random number generators for parallel processors abstract the fundamental requirements for the sequence of numbers produced by a random number generator in a computer program are that 1 the sequence be indistinguishable from that produced by an iid sequence of standard uniformly distributed random variables 2 the sequence be identically reproduced on a subsequent execution of the same computer program for computers with multiple processors it is sensible to add the additional requirement that 3 the sequences used by each of the several processors be indistinguishable from independent sequences if one uses a standard random number generator developed for a uniprocessor in an environment with multiple processors then each one of these requirements may be violated this paper contains a review of previous attempts to satisfy the three requirements for a multiprocessor and concludes that none are really successful

quantum stochastic integrals under standing hypotheses abstract we study the meaning of stochastic integrals when the integrator is a quantum stochastic process which is not quite a martingale in that it obeys estimates of the type advocated by mcshane in the classical case we define the integral and solve stochastic differential equations when the von neumann algebra is finite and when it has a cyclic and separating state or weight when conditional expectations exist a quantum martingale continuity theorem is proved

criteria for the assessment of random number generators abstract for any finite sequence of pseudo random numbers special simulation problems can be constructed such that this sequence yields useless results in order to study the quality of the result of a simulation the assessment of a pseudorandom number generator based on theoretical considerations is a great advantage several criteria for the assessment of random number generators are known the most important criteria are discussed

dynamic estimation of linear systems constrained by bounds this correspondence deals with the minimum variance estimation of a gaussian process constrained by bounds a special truncated gaussian probability is shown to be fairly well adapted to this filtering scheme as its set is linearly closed with respect to convolution and multiplication operations

management of constraints in optimization problems abstract optimization problems are encountered in all scientific disciplines and in many aspects of everyday life application of established optimization methods assumes that an expert can state the optimization problem correctly unfortunately this is not the case in reality below we consider how to help an expert state and solve optimization problems the proposed technique splits constraints of an optimization problem into soft manageable and rigid constraints and modifies the soft constraints in an interactive mode with the expert the technique is illustrated with a numeric example devoted to the optimization of a real life nonlinear system

the ito clifford integral abstract we present a theory of non commutative stochastic integration analogous to the ito theory it is shown that wick products of fermi fields define martingales and that stochastic integrals with respect to these are defined for adapted operatorvalued square integrable integrands for square integrable martingales associated with an arbitrary probability gage space a stochastic integral is defined and a doob meyer decomposition for supermartingales obtained

quantum stochastic calculus on full fock modules abstract we develop a quantum stochastic calculus on full fock modules over arbitrary hilbert b b modules we find a calculus of bounded operators where all quantum stochastic integrals are limits of riemann stieltjes sums after having estalished existence and uniqueness of solutions of a large class of quantum stochastic differential equations we find necessary and sufficient conditions for unitarity of a subclass of solutions as an application we find dilations of a conservative cp semigroup quantum dynamical semigroup on b with arbitrary bounded christensen evans generator we point out that in the case b b g the calculus may be interpreted as a calculus on the full fock space tensor initial space g with arbitrary degree of freedom dilating cp semigroups with arbitrary lindblad generator finally we show how a calculus on the boolean fock module reduces to our calculus as a special case this includes a calculus on the boolean fock space

comparison of three correlation coefficient estimators for gaussian stationary processes using independent samples from two stationary gaussian processes second order statistics are examined for the following three correlation estimators 1 the direct estimator 2 a hybrid sign estimator and 3 the polarity coincidence estimator in most cases increasing the number of samples by a factor of two or three allows one to use the simple polarity coincidence estimator with the same accuracy as the other two estimators

quantum poisson processes and dilations of dynamical semigroups the notion of a quantum poisson process over a quantum measure space is introduced this process is used to construct new quantum markov processes on the matrix algebram n with stationary faithful state if is the quantum measure space in question a von neumann algebra and a faithful normal weight then the semigroupe tl of transition operators on m n has generator whereu is an arbitrary unitary element of the centraliser of m n

