two three and four dimensional diffusion limited aggregation models abstract two three and four dimensional diffusion limited aggregation dla models with noise reduction and with growth probabilities proportional to small integer powers of the harmonic measure have been investigated using improved algorithms the results obtained from these simulations provide the basis for a more decisive test of theoretical results than ordinary dla simulations alone using off lattice models effective fractal dimensionalities d of about 1 41 and 1 29 were found for 2 and 3 respectively for a two dimensional d 2 embedding space for d 3 d 2 13 for 2 and d 1 90 for 3 similarly for d 4 d 2 97 for 2 and d 2 74 for 3 for the noise reduced dla lattice models our results are consistent with the idea that d d 1 in the asymptotic s m limit where s is the cluster size and m is the noise reduction parameter however for d 4 the effective fractal dimensionality is quite close to 3 for m 30

a new algebraic geometry algorithm for integer programming we propose a new algorithm for solving integer programming ip problems that is based on ideas from algebraic geometry the method provides a natural generalization of the farkas lemma for ip leads to a way of performing sensitivity analysis offers a systematic enumeration of all feasible solutions and gives structural information of the feasible set of a given ip we provide several examples that offer insights on the algorithm and its properties

the c 3 theorem and a d 2 algorithm for large scale stochastic mixed integer programming set convexification this paper considers the two stage stochastic integer programming problem with an emphasis on instances in which integer variables appear in the second stage drawing heavily on the theory of disjunctive programming we characterize convexifications of the second stage problem and develop a decomposition based algorithm for the solution of such problems in particular we verify that problems with fixed recourse are characterized by scenario dependent second stage convexifications that have a great deal in common we refer to this characterization as the c3 common cut coefficients theorem based on the c3 theorem we develop a decomposition algorithm which we refer to as disjunctive decomposition d2 in this new class of algorithms we work with master and subproblems that result from convexifications of two coupled disjunctive programs we show that when the second stage consists of 0 1 milp problems we can obtain accurate second stage objective function estimates after finitely many steps this result implies the convergence of the d2 algorithm

robust h sup spl infin filtering for uncertain markovian jump systems with mode dependent time delays this paper considers the problem of robust h sup spl infin filtering for uncertain markovian jump linear systems with time delays which are time varying and depend on the system mode the parameter uncertainties are time varying norm bounded the aim of this problem is to design a markovian jump linear filter that ensures robust exponential mean square stability of the filtering error system and a prescribed l sub 2 induced gain from the noise signals to the estimation error for all admissible uncertainties a sufficient condition for the solvability of this problem is obtained the desired filter can be constructed by solving a set of linear matrix inequalities an illustrative numerical example is provided to demonstrate the effectiveness of the proposed approach

impulsive control in this paper the concept and principles of impulsive control are presented impulsive control can be applied to a class of systems whose state variables are changeable in a very short time period in particular the asymptotic stability of the impulsive control of a nonlinear system is given

neighborhood systems for production sets with indivisibilities a production set with indivisibilities is described by an activity analysis matrix with activity levels which can assume arbitrary integral values a neighborhood system is an association with each integral vector of activity levels of a finite set of neighboring vectors the neighborhood relation is assumed to be symmetric and translation invariant each such neighborhood system can be used to define a local maximum for the associated integer programs obtained by selecting a single commodity whose level is to be maximized subject to specified factor endowments of the remaining commodities it is shown that each technology matrix subject to mild regularity assumptions has a unique minimal neighborhood system for which a local maximum is global the complexity of such minimal neighborhood systems is examined for several examples

on computing hilbert bases via the elliot macmahon algorithm the ways of using the elliot macmahon algorithm to compute the hilbert base of a system of linear diophantine equations known so far are either not efficient or can fail to terminate we present a version of an algorithm exploiting this range of ideas which however is reasonably efficient as well as finite

