continuum percolation threshold for interpenetrating squares and cubes monte carlo simulations are performed to determine the critical percolation threshold for interpenetrating square objects in two dimensions and cubic objects in three dimensions simulations are performed for two cases i objects whose edges are aligned parallel to one another and ii randomly oriented objects for squares whose edges are aligned the critical area fraction at the percolation threshold ensuremath varphi c 0 6666 ifmmode pm else textpm fi 0 0004 while for randomly oriented squares ensuremath varphi c 0 6254 ifmmode pm else textpm fi 0 0002 6 smaller for cubes whose edges are aligned the critical volume fraction at the percolation threshold ensuremath varphi c 0 2773 ifmmode pm else textpm fi 0 0002 while for randomly oriented cubes ensuremath varphi c 0 2168 ifmmode pm else textpm fi 0 0002 22 smaller

classical dirichlet forms on topological vector spaces closability and a cameron martin formula abstract we prove a sufficient condition for the closability of classical dirichlet forms on l 2 e which is also necessary if all components of the dirichlet form are closable here e is a locally convex topological vector space and a not necessarily quasi invariant probability measure on e the same condition is shown to imply the existence of a closed extension whose domain can be described explicitly in the special case where is quasi invariant with respect to certain vectors in e our result generalises previous theorems on closability in addition we prove a cameron martin type formula for a large class of measures if e is finite dimensional our characterisation of closability is the analogue of the corresponding one dimensional result applications to quantum fields and the connection with the well studied case of abstract wiener spaces are discussed

percolation of interacting classical dimers on the square lattice abstract we study the percolation properties of the interacting classical dimer model on the square lattice by means of monte carlo simulations and finite size scaling analysis we define ising clusters based on the dimer configuration the percolation point of the clusters coincides with the critical point of the kosterlitz thouless transition of the dimer model which is t c 0 654 2 furthermore we find that the largest cluster at the kosterlitz thouless point is a fractal with fractal dimension d c 1 874 2 which coincides with the critical exponent describing the critical behavior of the dimer dimer correlation function which is theoretically predicted to be 15 8

reflexive derivations and lattices of invariant subspaces of operator algebras associated with them the paper studies unbounded reflexive derivations of c algebras of bounded operators on hilbert spaces h whose domains d are weekly dense in b h and contain compact operators it describes a one to one correspondence between these derivations and pairs s l where s are symmetric densely operators on h and l are j orthogonal reflexive lattices of subspaces in the deficiency spaces of s the domains d of these derivations are associated with some non selfadjoint reflexive algebras a of bounded operators on h h the paper analyzes the structure of the lattices of invariant subspaces of a and of the normalizers of a the largest lie subalgebras of b h h such that a are their lie ideals

concentration of quantum states from quantum functional and transportation cost inequalities quantum functional inequalities e g the logarithmic sobolev and poincare inequalities have found widespread application in the study of the behavior of primitive quantum markov semigroups the classical counterparts of these inequalities are related to each other via a so called transportation cost inequality of order 2 tc2 the latter inequality relies on the notion of a metric on the set of probability distributions called the wasserstein distance of order 2 tc2 in turn implies a transportation cost inequality of order 1 tc1 in this paper we introduce quantum generalizations of the inequalities tc1 and tc2 making use of appropriate quantum versions of the wasserstein distances one recently defined by carlen and maas and the other defined by us we establish that these inequalities are related to each other and to the quantum modified logarithmic sobolev and poincare inequalities as in the classical case we also show that these inequalities imply certain concentration type results

definition of percolation thresholds on self affine surfaces we study the percolation transition on a two dimensional substrate with long range self affine correlations we find that the position of the percolation threshold on a correlated lattice is no longer unique and depends on the spanning rule employed numerical results are provided for spanning across the lattice in specified horizontal or vertical either or both directions

stochastic renormalization group in percolation i fluctuations and crossover abstract a generalization of the renormalization group which describes order parameter fluctuations in finite systems is developed in the specific context of percolation this stochastic renormalization group srg expresses statistical self similarity through a non stationary branching process the srg provides a theoretical basis for analytical or numerical approximations both at and away from criticality whenever the correlation length is much larger than the lattice spacing regardless of the system size for example the srg predicts order parameter distributions and finite size scaling functions for the complete crossover between phases for percolation the simplest srg describes structural quantities conditional on spanning such as the total cluster mass or the minimum chemical distance between two boundaries in these cases the central limit theorem for independent random variables holds at the stable off critical fixed points while a fractal central limit theorem describing long range correlations holds at the unstable critical fixed point this first part of a series of articles explains these basic concepts and a general theory of crossover subsequent parts will focus on limit theorems and comparisons of small cell srg approximations with simulation results

a blw inequality for vector bundles and applications to spectral bounds abstract we prove a non commutative version of the bochner lichnerowicz weitzenbock formula for the bochner laplacian acting on sections of a c algebra bundle or of a real euclidean bundle provided with a suitable connection we then use it to obtain a lower bound on the spectrum in terms of uniform or lp bounds on the curvature and current of the connection