a feynman kac formula for anticommuting brownian motion motivated by application to quantum physics anticommuting analogues of wiener measure and brownian motion are constructed the corresponding ito integrals are defined and the existence and uniqueness of solutions to a class of stochastic differential equations is established this machinery is used to provide a feynman kac formula for a class of hamiltonians several specific examples are considered

local shannon entropy measure with statistical tests for image randomness in this paper we propose a new image randomness measure using shannon entropy over local image blocks the proposed local shannon entropy measure overcomes several weaknesses of the conventional global shannon entropy measure including unfair randomness comparisons between images of different sizes failure to discern image randomness before and after image shuffling and possible inaccurate scores for synthesized images statistical tests pertinent to this new measure are also derived this new measure is therefore both quantitative and qualitative the parameters in the local shannon entropy measure are further optimized for a better capture of local image randomness the estimated statistics and observed distribution from 50 000 experiments match the theoretical ones finally two examples are given applying the proposed measure to image randomness among shuffled images and encrypted images both examples show that the proposed method is more effective and more accurate than the global shannon entropy measure

stochastic integration on the cuntz algebra o abstract we develop a theory of non commutative stochastic integration with respect to the creation and annihilation process on the full fock space over l2 r our theory largely parallels the theories of non commutative stochastic ito integration on boson and fermion fock space as developed by r hudson and k r parthasarathy it provides the first example of a non commutative stochastic calculus which does not depend on the quantum mechanical commutation or anticommutation relations but it is based on the theory of reduced free products of c algebras by d voiculescu this theory shows that the creation and annihilation processes on the full fock space over l2 r which generate the cuntz algebra o can be interpreted as a generalized brownian motion we should stress the fact that in contrast to the other theories of stochastic integration our integrals converge in the c norm on o i e uniformly rather than in some state dependent strong operator topology or non commutative l2 norm

a smoothly constrained kalman filter this paper presents the smoothly constrained kalman filter sckf for nonlinear constraints a constraint is any relation that exists between the state variables constraints can be treated as perfect observations but linearization errors can prevent the estimate from converging to the true value therefore the sckf iteratively applies nonlinear constraints as nearly perfect observations or equivalently weakened constraints integration of new measurements is interlaced with these iterations which reduces linearization errors and hence improves convergence compared to other iterative methods the weakening is achieved by artificially increasing the variance of the nonlinear constraint the paper explains how to choose the weakening values and when to start and stop the iterative application of the constraint

non commutative probability and non commutative processes beyond the heisenberg algebra a probability space is a pair a where a is an algebra and is a state on the algebra in classical probability a is the algebra of linear combinations of indicator functions on the sample space and in quantum probability a is the heisenberg or clifford algebra however other algebras are of interest in noncommutative probability after a short review of the framework of classical and quantum probability other noncommutative probability spaces are discussed in particular those associated with noncommutative space time a probability space is a pair a where a is an algebra and is a state on the algebra in classical probability a is the algebra of linear combinations of indicator functions on the sample space and in quantum probability a is the heisenberg or clifford algebra however other algebras are of interest in noncommutative probability after a short review of the framework of classical and quantum probability other noncommutative probability spaces are discussed in particular those associated with noncommutative space time

cluster monte carlo tscaling of systematic errors in the two dimensional ising model we present an extensive analysis of systematic deviations in wolff cluster simulations of the critical ising model using random numbers generated by binary shift registers we investigate how these deviations depend on the lattice size the shift register length and the number of bits correlated by the production rule they appear to satisfy scaling relations copyright ital 1997 ital the american physical society

target tracking problems subject to kinematic constraints filtering problems with kinematic constraints which may arise in target tracking problems are considered a novel approach which treats kinematic constraints as additional fictitious or pseudomeasurements is proposed a numerical example is provided to show the technical feasibility of the proposed idea for target tracking problems this example shows that the proposed method can improve estimation accuracy significantly for velocity and acceleration states in the tracking problem however it is noted that the tracking performance may be deteriorated if the constraints do not properly represent the target characteristics and a small r sub c is chosen

