detection of signals by information theoretic criteria a new approach is presented to the problem of detecting the number of signals in a multichannel time series based on the application of the information theoretic criteria for model selection introduced by akaike aic and by schwartz and rissanen mdl unlike the conventional hypothesis testing based approach the new approach does not requite any subjective threshold settings the number of signals is obtained merely by minimizing the aic or the mdl criteria simulation results that illustrate the performance of the new method for the detection of the number of signals received by a sensor array are presented

a fast high quality and reproducible parallel lagged fibonacci pseudorandom number generator we study the suitability of the additive lagged fibonacci pseudo random number generator for parallel computation this generator has relatively short period with respect to the size of its seed however the short period is more than made up for with the huge number of full period cycles it contains these different full period cycles are called equivalence classes we show how to enumerate the equivalence classes and how to compute seeds to select a given equivalence class in addition we present some theoretical measures of quality for this generator when used in parallel next we conjecture on the size of these measures of quality for this generator extensive empirical evidence supports this conjecture in addition a probabilistic interpretation of these measures leads to another conjecture similarly supported by empirical evidence finally we give an explicit parallelization suitable for a fully reproducible asynchronous mimd implementation

superpositions of multifractals generators of phase transitions in the generalized thermodynamic formalism we investigate the superposition of multifractals in the generalized thermodynamic formalism it is shown analytically that phase transitions of first and second order are obtained and that the topology of the corresponding critical lines endows bicritical behavior we demonstrate that these phase transitions can be observed in the spectrum of fractal dimensions and in the spectra of related quantities therefore the obtained results are of importance for the interpretation of experimental systems

multisource self calibration for sensor arrays calibration of a sensor array is more involved if the antennas have direction dependent gains and multiple calibrator sources are simultaneously present we study this case for a sensor array with arbitrary geometry but identical elements i e elements with the same direction dependent gain pattern a weighted alternating least squares wals algorithm is derived that iteratively solves for the direction independent complex gains of the array elements their noise powers and their gains in the direction of the calibrator sources an extension of the problem is the case where the apparent calibrator source locations are unknown e g due to refractive propagation paths for this case the wals method is supplemented with weighted subspace fitting wsf direction finding techniques using monte carlo simulations we demonstrate that both methods are asymptotically statistically efficient and converge within two iterations even in cases of low snr

thermodynamics of random number generation we analyze the thermodynamic costs of the three main approaches to generating random numbers via the recently introduced information processing second law given access to a specified source of randomness a random number generator rng produces samples from a desired target probability distribution this differs from pseudorandom number generators prng that use wholly deterministic algorithms and from true random number generators trng in which the randomness source is a physical system for each class we analyze the thermodynamics of generators based on algorithms implemented as finite state machines as these allow for direct bounds on the required physical resources this establishes bounds on heat dissipation and work consumption during the operation of three main classes of rng algorithms including those of von neumann knuth and yao and roche and hoshi and for prng methods we introduce a general trng and determine its thermodynamic costs exactly for arbitrary target distributions the results highlight the significant differences between the three main approaches to random number generation one is work producing one is work consuming and the other is potentially dissipation neutral notably trngs can both generate random numbers and convert thermal energy to stored work these thermodynamic costs on information creation complement landauer s limit on the irreducible costs of information destruction

interval algorithm for random number generation the problem of generating a random number with an arbitrary probability distribution by using a general biased m coin is studied an efficient and very simple algorithm based on the successive refinement of partitions of the unit interval 0 1 which we call the interval algorithm is proposed a fairly tight evaluation on the efficiency is given generalizations of the interval algorithm to the following cases are investigated 1 output sequence is independent and identically distributed i i d 2 output sequence is markov 3 input sequence is markov 4 input sequence and output sequence are both subject to arbitrary stochastic processes

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

a model selection rule for sinusoids in white gaussian noise the model selection problem for sinusoidal signals has often been addressed by employing the akaike 1974 information criterion aic and the minimum description length principle mdl the popularity of these criteria partly stems from the intrinsically simple means by which they can be implemented they can however produce misleading results if they are not carefully used the aic and mdl have a common form in that they comprise two terms a data term and a penalty term the data term quantifies the residuals of the model and the penalty term reflects the desideratum of parsimony while the data terms of the aic and mdl are identical the penalty terms are different in most of the literature the aic and mdl penalties are however both obtained by apportioning an equal weight to each additional unknown parameter be it phase amplitude or frequency by contrast we demonstrate that the penalties associated with the amplitude and phase parameters should be weighted differently than the penalty attached to the frequencies following the bayesian methodology we derive a model selection criterion for sinusoidal signals in gaussian noise which also contains the log likelihood and the penalty terms the simulation results disclose remarkable improvement in our selection rule over the commonly used mdl and aic

