averaged controllability of parameter dependent conservative semigroups abstract we consider the problem of averaged controllability for parameter depending either in a discrete or continuous fashion control systems the aim being to find a control independent of the unknown parameters so that the average of the states is controlled we do it in the context of conservative models both in an abstract setting and also analysing the specific examples of the wave and schrodinger equations our first result is of perturbative nature assuming the averaging probability measure to be a small parameter dependent perturbation in a sense that we make precise of an atomic measure given by a dirac mass corresponding to a specific realisation of the system we show that the averaged controllability property is achieved whenever the system corresponding to the support of the dirac is controllable similar tools can be employed to obtain averaged versions of the so called ingham inequalities particular attention is devoted to the 1d wave equation in which the time periodicity of solutions can be exploited to obtain more precise results provided the parameters involved satisfy diophantine conditions ensuring the lack of resonances

constant depth reducibility the purpose of this paper is to study reducibilities that can be computed by combinational logic networks of polynomial size and constant depth containing and s or s and not s with no bound placed on the fan in of and gates and or gates two such reducibilities are defined and reductions and equivalences among several common problems such as parity sorting integer multiplication graph connectivity bipartite matching and network flow are given certain problems are shown to be complete with respect to these reducibilities in the complexity classes deterministic logarithmic space nondeterministic logarithmic space and deterministic polynomial time new upper bounds on the size depth unbounded fan in circuit complexity of symmetric boolean functions are established

on efficient implicit obdd based algorithms for maximal matchings the maximal matching problem i e the computation of a matching that is not a proper subset of another matching is a fundamental optimization problem and maximal matching algorithms have been used as submodules for problems like maximal node disjoint paths or maximum flow since in some applications very large graphs have to be processed a research branch has emerged which is concerned with the design and analysis of implicit algorithms for classical graph problems input graphs are given as characteristic boolean functions of their edge sets and problems have to be solved by functional operations as obdds which are closely related to deterministic finite automata are a well known data structure for boolean functions obdd based algorithms are used as a heuristic approach to handle very large graphs here an implicit obdd based maximal matching algorithm is presented that uses only a polylogarithmic number of functional operations with respect to the number of vertices of the input graph in order to investigate the algorithm s behavior on large and structured networks it is analyzed on grid graphs it is shown that the overall running time and the space requirement is also polylogarithmic furthermore we present another algorithm similar to the well known karp sipser approach and we investigate the representation size of maximal matchings

boundary controllability of a hybrid system consisting in two flexible beams connected by a point mass we consider a hybrid system consisting of two flexible beams connected by a point mass the constant of rotational inertia is assumed to be nonzero in a previous paper we have proved that in the presence of the point mass the system is well posed in asymmetric spaces in which solutions have one more degree of regularity to one side of the mass we are interested in the problem of controllability when the control acts on the free extreme of one of the beams we prove that when the control time is large enough the system is exactly controllable in an asymmetric space this result is sharp the proofs combine classical techniques from asymptotic analysis and the theory of nonharmonic fourier series

null boundary controllability of a one dimensional heat equation with an internal point mass and variable coefficients in this paper we consider a linear hybrid system which is composed by two non homogeneous rods connected by a point mass with dirichlet boundary conditions on the left end and a boundary control acts on the right end we prove that this system is null controllable with dirichlet or neumann boundary controls our approach is mainly based on a detailed spectral analysis together with the moment method in particular we show that the associated spectral gap in both cases dirichlet or neumann boundary controls is positive without further conditions on the coefficients other than the regularities

using interior point methods for fast parallel algorithms for bipartite matching and related problems in this paper interior point methods for linear programming developed in the context of sequential computation are used to obtain a parallel algorithm for the bipartite matching problem this algorithm finds a maximum cardinality matching in a bipartite graph with n nodes and m edges in o sqrt m log 3 n time on a crcw pram the results here extend to the weighted bipartite matching problem and to the zero one minimum cost flow problem yielding o sqrt m log 2 n log nc algorithms where c 1 is an upper bound on the absolute value of the integral weights or costs in the two problems respectively the results here improve previous bounds on these problems and introduce interior point methods to the context of parallel algorithm design

