technical note the stochastic discrete dynamic lot size problem an open loop solution we investigate the stochastic dynamic lot size model taking into account probabilistic constraints on the state variable our approach is to obtain an open loop solution by solving a new equivalent deterministic dynamic lot size problem with new parameters we also discuss characteristics of the new equivalent deterministic problem and note in particular that the new formulation preserves concavity or convexity

a semismooth newton cg method for constrained parameter identification in seismic tomography seismic tomography is a technique to determine the material properties of the earth s subsurface based on the observation of seismograms this can be stated as a pde constrained optimization problem governed by the elastic wave equation we present a semismooth newton pcg method with a trust region globalization for full waveform seismic inversion that uses a moreau yosida regularization to handle additional constraints on the material parameters we establish results on the differentiability of the parameter to state operator and analyze the proposed optimization method in a function space setting the elastic wave equation is discretized by a high order continuous galerkin method in space and an explicit newmark time stepping scheme the matrix free implementation relies on the adjoint based computation of the gradient and hessian vector products and on an mpi based parallelization numerical results are shown for an application in geophysical exploration at reservoir scale

a six state minimal time solution to the firing squad synchronization problem abstract from balzer s work 1967 we know that the firing squad synchronization problem has a minimal time solution with eight states we show that such a solution exists with only six states our method is somewhat different from all previous ones the initial line is iteratively divided in two inequal parts so that each new right part can be treated as the homothetical image of a shorter initial line

stochastic algorithms for inverse problems involving pdes and many measurements inverse problems involving systems of partial differential equations pdes can be very expensive to solve numerically this is so especially when many experiments involving different combinations of sources and receivers are employed in order to obtain reconstructions of acceptable quality the mere evaluation of a misfit function the distance between predicted and observed data often requires hundreds and thousands of pde solves this article develops and assesses dimensionality reduction methods both stochastic and deterministic to reduce this computational burden we assume that all experiments share the same set of receivers and concentrate on methods for reducing the number of combinations of experiments called simultaneous sources that are used at each stabilized gauss newton iteration algorithms for controlling the number of such combined sources are proposed and justified evaluating the misfit approximately except for the final verification for terminating the process always involves

invertible cellular automata a review abstract in the light of recent developments in the theory of invertible cellular automata we attempt to give a unified presentation of the subject and discuss its relevance to computer science and mathematical physics

universality and complexity in cellular automata abstract cellular automata are discrete dynamical systems with simple construction but complex self organizing behaviour evidence is presented that all one dimensional cellular automata fall into four distinct universality classes characterizations of the structures generated in these classes are discussed three classes exhibit behaviour analogous to limit points limit cycles and chaotic attractors the fourth class is probably capable of universal computation so that properties of its infinite time behaviour are undecidable

additive conserved quantities in discrete time lattice dynamical systems abstract we give a necessary and sufficient condition for the existence of additive conserved quantities for one dimensional discrete time lattice dynamical systems such as cellular automata ca and coupled map lattices proof is given for the case of nearest neighbor interaction rules the obtained condition guarantees the existence of the current conservation law and is useful for finding additive conserved quantities for ca applications are made to wolfram s elementary ca and elementary reversible ca of takesue in the latter case the additive conserved quantities are classified into those induced by local conservation laws and propagative ones

physics like models of computation abstract reversible cellular automata are computer models that embody discrete analogues of the classical physics notions of space time locality and microscopic reversibility they are offered as a step towards models of computation that are closer to fundamental physics

optimality of quasi open loop policies for discounted semi markov decision processes quasi open loop policies consist of sequences of markovian decision rules that are insensitive to one component of the state space given a semi markov decision process smdp we distinguish between exogenous and endogenous state components as follows i the decision maker s actions do not impact the evolution of an exogenous state component and ii between consecutive decision epochs the exogenous and endogenous state components are conditionally independent given the decision maker s latest action for simplicity we consider an smdp with one exogenous and one endogenous state component when transition times between epochs are conditionally independent of the exogenous state given the most recent action and the exogenous component is a multiplicative compound poisson process we provide an almost everywhere condition on the reward function sufficient for the optimality of a quasi open loop policy after adjusting the discount factor to account for the statistical properties of the exogenous state process obtaining this policy amounts to solving a reduced smdp in which the exogenous state is static depending on the relationship between the structure of the exogenous state process and the shape of the reward function we can replace the almost everywhere condition with one that applies only in expectation quasi open loop optimality holds even if the times between decision epochs depend on the poisson process underlying the exogenous state component and or the poisson process is replaced with a generic counting process