symmetric operator extensions of unbounded derivations of c algebras abstract let be a closed derivation from a c subalgebra a of b h into b h and let there exist a closed symmetric operator s such that is that is for a d ad s d s and a d s i s a d s symmetric extensions of s are investigated i e such symmetric extensions t of s that it in particular it is shown that if s has equal and finite deficiency indices and if i a and a does not have finite dimensional representations a c h for example then there exists a self adjoint extension of s

a critical exponent for shortest path scaling in continuum percolation we carry out monte carlo experiments to study the scaling behavior of shortest path lengths in continuum percolation these studies suggest that the critical exponent governing this scaling is the same for both continuum and lattice percolation we use splitting a technique that has not yet been fully exploited in the physics literature to increase the speed of our simulations this technique can also be applied to other models where clusters are grown sequentially

fast monte carlo algorithm for site or bond percolation we describe in detail an efficient algorithm for studying site or bond percolation on any lattice the algorithm can measure an observable quantity in a percolation system for all values of the site or bond occupation probability from zero to one in an amount of time that scales linearly with the size of the system we demonstrate our algorithm by using it to investigate a number of issues in percolation theory including the position of the percolation transition for site percolation on the square lattice the stretched exponential behavior of spanning probabilities away from the critical point and the size of the giant component for site percolation on random graphs

superderivations and symmetric markov semigroups unbounded superderivations are used to construct non commutative elliptic operators on semi finite von neumann algebras the method exploits the interplay between dynamical semigroups and dirichlet forms the elliptic operators may be viewed as generators of irreversible dynamics for fermion systems with infinite degrees of freedom

boundary observer design for hyperbolic pde ode cascade systems the paper presents an observer design for a class of hyperbolic pde ode cascade systems with a boundary measurement the cascade systems consist of coupled pdes featuring one rightward and one leftward convecting first order transport pdes and a set of odes which enter the pdes through the left boundary of the systems the design which is based on the volterra integral transformation relies only on a single sensor at the right boundary of the system the observer consists of a copy of the plant plus output injection terms both in the pdes and the odes the observer is constructed in a collocated setup which means both sensing and actuation are located at the same boundary the observer gains are computed analytically by solving goursat type pdes in terms of bessel function of the first kind the observer design is tested against a field scale flow loop test experiment in stavanger by statoil oil company the results show that the observer converges to the actual values and that the design can be used as a process monitoring tool in oil well drilling

noncommutative martingale deviation and poincare type inequalities with applications we prove a deviation inequality for noncommutative martingales by extending oliveira s argument for random matrices by integration we obtain a burkholder type inequality with satisfactory constant using continuous time we establish noncommutative poincare type inequalities for nice semigroups with a positive curvature condition these results allow us to prove a general deviation inequality and a noncommutative transportation inequality due to bobkov and gotze in the commutative case to demonstrate our setting is general enough we give various examples including certain group von neumann algebras random matrices and classical diffusion processes among others

universality of the crossing probability for the potts model for q 1 2 3 4 the universality of the crossing probability pi hs of a system to percolate only in the horizontal direction was investigated numerically by a cluster monte carlo algorithm for the q state potts model for q 2 3 4 and for percolation q 1 we check the percolation through fortuin kasteleyn clusters near the critical point on the square lattice by using representation of the potts model as the correlated site bond percolation model it was shown that probability of a system to percolate only in the horizontal direction pi hs has the universal form pi hs a q q z for q 1 2 3 4 as a function of the scaling variable z b q l 1 nu q p p c q l zeta q here p 1 exp beta is the probability of a bond to be closed a q is the nonuniversal crossing amplitude b q is the nonuniversal metric factor nu q is the correlation length index and zeta q is the additional scaling index the universal function q x approximately equal exp z the nonuniversal scaling factors were found numerically

continuum percolation thresholds in two dimensions a wide variety of methods have been used to compute percolation thresholds in lattice percolation the most powerful of these methods consists of microcanonical simulations using the union find algorithm to efficiently determine the connected clusters and in two dimensions using exact values from conformal field theory for the probability at the phase transition that various kinds of wrapping clusters exist on the torus we apply this approach to percolation in continuum models finding overlaps between objects with real valued positions and orientations in particular we find precise values of the percolation transition for disks squares rotated squares and rotated sticks in two dimensions and confirm that these transitions behave as conformal field theory predicts the running time and memory use of our algorithm are essentially linear as a function of the number of objects at criticality

invaded cluster algorithm for potts models the invaded cluster algorithm a method for simulating phase transitions is described in detail theoretical albeit nonrigorous justification of the method is presented and the algorithm is applied to potts models in two and three dimensions the algorithm is shown to be useful for both first order and continuous transitions and evidently provides an efficient way to distinguish between these possibilities the dynamic properties of the invaded cluster algorithm are studied numerical evidence suggests that the algorithm has no critical slowing for ising models s1063 651x 96 09208 2