tree algorithms for unbiased coin tossing with a biased coin we give new algorithms for simulating a flip of an unbiased coin by flipping a coin of unknown bias we are interested in efficient algorithms where the expected number of flips is our measure of efficiency other authors have represented algorithms as lattices but by representing them instead as trees we are able to produce an algorithm more efficient than any previously appearing we also prove a conjecture of hoeffding and simons that there is no optimal algorithm further we consider generalizations where the input is a sequence of iid discrete random variables and the output is a uniform random variable with n possible outcomes in this setting we provide an algorithm significantly superior to those previously published

on the behavior of information theoretic criteria for model order selection the akaike 1974 information criterion aic and the minimum description length mdl are two well known criteria for model order selection in the additive white noise case our aim is to study the influence on their behavior of a large gap between the signal and the noise eigenvalues and of the noise eigenvalue dispersion our results are mostly qualitative and serve to explain the behavior of the aic and the mdl in some cases of great practical importance we show that when the noise eigenvalues are not clustered sufficiently closely then the aic and the mdl may lead to overmodeling by ignoring an arbitrarily large gap between the signal and the noise eigenvalues for fixed number of data samples overmodeling becomes more likely for increasing the dispersion of the noise eigenvalues for fixed dispersion overmodeling becomes more likely for increasing the number of data samples undermodeling may happen in the cases where the signal and the noise eigenvalues are not well separated and the noise eigenvalues are clustered sufficiently closely we illustrate our results by using simulations from the effective channel order determination area

automatic determination of the number of targets present when using the time reversal operator acoustical time reversal mirrors have been shown to provide a highly accurate means of studying and focusing on acoustical sources the dort method is a derivation of the time reversal process which allows for focusing on multiple targets an important step in this process is the determination of the number of targets or sources present this is achieved by examining the eigenvalues of the time reversal operator tro the number of significant eigenvalues is then chosen as the number of sources present however as mentioned in n mordant c prada and m fink j acoust soc am 105 2634 2642 1999 and c prada m tanter and m fink in proceedings of the ieee symposium 1997 pp 679 683 factors such as low signal to noise ratio snr small data sample array configuration and the target location may result in the eigenvalues corresponding to the targets no longer being distinguishable from the background noise eigenvalues this paper proposes a robust method of automatically determining the

detection of the number of coherent signals by the mdl principle an approach is presented to the problem of detecting the number of sources impinging on a passive sensor array that is based on j rissanen s 1983 minimum description length mdl principle the approach is applicable to any type of sources including the case of sources which are fully correlated referred to as the coherent signals case two slightly different detection criteria are derived both requiring the estimation of the locations of the sources the first is tailored to the detection problem per se whereas the second is tailored to the combined detection estimation problem consistency of the two criteria is proved and their performance is demonstrated by computer simulations

blind channel approximation effective channel order determination a common assumption of blind channel identification methods is that the order of the true channel is known this information is not available in practice and we are obliged to estimate the channel order by applying a rank detection procedure to an overmodeled data covariance matrix information theoretic criteria have been widely suggested approaches for this task we check the quality of their estimates in the context of order estimation of measured microwave radio channels and confirm that they are very sensitive to variations in the snr and the number of data samples this fact has prohibited their successful application for channel order estimation and hits created some confusion concerning the classification into under and over modeled cases recently it has been shown that blind channel approximation methods should attempt to model only the significant part of the channel composed of the large impulse response terms because efforts toward modeling small leading and or trailing terms lead to effective overmodeling which is generically ill conditioned and thus should be avoided this can be achieved by applying blind identification methods with model order equal to the order of the significant part of the true channel called the effective channel order toward developing an efficient approach for the detection of the effective channel order we use numerical analysis arguments the derived criterion provides a maximally stable decomposition of the range space of an overmodeled data covariance matrix into signal and noise subspaces it is shown to be robust to variations in the snr and the number of data samples furthermore it provides useful effective channel order estimates leading to sufficiently good blind approximation equalization of measured real world microwave radio channels

an information theoretic approach to source enumeration in array signal processing in this paper a new information theoretic algorithm is proposed for signal enumeration in array processing the approach is based on predictive description length pdl that is defined as the length of a predictive code for the set of observations we assume that several models with each model representing a certain number of sources will compete the pdl criterion is computed for the candidate models and is minimized over all models to select the best model and to determine the number of signals in the proposed method the correlation matrix is decomposed into two orthogonal components in the signal and noise subspaces the maximum likelihood ml estimates of the angles of arrival are used to find the projection of the sample correlation matrix onto the signal and noise subspaces the summation of the ml estimates of these matrices is the ml estimate of the correlation matrix this method can detect both coherent and noncoherent signals the proposed method can be used online and can be applied to time varying systems and target tracking

