monopoles and the gibbons manton metric we show that in the region where monopoles are well separated the l 2 metric on the moduli space of n monopoles is exponentially close to the l 2 invariant hyperkahler metric proposed by gibbons and manton the proof is based on a description of the gibbons manton metric as a metric on a certain moduli space of solutions to nahm s equations and on twistor methods in particular we show how the twistor description of monopole metrics determines the asymptotic metric the construction of the gibbons manton metric in terms of nahm s equations yields a class of interesting pseudo hyperkahler metrics for example we show for each semisimple lie group g and a maximal torus t g the existence of a g t invariant pseudo hyperkahler manifold whose hyperkahler quotients by t are precisely kronheimer s hyperkahler metrics on g t a similar result holds for kronheimer s ale spaces

alternative semantics for temporal logics abstract the relationship between alternative underlying semantics for temporal logics is studied a number of constraints on the allowable sets of computation paths can be built into a logic to try to ensure that the abstract computation path semantics of a concurrent program accurately reflects essential aspects of real concurrent programs three such constraints are suffix closure lamport 1980 fusion closure pratt 1979 and limit closure abrahamson 1980 another common constraint is that the set of paths be r generable i e generated by some binary relation manna and pnueli 1979 we show that each of the first three constraints is independent of the others and their conjunction is precisely equivalent to the fourth constraint

a note on monopole moduli spaces we discuss the structure of the framed moduli space of bogomolny monopoles for arbitrary symmetry breaking and extend the definition of its stratification to the case of arbitrary compact lie groups we show that each stratum is a union of submanifolds for which we conjecture that the natural l2 metric is hyper kahler the dimensions of the strata and of these submanifolds are calculated and it is found that for the latter the dimension is always a multiple of four

deciding full branching time logic in this paper the full branching time logic ctl is studied it has basic modalities consisting of a path quantifier either a for all paths of e for some path followed by an arbitrary linear time assertion composed of unrestricted combinations of the usual linear temporal operators f sometime g always x nexttime and u until it is shown that the problem of determining if a ctl formula is satisfiable in a structure generated by a binary relation is decidable in triple exponential time the decision procedure exploits the special structure of the finite state automata for linear temporal formulae which allows them to be determinized with only a single exponential blowup in size also the expressive power of tree automata is compared with that of ctl augmented by quantified auxillary propositions

monopoles and rational maps a note on a theorem of donaldson in a recent paper donaldson gave a description of the moduli space of su 2 monopoles in terms of rational maps this was done indirectly via the associated solution of nahm s equations we give here an interpretation of these rational maps in terms of the monopole s spectral curve and then as scattering data for the monopole itself

inconsistency tolerant temporal reasoning with hierarchical information this paper introduces a new temporal logic spctl spctl is an extension of the well known computation tree logic ctl the complexity of the model checking problem of spctl is settled an illustrative example for medical diagnosis is presented based on spctl a formal method is proposed for modeling and verifying inconsistency tolerant temporal reasoning with hierarchical information for this purpose temporal logic called sequential paraconsistent computation tree logic spctl is obtained from computation tree logic by adding a paraconsistent negation connective and some sequence modal operators spctl can appropriately represent both inconsistency tolerant reasoning by the paraconsistent negation connective and hierarchical information by the sequence modal operators the validity satisfiability and model checking problems of spctl are shown to be exptime complete deterministic exptime complete and deterministic ptime complete respectively illustrative examples for inconsistency tolerant temporal reasoning with hierarchical information are presented using the proposed spctl

mean field self organized criticality the authors consider a variant of directed percolation in which the set of nodes is itself dependent on the progress of the percolation process for the mean field model studied the system is driven to its critical point from a broad range of initial conditions an advantage of the model is its explicit and easy solvability

exact solution of a deterministic sandpile model in one dimension we present an exact solution of a one dimensional sandpile model for which sand is dropped along the wall and n 2 grains of sand fall over the neighboring downhill sites when the critical slope is exceeded the slopes of n consecutive sites organize into a local state the time evolution of the local states along the spatial direction shows a natural tree structure as a result various multifractals can be identified the spatial two point correlation function decreases exponentially with a correlation length of the order of the lattice spacing

critical exponents of the sand pile models in two dimensions abstract we study three sand pile automaton models namely the critical height critical slope and the critical laplacian models in two dimensions in which the stability criterion of the sand columns depend on the zeroth first and the second derivatives of the sand height function we carried out simulations on system sizes up to 2048 2048 and up to 108 avalanches were generated the exponents of the critical height model were calculated by taking into account the strong corrections to scaling in order to determine the exponents of the critical laplacian model accurately we introduced a height restriction in the toppling criterion that maintains universality but accelerates convergence to the steady state by orders of magnitude we see clear scaling in the critical height and the critical laplacian models and find that they belong to different universality classes however we do not find any scaling in the critical slope model