stability of switched linear hyperbolic systems by lyapunov techniques switched linear hyperbolic partial differential equation sa re considered in this technical note they model infinite dimensional systems of conservation laws and balance laws which are potentially affecte db y a distributed source or sink term the dynamics and the boundary condi tions are subject to abrupt changes given by a switching signal modeled as a piecewise constant function and possibly a dwell time by means of lyapunov techniques some sufficient conditions are obtained for the expo nential stability of the switching system uniformly for all switching signals different cases are considered with or without a dwell time assumption on the switching signals and on the number of positive characteristic veloci ties which may also depend on the switching signal some numerical sim ulations are also given to illustrate some main results and to motivate this study

passage times exit times and dirichlet problems for open quantum walks we consider open quantum walks on a graph and consider the random variables defined as the passage time and number of visits to a given point of the graph we study in particular the probability that the passage time is finite the expectation of that passage time and the expectation of the number of visits and discuss the notion of recurrence for open quantum walks we also study exit times and exit probabilities from a finite domain and use them to solve dirichlet problems and to determine harmonic measures we consider in particular the case of irreducible open quantum walks the results we obtain extend those for classical markov chains

largest cluster in subcritical percolation the statistical behavior of the size or mass of the largest cluster in subcritical percolation on a finite lattice of size n is investigated below the upper critical dimension presumably d c 6 it is argued that as stackrel ensuremath rightarrow n ensuremath infty the cumulative distribution function converges to the fisher tippett or gumbel distribution e ensuremath e ensuremath z in a certain weak sense when suitably normalized the mean grows as s ensuremath xi mathrm log n where s ensuremath xi p is a crossover size the standard deviation is bounded near s ensuremath xi ensuremath pi sqrt 6 with persistent fluctuations due to discreteness these predictions are verified by monte carlo simulations on d 2 square lattices of up to 30 million sites which also reveal finite size scaling the results are explained in terms of a flow in the space of probability distributions as stackrel ensuremath rightarrow n ensuremath infty the subcritical segment of the physical manifold 0lpl p c approaches a line of limit cycles where the flow is approximately described by a renormalization group from the classical theory of extreme order statistics

precise percolation thresholds of two dimensional random systems comprising overlapping ellipses abstract this work explores the percolation thresholds of continuum systems consisting of randomly oriented overlapping ellipses high precision percolation thresholds for various homogeneous ellipse systems with different aspect ratios are obtained from extensive monte carlo simulations based on the incorporation of vieillard baron s contact function of two identical ellipses with our efficient algorithm for continuum percolation in addition we generalize vieillard baron s contact function from identical ellipses to unequal ellipses and extend the monte carlo algorithm to heterogeneous ellipse systems where the ellipses have different dimensions and or aspect ratios based on the concept of modified excluded area a general law is verified for precise prediction of percolation threshold for many heterogeneous ellipse systems in particular the study of heterogeneous ellipse systems gains insight into the apparent percolation threshold symmetry observed earlier in systems comprising unequal circles consiglio et al 2004

generators of kms symmetric markov semigroups on mathcal b rm h symmetry and quantum detailed balance we find the structure of generators of norm continuous quantum markov semigroups on mathcal b rm h that are symmetric with respect to the scalar product tr 1 2x 1 2y induced by a faithful normal invariant state and satisfy two quantum generalisations of the classical detailed balance condition related with this non commutative notion of symmetry the so called standard detailed balance condition and the standard detailed balance condition with an antiunitary time reversal

critical percolation on the torus we compute the various crossing probabilities defined by r langlands p pouliot and y saint aubin for the critical percolation on the torus

dirichlet forms and markovian semigroups on standard forms of von neumann algebras we characterize w continuous markovian semigroups on a von neumann algebra m which are 0 symmetric w r t a faithful normal state 0in m in terms of quadratic forms on the hilbert space h of a standard form m h p j we characterize also symmetric strongly continuous contraction semigroups on a real hilbert space h which leave invariant a closed convex set in h in terms of a contraction property of the associated quadratic forms we apply the results to give criteria of essential selfadjointness for quadratic form sums and to give a characterization of w continuous markovian semigroups on m which commute with the modular automorphism group 0t

percolation threshold parameters of fluids extensive monte carlo simulations on three qualitatively different model supercritical fluids square well fluid lennard jonesium and primitive water have been performed to examine percolation threshold parameters for continuum correlated models and their relation to general results valid for random lattice models random site percolation simple cubic lattice has therefore been considered as well two different bond criteria the configurational and self bound ones defining a cluster have been used in addition to the percolation threshold occupation probability p c and the percolation threshold fluid density ensuremath rho c the correlation length exponent ensuremath nu and the wrapping probability at the percolation threshold r w c have also been evaluated it is found that parameters ensuremath nu and r w c exhibit not only strong temperature dependence but also unlike the case of lattice systems dependence on the nature of the system considered and the employed definition of the cluster