an effective method for parameter estimation with pde constraints with multiple right hand sides often parameter estimation problems of parameter dependent pdes involve multiple right hand sides the computational cost and memory requirements of such problems increase linearly with the number

a complete and efficiently computable topological classification of d dimensional linear cellular automata over z m we study the dynamical behavior of d dimensional linear cellular automata over zm we provide easy to check necessary and sufficient conditions for a d dimensional linear cellular automata over zm to be sensitive to initial conditions positively expansive strongly transitive and equicontinuous as a consequence of our results we have a complete and efficiently computable topological classification of d dimensional linear cellular automata over zm according to the most important dynamical properties studied in the theory of discrete time dynamical systems

classifying circular cellular automata we introduce a hierarchy of linear cellular automata based on their limiting behavior on spatially periodic configurations we show that it is undecidable to which class in the hierarchy a cellular automaton belongs in particular it is undecidable whether all spatially periodic configurations evolve to a fixed point furthermore there is no computable bound on the period lengths of these configurations our arguments are based on a non standard simulation of turing machines on circular cellular automata

optimal regularized low rank inverse approximation abstract in this paper we consider the problem of finding approximate inverses of a given matrix we give an explicit solution to the rank constrained regularized inverse approximation problem and obtain an inverse regularized eckart young like theorem

stochastic sampling for deterministic structural topology optimization with many load cases density based and ground structure approaches abstract we propose an efficient probabilistic method to solve a fully deterministic problem we present a randomized optimization approach that drastically reduces the enormous computational cost of optimizing designs under many load cases for both continuum and truss topology optimization practical structural designs by deterministic topology optimization typically involve many load cases possibly hundreds or more the optimal design minimizes a possibly weighted average of the compliance under each load case or some other objective this means that in each optimization step a large finite element problem must be solved for each load case leading to an enormous computational effort on the contrary the proposed randomized optimization method with stochastic sampling requires the solution of only a few e g 5 or 6 finite element problems large linear systems per optimization step based on simulated annealing we introduce a damping scheme for the randomized approach through numerical examples in two and three dimensions we demonstrate that the randomization algorithm drastically reduces computational cost to obtain similar final topologies and results e g compliance to those of standard algorithms the results indicate that the damping scheme is effective and leads to rapid convergence of the proposed algorithm

on the limit sets of cellular automata the limit sets of cellular automata defined by wolfram play an important role in applications of cellular automata to complex systems a number of results on limit sets are proved considering both finite and infinite configurations of cellular automata the main concern of this paper is with testing membership and essential emptiness of limit sets for linear and two dimensional cellular automata

ergodicity transitivity and regularity for linear cellular automata over z m 1 we study the dynamical behavior of d dimensional linear cellular automata over zm we provide an easy to check necessary and sufficient condition for a d dimensional linear cellular automata over zm to be ergodic and topologically transitive as a byproduct we get that for linear cellular automata ergodicity is equivalent to topological transitivity finally we prove that for 1 dimensional linear cellular automata over zm regularity denseness of periodic orbits is equivalent to surjectivity

optimal information acquisition for a linear quadratic control problem this paper develops a generalization of the linear quadratic control problem with partial information as in the standard partial information setting it is assumed that the state variable is only observed with noise the idea in this paper is that the information level may be chosen optimally in real life information is costly to acquire it is therefore a trade off between the costs of getting detailed information and the increased value this information gives we believe that the technique we present should have potential for application within both economics and engineering