a non commutative martingale representation theorem for non fock quantum brownian motion abstract a non commutative theory of stochastic integration is constructed in which the integrators are the components of the quantum brownian motion with non unit variance unlike the unit variance fock case there is a kunita watanabe type representation theorem for processes which are martingales with respect to the generated filtration

the optional stopping theorem for quantum martingales in classical probability theory a random time t is a stopping time in a filtration ft t 0 if and only if the optional sampling holds at t for all bounded martingales furthermore if a process xt t 0 is progressively measurable with respect to ft t 0 then xt is ft measurable unfortunately this is not the case in noncommutative probability with the definition of stopped process used until now it is shown in this article that we can define the stopping of noncommutative processes in fock space in such a way that all the bounded martingales can be stopped at any stopping time t are adapted to the filtration of the past before t and satisfy the optional stopping theorem

some aspects of the boson fermion in equivalence a remark on the paper by hudson and parthasarathy for original paper see commun math phys vol 104 p 457 70 1986 the author links the recently proposed unification of the boson and fermion stochastic calculus with the general problem of boson fermion equivalence duality reciprocity etc for quantum fields even if via the fock construction the common fock space for bosons and fermions can be introduced it still does not allow for the unrestricted boson fermion equivalence for field theory models all local fermion field theory models thus have boson equivalents violating the weak local commutativity condition for space dimension three the reverse statement is not valid not all boson models admit a pure fermion reconstruction

multiplicative congruential random number generators with modulus 2 an exhaustive analysis for 32 and a partial analysis for 48 this paper presents the results of a search to find optimal maximal period multipliers for multiplicative congruential random number generators with moduli 2 32 and 2 48 here a multiplier is said to be optimal if the distance between adjacent parallel hyperplanes on which k tuples lie does not exceed the minimal achievable distance by more than 25 percent for k 2 6

maximally equidistributed combined tausworthe generators tausworthe random number generators based on a primitive trinomial allow an easy and fast implementation when their parameters obey certain restrictions however such generators with those restrictions have bad statistical properties unless we combine them a generator is called maximally equidistributed if its vectors of successive values have the best possible equidistribution in all dimensions this paper shows how to find maximally equidistributed combinations in an efficient manner and gives a list of generators with that property such generators have a strong theoretical support and lend themselves to very fast software implementations

the serial test for congruential pseudorandom numbers generated by inversions two types of congruential pseudorandom number generators based on inversions were introduced recently we analyze the statistical independence properties of these pseudorandom numbers by means of the serial test the results show that these pseudorandom numbers perform satisfactorily under the serial test the methods of proof rely heavily on bounds for character sums such as the weil stepanov bound for character sums over finite fields

time orthogonal unitary dilations and noncommutative feynman kac formulae an analysis of feynman kac formulae reveals that typically the unperturbed semigroup is expressed as the expectation of a random unitary evolution and the perturbed semigroup is the expectation of a perturbation of this evolution in which the latter perturbation is effected by a cocycle with certain covariance properties with respect to the group of translations and reflections of the line we consider generalisations of the classical commutative formalism in which the probabilistic properties are described in terms of non commutative probability theory based on von neumann algebras examples of this type are generated by means of second quantisation from a unitary dilation of a given self adjoint contraction semigroup called the time orthogonal unitary dilation whose key feature is that the dilation operators corresponding to disjoint time intervals act nontrivially only in mutually orthogonal supplementary hilbert spaces

an example of a generalized brownian motion we present an example of a generalized brownian motion it is given by creation and annihilation operators on a twisted fock space ofl2 these operators fulfill for a fixed 1 1 the relationsc f c g c g c f f g 1 f g l2 we show that the distribution of these operators with respect to the vacuum expectation is a generalized gaussian distribution in the sense that all moments can be calculated from the second moments with the help of a combinatorial formula we also indicate that our brownian motion is one component of ann dimensional brownian motion which is invariant under the quantum groups u n of woronowicz with v2