superderivations of c algebras implemented by symmetric operators the paper studies unbounded symmetric and dissipative implementations s g of superderivations ofc algebras mathfrak u it associates with them representations s of the domainsd of on the deficiency spacesn s of the symmetric operatorss a link is obtained between the deficiency indicesn s ofs and the dimensions of irreducible representations of mathfrak u for the case when s g is a maximal implementation and max n s some conditions are given for the representation s to be semisimple and to extend to a bounded representation of mathfrak u

switching rules for stabilization of linear systems of conservation laws in this paper the exponential convergence in l 2 norm is analyzed for a class of switched linear systems of conservation laws the boundary conditions are subject to switches we investigate the problem of synthesizing stabilizing switching controllers by means of lyapunov techniques three control strategies are developed based on steepest descent selection possibly combined with a hysteresis and a low pass filter for the first strategy we show the global exponential stabilizability but no result for the existence and uniqueness of trajectories can be stated for the other ones the problem is shown to be well posed and global exponential convergence can be obtained moreover we consider the robustness issues for these switching rules in presence of measurement noise some numerical examples illustrate our approach and show the merits of the proposed strategies particularly we have developed a model for a network of open channels with switching controllers in the gate operations

backstepping boundary control for first order hyperbolic pdes and application to systems with actuator and sensor delays abstract we consider a problem of boundary feedback stabilization of first order hyperbolic partial differential equations pdes these equations serve as a model for physical phenomena such as traffic flows chemical reactors and heat exchangers we design controllers using a backstepping method which has been recently developed for parabolic pdes with the integral transformation and boundary feedback the unstable pde is converted into a delay line system which converges to zero in finite time we then apply this procedure to finite dimensional systems with actuator and sensor delays to recover a well known infinite dimensional controller analog of the smith predictor for unstable plants we also show that the proposed method can be used for the boundary control of a korteweg de vries like third order pde the designs are illustrated with simulations

percolation thresholds on planar euclidean relative neighborhood graphs in the present article statistical properties regarding the topology and standard percolation on relative neighborhood graphs rngs for planar sets of points considering the euclidean metric are put under scrutiny rngs belong to the family of proximity graphs i e their edgeset encodes proximity information regarding the close neighbors for the terminal nodes of a given edge therefore they are e g discussed in the context of the construction of backbones for wireless ad hoc networks that guarantee connectedness of all underlying nodes here by means of numerical simulations we determine the asymptotic degree and diameter of rngs and we estimate their bond and site percolation thresholds which were previously conjectured to be nontrivial we compare the results to regular 2d graphs for which the degree is close to that of the rng finally we deduce the common percolation critical exponents from the rng data to verify that the associated universality class is that of standard 2d percolation

hypercontractivity in noncommutative lpspaces we introduce and study a setup for hypercontractivity in the interpolating family of noncommutative lpspaces associated to a locally normal state on an inductive limitc algebra

l 2 rigidity in von neumann algebras we introduce the notion of l2 rigidity for von neumann algebras a generalization of property t which can be viewed as an analogue for the vanishing of 1 cohomology into the left regular representation of a group we show that l2 rigidity passes to normalizers and is satisfied by nonamenable ii1 factors which are non prime have property or are weakly rigid as a consequence we obtain that if m is a free product of diffuse von neumann algebras or if m l where is a finitely generated group with 1 2 0 then any nonamenable regular subfactor of m is prime and does not have properties or t in particular this gives a new approach for showing solidity for a free group factor thus recovering a well known recent result of n ozawa

totally symmetric algebras and the similarity problem abstract for closed derivations on b h the algebras a a o a a a d are considered a new involution is introduced in b h h such that a a and that a is totally symmetric if is a closed involution it is proved that if an invertible operator belongs to d sca then its inverse also belongs to d sca for f a i f a where f are selfadjoint operators it is shown that a f are reflexive semi simple and totally symmetric algebras if f is unbounded then a f has a strictly irreducible representation which is not similar to representations

an inequality for hilbert schmidt norm for the absolute value c c c 1 2 and the hilbert schmidt norm c hs trc c 1 2 of an operatorc the following inequality is proved for any bounded linear operatorsa andb on a hilbert space a b hs leqq 2 1 2 a b hs the corresponding inequality for two normal state and of a von neumann algebram is also proved in the following form d varphi psi leqq xi varphi xi psi leqq 2 1 2 d varphi psi here denotes the unique vector representative of a state in a natural positive conep form andd denotes the bures distance defined as the infimum which is also the minimum of the distance of vector representatives of and in particular xi varphi 1 xi varphi 2 leqq 2 1 2 xi 1 xi 2 for any vector representatives j of j j 1 2

finite size scaling in stick percolation this work presents the generalization of the concept of universal finite size scaling functions to continuum percolation a high efficiency algorithm for monte carlo simulations is developed to inv

stochastic analysis on product manifolds dirichlet operators on differential forms abstract we define a de rham complex over a product manifold infinite product of compact manifolds and dirichlet operators on differential forms associated with differentiable measures in particular gibbs measures which generalize the notions of bochner and de rham laplacians we give probabilistic representations for corresponding semigroups and study properties of the corresponding stochastic dynamics

