Showing papers on "Randomness published in 2007"

Localization of interacting fermions at high temperature

Abstract: We suggest that if a localized phase at nonzero temperature $Tg0$ exists for strongly disordered and weakly interacting electrons, as recently argued, it will also occur when both disorder and interactions are strong and $T$ is very high. We show that in this high-$T$ regime, the localization transition may be studied numerically through exact diagonalization of small systems. We obtain spectra for one-dimensional lattice models of interacting spinless fermions in a random potential. As expected, the spectral statistics of finite-size samples cross over from those of orthogonal random matrices in the diffusive regime at weak random potential to Poisson statistics in the localized regime at strong randomness. However, these data show deviations from simple one-parameter finite-size scaling: the apparent mobility edge ``drifts'' as the system's size is increased. Based on spectral statistics alone, we have thus been unable to make a strong numerical case for the presence of a many-body localized phase at nonzero $T$.

Exploiting Nonlinear Recurrence and Fractal Scaling Properties for Voice Disorder Detection

Abstract: Voice disorders affect patients profoundly, and acoustic tools can potentially measure voice function objectively. Disordered sustained vowels exhibit wide-ranging phenomena, from nearly periodic to highly complex, aperiodic vibrations, and increased "breathiness". Modelling and surrogate data studies have shown significant nonlinear and non-Gaussian random properties in these sounds. Nonetheless, existing tools are limited to analysing voices displaying near periodicity, and do not account for this inherent biophysical nonlinearity and non-Gaussian randomness, often using linear signal processing methods insensitive to these properties. They do not directly measure the two main biophysical symptoms of disorder: complex nonlinear aperiodicity, and turbulent, aeroacoustic, non-Gaussian randomness. Often these tools cannot be applied to more severe disordered voices, limiting their clinical usefulness. This paper introduces two new tools to speech analysis: recurrence and fractal scaling, which overcome the range limitations of existing tools by addressing directly these two symptoms of disorder, together reproducing a "hoarseness" diagram. A simple bootstrapped classifier then uses these two features to distinguish normal from disordered voices. On a large database of subjects with a wide variety of voice disorders, these new techniques can distinguish normal from disordered cases, using quadratic discriminant analysis, to overall correct classification performance of 91.8 ± 2.0%. The true positive classification performance is 95.4 ± 3.2%, and the true negative performance is 91.5 ± 2.3% (95% confidence). This is shown to outperform all combinations of the most popular classical tools. Given the very large number of arbitrary parameters and computational complexity of existing techniques, these new techniques are far simpler and yet achieve clinically useful classification performance using only a basic classification technique. They do so by exploiting the inherent nonlinearity and turbulent randomness in disordered voice signals. They are widely applicable to the whole range of disordered voice phenomena by design. These new measures could therefore be used for a variety of practical clinical purposes.

Algorithmic Learning in a Random World

Abstract: Algorithmic Learning in a Random World describes recent theoretical and experimental developments in building computable approximations to Kolmogorov's algorithmic notion of randomness. Based on these approximations, a new set of machine learning algorithms have been developed that can be used to make predictions and to estimate their confidence and credibility in high-dimensional spaces under the usual assumption that the data are independent and identically distributed (assumption of randomness). Another aim of this unique monograph is to outline some limits of predictions: The approach based on algorithmic theory of randomness allows for the proof of impossibility of prediction in certain situations. The book describes how several important machine learning problems, such as density estimation in high-dimensional spaces, cannot be solved if the only assumption is randomness.

Linear Degree Extractors and the Inapproximability of Max Clique and Chromatic Number

Abstract: A randomness extractor is an algorithm which extracts randomness from a low-quality random source, using some additional truly random bits. We construct new extractors which require only log n + O(1) additional random bits for sources with constant entropy rate. We further construct dispersers, which are similar to one-sided extractors, which use an arbitrarily small constant times log n additional random bits for sources with constant entropy rate. Our extractors and dispersers output 1-α fraction of the randomness, for any α>0.We use our dispersers to derandomize results of Hastad [23] and Feige-Kilian [19] and show that for all e>0, approximating MAX CLIQUE and CHROMATIC NUMBER to within n1-e are NP-hard. We also derandomize the results of Khot [29] and show that for some γ > 0, no quasi-polynomial time algorithm approximates MAX CLIQUE or CHROMATIC NUMBER to within n/2(log n)1-γ, unless NP = P.Our constructions rely on recent results in additive number theory and extractors by Bourgain-Katz-Tao [11], Barak-Impagliazzo-Wigderson [5], Barak-Kindler-Shaltiel-Sudakov-Wigderson [6], and Raz [36]. We also simplify and slightly strengthen key theorems in the second and third of these papers, and strengthen a related theorem by Bourgain [10].