a simple unpredictable pseudo random number generator two closely related pseudo random sequence generators are presented the 1 p generator with input p a prime outputs the quotient digits obtained on dividing 1 by p the x 2 bmod n generato

the functional ito formula in quantum stochastic calculus using an op algebraic approach noncommutative analogs of the ito formula of classical stochastic calculus within the framework of the hudson parthasarathy formulation of boson quantum stochastic calculus are proven

the strong markov property for fermion brownian motion abstract a concept of independence of w 2 algebras is developed which is the fermion analogue of independence of von neumann algebras for bosons for a fermion brownian motion process a t a t t r d applebaum fermion stochastic calculus ph d thesis university of nottingham 1984 and a markov time t 0 de it is shown that the process a t t a t a t t a t t r whose components are defined as spectral integrals with operator valued integrands as in r l hudson j funct anal 34 1979 266 constitutes a new fermion brownian motion process such that the pre t and post t w 2 algebras are independent

the ito clifford integral iii the markov property of solutions to stochastic differential equations it is shown that the solution to the ito clifford stochastic differential equationdx t f x t t d t d t g x t t h x t t dt wheref g h are suitable lipschitz functions and t is the fermion martingale satisfies a markov property

on the discrepancy of gfsr pseudorandom numbers a new summation formula based on the orthogonal property of walsh functions is devised using this formula the k dimensional discrepancy of the generalized feedback shift register gfsr pseudorandom numbers is derived the relation between the discrepancy and k distribution of gfsr sequences is also obtained finally the definition of optimal gpsr pseudorandom number generators is introduced

on martingale inequalities in non commutative stochastic analysis we develop a non commutativelpstochastic calculus for the clifford stochastic integral anl2theory of which has been developed by barnett streater and wilde the main results are certain non commutativelpinequalities relating clifford integrals and their integrands these results are applied to extend the domain of the clifford integral froml2tol1integrands and we give applications to optional stopping of clifford martingales proving an analog of a theorem of burkholder the stopped clifford processfthas zero expectation providedet in proving these results we establish a number of results relating the clifford integral to the differential calculus in the clifford algebra in particular we show that the clifford integral is given by the divergence operator and we prove an explicit martingale representation theorem both of these results correspond closely to basic results for stochastic analysis on wiener space thus furthering the analogy between the clifford process and brownian motion

stochastic integral representation theorem for quantum semimartingales abstract the quantum stochastic integral of ito type formulated by hudson and parthasarathy is extended to a wider class of adapted quantum stochastic processes on boson fock space an ito formula is established and a quantum stochastic integral representation theorem is proved for a class of unbounded semimartingales which includes polynomials and wick exponentials of the basic martingales in quantum stochastic calculus

stochastic schrodinger and heisenberg equations a martingale problem in quantum stochastic processes the relation between a quantum dynamical semigroup and the associated quantum stochastic processes can be formulated by an analogy in operator algebras to the martingale problem of stroock and varadhan 1969 for classical diffusions it is shown that under simple circumstances the formulation yields the explicit solution the authors give three such examples

markov dilations and quantum detailed balance we construct quantum stochastic processes whose multi time correlation functions with suitable time ordering can be obtained from a quantum dynamical semigroup we prove that such a process defines a stationary markov dilation of the associated semigroup if and only if up to technicalities the semigroup satisfies the quantum detailed balance condition with respect to its stationary state

the hierarchy of correlations in random binary sequences the meaning of randomness is studied for the simple case of binary sequences ensemble theory is used together with correlation coefficients of any order conservation laws for the total amount of correlation are obtained they imply that true randomness is an ensemble property and can never be achieved in a single sequence the relation with entropy is discussed for different ensembles well tempered pseudorandom sequences turn out to be suitable sources of random numbers and practical recipes to generate them for use in large scale monte carlo simulations are found