the complexity of generic primal algorithms for solving general integer programs primal methods constitute a common approach to solving combinatorial optimization problems starting from a given feasible solution they successively produce new feasible solutions with increasingly better objective function value until an optimal solution is reached from an abstract point of view an augmentation problem is solved in each iteration that is given a feasible point these methods find an augmenting vector if one exists usually augmenting vectors with certain properties are sought to guarantee the polynomial running time of the overall algorithm in this paper we show that one can solve every integer programming problem in polynomial time provided one can efficiently solve the directed augmentation problem the directed augmentation problem arises from the ordinary augmentation problem by splitting each direction into its positive and its negative part and by considering linear objectives on these parts our main result states that in order to get a polynomial time algorithm for optimization it is sufficient to efficiently find for any linear objective function in the positive and negative part an arbitrary augmenting vector this result also provides a general framework for the design of polynomial time algorithms for specific combinatorial optimization problems we demonstrate its applicability by considering the min cost flow problem by giving a novel algorithm for linear programming over unimodular spaces and by providing a different proof that for 0 1 integer programming an efficient algorithm solving the ordinary augmentation problem suffices for efficient optimization our main result also implies that directed augmentation is at least as hard as optimization in other words for an np hard problem already the task of finding a directed augmenting vector in polynomial time is hopeless unless p np we illustrate this kind of consequence with the help of the knapsack problem

razumikhin type theorems on p th moment exponential stability of impulsive stochastic delay differential equations this note develops razumikhin type theorems on pth moment exponential stability for general impulsive stochastic delay differential equations some applications are also given to some special types of impulsive stochastic delay differential equations two examples illustrate the effectiveness of the proposed results

sensitivity theorems in integer linear programming we consider integer linear programming problems with a fixed coefficient matrix and varying objective function and right hand side vector among our results we show that for any optimal solution to a linear program max wx ax b the distance to the nearest optimal solution to the corresponding integer program is at most the dimension of the problem multiplied by the largest subdeterminant of the integral matrixa using this we strengthen several integer programming proximity results of blair and jeroslow graver and wolsey we also show that the chvatal rank of a polyhedron x ax b can be bounded above by a function of the matrixa independent of the vectorb a result which as blair observed is equivalent to blair and jeroslow s theorem that each integer programming value function is a gomory function

variation of cost functions in integer programming we study the problem of minimizingc x subject toa x b x 0 andx integral for a fixed matrixa two cost functionsc andc are considered equivalent if they give the same optimal solutions for eachb we construct a polytopest a whose normal cones are the equivalence classes explicit inequality presentations of these cones are given by the reduced grobner bases associated witha the union of the reduced grobner bases asc varies called the universal grobner basis consists precisely of the edge directions ofst a we present geometric algorithms for computingst a the graver basis and the universal grobner basis

finite size effect of harmonic measure estimation in a dla model variable size of probe particles abstract a finite size effect in the probing of the harmonic measure in simulation of diffusion limited aggregation dla growth is investigated we introduce a variable size of probe particles to estimate harmonic measure and extract the fractal dimension of dla clusters taking two limits of vanishingly small probe particle size and of infinitely large size of a dla cluster we generate 1000 dla clusters consisting of 50 million particles each using an off lattice killing free algorithm developed in the early work the introduced method leads to unprecedented accuracy in the estimation of the fractal dimension we discuss the variation of the probability distribution function with the size of probing particles

algebraic algorithms for sampling from conditional distributions we construct markov chain algorithms for sampling from discrete exponential families conditional on a sufficient statistic examples include contingency tables logistic regression and spectral analysis of permutation data the algorithms involve computations in polynomial rings using grobner bases

permutohedra and minimal matrices the notions of minimality uniqueness and additivity originated in discrete tomography they have applications to kronecker products of characters of the symmetric group and arise as the optimal solutions of quadratic transportation problems here we introduce the notion of real minimality and give geometric characterizations of all these notions for a matrix a by considering the intersection of the permutohedron determined by a with the transportation polytope in which a lies we also study the computational complexity of deciding if the properties of being additive real minimal unique and minimal hold for a given matrix and show how to efficiently construct some matrix with any of these properties

test sets for integer programs in this paper i discuss various properties of the simplicial complex of maximal lattice free bodies associated with a matrix a if the matrix satisfies some mild conditions and is generic the edges of the complex form the minimal test set for the family of integer programs obtained by selecting a particular row of a as the objective function and using the remaining rows to impose constraints on the integer variables 1997 the mathematical programming society inc published by elsevier science b v