Microstructural Randomness and Scaling in Mechanics of Materials

Abstract: PREFACE BASIC RANDOM MEDIA MODELS Probability Measure of Geometric Objects Basic Point Fields Directional Data Random Fibers, Random Line Fields, Tessellations Basic Concepts and Definitions of Random Microstructures RANDOM PROCESSES AND FIELDS Elements of One-Dimensional Random Fields Mechanics Problems on One-Dimensional Random Fields Elements of Two- and Three-Dimensional Random Fields Mechanics Problems on Two- and Three-Dimensional Random Fields Ergodicity The Maximum Entropy Method PLANAR LATTICE MODELS: PERIODIC TOPOLOGIES AND ELASTOSTATICS One-Dimensional Lattices Planar Lattices: Classical Continua Applications in Mechanics of Composites Planar Lattices: Nonclassical Continua Extension-Twist Coupling in a Helix LATTICE MODELS: RIGIDITY, RANDOMNESS, DYNAMICS, AND OPTIMALITY Rigidity of Networks Spring Network Models for Disordered Topologies Particle Models Michell Trusses: Optimal Use of Material TWO- VERSUS THREE-DIMENSIONAL CLASSICAL ELASTICITY Basic Relations The CLM Result and Stress Invariance Poroelasticity TWO- VERSUS THREE-DIMENSIONAL MICROPOLAR ELASTICITY Micropolar Elastic Continua Classical vis-a-vis Nonclassical (Elasticity) Models Planar Cosserat Elasticity The CLM Result and Stress Invariance Effective Micropolar Moduli and Characteristic Lengths of Composites MESOSCALE BOUNDS FOR LINEAR ELASTIC MICROSTRUCTURES Micro-, Meso-, and Macroscales Volume Averaging Spatial Randomness Hierarchies of Mesoscale Bounds Examples of Hierarchies of Mesoscale Bounds Moduli of Trabecular Bone RANDOM FIELD MODELS AND STOCHASTIC FINITE ELEMENTS Mesoscale Random Fields Second-Order Properties of Mesoscale Random Fields Does There Exist a Locally Isotropic, Smooth Elastic Material? Stochastic Finite Elements for Elastic Media Method of Slip-Lines for Inhomogeneous Plastic Media Michell Trusses in the Presence of Random Microstructure HIERARCHIES OF MESOSCALE BOUNDS FOR NONLINEAR AND INELASTIC MICROSTRUCTURES Physically Nonlinear Elastic Microstructures Finite Elasticity of Random Composites Elastic-Plastic Microstructures Rigid-Perfectly Plastic Microstructures Viscoelastic Microstructures Stokes Flow in Porous Media Thermoelastic Microstructures Scaling and Stochastic Evolution in Damage Phenomena Comparison of Scaling Trends MESOSCALE RESPONSE IN THERMOMECHANICS OF RANDOM MEDIA From Statistical Mechanics to Continuum Thermodynamics Extensions of the Hill Condition Legendre Transformations in (Thermo)Elasticity Thermodynamic Orthogonality on the Mesoscale Complex versus Compound Processes: The Scaling Viewpoint Toward Continuum Mechanics of Fractal Media WAVES AND WAVEFRONTS IN RANDOM MEDIA Basic Methods in Stochastic Wave Propagation Toward Spectral Finite Elements for Random Media Waves in Random 1D Composites Transient Waves in Heterogeneous Nonlinear Media Acceleration Wavefronts in Nonlinear Media BIBLIOGRAPHY INDEX

Algorithmic information theory

Abstract: This article is a brief guide to the field of algorithmic information theory (AIT), its underlying philosophy, and the most important concepts. AIT arises by mixing information theory and computation theory to obtain an objective and absolute notion of information in an individual object, and in so doing gives rise to an objective and robust notion of randomness of individual objects. This is in contrast to classical information theory that is based on random variables and communication, and has no bearing on information and randomness of individual objects. After a brief overview, the major subfields, applications, history, and a map of the field are presented.