stop times in fock space stochastic calculus a stop time s in the boson fock space over l 2 is a spectral measure in 0 such that s 0 t is an adapted process following the ideas of hudson 6 to each stop time s a canonical shift operator u sis constructed in when s has the vacuum as a null vector u sbecomes an isometry when s 0 it is shown that admits a factorisation s s where s is the range of u sand s is a suitable subspace of called the fock space upto time s this in particular implies the strong markov property of quantum brownian motion in the boson as well as fermion sense and the dynkin hunt property that the classical brownian motion begins afresh at each stop time the stopped weyl and fermion processes are defined and their properties studied a composition operation is introduced in the space of stop time to make it a semigroup stop time integrals are introduced and their properties constitute the basic tools for the subject

quantum stratonovich calculus and the quantum wong zakai theorem we extend the it to stratonovich analysis or quantum stochastic differential equations introduced by gardiner and collett for emission creation absorption annihilation processes to include scattering conservation processes working within the framework of quantum stochastic calculus we define stratonovich calculus as an algebraic modification of the it one and give conditions for the existence of stratonovich time ordered exponentials we show that conversion formula for the coefficients has a striking resemblance to green s function formulas from standard perturbation theory we show that the calculus conveniently describes the markov limit of regular open quantum dynamical systems in much the same way as in the wong zakai approximation theorems of classical stochastic analysis we extend previous limit results to multiple dimensions with a proof that makes use of diagrammatic conventions

the serial test for pseudo random numbers generated by the linear congruential method we consider the linear congruential method for pseudo random number generation and establish effective criteria for the choice of parameters in this method which guarantee statistical almost independence of successive pseudo random numbers applications to numerical integration are also discussed

on a nonlinear congruential pseudorandom number generator a nonlinear congruential pseudorandom number generator with modulus m 2 w is proposed which may be viewed to comprise both linear as well as inversive congruential generators the condition for it to generate sequences of maximal period length is obtained it is akin to the inversive one and bears a remarkable resemblance to the latter

classical and quantum probability we follow the development of probability theory from the beginning of the last century emphasizing that quantum theory is really a generalization of this theory the great achievements of probability theory such as the theory of processes generalized random fields estimation theory and information geometry are reviewed their quantum versions are then described

the exact determination of rectangle discrepancy for linear congruential pseudorandom numbers l algorithme presente peut etre utilise dans les cas de grands generateurs avec un temps de calcul tres raisonnable

a characterization of stopping times left r be a random time in f the terminal element of a filtration f t satisfying the usual hypotheses it is shown that if optional sampling holds at r for all bounded martingales then r is optional if f t is the natural pseudo path filtration of a measurable process x t then r is optional if and only if the conditional distribution of x r given f r is z r where z t is an optional version of the conditional distribution of x t given f t

periodic orbits of the ensemble of sinai arnold cat maps and pseudorandom number generation we propose methods for constructing high quality pseudorandom number generators rngs based on an ensemble of hyperbolic automorphisms of the unit two dimensional torus sinai arnold map or cat map while keeping a part of the information hidden the single cat map provides the random properties expected from a good rng and is hence an appropriate building block for an rng although unnecessary correlations are always present in practice we show that introducing hidden variables and introducing rotation in the rng output accompanied with the proper initialization dramatically suppress these correlations we analyze the mechanisms of the single cat map correlations analytically and show how to diminish them we generalize the percival vivaldi theory in the case of the ensemble of maps find the period of the proposed rng analytically and also analyze its properties we present efficient practical realizations for the rngs and check our predictions numerically we also test our rngs using the known stringent batteries of statistical tests and find that the statistical properties of our best generators are not worse than those of other best modern generators

