Statistical mechanics in the extended Gaussian ensemble

The extended Gaussian ensemble (EGE) is introduced as a generalization of the canonical ensemble. This ensemble is a further extension of the Gaussian ensemble introduced by Hetherington [J. Low Temp. Phys. 66, 145 (1987)]. The statistical mechanical formalism is derived both from the analysis of the system attached to a finite reservoir and from the maximum statistical entropy principle. The probability of each microstate depends on two parameters ß and ¿ which allow one to fix, independently, the mean energy of the system and the energy fluctuations, respectively. We establish the Legendre transform structure for the generalized thermodynamic potential and propose a stability criterion. We also compare the EGE probability distribution with the q-exponential distribution. As an example, an application to a system with few independent spins is presented.

Bistability driven by Gaussian colored noise: First-passage times

Herein we present a calculation of the mean first-passage time for a bistable one-dimensional system driven by Gaussian colored noise of strength D and correlation time ¿c. We obtain quantitative agreement with experimental analog-computer simulations of this system. We disagree with some of the conclusions reached by previous investigators. In particular, we demonstrate that all available approximations that lead to a state-dependent diffusion coefficient lead to the same result for small D¿c.

Exact solution to the mean exit time problem for free inertial processes driven by Gaussian white noise

We obtain the exact analytical expression, up to a quadrature, for the mean exit time, T(x,v), of a free inertial process driven by Gaussian white noise from a region (0,L) in space. We obtain a completely explicit expression for T(x,0) and discuss the dependence of T(x,v) as a function of the size L of the region. We develop a new method that may be used to solve other exit time problems.

Fractal dimension for Gaussian colored processes

The exact analytical expression for the Hausdorff dimension of free processes driven by Gaussian noise in n-dimensional space is obtained. The fractal dimension solely depends on the time behavior of the arbitrary correlation function of the noise, ranging from DX=1 for Orstein-Uhlenbeck input noise to any real number greater than 1 for fractional Brownian motions.

Free inertial processes driven by Gaussian noise: Probability distributions, anomalous diffusion and fractal behavior

We study the motion of an unbound particle under the influence of a random force modeled as Gaussian colored noise with an arbitrary correlation function. We derive exact equations for the joint and marginal probability density functions and find the associated solutions. We analyze in detail anomalous diffusion behaviors along with the fractal structure of the trajectories of the particle and explore possible connections between dynamical exponents of the variance and the fractal dimension of the trajectories.

Exact solution to the exit-time problem for an undamped free particle driven by Gaussian white noise

In a recent paper [Phys. Rev. Lett. 75, 189 (1995)] we have presented the exact analytical expression for the mean exit time, T(x,v), of a free inertial process driven by Gaussian white noise out of a region (0,L) in space. In this paper we give a detailed account of the method employed and present results on asymptotic properties and averages of T(x,v).

The Gaussian assumption in second-order estimation problems in digital communications

This paper deals with the goodness of the Gaussian assumption when designing second-order blind estimationmethods in the context of digital communications. The low- andhigh-signal-to-noise ratio (SNR) asymptotic performance of the maximum likelihood estimator—derived assuming Gaussiantransmitted symbols—is compared with the performance of the optimal second-order estimator, which exploits the actualdistribution of the discrete constellation. The asymptotic study concludes that the Gaussian assumption leads to the optimalsecond-order solution if the SNR is very low or if the symbols belong to a multilevel constellation such as quadrature-amplitudemodulation (QAM) or amplitude-phase-shift keying (APSK). On the other hand, the Gaussian assumption can yield importantlosses at high SNR if the transmitted symbols are drawn from a constant modulus constellation such as phase-shift keying (PSK)or continuous-phase modulations (CPM). These conclusions are illustrated for the problem of direction-of-arrival (DOA) estimation of multiple digitally-modulated signals.

Joint array combining and MLSE for single-user receivers in multipath Gaussian multiuser channels

The well-known structure of an array combiner along with a maximum likelihood sequence estimator (MLSE) receiveris the basis for the derivation of a space-time processor presentinggood properties in terms of co-channel and intersymbol interferencerejection. The use of spatial diversity at the receiver front-endtogether with a scalar MLSE implies a joint design of the spatialcombiner and the impulse response for the sequence detector. Thisis faced using the MMSE criterion under the constraint that thedesired user signal power is not cancelled, yielding an impulse responsefor the sequence detector that is matched to the channel andcombiner response. The procedure maximizes the signal-to-noiseratio at the input of the detector and exhibits excellent performancein realistic multipath channels.