High-Speed True Random Number Generation with Logic Gates Only

Abstract: It is shown that the amount of true randomness produced by the recently introduced Galois and Fibonacci ring oscillators can be evaluated experimentally by restarting the oscillators from the same initial conditions and by examining the time evolution of the standard deviation of the oscillating signals. The restart approach is also applied to classical ring oscillators and the results obtained demonstrate that the new oscillators can achieve orders of magnitude higher entropy rates. A theoretical explanation is also provided. The restart and continuous modes of operation and a novel sampling method almost doubling the entropy rate are proposed. Accordingly, the new oscillators appear to be by far more effective than other known solutions for random number generation with logic gates only.

Exploiting Nonlinear Recurrence and Fractal Scaling Properties for Voice Disorder Detection

Abstract: Background: Voice disorders affect patients profoundly, and acoustic tools can potentially measure voice function objectively. Disordered sustained vowels exhibit wide-ranging phenomena, from nearly periodic to highly complex, aperiodic vibrations, and increased "breathiness". Modelling and surrogate data studies have shown significant nonlinear and non-Gaussian random properties in these sounds. Nonetheless, existing tools are limited to analysing voices displaying near periodicity, and do not account for this inherent biophysical nonlinearity and non-Gaussian randomness, often using linear signal processing methods insensitive to these properties. They do not directly measure the two main biophysical symptoms of disorder: complex nonlinear aperiodicity, and turbulent, aeroacoustic, non-Gaussian randomness. Often these tools cannot be applied to more severe disordered voices, limiting their clinical usefulness.Methods: This paper introduces two new tools to speech analysis: recurrence and fractal scaling, which overcome the range limitations of existing tools by addressing directly these two symptoms of disorder, together reproducing a "hoarseness" diagram. A simple bootstrapped classifier then uses these two features to distinguish normal from disordered voices.Results: On a large database of subjects with a wide variety of voice disorders, these new techniques can distinguish normal from disordered cases, using quadratic discriminant analysis, to overall correct classification performance of 91.8% plus or minus 2.0%. The true positive classification performance is 95.4% plus or minus 3.2%, and the true negative performance is 91.5% plus or minus 2.3% (95% confidence). This is shown to outperform all combinations of the most popular classical tools.Conclusions: Given the very large number of arbitrary parameters and computational complexity of existing techniques, these new techniques are far simpler and yet achieve clinically useful classification performance using only a basic classification technique. They do so by exploiting the inherent nonlinearity and turbulent randomness in disordered voice signals. They are widely applicable to the whole range of disordered voice phenomena by design. These new measures could therefore be used for a variety of practical clinical purposes.

Random access structure for wireless networks

Abstract: Apparatus and methods for accessing a wireless telecommunications network by transmitting a random access signal. The random access signal includes a random access preamble signal selected from a set of random access preamble signals constructed by cyclically shift selected root CAZAC sequences. The random access signal may be one or more transmission sub-frames in duration, the included random access preamble sequence's length being extended with the signal to provide improved signal detection performance in larger cells and in higher interference environments. The random access signal may include a wide-band pilot signal facilitating base station estimation of up-link frequency response in some situations. Each of the plurality of available random access preamble sequences may be assigned a unique information value. The base station may use the information encoded in the random access preamble to prioritize responses and resource allocations. Random access signal collisions are dealt with by a combination of preamble code space randomness and back-off procedures.

True Random Number Generator with a Metastability-Based Quality Control

Abstract: We present a metastability-based true random number generator that achieves high entropy and passes NIST randomness tests. The generator grades the probability of randomness regardless of the output bit value by measuring the metastable resolution time. The system determines the original random noise level at the time of metastability and tunes itself to achieve a high probability of randomness. Dynamic control enables the system to respond to deterministic noise and a qualifier module grades the individual metastable events to produce a high-entropy random bit-stream. The grading module allows the user to trade off output bit-rate with the quality of the bit-stream. A fully integrated true random number generator was fabricated in a 0.13 mum bulk CMOS technology with an area of 0.145 mm2.