constrained signal restoration via iterated extended kalman filtering the problem of estimating the input signal restoration to a known linear system point spread function given the noisy observations of the output is considered the input signal is assumed to satisfy certain known physical constraints such as positivity it is proposed to incorporate the constraints by introducing a memoryless non linearity in the system a statistical approach is taken leading to a closed form type of recursive solution in the form of iterated extended kalman filtering with two local iterations at every new data point a simulation example is presented which demonstrates the superiority of the proposed approach over the conventional kalman wiener filtering

pseudorandom vector generation by the multiple recursive matrix method pseudorandom vectors are of importance for parallelized simulation methods in this paper we carry out an in depth analysis of the multiple recursive matrix method for the generation of uniform pseudorandom vectors which was introduced in an earlier paper of the author we study in particular the periodicity properties the lattice structure and the behavior under the serial test for sequences of pseudorandom vectors generated by this method

a representation free quantum stochastic calculus abstract we develop a representation free stochastic calculus based on three inequalities semimartingale inequality scalar forward derivative inequality scalar conditional variance inequality we prove that our scheme includes all the previously developed stochastic calculi and some new examples the abstract theory is applied to prove a boson levy martingale representation theorem in bounded form and a general existence uniqueness and unitarity theorem for quantum stochastic differential equations

natural processes and doob meyer decompositions over a probability gage space wilde department of mathematics bedford college london nw1 4ns england communicated by l gross received february 21 1984 the notion of naturalness for l processes over a probability gage space is defined and the uniqueness of doob decompositions of supermartingales is discussed in particular it is shown that if a is an itbclifford stochastic integral martingale then x x has a unique decomposition into the sum of an l martingale and an increasing lx process null at

fermion ito s formula and stochastic evolutions an ito product formula is proved for stochastic integrals against fermion brownian motion and used to construct unitary processes satisfying stochastic differential equations as in the corresponding boson theory 10 11 these give rise to stochastic dilations of completely positive semigroups

arithmetical properties of strongly chaotic motions abstract the orbits of the generalized arnold sinai cat maps or hyperbolic automorphisms of the two dimensional torus typify purely chaotic anosov motion we transform the dynamics of the periodic orbits of these maps into modular arithmetic in suitable domains of quadratic integers classify all periodic orbits and show how to determine their periods and initial conditions the methods are based on ideal theory in quadratic fields which is reviewed it is shown that the structure of orbits rests upon some basic arithmetical notions such as unique factorization into prime ideals

good parameters and implementations for combined multiple recursive random number generators combining parallel multiple recursive sequences provides an efficient way of implementing random number generators with long periods and good structural properties such generators are statistically more robust than simple linear congruential generators that fit into a computer word we made extensive computer searches for good parameter sets with respect to the spectral test for combined multiple recursive generators of different sizes we also compare different implementations and give a specific code in c that is faster than previous implementations of similar generators

a nonlinear congruential pseudorandom number generator with power of two modulus a nonlinear congruential pseudorandom number generator is studied where the modulus is a power of two investigation of this generator was suggested by knuth 7 a simple necessary and sufficient condition is given for this generator to have the maximal period length

dilations of quantum dynamical semigroups with classical brownian motion we show that any quantum dynamical semigroup can be written with the help of the solution of a vector valued classical stochastic differential equation moreover this equation leads to a natural construction of a unitary dilation in term of wiener spaces

statistical independence properties of pseudorandom vectors produced by matrix generators abstract the uniformity test and the serial test are standard statistical tests for equidistribution and statistical independence respectively in sequences of uniform pseudorandom numbers we introduce analogues of these tests for sequences of uniform pseudorandom vectors and we apply these tests to matrix generators for uniform pseudorandom vector generation the results show that these generators behave well under these tests provided that the matrix in the generation algorithm is chosen carefully the essential condition is that a certain figure of merit attached to the matrix be large we also prove a general theorem which guarantees the existence of matrices with large figure of merit

