithmic cost

contact metric 5 manifolds cr twistor spaces and integrability the cr twistor space is defined over a contact metric 5 manifold m like the 4 dim twistor theory the integrability of the almost cr twistor structure is discussed in terms of the weyl conformal curvature and also the scalar curvature of m

the chern classes of sobolev connections assumef is the curvature field of a connection potential onr4 with finitel2 norm left int limits r 4 left f right 2 dx infty right we show the chern number c 2 1 mathord left vphantom 1 8 right kern nulldelimiterspace 8 pi 2 int limits r 4 f wedge f topological quantum number is an integer this generalizes previous results which showed that the integrality holds forf satisfying the yang mills equations we actually prove the natural general result in all even dimensions larger than 2

more choices allow more faults set consensus problems in totally asynchronous systems abstract we define the k set consensus problem as an extension of the consensus problem where each processor decides on a single value such that the set of decided values in any run is of size at most k we require the agreement condition that all values decided upon are initial values of some processor we show that the problem has a simple k 1 resilient protocol in a totally asynchronous system in an attempt to come up with a matching lower bound on the number of failures we study the uncertainty condition which requires that there must be some initial configuration from which all possible input values can be decided we prove using a combinatorial argument that any k resilient protocol for the k set agreement problem would satisfy the uncertainty condition while this is not true for any k 1 resilient protocol this result seems to strengthen the conjecture that there is no k resilient protocol for this problem we prove this result for a restricted class of protocols our motivation for studying this problem is to test whether the number of choices allowed to the processors is related to the number of faults we hope that this will provide intuition towards achieving better bounds for more practical problems that arise in distributed computing e g the renaming problem the larger goal is to characterize the boundary between possibility and impossibility in asynchronous systems given multiple faults

the combinatorial structure of wait free solvable tasks this paper presents a self contained study of wait free solvable tasks a new necessary condition for wait free solvability based on a restricted set of executions is proved this set of executions induces a very simple to understand structure which is used to prove tight bounds for k set consensus and renaming the framework is based on topology but uses only elementary combinatorics and in contrast to previous works does not rely on algebraic or geometric arguments

casimir operators induced by the maurer cartan equations it is shown that for inhomogeneous lie algebras with only one casimir operator the latter can be explicitly constructed from the maurer cartan equations by means of wedge products it is further proved that this constraint imposes sharp bounds for the dimension of the representation r defining the semidirect product the procedure is generalized to compute also the rational invariant of some lie algebras

a topological treatment of early deciding set agreement the k set agreement problem consists for a set of n processes to agree on less than k among n possibly different values each initially known to only one process the problem is at the heart of distributed computing and generalizes the celebrated consensus problem this paper considers the k set agreement problem in a synchronous message passing distributed system where up to t processes can fail by crashing we determine the number of communication rounds needed for all correct processes to reach a decision in a given run as a function of the degree of coordination k and the number of processes that actually fail in the run email protected t we prove that for any integer email protected k

computing with infinitely many processes we explore four classic problems in concurrent computing election mutual exclusion consensus and naming when the number of processes which may participate is unbounded partial information about the number of processes actually participating and the concurrency level is shown to affect the computability and complexity of solving these problems when using only atomic registers we survey and generalize work carried out in models with known bounds on the number of processes and prove several new results these include improved bounds for election when participation is required and a new adaptive starvation free mutual exclusion algorithm for unbounded concurrency we also survey results in models with shared objects stronger than atomic registers such as test set bits semaphores or read modify write registers and update them for the unbounded case

solving the at most once problem with nearly optimal effectiveness we present and analyze a wait free deterministic algorithm for solving the at most once problem how m shared memory fail prone processes perform asynchronously n jobs at most once our algorithmic strategy provides for the first time nearly optimal effectiveness which is a measure that expresses the total number of jobs completed in the worst case the effectiveness of our algorithm equals n 2m 2 this is up to an additive factor of m close to the known effectiveness upper bound n m 1 over all possible algorithms and improves on the previously best known deterministic solutions that have effectiveness only n logm o n we also present an iterative version of our algorithm that for any m o n logn3 is both effectiveness optimal and work optimal for any constant 0 we then employ this algorithm to provide a new algorithmic solution for the write all problem which is work optimal for any m o n logn3

wait free k set agreement is impossible the topology of public knowledge in the classical consensus problem each of n processors receives a private input value and produces a decision value which is one of the original input values with the requirement that all processors decide the same value a central result in distributed computing is that in several standard models including the asynchronous shared memory model this problem has no deterministic solution the k set agreement problem is a generalization of the classical consensus proposed by chaudhuri inform and comput 105 1993 pp 132 158 where the agreement condition is weakened so that the decision values produced may be different as long as the number of distinct values is at most k for n k geq 2 it was not known whether this problem is solvable deterministically in the asynchronous shared memory model in this paper we resolve this question by showing that for any k n there is no deterministic wait free protocol for n processors that solves the k set agreement problem the proof technique is new it is based on the development of a topological structure on the set of possible processor schedules of a protocol this topological structure has a natural interpretation in terms of the knowledge of the processors of the state of the system this structure reveals a close analogy between the impossibility of wait free k set agreement and the brouwer fixed point theorem for the k dimensional ball

instantons on mathbf cp _2 on decrit et on classe les instantons sur cp 2 pour les groupes de lie simples compacts unitaires et classiques

integer topological charges for finite energy fields in the o 3 σ model in the 2 1 dimensional classical o 3 model all finite energy fields have integer topological charges regardless of their asymptotic behavior at infinity the topological charge is conserved for the fields with the finite euclidean action without further assumptions on the field equations or asymptotics the fields with continuous first derivatives as well as fields in sobolev like spaces analogical to w1 2 are considered

a note and erratum concerning min max theory for the yang mills higgs equations an error in an argument which was used to prove the existence of non minimal solutions to thesu 2 yang mills higgs equations has been shown to the author a revised proof is presented here to establish the existence of infinitely many non minimal solutions to the afore mentioned equations

generalized magnetic monopoles over contact manifolds a generalization of magnetic monopoles is given over an odd dimensional contact manifold and we discuss whether the yang mills higgs functional attains at generalized monopoles the absolute minimal value the topological invariant

the geodesic approximation for the yang mills higgs equations in this paper we consider the dynamics of the monopole solutions of yang mills higgs theory on minkowski space the monopoles are solutions of the yang mills higgs equations on three dimensional euclidean space it is of interest to understand how they evolve in time when considered as solutions of the yang mills higgs equations on minkowski space i e the time dependent equations it was suggested by manton that in certain situations the monopole dynamics could be understood in terms of geodesics with respect to a certain metric on the space of guage equivalence classes of monopoles the moduli space the metric is defined by taking thel 2 inner product of tangent vectors to this space in this paper we will prove that manton s approximation is indeed valid in the right circumstances which correspond to the slow motion of monopoles the metric on the moduli space of monopoles was analysed in a book by atiyah and hitchin so together with the results of this paper a detailed and rigorous understanding of the low energy dynamics of monopoles in yang mills higgs theory is obtained the strategy of the proof is to develop asymptotic expansions using appropriate gauge conditions and then to use energy estimates to prove their validity for the case of monopoles to be considered here there is a technical obstacle to be overcome when the equations are linearised about the monopole the continuous spectrum extends all the way to the origin this is overcome by using a norm introduced by taubes in a discussion of index theory for the yang mills higgs functional