Showing papers on "Randomness published in 1988"
TL;DR: A new model for weak random physical sources is presented that strictly generalizes previous models and provides a fruitful viewpoint on problems studied previously such as Extracting almost-perfect bits from sources of weak randomness.
Abstract: A new model for weak random physical sources is presented. The new model strictly generalizes previous models (e.g., the Santha and Vazirani model [27]). The sources considered output strings according to probability distributions in which no single string is too probable.The new model provides a fruitful viewpoint on problems studied previously such as: • Extracting almost-perfect bits from sources of weak randomness. The question of possibility as well as the question of efficiency of such extraction schemes are addressed. • Probabilistic communication complexity. It is shown that most functions have linear communication complexity in a very strong probabilistic sense. • Robustness of BPP with respect to sources of weak randomness (generalizing a result of Vazirani and Vazirani [32], [33]).
537 citations
TL;DR: The relation of depth and thermodynamic depth to previously proposed definitions of complexity is discussed, and applications to physical, chemical, and mathematical problems are proposed.
524 citations
TL;DR: In this paper, a system of random walks or directed polymers interacting weakly with an environment which is random in space and time is considered and it is shown that the behavior is diffusive with probability one.
Abstract: We consider a system of random walks or directed polymers interacting weakly with an environment which is random in space and time. In spatial dimensionsd>2, we establish that the behavior is diffusive with probability one. The diffusion constant is not renormalized by the interaction.
254 citations
24 Oct 1988
TL;DR: A parallel algorithm for the Delta +1 vertex coloring problem with running time O(log/sup 3/ nlog log n) using a linear number of processors on a concurrent-read-concurrent-write parallel random-access machine.
Abstract: Some general techniques are developed for removing randomness from randomized NC algorithms without a blowup in the number of processors. One of the requirements for the application of these techniques is that the analysis of the randomized algorithm uses only pairwise independence. The main new result is a parallel algorithm for the Delta +1 vertex coloring problem with running time O(log/sup 3/ nlog log n) using a linear number of processors on a concurrent-read-concurrent-write parallel random-access machine. The techniques also apply to several other problems, including the maximal-independent-set problem and the maximal-matching problem. The application of the general technique to these last two problems is mostly of academic interest, because NC algorithms using a linear number of processors that have better running times have been previously found. >
210 citations
TL;DR: In this article, a random medium is considered, composed of identifiable interactive sites or obstacles equilibrated at a high temperature and then quenched rapidly to form a rigid structure, statistically homogeneous on all but molecular length scales.
Abstract: A random medium is considered, composed of identifiable interactive sites or obstacles equilibrated at a high temperature and then quenched rapidly to form a rigid structure, statistically homogeneous on all but molecular length scales. The equilibrium statistical mechanics of a fluid contained inside this quenched medium is discussed. Various particle-particle and particle-obstacle correlation functions, which differ from the corresponding functions for a fully equilibrated binary mixture, are defined through an averaging process over the static ensemble of obstacle configurations and application of topological reduction techniques. The Ornstein-Zernike equations also differ from their equilibrium counterparts.
207 citations
TL;DR: Algorithmic Definition of Randomness: Finite Case 400 2.2.
Abstract: CONTENTS Introduction 389 1. Algorithmic Definition of Randomness: Infinite Case 390 1.1. From finite chains to infinite sequences 390 1.2. Three properties of a random sequence 391 1.3. Typical sequences: definition 392 1.4. Chaotic sequences: equivalent definitions 393 1.5. Random sequences: definition 395 1.6. Stochastic sequences: attempts at a definition 396 1.7. Computable distributions and other generalizations 399 2. Algorithmic Definition of Randomness: Finite Case 400 2.
160 citations
TL;DR: In this paper, the limits of solid state order which are physically possible on cooling thermotropic random copolymers from the liquid crystalline phase were investigated using a two dimensional computer modelling routine.
109 citations
TL;DR: Probabilistic finite element method (PFEM), synthesizing the power of finite element methods with second-moment techniques, is formulated for various classes of problems in structural and solid mechanics as mentioned in this paper.