neighbors of the origin for four by three matrices scarf has defined a neighborhood system for families of integer programs where the right hand side is allowed to vary this system depends on a matrix a of constraint and objective function coefficients of the integer programs this paper characterizes the set of neighbors of the origin when a is four by three showing that it may be described as the set of integer vectors in a union of two dimensional polyhedra where the number of polyhedra is quadratic in the bit size of a

stochastic model for dielectric breakdown we discuss a model for the development of discharge patterns in dielectric breakdown based on the laplace equation associated with a probability field the model gives rise to random fractals with well defined hausdorff dimensions the relations of this model with the diffusion limited aggregation are discussed in detail the possibility of application to other stochastic phenomena like fracture propagation is proposed

decomposition of test sets in stochastic integer programming we study graver test sets for linear two stage stochastic integer programs and show that test sets can be decomposed into finitely many building blocks whose number is independent on the number of scenarios of the stochastic program we present a finite algorithm to compute the building blocks directly without prior knowledge of test set vectors once computed building blocks can be employed to solve the stochastic program by a simple augmentation scheme again without explicit knowledge of test set vectors finally we report preliminary computational experience

stability of a random diffusion with linear drift we consider a linear system with markovian switching which is perturbed by gaussian type noise if the linear system is mean square stable then we show that under certain conditions the perturbed system is also stable we also show that under certain conditions the linear system with markovian switching can be stabilized by such noisy perturbation

a geometric buchberger algorithm for integer programming let ip a c denote the family of integer programs of the form min cx ax b x nn obtained by varying the right hand side vector b but keeping a and c fixed a test set for ipa c is a set of vectors in zn such that for each nonoptimal solution to a program in this family there is at least one element g in this set such that g has an improved cost value as compared to we describe a unique minimal test set for this family called the reduced grobner basis of ip a c an algorithm for its construction is presented which we call a geometric buchberger algorithm for integer programming and we show how an integer program may be solved using this test set the reduced grobner basis is then compared with some other known test sets from the literature we also indicate an easy procedure to construct test sets with respect to all cost functions for a matrix a zn 2 n of full row rank

less conservative conditions for asymptotic stability of impulsive control systems this note studies the stability of impulsive control systems a new comparison theorem for asymptotic stability of impulsive differential system is presented based on the new result we derive some less conservative conditions for asymptotic stability of impulsive control systems with impulses at fixed times and the results are used to design impulsive control for a class of nonlinear systems the class of nonlinear systems considered is also enlarged

mean field analysis of the equilibrium of patterns growing in a laplacian field the properties of the shape of patterns generated by random growth in a laplacian field are investigated using a simple model the smoothed laplacian model the relation between this model and more complex systems such as saffman taylor fingers or diffusion limited aggregates stands in the recently recognized universality of patterns whose evolution is controlled by the laplace equation and in an analytical approximation for the laplacian field itself the smoothed laplacian model allows one to treat analytically the equilibrium of the structure in the smoothed laplacian field in a mean field approximation the results on this model are extended to radial geometry thus providing theoretical insight in the dependence of the shape on the geometry of boundary conditions in which the process takes place and on the parameter that tunes the strength of the laplacian field in the same way as the parameter eta does for the dielectric breakdown model this new picture is compared to numerical simulation results of dla and dbm and proves to be consistent with them

solving stochastic programs with integer recourse by enumeration a framework using gro bner basis reductions in this paper we present a framework for solving stochastic programs with complete integer recourse and discretely distributed right hand side vector using grobner basis methods from computational algebra to solve the numerous second stage integer programs using structural properties of the expected integer recourse function we prove that under mild conditions an optimal solution is contained in a finite set furthermore we present a basic scheme to enumerate this set and suggest improvements to reduce the number of function evaluations needed

p moment stability of stochastic differential equations with jumps in the paper p moment stability of stochastic differential equations with jumps is considered first some preliminary notes are given then several theorems on p moment stability of these equations are established using liapunov function at last an example is present to show application of the obtained results

two stage integer programs with stochastic right hand sides a superadditive dual approach we consider two stage pure integer programs with discretely distributed stochastic right hand sides we present an equivalent superadditive dual formulation that uses the value functions in both stages we give two algorithms for finding the value functions to solve the reformulation after obtaining the value functions we develop a global branch and bound approach and a level set approach to find an optimal tender we show that our method can solve randomly generated instances whose extensive forms are several orders of magnitude larger than the extensive forms of those instances found in the literature

