non finite specifiability of projections of functional dependency families abstract a functional dependency fd implicational dependency id family is a family of relational database instances consisting of all instances which satisfy a given set of fds ids an id family is finitely specifiable if it can be defined using a finite set of ids it is known that all fd families are finitely specifiable id families and also that each projection of each fd family while not necessarily an fd family is an id family it is shown here that if the projection of an fd family is not an fd family then it is not a finitely specifiable id family

extremely large scale simulation of a kardar parisi zhang model using graphics cards the octahedron model introduced recently has been implemented onto graphics cards which permits extremely large scale simulations via binary lattice gases and bit coded algorithms we confirm scaling behavior belonging to the two dimensional kardar parisi zhang universality class and find a surface growth exponent 0 2415 15 on 2 17 2 17 systems ruling out 1 4 suggested by field theory the maximum speedup with respect to a single cpu is 240 the steady state has been analyzed by finite size scaling and a growth exponent 0 393 4 is found correction to scaling exponent are computed and the power spectrum density of the steady state is determined we calculate the universal scaling functions and cumulants and show that the limit distribution can be obtained by the sizes considered we provide numerical fitting for the small and large tail behavior of the steady state scaling function of the interface width

small deviations from local equilibrium for a process which exhibits hydrodynamical behavior i the symmetric simple exclusion process on with sources at l l e is considered the stationary measure l is studied in the limit asl diverges the first order correction to its limit is proven to be of order 1 l and it is explicitly computed the result is in agreement with the analysis of the model from the hydrodynamical point of view initiated in ref 1

fluctuation properties of the tasep with periodic initial configuration we consider the joint distributions of particle positions for the continuous time totally asymmetric simple exclusion process tasep they are expressed as fredholm determinants with a kernel defining a signed determinantal point process we then consider certain periodic initial conditions and determine the kernel in the scaling limit this result has been announced first in a letter by one of us sasamoto in j phys a 38 l549 l556 2005 and here we provide a self contained derivation connections to last passage directed percolation and random matrices are also briefly discussed

generalized green functions and current correlations in the tasep we study correlation functions of the totally asymmetric simple exclusion process tasep in discrete time with backward sequential update we prove a determinantal formula for the generalized green function which describes transitions between positions of particles at different individual time moments in particular the generalized green function defines a probability measure at staircase lines on the space time plane the marginals of this measure are the tasep correlation functions in the space time region not covered by the standard green function approach as an example we calculate the current correlation function that is the joint probability distribution of times taken by selected particles to travel given distance an asymptotic analysis shows that current fluctuations converge to the airy2 process

supervisory control of a class of discrete event processes this paper studies the control of a class of discrete event processes i e processes that are discrete asynchronous and possibly nondeter ministic the controlled process is described as the generator of a formal language while the controller or supervisor is constructed from the grammar of a specified target language that incorporates the desired closed loop system behavior the existence problem for a supervisor is reduced to finding the largest controllable language contained in a given legal language two examples are provided

note a note on the reversibility and duality of some tandem blocking queueing systems in a previous paper yamazaki et al yamazaki g t kawashima h sakasegawa 1983 reversibility of tandem blocking queueing systems kogakuin university tokyo japan prove that a certain tandem blocking queueing system and its reversed counterpart have the same capacity throughput the purpose of this note is to offer an alternative viewpoint based on a concept of duality this leads to a more intuitive methodology and provides additional insight into the original and reversed systems

robust and nonblocking supervisor for discrete event systems with model uncertainty under partial observation addresses a robust and nonblocking supervisory control problem based on a framework of discrete event systems with model uncertainty under partial observation the uncertainty introduced in the paper is associated with internal and unobservable events occurring in systems the paper presents a systematic method for modeling uncertainty described as a spl delta transition representing the internal and unobservable events in particular at a state with the assigned positive integer value p a system is assumed to experience at most a p step state transition by the internal and unobservable event under the framework for model uncertainty the paper presents necessary and sufficient conditions for the existence of a robust supervisor with the nonblocking property

interacting particle systems at the edge of multilevel dyson brownian motions abstract we study the joint asymptotic behavior of spacings between particles at the edge of multilevel dyson brownian motions when the number of levels tends to infinity despite the global interactions between particles in multilevel dyson brownian motions we observe a decoupling phenomenon in the limit the global interactions become negligible and only the local interactions remain the resulting limiting objects are interacting particle systems which can be described as brownian versions of certain totally asymmetric exclusion processes this is the first appearance of a particle system with local interactions in the context of general random matrix models

microscopic shock structure in model particle systems the boghosian levermore cellular automation revisited we carried out new computer simulations of the boghosian levermore stochastic cellular automaton for the burgers equation the existence of an extra conservation law in the dynamics even and odd lattice sites exchange their contents at every time step implies that the automaton decomposes into two independent subsystems the simulations show that the density from each subsystem exhibits a shock front which does not broaden with time the location of the shock in a particular microscopic realization differs from that predicted by the burgers equation by an amount which depends only on the initial microscopic density of the particle system that is fluctuations in the stochastic dynamics do not affect the shock profile on the time scale considered this is in complete accord with theoretical expectations the apparent broadening of the shock in the original boghosian levermore simulations is shown to result from averaging the two subsystem densities