Abstract: Probabilistic finite element method (PFEM), synthesizing the power of finite element methods with second-moment techniques, are formulated for various classes of problems in structural and solid mechanics. Time-invariant random materials, geometric properties, and loads are incorporated in terms of their fundamental statistics viz. second-moments. Analogous to the discretization of the displacement field in finite element methods, the random fields are also discretized. Preserving the conceptual simplicity, the response moments are calculated with minimal computations. By incorporating certain computational techniques, these methods are shown to be capable of handling large systems with many sources of uncertainties. By construction, these methods are applicable when the scale of randomness is not very large and when the probabilistic density functions have decaying tails. The accuracy and efficiency of these methods, along with their limitations, are demonstrated by various applications. Results obtained are compared with those of Monte Carlo simulation and it is shown that good accuracy can be obtained for both linear and nonlinear problems. The methods are amenable to implementation in deterministic FEM based computer codes.
87 citations
TL;DR: In this article, the authors studied mutual synchronisation in a model of interacting limit cycle oscillators with random intrinsic frequencies, and showed rigorously that the model exhibits no long-range order in one dimension, and that in higher-dimensional lattices, large clusters of synchronised oscillators necessarily have a sponge-like structure.
Abstract: The authors study mutual synchronisation in a model of interacting limit cycle oscillators with random intrinsic frequencies. It is shown rigorously that the model exhibits no long-range order in one dimension, and that in higher-dimensional lattices, large clusters of synchronised oscillators necessarily have a sponge-like structure. Surprisingly, the phase-locking behaviour of the mean-field model is completely different from that of any finite-dimensional lattice, indicating that d= infinity is the upper critical dimension for phase locking.
87 citations
TL;DR: A survey of recent results and techniques for Schrodinger operators with random and quasiperiodic potentials can be found in this paper, where a new proof of localization for random potentials, established in collaboration with H. von Dreifus, is sketched.
Abstract: A survey is made of some recent mathematical results and techniques for Schrodinger operators with random and quasiperiodic potentials. A new proof of localization for random potentials, established in collaboration with H. von Dreifus, is sketched.
83 citations
AT&T1
TL;DR: The theoretical efficiency evaluation is encouraging: for 768 × 768 spins using a parallel processor with 256 processing elements, the estimated efficiency is not lower than 71%.
TL;DR: In this article, exact identities for a family of models including (a) a domain wall in a random field Ising model (RFIM), and (b) the random anisotropy model in the no-vortex approximation were derived.
Abstract: Exact identities are derived for a family of models including (a) a domain wall in a random field Ising model (RFIM), and (b) the random anisotropyXY model in the no-vortex approximation. In particular, the second moment of thermal fluctuations is not affected by frozen randomness. It is checked in a one-dimensional model that higher moments are on the contrary strongly enhanced. Thus, thermal fluctuations are strongly non-Gaussian. This reflects excursions between remote potential wells in the phase space. It is shown exactly that the Imry-Ma argument yields a correct evaluation of the field-induced fluctuations for the one-dimensional model.
01 Jan 1988
TL;DR: This work proves a lower bound for the entropy of a random source of any oblivious packet routing algorithm that routes an arbitrary permutation in T steps with probability 1 - Q and builds a family of oblivious algorithms that use less than a factor of log more random bits than the optimal algorithm achieving the same run-time.
Abstract: Three parameters characterize the performance of a probabilistic algorithm: T, the runtime of the algorithm; Q, the probability that the algorithm fails to complete the computation in the first T steps and R, the amount of randomness used by the algorithm, measured by the entropy of its random source.We present a tight tradeoff between these three parameters for the problem of oblivious packet routing on N-vertex bounded-degree networks. We prove a (1 - Q) log N/T - log Q - O(1) lower bound for the entropy of a random source of any oblivious packet routing algorithm that routes an arbitrary permutation in T steps with probability 1 - Q. We show that this lower bound is almost optimal by proving the existence, for every e3 log N ≤ T ≤ N1/2, of an oblivious algorithm that terminates in T steps with probability 1 - Q and uses (1-Q+o(1))logN/T-logQ independent random bits.We complement this result with an explicit construction of a family of oblivious algorithms that use less than a factor of log N more random bits than the optimal algorithm achieving the same run-time.