a robust null space method for linear equality constrained state estimation we present a robust null space method for linear equality constrained state space estimation exploiting a degeneracy in the estimator statistics an orthogonal factorization is used to decompose the problem into stochastic and deterministic components which are then solved separately the resulting dimension reduction algorithm has enhanced numerical stability solves the constrained problem completely and can reduce computational load by reducing the problem size the new method addresses deficiencies in commonly used pseudo observation or projection methods which either do not solve the constrained problem completely or have unstable numerical implementations due in part to the degeneracy in the estimator statistics we present a numerical example demonstrating the effectiveness of the new method compared to other current methods

quantum q white noise and a q central limit theorem we establish a connection between the azema martingales and certain quantum stochastic processes with increments satisfyingq commutation relations this leads to a theory ofq white noise onq bialgebras and to a generalization of the fock space representation theorem for white noise on bialgebras in particular quantum azema noise q interpolations between fermion and boson quantum brownian motion and unitary evolutions withq independent multiplicative increments are studied it follows from our results that the azema martingales and theq interpolations are central limits of sums ofq independent identically distributed quantum random variables

regular birth times for markov processes a random time r is called a regular birth time for a markov process if i the r past and r future are conditionally independent with respect to x r and ii the post r process evolves as a markov process perhaps with different probability laws in this paper we characterize each regular birth time in terms of an earlier coterminal time l it is shown theorem 4 2 that to the post l process r appears as an optional time perhaps with dependency on pre l information and on a certain invariant set

image restoration by the method of convex projections part 1ߞtheory a projection operator onto a closed convex set in hilbert space is one of the few examples of a nonlinear map that can be defined in simple abstract terms moreover it minimizes distance and is nonexpansive and therefore shares two of the more important properties of ordinary linear orthogonal projections onto closed linear manifolds in this paper we exploit the properties of these operators to develop several iterative algorithms for image restoration from partial data which permit any number of nonlinear constraints of a certain type to be subsumed automatically their common conceptual basis is as follows every known property of an original image f is envisaged as restricting it to lie in a well defined closed convex set thus m such properties place f in the intersection e0 ei of the corresponding closed convex sets e1 e2 em given only the projection operators pi onto the individual ei s i 1 m we restore f by recursive means clearly in this approach the realization of the pi s in a hilbert space setting is one of the major synthesis problems section i describes the geometrical significance of the three main theorems in considerable detail and most of the underlying ideas are illustrated with the aid of simple diagrams section ii presents rules for the numerical implementation of 11 specific projection operators which are found to occur frequently in many signal processing applications and the appendix contains proofs of all the major results

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

multicriteria analysis tools in real life problems applied optimization problems such as design identification design of controlled systems operational development of prototypes analysis of large scale systems and forecasting from observational data are multicriteria problems in essence construction of the feasible solution set is of primary importance in the above problems the definition of a feasible solution set is usually considered to be the skill of a designer even though this skill is essential it is by no means sufficient for the correct statement of the problem there are many antagonistic performance criteria and all kinds of constraints in these problems therefore it is quite difficult to correctly determine the feasible set as a result ill posed problems are solved and optimal solutions are searched for far from where they should be as a consequence the optimization results have no practical meaning in this work we propose methods and tools that will assist the designer in defining the feasible solution set correctly

constrained state estimation for nonlinear discrete time systems stability and moving horizon approximations state estimator design for a nonlinear discrete time system is a challenging problem further complicated when additional physical insight is available in the form of inequality constraints on the state variables and disturbances one strategy for constrained state estimation is to employ online optimization using a moving horizon approximation we propose a general theory for constrained moving horizon estimation sufficient conditions for asymptotic and bounded stability are established we apply these results to develop a practical algorithm for constrained linear and nonlinear state estimation examples are used to illustrate the benefits of constrained state estimation our framework is deterministic

physical tests for random numbers in simulations we propose three physical tests to measure correlations in random numbers used in monte carlo simulations the first test uses autocorrelation times of certain physical quantities when the ising model is simulated with the wolff algorithm the second test is based on random walks and the third on blocks of ital n successive numbers we apply the tests to show that recent errors in high precision ising simulations using generalized feedback shift register algorithms are due to short range correlations in random number sequences