centralized and decentralized supervisory control of nondeterministic systems under partial observation in this paper we extend our earlier work on supervisory control of nondeterministic systems using prioritized synchronization as the mechanism of control and trajectory model as the modeling formalism by considering design of supervisors under partial observation we introduce the notion of observation compatible systems and show that prioritized synchronous composition psc of observation compatible systems can be used as a mechanism of control of nondeterministic systems under partial observation in presence of driven events necessary and sufficient conditions that depend on the trajectory model as opposed to the language model of the plant are obtained for the existence of centralized as well as decentralized supervision our work on centralized control shows that the results of the traditional supervisory control can be extended to the above setting provided that the supervisor is deterministic and the observation mask is projection type on the other hand our work on decentralized control is based on a new relation between controllability observability co observability and psc that we derive in this paper

interface motion in a planar spin flip model derived from exclusion on the line we consider a two dimensional spin flip model which can be interpreted as the limit of the ising model at low temperature and a small nonzero external field in the hydrodynamic limit and for a special class of initial conditions the motion of the interface is governed by a nonlinear partial differential equation with a lattice distorted curvature term in our proofs we use results about the hydrodynamic behavior of the weakly asymmetric exclusion process on the integers and also on the nonnegative integers with a trap at the boundary

bound on the mass gap for a stochastic contour model at low temperature a two dimensional stochastic contour model is considered in which the state space consists of simple closed lattice contours about a fixed origin and the evolution in the state space is a continuous time reversible jump process an upper bound is obtained on the mass gap for the model which goes rapidly to zero in a low temperature limit a connection between this model and statistical mechanical and droplet models is discussed

shape fluctuations and random matrices we study a certain random growth model in two dimensions closely related to the one dimensional totally asymmetric exclusion process the results show that the shape fluctuations appropriately scaled converges in distribution to the tracy widom largest eigenvalue distribution for the gaussian unitary ensemble gue

correlations in the multispecies tasep and a conjecture by lam we study correlations in the multispecies tasep on a ring results on the correlation of two adjacent points prove two conjectures by thomas lam on a the limiting direction of a reduced random walk in a over tilde n 1 and b the asymptotic shape of a random integer partition with no hooks of length n a so called n core we further investigate two point correlations far apart and three point nearest neighbour correlations and prove explicit formulas in almost all cases these results can be seen as a finite strengthening of correlations in the tasep speed process by amir angel and valko we also give conjectures for certain higher order nearest neighbour correlations we find an unexplained independence property provably for two points conjecturally for more points between points that are closer in position than in value that deserves more study

exact field driven interface dynamics in the two dimensional stochastic ising model with helicoidal boundary conditions abstract we investigate the interface dynamics of the two dimensional stochastic ising model in an external field under helicoidal boundary conditions at sufficiently low temperatures and fields the dynamics of the interface is described by an exactly solvable high spin asymmetric quantum hamiltonian that is the infinitesimal generator of the zero range process generally the critical dynamics of the interface fluctuations is in the kardar parisi zhang universality class of critical behavior we remark that a whole family of rsos interface models similar to the ising interface model investigated here can be described by exactly solvable restricted high spin quantum x x z type hamiltonians

shock fluctuations in the asymmetric simple exclusion process we consider the one dimensional nearest neighbors asymmetric simple exclusion process with ratesq andp for left and right jumps respectively q p ferrari et al 1991 have shown that if the initial measure isv a product measure with densities and to the left and right of the origin respectively then there exists a microscopic shock for the system a shock is a random positionx t such that the system as seen from this position at timet has asymptotic product distributions with densities and to the left and right of the origin respectively uniformly int we compute the diffusion coefficient of the shockd lim t t 1 e x t 2 ex t 2 and findd p q 1 1 1 as conjectured by spohn 1991 we show that in the scale sqrt t the position ofx t is determined by the initial distribution of particles in a region of length proportional tot we prove that the distribution of the process at the average position of the shock converges to a fair mixture of the product measures with densities and this is the so called dynamical phase transition under shock initial conditions we show how the density fluctuation fields depend on the initial configuration

nonequilibrium measures which exhibit a temperature gradient study of a model we give some rules to define measures which could describe heat flow in homogeneous crystals we then study a particular model which is explicitly solvable the one dimensional nearest neighborhood ising model we analyze two cases in the first one the spins at the two boundaries interact with reservoirs at different temperatures in the thermodynamical limit the measure we introduce converges locally to gibbs measures and a temperature profile is so derived we obtain an explicit expression for the thermal conductivity coefficient which depends on the temperature in the second case we study the asymptotic behavior starting from an initial state in which each half of the space is at a different temperature we find again a temperature profile which asymptotically obeys the heat equation with the thermal conductivity coefficient previously derived from a mathematical point of view the analysis of the invariant measure is made possible by studying a time reversed process related to a graphical representation of an associated process this provides us with an explicit formula for then fold correlation function and we study the limiting behavior using both this representation for proving an exchangeability result and a donsker type spacetime renormalization procedure

moderate deviation and exit time estimates for stationary last passage percolation we consider planar stationary exponential last passage percolation in the positive quadrant with boundary weights for rho in 0 1 and points v n 1 rho 2 n rho 2 n going to infinity along the characteristic direction we establish right tail estimates with the optimal exponent for the exit time of the geodesic along with optimal exponent estimates for the upper tail moderate deviations for the passage time for the case rho frac 1 2 in the stationary model we establish the lower bound estimate with the optimal exponent for the lower tail of the passage time our arguments are based on moderate deviation estimates for point to point and point to line exponential last passage percolation which are obtained via random matrix estimates