monopoles and their spectral data a new definition of spectral data of a monopole is given for any compact lie or kac moody group it is shown that the spectral data determines the irreducible monopole in the case of maximal symmetry breaking the spectral data is shown to reduce to an earlier definition in terms of algebraic curves indexed by the nodes of the dynkin diagram of the group the structure of solutions to nahm s equations corresponding to the monopole is discussed

self organized critical state of sandpile automaton models we study a general bak tang wiesenfeld type automaton model of self organized criticality in which the toppling conditions depend on local height but not on its gradient we characterize the critical state and determine its entropy for an arbitrary finite lattice in any dimension the two point correlation function is shown to satisfy a linear equation the spectrum of relaxation times describing the approach to the critical state is also determined exactly

supervisory control of discrete event systems with ctl temporal logic specifications the supervisory control problem of discrete event systems with temporal logic specifications is studied the full branching time logic of ctl is used for expressing specifications of discrete event systems the control problem of ctl is reduced to the decision problem of ctl a small model theorem for the control of ctl is obtained it is shown that the control problem of ctl resp ctl is complete for deterministic double resp single exponential time a sound and complete supervisor synthesis algorithm for the control of ctl is provided special cases of the control of computation tree logic ctl and linear time temporal logic are also studied

hyperkahler quotient construction of bps monopole moduli spaces we use the hyperkahler quotient of flat space to obtain some monopole moduli space metrics in explicit form using this new description we discuss their topology completeness and isometries we construct the moduli space metrics in the limit when some monopoles become massless which corresponds to non maximal symmetry breaking of the gauge group we also introduce a new family of hyperkahler metrics which depending on the mass parameter being positive or negative tend to either the asymptotic metric on the moduli space of many su 2 monopoles or to previously unknown metrics these new metrics are singular or complete depending on the particular choice of the level set of the moment map the singular metrics are of relevance to the moduli spaces of vacua of three dimensional gauge theories for higher rank gauge groups finally we make a few comments concerning the existence of closed or bound orbits on some of these manifolds and the integrability of the geodesic flow

fractals and self organized criticality in dissipative dynamics abstract motivated by recent models of bak tang and wiesefneld we study fractal structures arising from dissipative transport in open systems a simple continuum equation is constructed to describe fluctuations around a steady state in a flowing sandpile formation of fractals is understood in terms of a conservation law in dynamics a dynamic renormalization group calculation allows us to determine fractal dimensions and various critical exponents exactly in all dimensions

a logic with revocable and refinable strategies in this article we present updatable strategy logic usl a multi agent temporal logic which subsumes the main propositions in this area such as atl atl atl sc and sl these logics allow to express the capabilities of agents to ensure the satisfaction of temporal properties usl mainly differs from sl in two ways semantically usl relies on multi strategies that is non deterministic strategies and the notion of strategy composition is extended to enable an agent to refine her strategy that is to update it without revoking it syntactically the logic features a binding operator enabling multi strategy refinements as well as an unbinding operator that allows an agent to explicitly revoke a multi strategy whereas revocation is implicit with the binding operator in sl we show that usl allows to express a notion of sustainable control for an agent i e a capability to always decide the satisfaction of a property that still holds even after the said capability has been employed furthermore usl allows the definition of a notion of equality between multi strategies that enables to consider quantification over deterministic strategies this makes usl strictly more expressive than sl finally we also show that the model checking problem for usl is decidable but non elementary as for sl

the classification of monopoles for the classical groups by studying a construction of nahm we compute the moduli spaces of monopoles with maximal symmetry breaking at infinity forsu n so n andsp n these are found to be equivalent to spaces of holomorphic maps from 1 into flag manifolds

invasion percolation a new form of percolation theory a new kind of percolation problem is described which differs from ordinary percolation theory in that it automatically finds the critical points of the system the model is motivated by the problem of one fluid displacing another from a porous medium under the action of capillary forces but in principle it may be applied to any kind of invasion process which proceeds along a path at least resistance the name invasion percolation is proposed for this new process similarities to and differences from ordinary percolation theory are discussed

monopoles and clusters we define and study certain hyperkahler manifolds which capture the asymptotic behaviour of the su 2 monopole metric in regions where monopoles break down into monopoles of lower charges the rate at which these new metrics approximate the monopole metric is exponential as for the gibbons manton metric

axiomatising extended computation tree logic we present a sound and complete axiomatisation for extended computation tree logic this language extends the standard computation tree logic ctl by allowing path formulae to be expressed in linear time mu calculus instead of linear time temporal logic the main novelties in the current paper are an inference rule in the axiom system reflecting the limit closure of paths a new strongly aconjunctive deterministic normal form for formulae and the way the completeness proof takes advantage of techniques provided by automata theory

on the construction of monopoles for the classical groups forg a classical group an equivalence is exhibited between a g monopoles over 3 with maximal symmetry breaking at infinity b families of rank g algebraic curves int 1 along with divisors on those curves satisfying certain constraints c solutions of nahm s equations over rank g intervals satisfying the appropriate boundary conditions a and b are linked by twistor techniques b and c via the krichever method for solving non linear differential equations and a and c via the adhmn construction providing a unified picture of techniques for solution amongst other things an asymptotic formula for the higgs field of the monopole is computed