control of homodirectional and general heterodirectional linear coupled hyperbolic pdes research on stabilization of coupled hyperbolic pdes has been dominated by the focus on pairs of counter convecting heterodirectional transport pdes with distributed local coupling and with controls at one or both boundaries a recent extension allows stabilization using only one control for a system containing an arbitrary number of coupled transport pdes that convect at different speeds against the direction of the pde whose boundary is actuated in this paper we present a solution to the fully general case in which the number of pdes in either direction is arbitrary and where actuation is applied on only one boundary to all the pdes that convect downstream from that boundary to solve this general problem we solve as a special case the problem of control of coupled homodirectional hyperbolic linear pdes where multiple transport pdes convect in the same direction with arbitrary local coupling our approach is based on pde backstepping and yields solutions to stabilization by both full state and observer based output feedback and trajectory tracking problems

spectral analysis and feller property for quantum ornstein uhlenbeck semigroups a class of dynamical semigroups arising in quantum optics models of masers and lasers is investigated the semigroups are constructed by means of noncommutative dirichlet forms on the full algebra of bounded operators on a separable hilbert space the explicit action of their generators on a core in the domain is used to demonstrate the feller property of the semigroups with respect to the c subalgebra of compact operators the dirichlet forms are analysed and the c 2 spectrum together with eigenspaces are found when reduced to certain maximal abelian subalgebras the semigroups give rise to the markov semigroups of classical ornstein uhlenbeck processes on the one hand and of classical birth and death processes on the other

stability analysis of discontinuous dynamical systems determined by semigroups we present lyapunov stability results for discontinuous dynamical systems dds determined by linear and nonlinear semigroups defined on banach space dds of the type considered herein arise in the modeling of a variety of finite and infinite dimensional systems including certain classes of hybrid systems discrete event systems switched systems systems subjected to impulse effects and the like we apply our results in the analysis of several important specific classes of dds

hyperbolic phase transitions in traffic flow this paper provides a mathematical model of the phenomenon of phase transitions in traffic flow the model consists of a scalar conservation law coupled with a 2 2 system of conservation laws the coupling is achieved via a free boundary where the phase transition takes place for this model the riemann problem is stated and globally solved the cauchy problem is proved to admit a solution defined globally in time without any assumption about the smallness of the initial data or the number of phase boundaries qualitative properties of real traffic flow are shown to agree with properties of the solutions of the model

scaling and universality in the spanning probability for percolation we discuss the spanning percolation probability function for three different spanning rules in general dimensions with both free and periodic boundary conditions our discussion relies on the renormalization group theory which indicates that apart from a few scale factors the scaling functions for the spanning probability are determined by the fixed point and therefore are universal for every system with the same dimensionality spanning rule aspect ratio and boundary conditions for square and rectangular systems we combine this theory with simple relations between the spanning rules and with duality arguments and find strong relations among different derivatives of the spanning function with respect to the scaling variables thus yielding several universal amplitude ratios and allowing a systematic study of the corrections to scaling both singular and analytic in the system size the theoretical predictions are numerically confirmed with excellent accuracy textcopyright 1996 the american physical society

dirichlet forms and symmetric markovian semigroups on ccr algebras with respect to quasi free states employing the construction method of dirichlet forms on standard forms of von neumann algebras developed in infinite dimensional analysis quantum probability and related topics 2000 vol 3 no 1 pp 1 14 ref 1 we construct dirichlet forms and associated symmetric markovian semigroups on ccr algebras with respect to quasi free states more precisely let a h0 be the ccr algebra over a complex separable pre hilbert space h0 and let be a quasi free state on a h0 for any normalized admissible function f and complete orthonormal system cons gn h0 we construct a dirichlet form and corresponding symmetric markovian semigroup on the natural standard form associated to the gns representation of a h0 it turns out that the form is independent of admissible function f and cons gn chosen by analyzing the spectrum of the generator dirichlet operator of the semigroup we show that the semigroup is ergodic and tends to the equilibrium exponentially fast

site bond percolation solution to preventing the propagation of p h y t o p h t h o r a zoospores on plantations we propose a strategy based on the site bond percolation to minimize the propagation of phytophthora zoospores on plantations consisting in introducing physical barriers between neighboring plants two clustering processes are distinguished i one of cells with the presence of the pathogen detected on soil analysis and ii that of diseased plants revealed from a visual inspection of the plantation the former is well described by the standard site bond percolation in the latter the percolation threshold is fitted by a tsallis distribution when no barriers are introduced we provide for both cases the formulas for the minimal barrier density to prevent the emergence of the spanning cluster though this work is focused on a specific pathogen the model presented here can also be applied to prevent the spreading of other pathogens that disseminate by other means from one plant to the neighboring ones finally the application of this strategy to three types of commercially important mexican chili plants is also shown