shocks in the asymmetric exclusion process in this paper we consider limit theorems for the asymmetric nearest neighbor exclusion process on the integers the initial distribution is a product measure with asymptotic density at and at earlier results described the limiting behavior in all cases except for 0 1 2 1 here we treat the exceptional case which is more delicate it corresponds to the one in which a shock wave occurs in an associated partial differential equation in the cases treated earlier the limit was an extremal invariant measure by contrast in the present case the limit is a mixture of two invariant measures our theorem resolves a conjecture made by the third author in 1975 7 the convergence proof is based on coupling and symmetry considerations

robust and nonblocking supervisory control of nondeterministic discrete event systems using trajectory models this note considers the robust supervisory control problems of uncertain nondeterministic discrete event systems dess the uncertain des to be controlled is assumed to be modeled as a set of some possible nondeterministic automata then the control objective is to achieve a given language specification and guarantee the nonblockingness of any nondeterministic automata of the set which are controlled by a robust nonblocking supervisor based on trajectory models this note presents the necessary and sufficient conditions for the existence of a robust nonblocking supervisor for a given uncertain nondeterministic des

current distribution and random matrix ensembles for an integrable asymmetric fragmentation process we calculate the time evolution of a discrete time fragmentation process in which clusters of particles break up and reassemble and move stochastically with size dependent rates in the continuous time limit the process turns into the totally asymmetric simple exclusion process only pieces of size 1 break off a given cluster we express the exact solution of the master equation for the process in terms of a determinant which can be derived using the bethe ansatz from this determinant we compute the distribution of the current across an arbitrary bond which after appropriate scaling is given by the distribution of the largest eigenvalue of the gaussian unitary ensemble of random matrices this result confirms universality of the scaling form of the current distribution in the kpz universality class and suggests that there is a link between integrable particle systems and random matrix ensembles

directed last passage percolation with discontinuous weights we prove that a directed last passage percolation model with discontinuous macroscopic non random inhomogeneities has a continuum limit that corresponds to solving a hamilton jacobi equation in the viscosity sense this hamilton jacobi equation is closely related to the conservation law for the hydrodynamic limit of the totally asymmetric simple exclusion process we also prove convergence of a numerical scheme for the hamilton jacobi equation and present an algorithm based on dynamic programming for finding the asymptotic shapes of maximal directed paths

around probabilistic cellular automata we survey probabilistic cellular automata with approaches coming from combinatorics statistical physics and theoretical computer science each bringing a different viewpoint some of the questions studied are specific to a domain and some others are shared most notably the ergodicity problem

heavy tails in last passage percolation we consider last passage percolation models in two dimensions in which the underlying weight distribution has a heavy tail of index 2 we prove scaling laws and asymptotic distributions both for the passage times and for the shape of optimal paths these are expressed in terms of a family indexed by of continuous last passage percolation models in the unit square in the extreme case 0 corresponding to a distribution with slowly varying tail the asymptotic distribution of the optimal path can be represented by a random self similar measure on 0 1 whose multifractal spectrum we compute by extending the continuous last passage percolation model to mathbb r 2 we obtain a heavy tailed analogue of the airy process representing the limit of appropriately scaled vectors of passage times to different points in the plane we give corresponding results for a directed percolation problem based on stable levy processes and indicate extensions of the results to higher dimensions

tools for template dependencies template dependencies td s are a class of data dependencies that include multivalued and join dependencies and embedded versions of these a collection of techniques examples and results about td s are presented the principal results are 1 finite implication implication over relations with a finite number of tuples is distinct from unrestricted implication for td s 2 there are for td s over three or more attributes infinite chains of increasingly weaker and increasingly stronger full td s 3 however there are weakest nontrivial and strongest full td s over any given set of attributes 4 over two attributes there are only three distinct td s 5 there is no weakest not necessarily full td over any set of three or more attributes 6 there is a finite relation that obeys every strictly partial td but no full td 7 the conjunction of each finite set of full td s is equivalent to a single full td however the conjunction of a finite set of not necessarily full td s is not necessarily e

reasoning about functional and full hierarchical dependencies over partial relations we study the implication problem for the combined class of functional and full hierarchical dependencies in the presence of sql s not null constraints two different notions of implication are addressed one where a dependency is implied by the given set of dependencies plus the underlying schema and one where a dependency is implied by the given set of dependencies alone we establish axiomatizations for both notions of implication and reveal deep relationships between them

limiting shapes of ising droplets ising fingers and ising solitons we examine the evolution of an ising ferromagnet endowed with zero temperature single spin flip dynamics a large droplet of one phase in the sea of the opposite phase eventually disappears an interesting behavior occurs in the intermediate regime when the droplet is still very large compared to the lattice spacing but already very small compared to the initial size in this regime the shape of the droplet is essentially deterministic fluctuations are negligible in comparison with characteristic size in two dimensions the shape is also universal that is independent of the initial shape we analytically determine the limiting shape of the ising droplet on the square lattice when the initial state is a semi infinite stripe of one phase in the sea of the opposite phase it evolves into a finger which translates along its axis we determine the limiting shape and the velocity of the ising finger on the square lattice an analog of the ising finger on the cubic lattice is the translating ising soliton we show that far away from the tip the cross section of the ising soliton coincides with the limiting shape of the two dimensional ising droplet and we determine a relation between the cross section area the distance from the tip and the velocity of the soliton