solving stochastic programs with integer recourse by enumeration a framework using grobner basis in this paper we present a framework for solving stochastic programs with complete integer recourse and discretely distributed right hand side vector using grobner basis methods from computational algebra to solve the numerous second stage integer programs using structural properties of the expected integer recourse function we prove that under mild conditions an optimal solution is contained in a finite set furthermore we present a basic scheme to enumerate this set and suggest improvements to reduce the number of function evaluations needed

fixed scale transformation approach to critical fluctuations and fractal growth abstract a geometrical approach to the study of critical phenomena calls for a fractal description of critical fluctuations the fixed scale transformation fst approach introduces such a description incorporating both the scale and translational invariance properties of the critical state besides providing a theoretical understanding of the genesis of fractal structures it enables one to compute the fractal dimension of the critical clusters to a high degree of accuracy in terms of the critical statistics of the underlying model laplacian models of irreversible fractal growth to which the fst approach was first applied are presented within the general framework of critical phenomena this geometrical approach links the growth rules which are fully nonlocal in both space and time measured in number of particles added to the morphology of the grown cluster and its scaling behaviour possible directions towards a more comprehensive theory of fractal growth are discussed

the value function of an integer program we consider integer programs in which the objective function and constraint matrix are fixed while the right hand side varies the value function gives for each feasible right hand side the criterion value of the optimal solution we provide a precise characterization of the closed form expression for any value function

controllability stabilizability and continuous time markovian jump linear quadratic control consideration is given to the control of continuous time linear systems that possess randomly jumping parameters which can be described by finite state markov processes the relationship between appropriately defined controllability stabilizability properties and the solution of the infinite time jump linear quadratic jlq optimal control problems is also examined although the solution of the continuous time markov jlq problem with finite or infinite time horizons is known only sufficient conditions for the existence of finite cost constant stabilizing controls for the infinite time problem appear in the literature in this paper necessary and sufficient conditions are established these conditions are based on new definitions of controllability observability stabilizability and detectability that are appropriate for continuous time markovian jump linear systems these definitions play the same role for the jlq problem as the deterministic properties do for the linear quadratic regulator lqr problem

stability analysis of impulsive stochastic cohen grossberg neural networks with mixed time delays abstract in this paper the problem of stability analysis for a class of impulsive stochastic cohen grossberg neural networks with mixed delays is considered the mixed time delays comprise both the time varying and infinite distributed delays by employing a combination of the m matrix theory and stochastic analysis technique a sufficient condition is obtained to ensure the existence uniqueness and exponential p stability of the equilibrium point for the addressed impulsive stochastic cohen grossberg neural network with mixed delays the proposed method which does not make use of the lyapunov functional is shown to be simple yet effective for analyzing the stability of impulsive or stochastic neural networks with variable and or distributed delays we then extend our main results to the case where the parameters contain interval uncertainties moreover the exponential convergence rate index is estimated which depends on the system parameters an example is given to show the effectiveness of the obtained results

a primal all integer algorithm based on irreducible solutions this paper introduces an exact primal augmentation algorithm for solving general linear integer programs the algorithm iteratively substitutes one column in a tableau by other columns that correspond to irreducible solutions of certain linear diophantine inequalities we prove that various versions of our algorithm are finite it is a major concern in this paper to show how the subproblem of replacing a column can be accomplished effectively an implementation of the presented algorithms is given computational results for a number of hard 0 1 integer programs from the miplib demonstrate the practical power of the method

particle aggregation versus cluster aggregation in high dimensions we distinguish two different types of irreversible aggregation accretion of individual particles and successive aggregation of clusters of comparable size in aggregation of particles which follow trajectories of fractal dimensiond 1 we show that physical limits on the aggregation rate impose a lower bound on the fractal dimensiond 0 of the aggregate ind dimensional space d 0 d d 1 1 thus aggregation of ballistic particles withd 1 1 is not fractal by contrast cluster aggregates appear to attain a finite limitingd 0 in high dimensions we present a soluble model with this property and argue that it should agree with sutherland s binary aggregation model in high dimensions for this model d 0 depends continuously on a parameter the exponent is not universal