on the construction of monopoles we show that any self dual su 2 monopole may be constructed either by ward s twistor method or nahm s use of the adhm construction the common factor in both approaches is an algebraic curve whose jacobian is used to linearize the non linear ordinary differential equations which arise in nahm s method we derive the non singularity condition for the monopole in terms of this curve and apply the result to prove the regularity of axially symmetric solutions

equivalence between the abelian sandpile model and the q 0 limit of the potts model abstract we establish an equivalence between the undirected abelian sandpile model and the q 0 limit of the q state potts model the equivalence is valid for arbitrary finite graphs two dimensional abelian sandpile models thus correspond to a conformal field theory with central charge c 2 the equivalence also gives a monte carlo algorithm to generate random spanning trees we study the growth process of the spread of fire under the burning algorithm in the background of a random recurrent configuration of the abelian sandpile model the average number of sites burnt upto time t varies at ta in two dimensions our numerically determined value of a agrees with the theoretical prediction a 8 5 we relate this exponent to the conventional exponents characterizing the distributions of avalanche sizes

characterizing finite kripke structures in propositional temporal logic abstract we show that if two finite kripke structures can be distinguished by some ctl formula that contains both branching time and linear time operators then the structures can be distinguished by a ctl formula that contains only branching time operators our proof involves showing that for any finite kripke structure m it is possible to construct a ctl formula f m that uniquely characterizes m since one kripke structure may be a trivial unrolling of another we use a notion of equivalence between kripke structures that is similar to the notion of bisimulation studied by milner 15 our first construction of f m requires the use of the nexttime operator we also consider the case in which the nexttime operator is disallowed in ctl formulas the proof in this case requires another notion of equivalence equivalence with respect to stuttering and is much more difficult since it is possible for two inequivalent states to have exactly the same finite behaviors modulo stuttering but different infinite behaviors we also give a polynomial algorithm for determining if two structures are stuttering equivalent and discuss the relevance of our results for temporal logic model checking and synthesis procedures

scaling and universality in statistical physics abstract the twin concepts of scaling and universality have played an important role in the description of statistical systems hydrodynamics contains many applications of scaling including descriptions of the behavior of boundary layers prandtl blasius and of the fluctuating velocity in turbulent flow kolmogorov heisenberg onsager phenomenological theories of behavior near critical points of phase transitions made extensive use of both scaling to define the size of various fluctuations and universality to say that changes in the model would not change the answers these two ideas were combined via the statement that elimination of degrees of freedom and a concomitant scale transformation left the answers quite unchanged in wilson s hands this mode of thinking led to the renormalization group approach to critical phenomena subsequently feigenbaum showed how scaling universality and renormalization group ideas could be applied to dynamical systems specifically this approach enabled us to see how chaos first arises in those systems in which but a few degrees of freedom are excited in parallel libchaber developed experiments aimed at understanding the onset of chaos the results of which were subsequently used to show that feigenbaum s universal behavior was in fact realized in honest to goodness hydrodynamical systems more recently gemunu gunaratne mogens jensen and itamar procaccia have indicated that they believe that a different and weaker universality might hold for the fully chaotic behavior of low dimensional dynamical systems dynamically generated situations often seem to show kinds of scaling and universality quite different from that seen in critical phenomena a technical difference which seems to arise in these intrinsically dynamical processes is that instead of having a denumerable list of different critical quantities each with their critical index instead there is continuum of critical indices this so called multifractal behavior may nonetheless show some kinds of universality and indeed this might be the kind of scaling and universality shown by those hydrodynamical systems in which many degrees of freedom are excited

exactly solved model of self organized critical phenomena we define a variant of the model of bak tang and wiesenfeld of self organized critial behavior by introducing a preferred direction we characterize the critical state and by establishing equivalence to a voter model determine the critical exponents exactly in arbitrary dimension d the upper critical dimension for this model is three in two dimensions the model is equivalent to an earlier solved special case of directed percolation

asymptotic metrics for su n monopoles with maximal symmetry breaking we compute the asymptotic metrics for moduli spaces of su n monopoles with maximal symmetry breaking these metrics are exponentially close to the exact monopole metric1 as soon as for each simple root the individual monopoles corresponding to that root are well separated we also show that the estimates can be differentiated term by term in natural coordinates which is a new result even for su 2 monopoles

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

nahm s equations and the classification of monopoles solutions of nahm s system of ordinary differential equations are produced by variational methods this leads to an explicit parametrisation of the solutions to the bogomolny equation over 3

reasoning about infinite computations we investigate extensions of temporal logic by connectives defined by finite automata on infinite words we consider three different logics corresponding to three different types of acceptance conditions finite looping and repeating for the automata it turns out however that these logics all have the same expressive power and that their decision problems are all pspace complete we also investigate connectives defined by alternating automata and show that they do not increase the expressive power of the logic or the complexity of the decision problem