Net spaces and boundedness of integral operators

In this paper we introduce new functional spaces which we call the net spaces. Using their properties, the necessary and sufficient conditions for the integral operators to be of strong or weak-type are obtained. The estimates of the norm of the convolution operator in weighted Lebesgue spaces are presented.

Estudio sobre la extracción de puntos característicos en imágenes y sus aplicaciones

En aquest treball realitzem un estudi sobre la detecció y la descripció de punts característics, una tecnologia que permet extreure informació continguda en les imatges. Primerament presentem l'estat de l'art juntament amb una avaluació dels mètodes més rellevants. A continuació proposem els nous mètodes que hem creat de detecció i descripció, juntament amb l'algorisme òptim anomenat DART, el qual supera l'estat de l'art. Finalment mostrem algunes aplicacions on s'utilitzen els punts DART. Basant-se en l'aproximació de l'espai d'escales Gaussià, el detector proposat pot extreure punts de distint tamany invariants davant canvis en el punt de vista, la rotació i la iluminació. La reutilització de l'espai d'escales durant el procés de descripció, així com l'ús d'estructures simplificades i optimitzades, permeten realitzar tot el procediment en un temps computacional menor a l'obtingut fins al moment. Així s'aconsegueixen punts invariants i distingibles de forma ràpida, el qual permet la seva utilització en aplicacions com el seguiment d'objectes, la reconstrucció d'escenaris 3D i en motors de cerca visual.

Extended truncated Tweedie-Poisson model

It has been argued that by truncating the sample space of the negative binomial and of the inverse Gaussian-Poisson mixture models at zero, one is allowed to extend the parameter space of the model. Here that is proved to be the case for the more general three parameter Tweedie-Poisson mixture model. It is also proved that the distributions in the extended part of the parameter space are not the zero truncation of mixed poisson distributions and that, other than for the negative binomial, they are not mixtures of zero truncated Poisson distributions either. By extending the parameter space one can improve the fit when the frequency of one is larger and the right tail is heavier than is allowed by the unextended model. Considering the extended model also allows one to use the basic maximum likelihood based inference tools when parameter estimates fall in the extended part of the parameter space, and hence when the m.l.e. does not exist under the unextended model. This extended truncated Tweedie-Poisson model is proved to be useful in the analysis of words and species frequency count data.

Spatial Analysis of Cell Composition Data

A version of Matheron’s discrete Gaussian model is applied to cell composition data.The examples are for map patterns of felsic metavolcanics in two different areas. Q-Qplots of the model for cell values representing proportion of 10 km x 10 km cell areaunderlain by this rock type are approximately linear, and the line of best fit can be usedto estimate the parameters of the model. It is also shown that felsic metavolcanics in theAbitibi area of the Canadian Shield can be modeled as a fractal

Resource dimensioning aspect of heterogeneous traffic with different service requirements: Integration versus segregation

In this paper, we consider the ATM networks in which the virtual path concept is implemented. The question of how to multiplex two or more diverse traffic classes while providing different quality of service requirements is a very complicated open problem. Two distinct options are available: integration and segregation. In an integration approach all the traffic from different connections are multiplexed onto one VP. This implies that the most restrictive QOS requirements must be applied to all services. Therefore, link utilization will be decreased because unnecessarily stringent QOS is provided to all connections. With the segregation approach the problem can be much simplified if different types of traffic are separated by assigning a VP with dedicated resources (buffers and links). Therefore, resources may not be efficiently utilized because no sharing of bandwidth can take place across the VP. The probability that the bandwidth required by the accepted connections exceeds the capacity of the link is evaluated with the probability of congestion (PC). Since the PC can be expressed as the CLP, we shall simply carry out bandwidth allocation using the PC. We first focus on the influence of some parameters (CLP, bit rate and burstiness) on the capacity required by a VP supporting a single traffic class using the new convolution approach. Numerical results are presented both to compare the required capacity and to observe which conditions under each approach are preferred

Estimation of the probability of congestion using Monte Carlo method in OPS networks

In networks with small buffers, such as optical packet switching based networks, the convolution approach is presented as one of the most accurate method used for the connection admission control. Admission control and resource management have been addressed in other works oriented to bursty traffic and ATM. This paper focuses on heterogeneous traffic in OPS based networks. Using heterogeneous traffic and bufferless networks the enhanced convolution approach is a good solution. However, both methods (CA and ECA) present a high computational cost for high number of connections. Two new mechanisms (UMCA and ISCA) based on Monte Carlo method are proposed to overcome this drawback. Simulation results show that our proposals achieve lower computational cost compared to enhanced convolution approach with an small stochastic error in the probability estimation