convergence to a non extremal equilibrium measure in the exclusion process it has been conjectured that the asymmetric exclusion process starting from certain product measures converges to a non extremal equilibrium measure in this paper we prove a weaker version of this conjecture

exact solution of the totally asymmetric simple exclusion process shock profiles the microscopic structure of macroscopic shocks in the one dimensional totally asymmetric simple exclusion process is obtained exactly from the complete solution of the stationary state of a model system containing two types of particles first and second class this nonequilibrium steady state factorizes about any second class particle which implies factorization in the one component system about the random shock position it also exhibits several other interesting features including long range correlations in the limit of zero density of the second class particles the solution also shows that a finite number of second class particles in a uniform background of first class particles form a weakly bound state

directed last passage percolation and random matrices this paper is a survey of various techniques recent results and applications of directed last passage percolation model and its relation to random matrices the connection can be explained mainly via the universality of famous tracy widom distribution and airy process some unsolved problems are also surveyed

longest increasing subsequences from patience sorting to the baik deift johansson theorem we describe a simple one person card game patience sorting its analysis leads to a broad circle of ideas linking young tableaux with the longest increasing subsequence of a random permutation via the schensted correspondence a recent highlight of this area is the work of baik deift johansson which yields limiting probability laws via hard analysis of toeplitz determinants

exclusion process and droplet shape we use a mathematical isomorphism between the one dimensional exclusion process and the two dimensional stochastic ising model in the low temperature limit to describe the typical instantaneous shape of a supercritical droplet we derive specifically the exact asymptotic distribution of the boundaries of a 1 spin region confined to z 2 and subjected to a positive magnetic field in an appropriate scaling the boundary distribution converges to a deterministic continuum limit

membership problem for embedded multivalued dependencies under some restricted conditions abstract it is known that there is no finite set of inference rules that is complete for embedded multivalued dependencies this paper considers the problem called membership problem of deciding whether a given embedded multivalued dependency x v on u or functional dependency x v is implied by a given set d of functional and embedded multivalued dependencies a new inference rule for embedded multivalued dependencies is presented and the following results about membership problems are shown let u be a set of attributes and let w n w 0 u let d f e e 1 e n where 1 i f is a set of functional dependencies y z satisfying y w 0 or z w 0 2 ii e is a set of embedded multivalued dependencies y z on t satisfying at least one of y w 0 t z w 0 and t y z w 0 and 3 iii each e 1 i n is a set of embedded multivalued dependencies on w 1 1 if x v u w 0 then the membership problem is solaable that is it is decidable whether x v on u or x v is implied by d 2 2 if x v u w n then the membership problem cah be solved in o d v x time where d is the size of the description of d 3 3 if x w n and x v u w 0 then the membership problem can be solved in o d 2 w n x n t 1 w 1 w 1 l 1 time

on the hydrodynamic limit of a ginzburg landau lattice model the law of large numbers in arbitrary dimensions a lattice system of interacting diffusion processes is investigated the evolution is attractive and time reversible the spin satisfies a conservation law it is shown that the rescaled spin field converges in probability to the corresponding solution to a nonlinear diffusion equation

supervisory control of nondeterministic systems with driven events via prioritized synchronization and trajectory models the supervisory control of nondeterministic discrete event dynamical systems dedss with driven events in the setting of prioritized synchronization and trajectory models introduced by heymann are studied prioritized synchronization captures the notions of controllable uncontrollable and driven events in a natural way and the authors use it for constructing supervisory controllers the trajectory model is used for characterizing the behavior of nondeterministic dedss since it is a sufficiently detailed model in contrast to the less detailed language or failures models and serves as a language congruence with respect to the operation of prioritized synchronization results concerning controllability and observability in this general setting are obtained

asymmetric attractive particle systems on z hydrodynamic limit for monotone initial profiles we extend previous results on the preservation of local equilibrium for one dimensional asymmetric attractive particle systems the hydrodynamic behavior is studied for general monotone initial profiles

rate of convergence of the mean for sub additive ergodic sequences abstract for sub additive ergodic processes x m n with weak dependence we analyze the rate of convergence of e x 0 n n to its limit g we define an exponent given roughly by e x 0 n n g n and assuming existence of a fluctuation exponent that gives var x 0 n n 2 we provide a lower bound for of the form the main requirement is that 1 2 in the case 1 2 and under the assumption var x 0 n o n log n for some 0 we prove c for a dependent constant c these results show in particular that non diffusive fluctuations are associated to non trivial various models including first passage percolation directed polymers the minimum of a branching random walk and bin packing fall into our general framework and the results apply assuming exists in the case of first passage percolation in z d we provide a version of 1 2 without assuming existence of

non equilibrium behaviour of a many particle process density profile and local equilibria one considers a simple exclusion particle jump process on where the underlying one particle motion is a degenerate random walk that moves only to the right one starts with the configuration in which the left halfline is completely occupied and the right one free it is shown that the number of particles at time t between site u t and v t divided by t converges a s to int limits u nu f w dw where f might be called the density profile it is explicitely determined and shown to be an affine function secondly we prove that the distribution of the process looked at by an observer travelling at constant speed u converges weakly to the bernoulli measure with density f u as the time tends to infinity