3d frequency domain seismic inversion with controlled sloppiness seismic waveform inversion aims at obtaining detailed estimates of subsurface medium parameters such as the spatial distribution of soundspeed from multiexperiment seismic data a formulation of this inverse problem in the frequency domain leads to an optimization problem constrained by a helmholtz equation with many right hand sides application of this technique to industry scale problems faces several challenges first we need to solve the helmholtz equation for high wave numbers over large computational domains second the data consist of many independent experiments leading to a large number of pde solves this results in high computational complexity both in terms of memory and cpu time as well as input output costs finally the inverse problem is highly nonlinear and a lot of art goes into preprocessing and regularization ideally an inversion needs to be run several times with different initial guesses and or tuning parameters in this paper we discuss the requirements of the various components pde solver optimization method dots when applied to large scale three dimensional seismic waveform inversion and combine several existing approaches into a flexible inversion scheme for seismic waveform inversion the scheme is based on the idea that in the early stages of the inversion we do not need all the data or very accurate pde solves we base our method on an existing preconditioned krylov solver carp cg and use ideas from stochastic optimization to formulate a gradient based quasi newton optimization algorithm that works with small subsets of the right hand sides and uses inexact pde solves for the gradient calculations we propose novel heuristics to adaptively control both the accuracy and the number of right hand sides we illustrate the algorithms on synthetic benchmark models for which significant computational gains can be made without being sensitive to noise and without losing the accuracy of the inverted model

the 4 way deterministic tiling problem is undecidable it is shown that the infinite tiling problem by wang tiles is undecidable even if the given tile set is deterministic by all four corners i e a tile is uniquely determined by the colors of any two adjacent edges the reduction is done from the turing machine halting problem and uses the aperiodic tile set of kari and papasoglu

relating the power of cellular arrays to their closure properties there are many fundamental open problems concerning cellular arrays ca s for example 1 is the class of real time ca languages closed under reversal concatenation 2 2 are linear time ca s more powerful than real time ca s 3 3 are nonlinear time ca s more powerful than linear time ca s 4 4 does one way communication reduce the computing power of a ca although some of these problems appear to be easier to resolve than the others e g problem 1 seems easier than 2 no solution to any of these problems is forthcoming in this paper we investigate the relationships among these problems as well as prove some positive results concerning ca s we show a a the class of real time ca languages is closed under reversal if and only if linear time ca s are equivalent to real time ca s b if ca s are more powerful than ca s restricted to one way data communication i e one way ca s then nonlinear time ca s are more powerful than linear time ca s c c if the class of real time ca languages is closed under reversal then it is also closed under concatenation in the case of unary ca languages we show that the class is closed under concatenation we also show that the languagel 0n1m m n 0 mdividesn is a real time ca language disproving a conjecture of bucher and culik

theory of cellular automata a survey this article surveys some theoretical aspects of cellular automata ca research in particular we discuss classical and new results on reversibility conservation laws limit sets decidability questions universality and topological dynamics of ca the selection of topics is by no means comprehensive and reflects the research interests of the author the main goal is to provide a tutorial of ca theory to researchers in other branches of natural computing to give a compact collection of known results with references to their proofs and to suggest some open problems

the nilpotency problem of one dimensional cellular automata the limit set of a celullar automaton consists of all the configurations of the automaton that can appear after arbitrarily long computations it is known that the limit set is never empty it contains at least one homogeneous configuration a ca is called nilpotent if its limit set contains just one configuration the present work proves that it is algorithmically undecidable whether a given one dimensional cellular automaton is nilpotent the proof is based on a generalization of the well known result about the undecidability of the tiling problem of the plane the generalization states that the tiling problem remains undecidable even if one considers only so called nw deterministic tile sets that is tile sets in which the left and upper neighbors of each tile determine the tile uniquely the nilpotency problem is known to be undecidable for d dimensional ca for d geq 2 the result is the basis of the proof of rice s theorem for ca limit sets which states that every nontrivial property of limit set

a new optimization approach for source encoding full waveform inversion waveform inversion is the method of choice for determining a highly heterogeneous subsurface structure however conventional waveform inversion requires that the wavefield for each source is computed separately this makes it very expensive for realistic 3d seismic surveys source encoding waveform inversion in which the sources are modeled simultaneously is considerably faster than conventional waveform inversion but suffers from artifacts these artifacts can partly be removed by assigning random weights to the source wavefields we found that the misfit function and therefore also its gradient for source encoding waveform inversion is an unbiased random estimation of the misfit function used in conventional waveform inversion we found a new method of source encoding waveform inversion that takes into account the random nature of the gradients used in the optimization in this new method the gradient at each iteration is a weighted average of past gradients such that the most recent gradients have the largest weights with exponential decay this way we damped the random fluctuations of the gradient by incorporating information from the previous iterations we compared this new method with existing source encoding waveform inversion methods as well as conventional waveform inversion and found that the model misfit reduction is faster and smoother than those of existing source encoding waveform inversion methods and it approaches the model misfit reduction obtained in conventional waveform inversion