fixed scale transformation applied to diffusion limited aggregation and dielectric breakdown model in three dimensions abstract we extend the method of the fixed scale transformation fst to the case of fractal growth in three dimensions and apply it to diffusion limited aggregation and to the dielectric breakdown model for different values of the parameter the scheme is formally similar to the two dimensional case with the following technical complications i the basis configurations for the fine graining process are five instead of two and consist of 2 2 cells ii the treatment of the fluctuations of boundary conditions is far more complex and requires new schemes of approximations in order to test the convergency of the theoretical results we consider three different schemes of increasing complexity for dbm in three dimensions the computed values of the fractal dimension for 1 2 and 3 result to be in very good agreement with corresponding values obtained by computer simulations these results provide an important test for the fst method as a new theoretical tool to study irreversible fractal growth

short rational generating functions for lattice point problems abstract we prove that for any xed d the generating function of the projectionof the set of integer points in a rational d dimensional polytope can be computed inpolynomial time as a corollary we deduce that various interesting sets of latticepoints notably integer semigroups and minimal hilbert bases of rational cones have short rational generating functions provided certain parameters the dimensionand the number of generators are xed it follows then that many computationalproblems for such sets for example nding the number of positive integers notrepresentable as a non negative integer combination of given coprime positive integersa 1 a d admit polynomial time algorithms we also discuss a related problem ofcomputing the hilbert series of a ring generated by monomials 1 introduction and main resultsour main motivation is the following question which goes back to frobenius andsylvester 1 1 the frobenius problem let a 1 a d be positive coprime integers andlets n

p moment stability of stochastic differential equations with impulsive jump and markovian switching this paper introduces some new concepts of p moment stability for stochastic differential equations with impulsive jump and markovian switching some stability criteria of p moment stability for stochastic differential equations with impulsive jump and markovian switching are obtained by using liapunov function method an example is also discussed to illustrate the efficiency of the obtained results

theory of laplacian fractals diffusion limited aggregation and dielectric breakdown model abstract we describe a new theoretical approach that clarifies the origin of fractal structures in irreversible growth models based on the laplace equation and a stochastic field this new theory provides a systematic method for the calculation of the fractal dimension d and of the multifractal spectrum of the growth probability a detailed application to the dielectric breakdown model and diffusion limited aggregation in two dimensions is presented our approach exploits the scale invariance of the laplace equation that implies that the structure is self similar both under growth and scale transformation this allows one to introduce a fixed scale transformation instead of coarse graining as in the renormalization group theory that defines a functional equation for the fixed point of the distribution of basic diagrams used in the coarse graining process for the calculation of the matrix elements of this transformation one has to consider an infinite but rapidly convergent number of processes that occurs outside a considered diagram

an algebraic geometry algorithm for scheduling in presence of setups and correlated demands we study here a problem of schedulingn job types onm parallel machines when setups are required and the demands for the products are correlated random variables we model this problem as a chance constrained integer program

brief continuous time state feedback h2 control of markovian jump linear systems via convex analysis continuous time h 2 control problem for the class of linear systems with markovian jumps mjls using convex analysis is considered in this paper the definition of the h 2 norm for continuous time mjls is presented and related to the appropriate observability and controllability gramians a convex programming formulation for the h 2 control problem of mjls is developed that enables us to tackle the optimization problem of mjls under the assumption that the transition rate matrix p p i j for the markov chain may not be exactly known but belongs to an appropriate convex set an equivalence between the convex formulation when p is exactly known and the usual dynamic programming approach of quadratic optimal control of mjls is established it is shown that there exists a solution for the convex programming problem if and only if there exists the mean square stabilizing solution for a set of coupled algebraic riccati equations these results are compared with other related works in the current literature

output feedback control of markov jump linear systems in continuous time this paper addresses the dynamic output feedback control problem of continuous time markovian jump linear systems the fundamental point in the analysis is an lmi characterization comprising all dynamical compensators that stabilize the closed loop system in the mean square sense the h sub 2 and h sub spl infin norm control problems are studied and the h sub 2 and h sub spl infin filtering problems are solved as a by product