an equivalence between relational database dependencies and a fragment of propositional logic it is known that there is an eqmvalence between functional dependencies m a relatmonal database and a certain fragment of proposmonal logic thins eqmvalence is extended to include both functional and multivalued dependencmes thus for each dependency there is a corresponding statement m proposmonal logic it ms then shown that a dependency funcuonal or multivalued is a consequence of a set of dependencies ff and only ff the corresponding proposiuonal statement s a consequence of the corresponding set of proposmonal statements examples are given to show that these techniques are valuable mn provmdmg much shorter proofs of theorems about dependencies than have been obtained by more tradmonal means it is shown that this eqmvalence cannot be extended to include either join dependencies or embedded multmvalued dependencies

decentralized control of discrete event systems using prioritized composition with exclusion a necessary and sufficient condition for decentralized control of discrete event systems via prioritized composition with exclusion pcx is provided pcx was extended from prioritized synchronous composition psc in order to model various boolean modes of decision fusion by allowing the exclusivity of participation in system interactions a notion of pcx coobservability is introduced that captures the nature of pcx based decision fusion and a testing algorithm with polynomial complexity in the states of plant and specification is presented the result is extended for multiple supervisors with multiple exclusivity sets based on an extended pcx definition

a proof procedure for data dependencies definition d une classe de dependances dependances generant l equalite et les triples et generalisation du processus de poursuite pour traiter ces dependances on montre quelques cas pour lesquels il y a une procedure de decision redondance de l egalite pour decider de l implication des dependances generant les triples et presque redondance pour decider de l implication des dependances generant l egalite

sort sets in the relational model the notion of sort set is introduced here to formalize the fact that certain database relations can be sorted so that two or more columns are simultaneously listed in order this notion is shown to be applicable in several ways to enhance the efficiency of an implemented database a characterization of when order dependency implies the existence of sort sets in a database is presented along with several corollaries concerning complexity armstrong relations and cliques of certain graphs sort set dependencies are then introduced a finite sound and complete set of inference rules for sort set dependencies is presented as well as a proof that there is no such set for functional and sort set dependencies taken together deciding logical implication for sort set dependencies is proved to be polynomial but if functional dependencies are included the problem is co np complete each set of sort set and functional dependencies is shown to have an armstrong relation a natural generalization of armstrong relation here called separator is given and then used to study the relationship between order and sort set dependencies

bisimilarity control of partially observed deterministic systems control for safety and nonblockingness using a deterministic supervisor requires the specification language be controllable and observable under the setting that marking is also decided by a supervisor we argue that there exist cases where the above properties do not hold yet a safe and nonblocking control can be synthesized by allowing the supervisor to be nondeterministic use of a nondeterministic supervisor yields a controlled system that is nondeterministic for which a language equivalence only preserve the safety but not the nonblocking property and so instead we require the stronger equivalence of bisimilarity which preserves sequential behavior such as safety as well as branching behavior such as nonblockingness this motivates us to consider control of deterministic systems for achieving bisimulation equivalence to possibly nondeterministic specifications we introduce the notions of state achievability sa and state achievability bisimilar sab as part of the existence condition and develop effective algorithms for verify the existence conditions as well as for synthesizing a supervisor when the existence condition holds we show that the complexity of verifying the existence of a controller is polynomial whereas that of computing a controller when one exists is singly exponential the proposed approach can be applied to enforce any property that depends on branching and sequential behavior

order dependency in the relational model abstract the relational model is formally extended to include fixed orderings on attribute domains a new constraint called order dependency is then introduced to incorporate semantic information involving these orderings it is shown that this constraint can be applied to enhance the efficiency of an implemented database the thrust of the paper is to study logical implication for order dependency the main theoretical results consist in i introducing a formalism analogous to propositional calculus for analyzing order dependency ii exhibiting a sound and complete set of inference rules for order dependency and iii demonstrating that determining logical implication for order dependency is co np complete it is also shown that there are sets of order dependencies for which no armstrong relations exist

equivalence reversibility symmetry and concavity properties in fork join queuing networks with blocking in this paper we study quantitative as well as qualitative properties of fork join queuing networks with blocking fjqn bs specifically we prove results regarding the equivalence of the behavior of a fjqn b and that of its duals and a strongly connected marked graph in addition we obtain general conditions that must be satisfied by the service times to guarantee the existence of a long term throughput and its independence on the initial configuration we also establish conditions under which the reverse of a fjqn b has the same throughput as the original network by combining the equivalence result for duals and the reversibility result we establish a symmetry property for the throughput of a fjqn b last we establish that the throughput is a concave function of the buffer sizes and the initial marking provided that the service times are mutually independent random variables belonging to the class of pert distributions that includes the erlang distributions this last result coupled with the symmetry property can be used to identify the initial configuration that maximizes the long term throughput in closed series parallel networks

functional dependencies and constraints on null values in database relations database relations with incomplete information are considered the no information interpretation of null values is adopted due to its characteristics of generality and naturalness coherently with the framework and its motivation two meaningful classes of integrity constraints are studied a functional dependencies which have been widely investigated in the classical relational theory and b constraints on null values which control the presence of nulls in the relations specifically three types of constraints on null values are taken into account nullfree subschemes existence constraints disjunctive existence constraints and the interaction of each of them with functional dependencies is studied in each of the three cases the inference problem is solved the complexity of the algorithms for its solution analyzed and the existence of a complete axiomatization discussed