Book•
01 Jan 1988TL;DR: The exact Hausdorff dimension function is determined for sets in R(m) constructed by using a recursion that is governed by some given law of randomness.
Abstract: The exact Hausdorff dimension function is determined for sets in Rm constructed by using a recursion that is governed by some given law of randomness.
TL;DR: In this paper, the authors describe the general mathematical methods required to do this, with one particular method (the nearest neighbor model) described in detail in one, two, and three dimensions.
Abstract: The spatial distribution of rock properties in porous media, such as permeability and porosity, often is strongly variable. Therefore, these properties usefully may be considered as a random field. However, this variability is correlated frequently on length scales comparable to geological lengths (for example, scales of sand bodies or facies). To solve various engineering problems (for example, in the oil recovery process) numerical models of a porous medium often are used. A need exists then to understand correlated random fields and to generate them over discretized numerical grids. The paper describes the general mathematical methods required to do this, with one particular method (the nearest neighbor model) described in detail. How parameters of the mathematical model may be related to rock property statistics for the nearest neighbor model is shown. The method is described in detail in one, two, and three dimensions. Examples are given of how model parameters may be determined from real data.
01 Jan 1988
TL;DR: This book contains papers presented at a conference on Computerized Simulation on the following topics: Model generating input processes; generalized zero invariance and intelligent random numbers; computerized simulation of array processors; andComputerized simulation for traffic control.
Abstract: This book contains papers presented at a conference on Computerized Simulation. Topics include the following: Model generating input processes; generalized zero invariance and intelligent random numbers; computerized simulation of array processors; and computerized simulation for traffic control.
TL;DR: A variety of measurements on fluid interface motion through model porous media are reported, finding that over a range of pressures randomness pins the interface and the dc response outside the pinned region is markedly nonlinear.
Abstract: We report a variety of measurements on fluid interface motion through model porous media. The dynamics shares many features with other systems pinned by random fields. Over a range of pressures randomness pins the interface. In this range there are many metastable interface configurations and relaxation is extremely slow. The dc response outside the pinned region is markedly nonlinear. Oscillations in the pressure occur at constant velocity which reflect the pore geometry.
TL;DR: In this article, the authors derived an asymptotic expansion of the Lifshitz tail to all orders in this logarithmic variable, for continuous distributions starting with a power law.
Abstract: In random systems, the density of states of various linear problems, such as phonons, tight-binding electrons, or diffusion in a medium with traps, exhibits an exponentially small Liftshitz tail at band edges. When the distribution of the appropriate random variables (atomic masses, site energies, trap depths) has a delta function at its lower (upper) bound, the Lifshitz singularities are pure exponentials. We study in a quantitative way how these singularities are affected by a universal logarithmic correction for continuous distributions starting with a power law. We derive an asymptotic expansion of the Lifshitz tail to all orders in this logarithmic variable. For distributions starting with an essential singularity, the exponent of the Lifshitz singularity itself is modified. These results are obtained in the example of harmonic chains with random masses. It is argued that analogous results hoid in higher dimensions. Their implications for other models, such as the long-time decay in trapping problems, are also discussed.
01 Jan 1988
TL;DR: In this paper, the behavior of generalized Lyapunov exponents for chaotic symplectic dynamical systems and products of random matrices in the limit of large dimensions was studied.
Abstract: We study the behavior of the generalized Lyapunov exponents for chaotic symplectic dynamical systems and products of random matrices in the limit of large dimensionsD. For products of random matrices without any particular structure the generalized Lyapunov exponents become equal in this limit and the value of one of the generalized Lyapunov exponents is obtained by simple arguments. On the contrary, for random symplectic matrices with peculiar structures and for chaotic symplectic maps the generalized Lyapunov exponents remains different forD → ∞, indicating that high dimensionality cannot always destroy intermittency.
01 Jan 1988
TL;DR: Randomness is inherent in all natural phenomena as mentioned in this paper and even the most perfect crystal has many impurities and other defects placed at random, and even if the crystal was perfect with each atom in its proper place, it would be there only on the average since the atoms axe in constant thermal motion.