Randomness enhances cooperation: a resonance-type phenomenon in evolutionary games.

Abstract: We investigate the effect of randomness in both relationships and decisions on the evolution of cooperation. Simulation results show, in such randomness' presence, the system evolves more frequently to a cooperative state than in its absence. Specifically, there is an optimal amount of randomness, which can induce the highest level of cooperation. The mechanism of randomness promoting cooperation resembles a resonancelike fashion, which could be of particular interest in evolutionary game dynamics in economic, biological, and social systems.

Entropy production and time asymmetry in nonequilibrium fluctuations.

Abstract: The time-reversal symmetry of nonequilibrium fluctuations is experimentally investigated in two out-of-equilibrium systems: namely, a Brownian particle in a trap moving at constant speed and an electric circuit with an imposed mean current. The dynamical randomness of their nonequilibrium fluctuations is characterized in terms of the standard and time-reversed entropies per unit time of dynamical systems theory. We present experimental results showing that their difference equals the thermodynamic entropy production in units of Boltzmann's constant.

Multiple scattering by random particulate media: exact 3D results

Abstract: We use the numerically exact superposition T-matrix method to perform extensive computations of electromagnetic scattering by a 3D volume filled with randomly distributed wavelength-sized particles. These computations are used to simulate and analyze the effect of randomness of particle positions as well as the onset and evolution of various multiple-scattering effects with increasing number of particles in a statistically homogeneous volume of discrete random medium. Our exact results illustrate and substantiate the methodology underlying the microphysical theories of radiative transfer and coherent backscattering. Furthermore, we show that even in densely packed media, the light multiply scattered along strings of widely separated particles still provides a significant contribution to the total scattered signal and thereby makes quite pronounced the classical radiative transfer and coherent backscattering effects.

The Communication Complexity of Correlation

Abstract: We examine the communication required for generating random variables remotely. One party Alice is given a distribution D, and she has to send a message to Bob, who is then required to generate a value with distribution exactly D. Alice and Bob are allowed to share random bits generated without the knowledge of D. There are two settings based on how the distribution D provided to Alice is chosen. If D is itself chosen randomly from some set (the set and distribution are known in advance) and we wish to minimize the expected communication in order for Alice to generate a value y, with distribution D, then we characterize the communication required in terms of the mutual information between the input to Alice and the output Bob is required to generate. If D is chosen from a set of distributions D, and we wish to devise a protocol so that the expected communication (the randomness comes from the shared random string and Alice's coin tosses) is small for each D isin D, then we characterize the communication required in this case in terms of the channel capacity associated with the set D. Our proofs are based on an improved rejection sampling procedure that relates the relative entropy between two distributions to the communication complexity of generating one distribution from the other. As an application of these results, we derive a direct sum theorem in communication complexity that substantially improves the previous such result shown by Jain et al. (2003).

Quantum random number generator based on photonic emission in semiconductors

Abstract: We report upon the realization of a novel fast nondeterministic random number generator whose randomness relies on the intrinsic randomness of the quantum physical processes of photonic emission in semiconductors and subsequent detection by the photoelectric effect. Timing information of detected photons is used to generate binary random digits-bits. The bit extraction method based on the restartable clock method theoretically eliminates both bias and autocorrelation while reaching efficiency of almost 0.5 bits per random event. A prototype has been built and statistically tested.

Unbalanced Expanders and Randomness Extractors from Parvaresh-Vardy Codes

Abstract: We give an improved explicit construction of highly unbalanced bipartite expander graphs with expansion arbitrarily close to the degree (which is polylogarithmic in the number of vertices). Both the degree and the number of right-hand vertices are polynomially close to optimal, whereas the previous constructions of Ta-Shma, Umans, and Zuckerman (STOC "01) required at least one of these to be quasipolynomial in the optimal. Our expanders have a short and self-contained description and analysis, based on the ideas underlying the recent list-decodable error-correcting codes of Parvaresh and Vardy (FOCS "05). Our expanders can be interpreted as near-optimal "randomness condensers," that reduce the task of extracting randomness from sources of arbitrary min-entropy rate to extracting randomness from sources of min-entropy rate arbitrarily close to 1, which is a much easier task. Using this connection, we obtain a new construction of randomness extractors that is optimal up to constant factors, while being much simpler than the previous construction of Lu et al. (STOC "03) and improving upon it when the error parameter is small (e.g. 1/poly(n)).