geodesics and the competition interface for the corner growth model we study the directed last passage percolation model on the planar integer lattice with nearest neighbor steps and general i i d weights on the vertices outside the class of exactly solvable models in georgiou et al probab theory relat fields 2016 doi 10 1007 s00440 016 0729 x we constructed stationary cocycles and busemann functions for this model using these objects we prove new results on the competition interface on existence uniqueness and coalescence of directional semi infinite geodesics and on nonexistence of doubly infinite geodesics

stationary cocycles and busemann functions for the corner growth model we study the directed last passage percolation model on the planar square lattice with nearest neighbor steps and general i i d weights on the vertices outside of the class of exactly solvable models stationary cocycles are constructed for this percolation model from queueing fixed points these cocycles serve as boundary conditions for stationary last passage percolation solve variational formulas that characterize limit shapes and yield existence of busemann functions in directions where the shape has some regularity in a sequel to this paper the cocycles are used to prove results about semi infinite geodesics and the competition interface

on the undecidability of implications between embedded multivalued database dependencies the implication and finite implication problems for embedded multivalued database dependencies are both shown to be algorithmically undecidable the proof is by an interpretation of semigroup word problems via systems of permuting equivalence relations into database dependencies in contrast it is shown that for each fixed premise h one has a decision procedure for implications h f

delocalization of polymers in lower tail large deviation directed last passage percolation models on the plane where one studies the weight as well as the geometry of optimizing paths called polymers in a field of i i d weights are paradigm examples of models in kpz universality class in this article we consider the large deviation regime i e when the polymer has a much smaller lower tail or larger upper tail weight than typical precise asymptotics of large deviation probabilities have been obtained in a handful of the so called exactly solvable scenarios including the exponential johansson in commun math phys 209 2 437 476 2000 and poissonian deuschel and zeitouni in comb probab comput 8 03 247 263 1999 seppalainen in probab theory relat fields 112 2 221 244 1998 cases how the geometry of the optimizing paths change under such a large deviation event was considered in deuschel and zeitouni 1999 where it was shown that the paths from 0 0 to n n say remain concentrated around the straight line joining the end points in the upper tail large deviation regime but the corresponding question in the lower tail was left open we establish a contrasting behaviour in the lower tail large deviation regime showing that conditioned on the latter in both the models the optimizing paths are not concentrated around any deterministic curve our argument does not use any ingredient from integrable probability and hence can be extended to other planar last passage percolation models under fairly mild conditions and also to other non integrable settings such as last passage percolation in higher dimensions

an exact solution of a one dimensional asymmetric exclusion model with open boundaries a simple asymmetric exclusion model with open boundaries is solved exactly in one dimension the exact solution is obtained by deriving a recursion relation for the steady state if the steady state is known for all system sizes less thann then our equation 8 gives the steady state for sizen using this recursion we obtain closed expressions 48 for the average occupations of all sites the results are compared to the predictions of a mean field theory in particular for infinitely large systems the effect of the boundary decays as the distance to the power 1 2 instead of the inverse of the distance as predicted by the mean field theory

inferences for numerical dependencies abstract we introduce and motivate the study of numerical dependencies which are a generalization of functional dependencies we prove that there does not exist a finite set of sound and complete inference rules for numerical dependencies in contrast to the case of functional dependencies we also prove that nontrivial numerical dependencies which are not functional dependencies cannot be expressed by horn formulas in first order logic and show some applications of numerical dependencies

statistical self similarity of one dimensional growth processes abstract for one dimensional growth processes we consider the distribution of the height above a given point of the substrate and study its scale invariance in the limit of large times we argue that for self similar growth from a single seed the universal distribution is the tracy widom distribution from the theory of random matrices and that for the growth from a flat substrate it is some other only numerically determined distribution in particular for the polynuclear growth model in the droplet geometry the height maps onto the longest increasing subsequence of a random permutation from which the height distribution is identified as the tracy widom distribution

on the supermal controllable sublanguage of a given language the concept of controllable language has been shown to play a basic role in the existence theory of supervisory controls for discrete event processes in this paper the supremal controllable sublanguage s of a given language l is characterized as the largest fixpoint of a monotone operator omega in the case where the languages involved are regular it is shown that the fixpoint s can be computed as the limit of the finite sequence k j given by k j 1 omega k j k 0 l an effective computational algorithm is developed and three examples are provided for illustration

exact solution of the master equation for the asymmetric exclusion process using the bethe ansatz we obtain the exact solution of the master equation for the totally asymmetric exclusion process on an infinite one dimensional lattice we derive explicit expressions for the conditional probabilitiesp x1 xn t y1 yn 0 of findingn particles on lattices sitesx1 xn at timet with initial occupationy1 yn at timet 0

axioms and algorithms for inferences involving probabilistic independence abstract this paper offers an axiomatic characterization of the probabilistic relation x is independent of y written x y where x and y are two disjoint sets of variables four axioms for x y are presented and shown to be complete based on these axioms a polynomial membership algorithm is developed to decide whether any given independence statement x y logically follows from a set of such statements i e whether x y holds in every probability distribution that satisfies the complexity of the algorithm is o k2 n where is the number of given statements n is the number of variables in x y and k is the number of variables in x y