robust inversion dimensionality reduction and randomized sampling we consider a class of inverse problems in which the forward model is the solution operator to linear odes or pdes this class admits several dimensionality reduction techniques based on data averaging or sampling which are especially useful for large scale problems we survey these approaches and their connection to stochastic optimization the data averaging approach is only viable however for a least squares misfit which is sensitive to outliers in the data and artifacts unexplained by the forward model this motivates us to propose a robust formulation based on the student s t distribution of the error we demonstrate how the corresponding penalty function together with the sampling approach can obtain good results for a large scale seismic inverse problem with 50 corrupted data

complexities for generalized models of self assembly in this paper we study the complexity of self assembly under models that are natural generalizations of the tile self assembly model in particular we extend rothemund and winfree s study of the tile complexity of tile self assembly proceedings of the 32nd annual acm symposium on theory of computing portland or 2000 pp 459 468 they provided a lower bound of omega frac log n log log n on the tile complexity of assembling an n times n square for almost all n adleman et al proceedings of the 33rd annual acm symposium on theory of computing heraklion greece 2001 pp 740 748 gave a construction which achieves this bound we consider whether the tile complexity for self assembly can be reduced through several natural generalizations of the model one of our results is a tile set of size o sqrt log n which assembles an n times n square in a model which allows flexible glue strength between nonequal glues this result is matched for almost all n by a lower bound dictated by kolmogorov complexity for three other generalizations we show that the omega frac log n log log n lower bound applies to n times n squares at the same time we demonstrate that there are some other shapes for which these generalizations allow reduced tile sets specifically for thin rectangles with length n and width k we provide a tighter lower bound of omega frac n 1 k k for the standard model yet we also give a construction which achieves o frac log n log log n complexity in a model in which the temperature of the tile system is adjusted during assembly we also investigate the problem of verifying whether a given tile system uniquely assembles into a given shape we show that this problem is np hard for three of the generalized models

an optimal solution for the stochastic version of the wagner whitin dynamic lot size model we present an algorithm for determining the optimal solution over the entire planning horizon for the dynamic lot size model where demand is stochastic and non stationary the optimal solution to the deterministic problem is the well known wagner whitin algorithm the present work contributes principally to knowledge building and provides a tool for researchers one potentially useful contribution to practice is the solution to an important special case where demand follows normal distributions other contributions to practice will likely flow from the development of improved heuristics and the improved basis to evaluate heuristic performance

rice s theorem for the limit sets of cellular automata abstract rice s theorem is a well known result in the theory of recursive functions a corresponding theorem for cellular automata limit sets is proved all nontrivial properties of limit sets of cellular automata cas are shown undecidable the theorem remains valid even if only one dimensional cas are considered

dipole codes attractively encode glue functions dipole words are sequences of magnetic dipoles in which alike elements repel and opposite elements attract magnetic dipoles contrast with more general sets of bonding types called glues in which pairwise bonding strength is specified by a glue function we prove that every glue function g has a set of dipole words called a dipole code that attractively encodes g the pairwise attractions positive or non positive bond strength between the words are identical to those of g moreover we give such word sets of asymptotically optimal length similar results are obtained for a commonly used subclass of glue functions

formal languages and global cellular automaton behavior abstract a connection is made between the description of one dimensional cellular automata as dynamical systems acting on a compact metric space and as computational systems acting on strings operators are defined which determine a bijective correspondence between subshifts of infinite configurations and languages of finite strings under this correspondence families of languages give rise to families of subshifts regular languages correspond to sofic subshifts families of subshifts corresponding to context free context sensitive and recursively enumerable languages are introduced and their closure properties under forward and backward cellular automaton images studied