locality in distributed graph algorithms this paper concerns a number of algorithmic problems on graphs and how they may be solved in a distributed fashion the computational model is such that each node of the graph is occupied by a processor which has its own id processors are restricted to collecting data from others which are at a distance at most t away from them in t time units but are otherwise computationally unbounded this model focuses on the issue of locality in distributed processing namely to what extent a global solution to a computational problem can be obtained from locally available data three results are proved within this model a 3 coloring of an n cycle requires time omega log n this bound is tight by previous work of cole and vishkin any algorithm for coloring the d regular tree of radius r which runs for time at most 2r 3 requires at least omega sqrt d colors in an n vertex graph of largest degree delta an o delta 2 coloring may be found in time o log n

on the simplicity of eigenvalues of two nonhomogeneous euler bernoulli beams connected by a point mass abstract in this paper we consider a linear system modeling the vibrations of two nonhomogeneous euler bernoulli beams connected by a point mass this system is generated by the following equations x y t t t x x y x x t x x x q x y x t x x 0 t 0 x 1 0 0 1 m y t t t 0 t y t x x 0 t y t x x 0 t 0 with hinged boundary conditions at both ends where m 0 x 0 x 0 q x 0 and t y x y x x x q x y x for x 1 0 0 1 we prove that all the associated eigenvalues n n 1 are algebraically simple furthermore the corresponding eigenfunctions n n 1 satisfy n 1 t n 1 0 and n 1 t n 1 0 for all n 1 these results are essential for the proof of the exact boundary controllability problem related to this system by means of the non harmonic fourier series method

analysis of a viscoelastic spring mass model in this paper we consider a linear wave equation with strong damping and dynamical boundary conditions as an alternative model for the classical spring mass damper ode our purpose is to compare analytically these two approaches to the same physical system we take a functional analysis point of view based on semigroup theory spectral perturbation analysis and dominant eigenvalues

on universal classes of extremely random constant time hash functions a family of functions f that map 0 m 1 into 0 n 1 is said to be h wise independent if any tuple of h distinct points in 0 m 1 have a corresponding image for a randomly selected f in f that is uniformly distributed in 0 n 1 h this paper shows that for suitably fixed epsilon 1 and any h m epsilon there are families of h wise independent functions that can be evaluated in constant time for the standard random access model of computation it is also proven that any such family requires a storage array of m delta random seeds for a suitable delta 1 these seeds can be pseudorandom values precomputed from an initial o h random seeds a simple adaptation yields n epsilon wise independent functions that require n delta storage in many cases where m gg n lower bounds are presented to show that neither storage requirement can be materially reduced previous constructions of random functions having constant evaluation time and sublinear storage exhibited only a constant degree of independence unfortunately the explicit randomized constructions while requiring a constant number of operations are far too slow for any practical application however nonconstructive existence arguments are given which suggest that this factor might be eliminated the problem of eliminating this factor is shown to be equivalent to a fundamental open question in graph theory as a consequence of these constructions many probabilistic algorithms from traditional hashing to ranade s emulation of common pram algorithms can for the first time be shown to achieve up to constant factors their expected asymptotic performance for a programmable albeit formal and currently impractical model of computation and a research direction is now available that may eventually lead to implementations that are fast and provably sound

small bias probability spaces efficient constructions and applications it is shown how to efficiently construct a small probability space on n binary random variables such that for every subset its parity is either zero or one with almost equal probability they are called epsilon biased random variables the number of random bits needed to generate the random variables is o log n log frac 1 epsilon thus if epsilon is polynomially small then the size of the sample space is also polynomial random variables that are epsilon biased can be used to construct almost k wise independent random variables where epsilon is a function of k these probability spaces have various applications l derandomization of algorithms many randomized algorithms that require only k wise independence of their random bits where k is bounded by o log n can be derandomized by using epsilon biased random variables 2 reducing the number of random bits required by certain randomized algorithms e g verification of matrix multiplication 3 exhaustive tes