feynman kac representation of some noncommutative elliptic operators abstract gaussian averages of automorphisms of a von neumannn algebra yield markov semigroups by the well known procedure of subordination we construct operator valued martingales to realise perturbations of such semigroups through feynman kac formulae the perturbations are noncommutative vector fields and the martingales are operator families which are determined by an ito equation on each vector and satisfy cocycle relations with respect to a randomised flow on the algebra in particular this gives a probabilistic representation of some symmetric markov semigroups considered by davies and lindsay

a note about proving non γ under a finite non microstates free fisher information assumption we prove that if x1 xn n 1 are self adjoints in a w probability space with finite non microstates free fisher information then the von neumann algebra w x1 xn they generate doesn t have property especially is not amenable this is an analog of a well known result of voiculescu for microstates free entropy we also prove factoriality under finite non microstates entropy

extension of derivations in the algebra of compact operators let c h denote the c algebra of all compact linear operators on a complex hilbert space h if is a closable derivation in c h which anti commutes with an involutive antiautomorphism and has finite spatial deficiency indices then there exists an infinitesimal generator 0 of a continuous action of r on c h which extends and anti commutes with this is an analogue of the von neumann s theorem which states that a symmetric operator commuting with a conjugation j has a self adjoint extension which also commutes with j

variations in noncommutative potential theory finite energy states potentials and multipliers in this work we undertake an extension of various aspects of the potential theory of dirichlet forms from locally compact spaces to noncommu tative c algebras with trace in particular we introduce finite energy states potentials and multipliers of dirichlet spaces we prove several results among which the celebrated deny s embedding theorem and the deny s inequality the fact that the carre du champ of bounded potentials are finite energy func tionals and the relative supply of multipliers 1 introduction and description of the results in the present work we develop further the potential theory of dirichlet forms on noncommutative c algebras with trace we introduce and investigate finite energy states potentials and multipliers objects naturally associated to dirichlet spaces and which are meant to encode or reveal the geometric nature of the latter in a companion work the results here obtained will be crucial to construct on c algebras endowed with a dirichlet form the building blocks of a metric differential geometry dirac operators and spectral triples and topological invariants sum mable fredholm modules in k homology in the framework of the noncommutative geometry developed by a connes co classical potential theory studying harmonic functions on euclidean spaces r n finite energy measures and their potentials was based on the properties of kernel x y 1 the so called green function to understood as the integral kernel of the

the number of incipient spanning clusters in two dimensional percolation using methods of conformal field theory we conjecture an exact form for the probability that n distinct clusters span a large rectangle or open cylinder of aspect ratio k i n the limit when k is large the study of the structure of large clusters at the percolation threshold continues to pose interesting problems whose solution sheds light on the nature of the critical state in general recently some attention has been paid to incipient spanning clusters iscs these are clusters which connect two disjoint segments of the boundary of a macroscopically large region langlands et al 1 conjectured that the probability that at least one such cluster exists that is that the segments are connected is invariant under conformal transformations this statement was placed in the context of conformal field theory in 2 where an explicit formula was given for this crossing probability for a review of the status of conformal invariance in critical percolation see 3 more recently aizenman 4 has considered among other things the probability that there exist n distinct iscs connecting the two segmentsy in the case of a rectangular region 0 kl 0 l he has proved that the probability p n k l that the strip is traversed in the direction of length kl b y nindependent clusters satisfies the bounds a e n 2 k

gradient flow and entropy inequalities for quantum markov semigroups with detailed balance abstract we study a class of ergodic quantum markov semigroups on finite dimensional unital c algebras these semigroups have a unique stationary state and we are concerned with those that satisfy a quantum detailed balance condition with respect to we show that the evolution on the set of states that is given by such a quantum markov semigroup is gradient flow for the relative entropy with respect to in a particular riemannian metric on the set of states this metric is a non commutative analog of the 2 wasserstein metric and in several interesting cases we are able to show in analogy with work of otto on gradient flows with respect to the classical 2 wasserstein metric that the relative entropy is strictly and uniformly convex with respect to the riemannian metric introduced here as a consequence we obtain a number of new inequalities for the decay of relative entropy for ergodic quantum markov semigroups with detailed balance

contractivity properties of a quantum diffusion semigroup we consider a quantum generalization of the classical heat equation and study contractivity properties of its associated semigroup we prove a nash inequality and a logarithmic sobolev inequality the former leads to an ultracontractivity result this in turn implies that the largest eigenvalue and the purity of a state with positive wigner function evolving under the action of the semigroup decrease at least inverse polynomially in time while its entropy increases at least logarithmically in time

gas flow in fan shaped networks classical solutions and feedback stabilization we analyze the subcritical gas flow through fan shaped networks of pipes that is through tree shaped networks with exactly one node where more than two pipes meet the gas flow in pipe networks is modeled by the isothermal euler equations a hyperbolic pde system of balance laws for this system we analyze stationary states and classical nonstationary solutions locally around a stationary state on a finite time interval furthermore we present a lyapunov function and boundary feedback laws to stabilize a fan shaped network around a given stationary state