existence of hydrodynamics for the totally asymmetric simple k exclusion process in a totally asymmetric simple k exclusion process particles take nearest neighbor steps to the right on the lattice z under the constraint that each site contain at most k particles we prove that such processes satisfy hydrodynamic limits under euler scaling and that the limit of the empirical particle profile is the entropy solution of a scalar conservation law with a concave flux function our technique requires no knowledge of the invariant measures of the process which is essential because the equilibria of asymmetric k exclusion are unknown but we cannot calculate the flux function precisely the proof proceeds via a coupling with a growth model on the two dimensional lattice in addition to the basic k exclusion with constant exponential jump rates we treat the site disordered case where each site has its own jump rate randomly chosen but frozen for all time the hydrodynamic limit under site disorder is new even for the simple exclusion process the case k 1 our proof makes no use of the markov property so at the end of the paper we indicate how to treat the case with arbitrary waiting times

nonblocking supervisory control of nondeterministic systems via prioritized synchronization shayman and kumar 1995 showed that supervisory control of nondeterministic discrete event systems in the presence of driven events can be achieved using prioritized synchronous composition as a mechanism of control and trajectory models as a modeling formalism first introduced by heymann 1990 the specifications considered in this earlier work were given by prefix closed languages in this paper we extend this work to include markings so that nonclosed specifications and issues such as blocking can be addressed it is shown that the usual notion of nonblocking called language model nonblocking may not be adequate in the setting of nondeterministic systems and a stronger notion called trajectory model nonblocking is introduced necessary and sufficient conditions for the existence of language model nonblocking as well as trajectory model nonblocking supervisors are obtained for nondeterministic systems in the presence of driven events in terms of extended controllability and relative closure conditions and a new condition called the trajectory closure condition

ground state energy anisotropy for directed polymers in random media the orientation dependence of the line energy of zero temperature directed polymers is studied analytically and numerically for the two dimensional square lattice with site disorder using the equivalence to single step growth models the exact line energy of maximum energy paths is computed for exponential and geometric disorder distributions the resulting expression depends on the distributions only through their mean and variance a universal square root singularity appears in the ground state energy as the line orientation approaches the edges of the wedge shaped lattice we also discuss the relationship between point to point and point to line optimization problems as well as their connection to the classic wulff construction for crystal shapes in addition we derive some general distribution independent properties of the optimal path angle in the point to line configuration this angle is argued to be directly measurable in fracture experiments of anisotropic materials such as paper

entropy large deviations and scaling limits we often model the evolution of a complex system at the lowest or micro level because that is what makes the most physical sense but if the system is large we invariably want answers to questions posed on the larger macro or global scale this then involves the study of equations with a large number of variables and extracting useful information from their solutions the macroscopic quantities of interest may not contain complete information about the microscopic variables that drive their evolution something has to be done to obtain a closed system of equations for quantities of interest different contexts require different approaches we are concerned here with the evolution of large systems of interacting particles or field variables that have some built in noise and outline some of the work done at the institute during the last 25 years 2013 wiley periodicals inc

hammersley s interacting particle process and longest increasing subsequences in a famous paper 8 hammersley investigated the lengthl n of the longest increasing subsequence of a randomn permutation implicit in that paper is a certain one dimensional continuous space interacting particle process by studying a hydrodynamical limit for hammersley s process we show by fairly soft arguments that limn 1 2 el n 2 this is a known result but previous proofs 14 11 relied on hard analysis of combinatorial asymptotics

characterizations for functional dependency and boyce codd normal form families abstract a functional dependency fd family was recently defined 20 as the set of all instances satisfying some set of functional dependencies a boyce codd normal form abbreviated bcnf family is defined here as an fd family specified by some bcnf set of functional dependencies the purpose of this paper is to present set theoretic algebraic characterizations relating to both types of families two characterizations of f i the smallest fd family containing the family i of instances are established the first involves the notion of agreement a concept related to that of a closed set of attributes the second describes f i as the smallest family of instances containing i and closed under four specific operations on instances companion results are also given for bcnf families the remaining results concern characterizations involving the well known operations of projection join and union two characterizations for when the projection of an fd family is again an fd family are given several corollaries are obtained including the effective decidability of whether a projection of an fd family is an fd family the problem for bcnf families disappears since it is shown that the projection of a bcnf family is always a bcnf family analogous to results for fd families presented in 20 characterizations of when the join and union of bcnf families are bcnf families are given finally the collections of all fd families and all bcnf families are characterized in terms of inverse projection operations and intersection

on controllability and normality of discrete event dynamical systems abstract this paper studies the supervisor synthesis problem of discrete event dynamical systems deds s through the use of synchronous composition of the plant and the supervisor and discusses some of the simplifications achieved by using the synchronous composition to model supervisory control an alternate definition of controllability is presented this definition of controllability is then used to derive an algorithm that is computationally more efficient than previously existing ones for the construction of the supremal controllable sublanguage the algorithm is also shown to be optimal the observability and normality issues arising due to the partial observation of the system dynamics under an arbitrary mask are then investigated closed form representations of the supremal normal and supremal closd and normal sublanguages are derived in the more general setting of arbitrary mask and nonclosed languages thus extending earlier results of the authors and others