the size of reduced obdd s and optimal read once branching programs for almost all boolean functions boolean functions are often represented by ordered binary decision diagrams obdds introduced by bryant 1986 liaw and lin 1992 have proved upper and lower bounds on the minimal obdd size of almost all boolean functions now tight bounds are proved for the minimal obdd size for arbitrary or optimal variable orderings and for the minimal read once branching program size of almost all functions almost all boolean functions have a sensitivity of almost 1 i e the minimal obdd size for an optimal variable ordering differs from the minimal obdd size for a worst variable ordering by a factor of at most 1 spl epsi n where spl epsi n converges exponentially fast to 0

implicit computation of maximum bipartite matchings by sublinear functional operations the maximum bipartite matching problem an important problem in combinatorial optimization has been studied for a long time in order to solve problems for very large structured graphs in reasonable time and space implicit algorithms have been investigated any object to be manipulated is binary encoded and problems have to be solved mainly by functional operations on the corresponding boolean functions obdds are a popular data structure for boolean functions therefore obdd based algorithms have been used as a heuristic approach to handle large input graphs here two obdd based maximum bipartite matching algorithms are presented which are the first ones using only a sublinear number of operations with respect to the number of vertices of the input graph for a problem unknown to be in nc the complexity class that contains all problems computable in deterministic polylogarithmic time with polynomially many processors furthermore the algorithms are experimentally evaluated

a sublinear parallel algorithm for stable matching abstract a parallel algorithm for the stable matching problem is presented the algorithm is based on the primal dual interior path following method for linear programming the main result is that a stable matching can be found in o m time by a polynomial number of processors where m is the total length of preference lists of individuals

asymptotic stability and blow up for a semilinear damped wave equation with dynamic boundary conditions abstract in this paper we consider a multi dimensional wave equation with dynamic boundary conditions related to the kelvin voigt damping global existence and asymptotic stability of solutions starting in a stable set are proved blow up for solutions of the problem with linear dynamic boundary conditions with initial data in the unstable set is also obtained

exact controllability and stabilization of a vibrating string with an interior point mass in this article we examine the problems of boundary control and stabilization for a one dimensional wave equation with interior point masses we show that singularities in waves are smoothed one order as they cross a point mass thus in the case of one interior point mass with e g l 2 dirichlet control at the left end the most general reachable space from 0 that one can expect is l 2 times h 1 to the left of the mass and h 1 times l 2 to the right of the mass we show that this is in fact the optimal result modulo certain compatibility conditions several related results for both control and stabilization of such systems are also given

numerical approximation schemes for multi dimensional wave equations in asymmetric spaces we develop finite difference numerical schemes for a model arising in multi body structures previously analyzed by h koch and e zuazua 13 constituted by two n dimensional wave equations coupled with a n 1 dimensional one along a flexible interface that model under suitable assumptions on the speed of propagation in each media is well posed in asymmetric spaces in which the regularity of solutions differs by one derivative from one medium to the other here we consider a flat interface and analyze this property at a discrete level for finite difference and mixed finite element methods on regular meshes parallel to the interface we prove that those methods are well posed in such asymmetric spaces uniformly with respect to the mesh size parameters and we prove the convergence of the numerical solutions towards the continuous ones in these spaces in other words these numerical methods that are well behaved in standard energy spaces preserve the convergence properties in these asymmetric spaces too these results are illustrated by several numerical experiments

quasi proper meromorphic equivalence relations the aim of this article is to complete and generalize results of mathieu ann inst fourier grenoble t 50 1155 1189 2000 and barlet comment math helv 83 869 888 2008 and to show that they imply a rather general existence theorem for meromorphic quotients of strongly quasi proper meromorphic equivalence relations in this context generic equivalence classes are asked to be pure dimensional closed analytic subset with finitely many irreducible components as an application of these methods we prove a stein factorization theorem for a strongly quasi proper map