Chaotic behavior of a random laser with static disorder

Abstract: We report on an experimental and numerical study of chaotic behavior in random lasers. The complex emission spectra from a disordered amplifying material with static disorder are investigated in a configuration with controlled, stable experimental conditions. It is found that, upon repeated identical excitation, the emission spectra are distinct and uncorrelated. This behavior can be understood in terms of strongly coupled modes that are triggered by spontaneous emission, and is expected to play an important role in most pulsed random lasers.

Using random sets as oracles

Abstract: Let R be a notion of algorithmic randomness for individual subsets of ℕ. A set B is a base for R randomness if there is a Z ≥ T B such that Z is R random relative to B. We show that the bases for 1-randomness are exactly the K-trivial sets, and discuss several consequences of this result. On the other hand, the bases for computable randomness include every Δ 2 0 set that is not diagonally noncomputable, but no set of PA-degree. As a consequence, an n-c.e. set is a base for computable randomness if and only if it is Turing incomplete.

Computability of probability measures and Martin-Lof randomness over metric spaces

Abstract: In this paper we investigate algorithmic randomness on more general spaces than the Cantor space, namely computable metric spaces. To do this, we first develop a unified framework allowing computations with probability measures. We show that any computable metric space with a computable probability measure is isomorphic to the Cantor space in a computable and measure-theoretic sense. We show that any computable metric space admits a universal uniform randomness test (without further assumption).

Bose-Einstein-condensed systems in random potentials

Abstract: The properties of systems with Bose-Einstein condensate in external time-independent random potentials are investigated in the frame of a self-consistent stochastic mean-field approximation. General considerations are presented, which are valid for finite temperatures, arbitrary strengths of the interaction potential, and for arbitrarily strong disorder potentials. The special case of a spatially uncorrelated random field is then treated in more detail. It is shown that the system consists of three components, condensed particles, uncondensed particles, and a glassy density fraction, but that the pure Bose glass phase with only a glassy density does not appear. The theory predicts a first-order phase transition for increasing disorder parameter, where the condensate fraction and the superfluid fraction simultaneously jump to zero. The influence of disorder on the ground-state energy, the stability conditions, the compressibility, the structure factor, and the sound velocity are analyzed. The uniform ideal condensed gas is shown to be always stochastically unstable, in the sense that an infinitesimally weak disorder destroys the Bose-Einstein condensate, returning the system to the normal state; but the uniform Bose-condensed system with finite repulsive interactions becomes stochastically stable and exists in a finite interval of the disorder parameter.

Colloquium: Random matrices and chaos in nuclear spectra

Abstract: Chaos occurs in quantum systems if the statistical properties of the eigenvalue spectrum coincide with predictions of random-matrix theory. Chaos is a typical feature of atomic nuclei and other self-bound Fermi systems. How can the existence of chaos be reconciled with the known dynamical features of spherical nuclei? Such nuclei are described by the shell model (a mean-field theory) plus a residual interaction. The question is answered using a statistical approach (the two-body random ensemble): The matrix elements of the residual interaction are taken to be random variables. Chaos is shown to be a generic feature of the ensemble and some of its properties are displayed, emphasizing those which differ from standard random-matrix theory. In particular, the existence of correlations among spectra carrying different quantum numbers is demonstrated. These are subject to experimental verification.

Secure self-calibrating quantum random-bit generator

Abstract: Random-bit generators (RBGs) are key components of a variety of information processing applications ranging from simulations to cryptography. In particular, cryptographic systems require ``strong'' RBGs that produce high-entropy bit sequences, but traditional software pseudo-RBGs have very low entropy content and therefore are relatively weak for cryptography. Hardware RBGs yield entropy from chaotic or quantum physical systems and therefore are expected to exhibit high entropy, but in current implementations their exact entropy content is unknown. Here we report a quantum random-bit generator (QRBG) that harvests entropy by measuring single-photon and entangled two-photon polarization states. We introduce and implement a quantum tomographic method to measure a lower bound on the ``min-entropy'' of the system, and we employ this value to distill a truly random-bit sequence. This approach is secure: even if an attacker takes control of the source of optical states, a secure random sequence can be distilled.