Abstract: Randomness is inherent in all natural phenomena. Even the most perfect crystal has many impurities and other defects placed at random. In fact, even if the crystal was perfect with each atom in its proper place, it would be there only on the average since the atoms axe in constant thermal motion. Therefore the actual state of even the most perfect system has elements of randomness. There is good evidence that many natural phenomena are best described as fractals. However, if fractals axe to be useful in the description of nature we must develop the concepts of random fractals.
TL;DR: The main result of this paper is to establish the equivalence of the sequences which appear random to all FPMs and the ∞-distributed sequences, where every string of length k occurs in the sequence with frequency 2 − k , for all positive integers k .
TL;DR: In this paper, a simple model to handle fatigue-life length problems is discussed, which combines the Palmgren-Miner rule with time invariance, and is applied to situations with both random strength and random load.
Abstract: A simple model to handle fatigue-life length problems is discussed. The characteristic property of the model is that it combines the Palmgren-Miner rule with time invariance. The model is applied to situations with both random strength and random load. The randomness in the life is generated by the random strength and not by the random load. The only property of the random load that affects the life is its damage intensity, which is independent of the particular realization in the ergodic-load case. The damage intensity is even independent of the distribution of the random function, provided its level-crossing intensity is known. Particular attention is given to simple random strength models. In general, the exhaustion density is a random function, but in the simple models the only randomness that appears in the strength is either randomness in the time scale or randomness in the amplitude scale. The model is well-suited for comparative calculations under different load conditions, since it connects fatigue life for random loads to fatigue life for periodically oscillating loads, which is usually measured in experiments. >
TL;DR: In this article, a method for estimating the uncertainty in the prediction of indoor air quality is described, which is based on Ito stochastical differential equations which provides the statistical characteristics of variables of interest.
TL;DR: In this paper, the intrinsic randomness of the thermal conductivity k(x) is considered to be a distribution function with random amplitude in the solid, and several typical stochastic processes are considered in the numerical examples.
Abstract: Stochastic temperature distribution in a solid medium with random heat conductivity is investigated by the method of perturbation. The intrinsic randomness of the thermal conductivity k(x) is considered to be a distribution function with random amplitude in the solid, and several typical stochastic processes are considered in the numerical examples. The formulation used in the present analysis describes a situation that the statistical orders of the random response of the system are the same as those of the intrinsic random excitations, which is characteristic for the problem with extrinsic randomness. The maximum standard deviation of the temperature distribution from the mean value in the solid medium reveals the amount of unexpected energy experienced by the solid continuum, which should be carefully inspected in the thermal-failure design of structures with intrinsic randomness.
TL;DR: A procedure is outlined for the assessment of differences between entropy values obtained from a data set and Monte Carlo simulations were used, through which the maximum and minimum entropy values that could be obtained from each data set were estimated.
TL;DR: In this article, two groups of features with different time evolution characteristics were identified in the low-field microwave absorption signal in ceramic Y1Ba2Cu3Oy and they cannot be explained by the usual concepts of randomness in superconducting network models.
Abstract: Two groups of features with different time evolution characteristics can be identified in the low-field microwave absorption signal in ceramic Y1Ba2Cu3Oy. One set of features has its origin in the flux reconfiguration in a magnetically viscous medium while the second set of features arise from the flux quantisation through the random Josephson current network. The periodicity and existence of these features cannot be explained by the usual concepts of randomness in superconducting network models.
01 Jan 1988
TL;DR: This work considers the case where the minimization is carried out over a finite domain and presents a survey of several results and analytical tools for studying the asymptotic behavior of the simulated annealing algorithm, as time goes to infinity and temperature approaches zero.
Abstract: Simulated annealing is a probabilistic algorithm for minimizing a general cost function which may have multiple local minima The amount of randomness in this algorithm is controlled by the “temperature”, a scalar parameter which is decreased to zero as the algorithm progresses We consider the case where the minimization is carried out over a finite domain and we present a survey of several results and analytical tools for studying the asymptotic behavior of the simulated annealing algorithm, as time goes to infinity and temperature approaches zero