a simple parallel algorithm for the maximal independent set problem two basic design strategies are used to develop a very simple and fast parallel algorithms for the maximal independent set mis problem the first strategy consists of assigning identical copies o

almost k wise independence and hard boolean functions we construct boolean functions computable by polynomial size circuits with large lower bounds for read once branching program 1 b p s a function in p with the lower bound 2n polylog n a function in quasipolynomial time with the lower bound 2n o log n and a function in linspace with the lower bound 2n log n o 1 our constructions are simpler than those of andreev et al electronic colloq on computational complexity tr97 053 1997 as we apply the idea of almost k wise independence more directly without the use of discrepancy set generators for large affine subspaces the simplicity of our constructions also allows us to observe that there exists a boolean function in ac0 2 computable by a depth 3 polynomial size circuit over the basis 1 with the optimal lower bound 2n log n o 1 for 1 b p s

randomized obdd based graph algorithms abstract implicit graph algorithms deal with the characteristic function e of the edge set e of a graph g v e encoding the nodes by binary vectors e can be represented by an ordered binary decision diagram obdd which is a well known data structure for boolean functions obdd based graph algorithms solve graph optimization problems by mainly using functional operations and are a heuristic approach to cope with massive graphs these algorithms heavily rely on a compact representation of the underlying boolean functions which is why all previously known obdd based algorithms are deterministic since random functions are not compressible in general here the first randomized obdd based algorithms are presented where random functions with limited independence are used to overcome the large representation size on the theoretical part we investigate the size of obdds representing k wise independent random functions in addition we give a construction of almost k wise independent random functions by means of a random obdd generation and show an almost matching lower bound of the obdd size representing such random functions on the algorithmic part randomization often facilitates the design of simple algorithms which in the context of obdd based algorithms means a small number of functional operations and as few input variables of the used boolean functions as possible we present two randomized implicit algorithms a randomized minimum spanning tree algorithm and a maximal matching algorithm the matching algorithm needs o log 3 v functional operations in expectation and uses functions with at most 3 log v variables which is both better than the best known deterministic algorithms w r t functional operations and variables the algorithm may be of independent interest the experimental evaluation of the algorithms shows that they outperform known obdd based algorithms for the maximal matching problem and the minimum spanning tree problem

on symbolic obdd based algorithms for the minimum spanning tree problem the minimum spanning tree problem is one of the most fundamental algorithmic graph problems and obdds are a very common dynamic data structure for boolean functions since in some applications graphs become larger and larger a research branch has emerged which is concerned with the design and analysis of so called symbolic algorithms for classical graph problems on obdd represented graph instances here a symbolic minimum spanning tree algorithm using o log 3 v functional operations is presented where v is the set of vertices of the input graph moreover the computation of the transitive closure is investigated and it is proved that there can be an exponential blow up from input to output size furthermore answering an open problem posed by sawitzki 37 it is shown that every symbolic obdd based algorithm for the minimum spanning tree problem needs exponential space with respect to the obdd size of the input graph this result even holds for planar input graphs

periodic solutions for a weakly dissipated hybrid system abstract we consider the motion of a stretched string coupled with a rigid body at one end and we study the existence of periodic solution when a periodic force f acts on the body the main difficulty of the study is related to the weak dissipation that characterizes this hybrid system which does not ensure a uniform decay rate of the energy under additional regularity conditions on f we use a perturbation argument in order to prove the existence of a periodic solution in the last part of the paper we present some numerical simulations based on the theoretical results

a randomized linear time algorithm to find minimum spanning trees we present a randomized linear time algorithm to find a minimum spanning tree in a connected graph with edge weights the algorithm uses random sampling in combination with a recently discovered linear time algorithm for verifying a minimum spanning tree our computational model is a unit cost random access machine with the restriction that the only operations allowed on edge weights are binary comparisons