gaussian hypercontractivity revisited abstract recent work on convolution type products on fock space allow an elementary treatment of hypercontractivity for second quantised contractions in the fermi case new results are obtained lending further support to a conjecture of l gross

worst case analysis of set union algorithms this paper analyzes the asymptotic worst case running time of a number of variants of the well known method of path compression for maintaining a collection of disjoint sets under union we show that two one pass methods proposed by van leeuwen and van der weide are asymptotically optimal whereas several other methods including one proposed by rein and advocated by dijkstra are slower than the best methods

existence of quantum diffusions a quantum diffusion a a j comprises of unital algebras a and a and a family of identity preserving homomorphisms j j t t 0 from a into a also j satisfies a system of quantum stochastic differential equations dj t x 0 j t x 0 dm j 0 x 0 x 0 i for all x 0 a where 1 i j n are maps from a to itself and are known as the structure maps in this paper an existence proof is given for a class of quantum diffusions for which the structure maps are bounded in the operator norm sense a solution to the system of quantum stochastic differential equations is first produced using a variation of the picard iteration method another application of this method shows that the solution is a quantum diffusion

asymmetry in the percolation thresholds of fully penetrable disks with two different radii we perform simulations of continuum gradient percolation to measure the percolation threshold of systems of fully penetrable disks of two different radii as a function of volumetric proportion v the percolation threshold phic v lambda is approximately symmetric about v 0 5 for a fixed ratio lambda of the radii however the difference from symmetry is strongly statistically significant we also improve by an order of magnitude the measurement of the percolation threshold for disks of equal radius phic 0 676 347 5 6

percolation of the site random cluster model by monte carlo method we propose a site random cluster model by introducing an additional cluster weight in the partition function of the traditional site percolation to simulate the model on a square lattice we combine the color assignation and the swendsen wang methods to design a highly efficient cluster algorithm with a small critical slowing down phenomenon to verify whether or not it is consistent with the bond random cluster model we measure several quantities such as the wrapping probability re the percolating cluster density p and the magnetic susceptibility per site p as well as two exponents such as the thermal exponent yt and the fractal dimension yh of the percolating cluster we find that for different exponents of cluster weight q 1 5 2 2 5 3 3 5 and 4 the numerical estimation of the exponents yt and yh are consistent with the theoretical values the universalities of the site random cluster model and the bond random cluster model are completely identical for larger values of q we find obvious signatures of the first order percolation transition by the histograms and the hysteresis loops of percolating cluster density and the energy per site our results are helpful for the understanding of the percolation of traditional statistical models

disturbance rejection in 2 x 2 linear hyperbolic systems many interesting problems in the oil and gas industry face the challenge of responding to disturbances from afar typically the disturbance occurs at the inlet of a pipeline or the bottom of an oil well while sensing and actuation equipment is installed at the outlet only kilometers away from the disturbance the present paper develops an output feedback control law for such cases based on modelling the transport phenomenon as a 2 times 2 linear partial differential equation pde of hyperbolic type and the disturbance as a finite dimensional linear system affecting the left boundary of the pde sensing and actuation are co located at the right boundary of the pde the design provides a separation principle allowing a disturbance attenuating full state feedback control law to be combined with an observer the results are applied to a relevant problem from the oil and gas industry and demonstrated in simulations

markov semigroups on c bundles abstract we develop a non commutative theory of dirichlet forms and symmetric markov semigroups acting on the smooth sections of a c algebra bundle we show that the bochner laplacian associated to a suitable connection on a clifford algebra bundle induces a dirichlet form and describe some properties of the associated markov semigroup

quantum ito s formula and stochastic evolutions using only the boson canonical commutation relations and the riemann lebesgue integral we construct a simple theory of stochastic integrals and differentials with respect to the basic field operator processes this leads to a noncommutative ito product formula a realisation of the classical poisson process in fock space which gives a noncommutative central limit theorem the construction of solutions of certain noncommutative stochastic differential equations and finally to the integration of certain irreversible equations of motion governed by semigroups of completely positive maps the classical ito product formula for stochastic differentials with respect to brownian motion and the poisson process is a special case

derivations as square roots of dirichlet forms abstract the aim of this work is to analyze the structure of a tracially symmetric dirichlet form on a c algebra in terms of a killing weight and a closable derivation taking values in a hilbert space with a bimodule structure it is shown that the generator of the associate markovian semigroup always appears in a natural way as the divergence of a closable derivation applications are shown to the decomposition of dirichlet forms and to the construction of differential calculus on metric spaces

remarks on the decomposition of dirichlet forms on standard forms of von neumann algebras for a bounded generator g of a weakly continuous completely positive kms symmetric markovian semigroup on a von neumann algebra m acting on a separable hilbert space h let h be the operator induced by g via the symmetric embedding of m into h we decompose the dirichlet form associated with h into a direct integral of forms whose associated generators are divergences of derivations moreover if the derivations are inner then the dirichlet form can be written as the form given by park infinite dimen anal quantum probab relat top 3 1 2000 8 179 2005