noncommutative brownian motion in monotone fock space an example of noncommutative brownian motion is constructed on the monotone fock space which is a kind of fock space generated by all the decreasing finite sequences of positive real numbers the probability distribution at time associated to this brownian motion is shown to be the arcsine law normalized to mean 0 and variance t

noncommutative stochastic integration through decoupling abstract we present an abstract approach to noncommutative stochastic integration in the context of a finite von neumann algebra equipped with a normal faithful tracial state with respect to processes with tensor or freely independent increments satisfying a stationarity condition using a decoupling technique we obtain necessary and sufficient conditions for stochastic integrability of l p processes with respect to such integrators we apply the theory to stochastic integration with respect to boson and free brownian motion

minimum variance estimation of parameters constrained by bounds this correspondence deals with an extension of minimum variance estimation when the parameter to be estimated is constrained by bounds it is shown that a particular initial distribution allows finite dimensional calculation and leads to a nonlinear filter more precisely it is shown that a truncated gaussian distribution is preserved a long time leading to a finite number of parameters to be computed proof of the main theorem is straightforward with significant application such as positive real amplitude estimation performance gains are shown on the loran c signal reception example

factorization of polynomials and some linear algebra problems over finite fields abstract the recently developed algorithm of niederreiter for the factorization of polynomials over finite fields provides a linearization of the factorization problem via differential equations in rational function fields we show that the range of applicability of this algorithm can be extended by various techniques such as the application of normal bases and the use of hasse teichmuller derivatives we also discuss topics from pseudorandom vector generation and combinatorial linear algebra that lead to interesting linear algebra problems over finite fields

quasi free quantum stochastic integrals for the car and ccr abstract a theory of quantum martingales and quantum stochastic integrals in quasi free representations of the car and ccr is presented for the car the results generalize some of those developed in barnett streater and wilde j funct anal 48 1982 172 212 j london math soc 27 1983 373 384 and for the ccr the results contain the standard ito theory of stochastic integration with respect to brownian motion as a special case

simulation of a directed random walk model the effect of pseudo random number correlations abstract we investigate the mechanism that leads to systematic deviations in cluster monte carlo simulations when correlated pseudo random numbers are used we present a simple model which enables an analysis of the effects due to correlations in several types of pseudo random number sequences this model provides qualitative understanding of the bias mechanism in a class of cluster monte carlo algorithms

the lattice structure of pseudo random vectors generated by matrix generators abstract in many areas of science the problems treated by monte carlo simulations become more and more complex and more extensive because of that generators like linear congruential matrix generators are needed which produce enormously many pseudo random numbers in order to assess stochastical properties of the generated pseudo random vectors the lattice structure of these matrix generators is studied here

quantum and non causal stochastic calculus the quantum stochastic calculus initiated by hudson and parthasarathy and the non causal stochastic calculus originating with the papers of hitsuda and skorohod are two potent extensions of the ito calculus currently enjoying intensive development the former provides a quantum probabilistic extension of schrodinger s equation enabling the construction of a markov process for a quantum dynamical semigroup the latter allows the treatment of stochastic differential equations which involve terms which anticipate the future in this paper the close relationship between these theories is displayed and a noncausal quantum stochastic calculus already in demand from physics is described

random number generations generators on vector supercomputers and other advanced architectures this paper is divided into three parts the first part surveys the more common techniques for generating and testing uniformly distributed random numbers the second part considers the efficient ge

a new example of independence and white noise we examine the notion of free independence according to voiculescu this form of independence is used for defining free white noise or process with stationary and freely independent increments we prove a general limit theorem giving the combinatorics of infinitely freely divisible states and thus of free white noises with the help of admissible partitions we realize the free analogues of the wiener process and of the poisson process as processes on the full fock space ofl2