Random matrix eigenvalue problems in structural dynamics

Abstract: Natural frequencies and mode shapes play a fundamental role in the dynamic characteristics of linear structural systems. Considering that the system parameters are known only probabilistically, we obtain the moments and the probability density functions of the eigenvalues of discrete linear stochastic dynamic systems. Current methods to deal with such problems are dominated by mean-centred perturbation-based methods. Here two new approaches are proposed. The first approach is based on a perturbation expansion of the eigenvalues about an optimal point which is 'best' in some sense. The second approach is based on an asymptotic approximation of multidimensional integrals. A closed-form expression is derived for a general rth-order moment of the eigenvalues. Two approaches are presented to obtain the probability density functions of the eigenvalues. The first is based on the maximum entropy method and the second is based on a chi-square distribution. Both approaches result in simple closed-form expressions which can be easily calculated. The proposed methods are applied to two problems and the analytical results are compared with Monte Carlo simulations. It is expected that the 'small randomness' assumption usually employed in mean-centred-perturbation-based methods can be relaxed considerably using these methods.

Statistical regimes of random laser fluctuations

Abstract: Statistical fluctuations of the light emitted from amplifying random media are studied theoretically and numerically. The characteristic scales of the diffusive motion of light lead to Gaussian or power-law (Levy) distributed fluctuations depending on external control parameters. In the Levy regime, the output pulse is highly irregular leading to huge deviations from a mean-field description. Monte Carlo simulations of a simplified model which includes the population of the medium demonstrate the two statistical regimes and provide a comparison with dynamical rate equations. Different statistics of the fluctuations helps to explain recent experimental observations reported in the literature.

Entanglement Entropy at Infinite-Randomness Fixed Points in Higher Dimensions

Abstract: The entanglement entropy of the two-dimensional random transverse Ising model is studied with a numerical implementation of the strong-disorder renormalization group. The asymptotic behavior of the entropy per surface area diverges at, and only at, the quantum phase transition that is governed by an infinite-randomness fixed point. Here we identify a double-logarithmic multiplicative correction to the area law for the entanglement entropy. This contrasts with the pure area law valid at the infinite-randomness fixed point in the diluted transverse Ising model in higher dimensions.

Uncertainty Quantification with Stochastic Finite Elements

Abstract: Uncertainty estimation arises at least implicitly in any kind of modeling of the real-world, and it is desirable to actually quantify the uncertainty in probabilistic terms. Here the emphasis is on uncertain systems, where the randomness is assumed spatial. Traditional computational approaches usually use some form of perturbation or Monte Carlo simulation. This is contrasted here with more recent methods based on stochastic Galerkin approximations. Also some approaches to an adaptive uncertainty quantification are pointed out. Keywords: uncertainty quantification; spatially stochastic systems; stochastic elliptic partial differential equations; stochastic Galerkin methods; Karhunen–Loeve expansion; Wiener's polynomial chaos; white noise analysis; sparse Smolyak quadrature; Monte Carlo methods; stochastic finite elements

On the diffuse field reciprocity relationship and vibrational energy variance in a random subsystem at high frequencies.

Abstract: A recent paper has shown that under certain conditions the cross-spectral matrix of the forces exerted by a vibrational or acoustic wave field on its surrounding boundaries can be expressed in terms of (i) the energy of the wave field, and (ii) the direct field dynamic stiffness matrix of the boundary. This “diffuse field reciprocity relation” was derived using wave mechanics, and it is not immediately clear how the required wave field properties translate to conditions on the vibrational modes of the system or the applied forcing. This issue is addressed here by deriving an extended version of the reciprocity relation using modal methods, and the conditions required for the extended version to reduce to the existing relation are delineated. It is shown that the existing diffuse field reciprocity relation leads to an anomalous result when used to predict the energy variance of a subsystem, and that this anomaly is resolved by using the present extended version of the relation. A supplementary result arising from the analysis is that for systems with a sufficient degree of randomness the ensemble average of the dynamic stiffness matrix of a random subsystem is equal to the inverse of the ensemble average of the receptance matrix.