multifractal analysis in reciprocal space and the nature of the fourier transform of self similar structures the authors propose to use multifractal analysis in reciprocal space as a tool to characterise in a statistical and global sense the nature of the fourier transform of geometrical models for atomic structures this approach is especially adequate for shedding some new light on a class of structures introduced recently which exhibit singular scattering using the language of measure theory the fourier intensity of these models is presumably singular continuous and therefore represents an intermediate type of order between periodic or quasiperiodic structures characterised by bragg peaks atomic fourier transform and amorphous structures which exhibit diffuse scattering absolutely continuous fourier transform this general approach is illustrated in several examples of self similar one dimensional sequences and structures generated by substitutions a special emphasis is put on the relationship between the nature of the fourier intensity of these models and the f alpha spectrum obtained by multifractal analysis in reciprocal space

streaming universal distortion free entanglement concentration this paper presents a streaming sequential protocol for universal entanglement concentration at the shannon bound alice and bob begin with n identical but unknown two qubit pure states each containing e ebits of entanglement they each run a reversible algorithm on their qubits and end up with y perfect epr pairs where y ne o n our protocol is streaming so the n input systems are fed in one at a time and perfect epr pairs start popping out almost immediately it matches the optimal block protocol exactly at each stage so the average yield after n inputs is y ne o logn so somewhat surprisingly there is no tradeoff between yield and lag our protocol optimizes both in contrast the optimal n qubit block protocol achieves the same yield but since no epr pairs are produced until the entire input block is read its lag is o n finally our algorithm runs in o log n space so a lot of entanglement can be efficiently concentrated using a very small e g current or near future technology quantum processor along the way we find an optimal streaming protocol for extracting randomness from classical i i d sources and a more space efficient implementation of the schur transform

on convex hull violation by superpositions recently we observed a violation of the convex hull principle for the super imposed multifractals with measure which we found difficult to explain in a simple way using the generalized entropy point of view for the description we are able to resolve this problem

experimental subwavelength localization of scatterers by decomposition of the time reversal operator interpreted as a covariance matrix the d o r t method french acronym for decomposition of the time reversal operator is an active remote sensing technique using arrays of antennas for the detection and localization of scatterers prada et al j acoust soc am 99 2067 2076 1996 the analogy between the time reversal operator and the covariance matrix used for classical sources separation in passive remote sensing bienvenu et al ieee trans assp 31 1235 1247 1983 is established then an experiment of subwavelength detection and localization of point like scatterers with a linear array of transducers is presented using classical estimators in reception like maximum likelihood and multiple signal characterization music two point like scatterers separated by 3 and placed at 100 from the array of transducers are resolved in these experiments the role of multiple scattering and the existence of additional eigenvectors associated with dipolar and monopolar radiation of each scatterer is discussed

detection of the number of signals a predicted eigen threshold approach a novel method for detecting the number of signals incident upon an array of sensors is described the method is based on finding upper thresholds for the observed eigenvalues of the correlation matrix of the array output the asymptotic normality of the multifold eigenvalue estimate is used to derive a prediction formula for the thresholds due to the fact that the detection error of the method can be controlled by a parameter t the performance of the method is superior to the mdl minimum description length under low snr signal to noise ratio and superior to an aic akaike information criterion under high snr the distribution functions of both missing and false alarm errors are evaluated so that the performance of the method can be analyzed and so that t can be chosen simulation results are presented to confirm the analysis

evaluation of probabilistic and dynamical invariants from finite symbolic substrings comparison between two approaches abstract while evaluating scaling functions of fractal dimensions and lyapunov exponents from time series in the traditional way assumptions are made concerning the grammar of the underlying dynamical system it is implicitly assumed that the length of the substrings considered is sufficient to capture the grammatical properties of the system in this contribution we show where this assumption becomes relevant we give an example of a simple grammatical rule which leads to badly behaving convergence properties of the associated scaling functions as another consequence of our investigations we conclude that whenever a finite grammar is encountered the cycle expansion approach of cvitanovic using periodic orbits should preferably be used

on the periods of generalized fibonacci recurrences we give a simple condition for a linear recurrence mod 2w of degree r to have the maximal possible period 2m 1 2 1 it follows that the period is maximal in the cases of interest for pseudorandom number gen eration i e for three term linear recurrences defined by trinomials which are primitive mod 2 and of degree r 2 we consider the enumeration of cer tain exceptional polynomials which do not give maximal period and list all such polynomials of degree less than 15

multiple source location a matrix decomposition approach in this paper we present a new method without using the eigenstructure of the sensor covariance matrix for estimating the number of sources d and the direction of arrival of sources based on the matrix decomposition this method uniformly handles coherent and noncoherent sources alike in our procedure a number p is calculated and used for determination of the maximum number of distinguishable sources by a given linear array system