transience of second class particles and diffusive bounds for additive functionals in one dimensional asymmetric exclusion processes consider a one dimensional exclusion process with finite range translation invariant jump rates with nonzero drift let the process be stationary with product bernoulli invariant distribution at density place a second class particle initially at the origin for the case 1 2 we show that the time spent by the second class particle at the origin has finite expectation this strong transience is then used to prove that variances of additive functionals of local mean zero functions are diffusive when 1 2 as a corollary to previous work we deduce the invariance principle for these functionals the main arguments are comparisons of h 1 norms a large deviation estimate for second class particles and a relation between occupation times of second class particles and additive functional variances

second class particles as microscopic characteristics in totally asymmetric nearest neighbor k exclusion processes summary we study aspects of the hydrodynamics of one dimensional totally asym metric k exclusion building on the hydrodynamic limit of seppalainen 1999 we prove that the weak solution chosen by the particle system is the unique one with maximal current past any fixed location a uniqueness result is needed because we can prove neither differentiability nor strict concavity of the flux function so we cannot use the lax oleinik formula or jump conditions to define entropy solutions next we prove laws of large numbers for a second class particle in k exclusion the macroscopic trajectories of second class particles are characteristics and shocks of the conservation law for the particle density in particular we extend tok exclusion ferrari s result that the second class particle follows a macroscopic shock in the rie mann solution the technical novelty of the proofs is a variational representation for the position of a second class particle in the context of the variational coupling method

on the structure of armstrong relations for functional dependencies an armstrong relation for a set of functional dependencies fds is a relation that satisfies each fd implied by the set but no fd that is not implied by it the structure and size number of tuples of armstrong relatsons are investigated upper and lower bounds on the size of minimal sized armstrong relations are derived and upper and lower bounds on the number of distinct entries that must appear m an armstrong relation are given it is shown that the time complexity of finding an armstrong relation gwen a set of functional dependencies is precisely exponential in the number of attributes also shown s the falsity of a natural conjecture which says that almost all relations obeying a given set of fds are armstrong relations for that set of fds finally armstrong relations are used to generahze a result obtained by demetrovics using quite complicated methods about the possible sets of keys for a relauon

contact processes in several dimensions this paper deals primarily with the basic contact processes introduced and studied by harris 12t4 these are random evolutions on the state space s a l l subsets of z a zd the d dimensional integer lattice with extremely simple local dynamics namely if we think of the contact process as representing the spread of an infection t es denoting the set of infected sites at time t then x e it becomes healthy at exponential rate 1 while x z a t is infected at a rate proport ional to the number of sites neighboring x where infection is present the proportionali ty constant 2 is called the infection parameter contact processes are perhaps the simplest s valued markov processes which exhibit a critical phenomenon infection emanating from a single site dies out with probabili ty one for small positive 2 but has positive probability of surviving for all time when is large there is a critical value 2 d where the transition occurs principal objectives of analysis are the precise formulation of the critical phenomenon and detailed description of the ergodic behavior both below and above a c our recent survey articles 10 and i 6 provide introductions to contact processes and to the general field of interacting s valued systems respectively we will make constant use of notation and techniques from the surveys assuming that the reader is familiar with thern the article 10 describes in some detail the current state of knowledge concerning one dimensional contact processes the theory for d 1 is now fairly complete with two major exceptions 1 is not even determined to one decimal place 1 18 2 e there is an

one dimensional hard rod caricature of hydrodynamics we give here a rigorous deduction of the hydrodynamic equation which holds in the hydrodynamic limit for a model system of one dimensional identical hard rods interacting through elastic collisions the equation should be considered as the analog of the euler equation of real hydrodynamics owing to the degeneracy of the model it is written in terms of a functiong q v t expressing the density of particles with velocityv at the pointq at timet for this equation we prove an existence and uniqueness theorem in some natural class of functions our main result is the proof that if 0 is a class of initial states which are homogeneous on a scale much less than e 1 and if the corresponding particle densities tend ase 0 in the proper scale to the initial hydrodynamic densitygo q v then under some general assumptions on the states and ong0 the particle densities of the evolved states at timee 1t tend ase 0 to the unique solution of the hydrodynamic equation with initial conditiong0 the proof is completed by exhibiting a large class of initial families 0 which possess the required properties

variational formulas and cocycle solutions for directed polymer and percolation models we discuss variational formulas for the law of large numbers limits of certain models of motion in a random medium namely the limiting time constant for last passage percolation and the limiting free energy for directed polymers the results are valid for models in arbitrary dimension steps of the admissible paths can be general the environment process is ergodic under spatial translations and the potential accumulated along a path can depend on the environment and the next step of the path the variational formulas come in two types one minimizes over gradient like cocycles and another one maximizes over invariant measures on the space of environments and paths minimizing cocycles can be obtained from busemann functions when these can be proved to exist the results are illustrated through 1 1 dimensional exactly solvable examples periodic examples and polymers in weak disorder

formulas for calculating supremal controllable and normal sublanguages abstract supremal controllable and normal sublanguages have been shown to play an important role in supervisor synthesis in this paper we discuss the computation of supremal controllable and normal sublanguages we derive formulas for both supremal controllable sublanguages and supremal normal sublanguages when the languages involved are closed as a result those languages can be computed without applying recursive algorithms we also discuss those aspects of these formulas