minireview new results for old percolation abstract percolation theory deals with the formation of clusters in disordered media at the percolation threshold for the first time an infinite cluster appears however research of the last years showed that at this phase transition some old ideas were wrong there can also be two or three clusters spanning from top to bottom even in large two dimensional lattices and the probability of spanning is not given by simple real space renormalization ideas

shortest path distance in manhattan poisson line cox process while the euclidean distance characteristics of the poisson line cox process plcp have been investigated in the literature the analytical characterization of the path distances is still an open problem in this paper we solve this problem for the stationary manhattan poisson line cox process mplcp which is a variant of the plcp specifically we derive the exact cumulative distribution function cdf for the length of the shortest path to the nearest point of the mplcp in the sense of path distance measured from two reference points i the typical intersection of the manhattan poisson line process mplp and ii the typical point of the mplcp we also discuss the application of these results in infrastructure planning wireless communication and transportation networks

effect of anisotropy on the scaling of connectivity and conductivity in continuum percolation theory we investigate the effects of anisotropy on the finite size scaling of connectivity and conductivity of continuum percolation in three dimensions we consider a system of size x ifmmode times else texttimes fi y ifmmode times else texttimes fi z in which cubic bodies of size a ifmmode times else texttimes fi b ifmmode times else texttimes fi c are placed randomly we define two aspect ratios to request anisotropy then we expect that the displacement of average connected fraction p averaged over the realizations about the isotropic universal curves will be a function of the two aspect ratios this is accounted by considering an apparent percolation threshold in each direction which leads to 50 of realizations connecting in that direction we find the aspect ratios dependency of the apparent threshold and investigate the finite size scaling transformations for the mean connected fraction and its associated fluctuations moreover we apply a single phase pressure solver to determine the conductivity of various realizations of the system finally we apply the same idea to account for the effect of anisotropy on the conductivity scaling

non symmetric dirichlet forms on semifinite von neumann algebras abstract the theory of non symmetric dirichlet forms is generalized to the non abelian setting also establishing the natural correspondences among dirichlet forms sub markovian semigroups and sub markovian resolvents within this context some results on the allowed functional calculus for closed derivations on hilbert algebras are obtained examples of non symmetric dirichlet forms given by derivations on hilbert algebras are studied

exponential stability of switched linear hyperbolic initial boundary value problems we consider the initial boundary value problem governed by systems of linear hyperbolic partial differential equations in the canonical diagonal form and study conditions for exponential stability when the system discontinuously switches between a finite set of modes the switching system is fairly general in that the system matrix functions as well as the boundary conditions may switch in time we show how the stability mechanism developed for classical solutions of hyperbolic initial boundary value problems can be generalized to the case in which weaker solutions become necessary due to arbitrary switching we also provide an explicit dwell time bound for guaranteeing exponential stability of the switching system when for each mode the system is exponentially stable our stability conditions only depend on the system parameters and boundary data these conditions easily generalize to switching systems in the nondiagonal form under a simple commutativity assumption we present tutorial examples to illustrate the instabilities that can result from switching

potts and percolation models on bowtie lattices we give the exact critical frontier of the potts model on bowtie lattices for the case of q 1 the critical frontier yields the thresholds of bond percolation on these lattices which are exactly consistent with the results given by ziff et al j phys a 39 15083 2006 for the q 2 potts model on a bowtie a lattice the critical point is in agreement with that of the ising model on this lattice which has been exactly solved furthermore we do extensive monte carlo simulations of the potts model on a bowtie a lattice with noninteger q our numerical results which are accurate up to seven significant digits are consistent with the theoretical predictions we also simulate the site percolation on a bowtie a lattice and the threshold is s c 0 5479148 7 in the simulations of bond percolation and site percolation we find that the shape dependent properties of the percolation model on a bowtie a lattice are somewhat different from those of an isotropic lattice which may be caused by the anisotropy of the lattice

boundary observer based control for hyperbolic pde ode cascade systems with stochastic jumps abstract this work is concerned with the boundary observer based control for a category of cascade systems with stochastic jumps the cascade system consists of ordinary differential equations odes entering the hyperbolic partial differential equations pdes through the boundary a continuous time discrete state homogeneous markov process models the jumping parameters of the system and its right continuous trajectory candidate values are taken from a finite set a boundary observer is designed which relies only on limited quantity of sensors at the boundary of the pdes based on the lyapunov functional approach the observer error system is firstly proved to be exponentially mean square stable then the controller is presented by utilizing the estimated states of the odes as feedback variables the evolution profiles of the pdes in the closed loop are proved to be exponentially mean square stable at the desired steady state the existence conditions of the boundary observer and the stability conditions of the pdes in the closed loop form are presented via a set of compact space varying linear matrix inequalities svlmis the svlmis are then approximated by a finite number of lmis which guarantee the svlmis and the computational cost is reduced greatly finally the obtained theoretical results are applied to a traffic flow control system which confirms that the proposed estimation and control methods are effective