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.

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).

Realizations of Poincar group induced by second order differential systems. Non interaction theorem

A generalization of the predictive relativistic mechanics is studied where the initial conditions are taken on a general hypersurface of M4. The induced realizations of the Poincar group are obtained. The same procedure is used for the Galileo group. Noninteraction theorems are derived for both groups.

Enhanced pulse propagation in non-linear arrays of oscillators

The propagation of a pulse in a nonlinear array of oscillators is influenced by the nature of the array and by its coupling to a thermal environment. For example, in some arrays a pulse can be speeded up while in others a pulse can be slowed down by raising the temperature. We begin by showing that an energy pulse (one dimension) or energy front (two dimensions) travels more rapidly and remains more localized over greater distances in an isolated array (microcanonical) of hard springs than in a harmonic array or in a soft-springed array. Increasing the pulse amplitude causes it to speed up in a hard chain, leaves the pulse speed unchanged in a harmonic system, and slows down the pulse in a soft chain. Connection of each site to a thermal environment (canonical) affects these results very differently in each type of array. In a hard chain the dissipative forces slow down the pulse while raising the temperature speeds it up. In a soft chain the opposite occurs: the dissipative forces actually speed up the pulse, while raising the temperature slows it down. In a harmonic chain neither dissipation nor temperature changes affect the pulse speed. These and other results are explained on the basis of the frequency vs energy relations in the various arrays

Stochastic delay equations with non-negativity constraints driven by fractional Brownian motion

In this note we prove an existence and uniqueness result for the solution of multidimensional stochastic delay differential equations with normal reflection. The equations are driven by a fractional Brownian motion with Hurst parameter H > 1/2. The stochastic integral with respect to the fractional Brownian motion is a pathwise Riemann¿Stieltjes integral.

Post-Nonlinear Mixtures and Beyond

Although sources in general nonlinear mixturm arc not separable iising only statistical independence, a special and realistic case of nonlinear mixtnres, the post nonlinear (PNL) mixture is separable choosing a suited separating system. Then, a natural approach is based on the estimation of tho separating Bystem parameters by minimizing an indcpendence criterion, like estimated mwce mutual information. This class of methods requires higher (than 2) order statistics, and cannot separate Gaarsian sources. However, use of [weak) prior, like source temporal correlation or nonstationarity, leads to other source separation Jgw rithms, which are able to separate Gaussian sourra, and can even, for a few of them, works with second-order statistics. Recently, modeling time correlated s011rces by Markov models, we propose vcry efficient algorithms hmed on minimization of the conditional mutual information. Currently, using the prior of temporally correlated sources, we investigate the fesihility of inverting PNL mixtures with non-bijectiw non-liacarities, like quadratic functions. In this paper, we review the main ICA and BSS results for riunlinear mixtures, present PNL models and algorithms, and finish with advanced resutts using temporally correlated snu~sm

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.

Post-market environmental monitoring of Bt maize in Spain: Non-target effects of varieties derived from the event MON810 on predatory fauna

The Spanish Government has established post-market environmental monitoring (PMEM) as mandatory for genetically modified (GM) crop varieties cultivated in Spain. In order to comply with this regulation, effects of Bt maize varieties derived from the event MON810 on the predatory fauna were monitored for two years in northeast and central Spain. The study was carried out with a randomized block design in maize fields of 3-4 ha on which the abundance of plant-dwelling predators and the activity-density of soil-dwelling predators in Bt vs. non-Bt near-isogenic varieties were compared. To this end, the plots were sampled by visual inspection of a certain number of plants and pitfall traps 6 or 7 times throughout two seasons. No significant differences in predator densities on plants were found between Bt and non-Bt varieties. In the pitfall traps, significant differences between the two types of maize were found only in Staphylinidae, in which trap catches in non-Bt maize were higher than in Bt maize in central Spain. Based on the statistical power of the assays, surrogate arthropods for PMEM purposes are proposed; Orius spp. and Araneae for visual sampling and Carabidae, Araneae, and Staphylinidae for pitfall trapping. The other predator groups recorded in the study, Nabis sp. and Coccinellidae in visual sampling and Dermaptera in pitfall trapping, gave very poor power results. To help to establish a standardized protocol for PMEM of genetically modified crops, the effect-detecting capacity with a power of 0.8 of each predator group is given.

Hardness of FRHC-Cu determined by statistical analysis

A statistical indentation method has been employed to study the hardness value of fire-refined high conductivity copper, using nanoindentation technique. The Joslin and Oliver approach was used with the aim to separate the hardness (H) influence of copper matrix, from that of inclusions and grain boundaries. This approach relies on a large array of imprints (around 400 indentations), performed at 150 nm of indentation depth. A statistical study using a cumulative distribution function fit and Gaussian simulated distributions, exhibits that H for each phase can be extracted when the indentation depth is much lower than the size of the secondary phases. It is found that the thermal treatment produces a hardness increase, due to the partly re-dissolution of the inclusions (mainly Pb and Sn) in the matrix.

Little evidence for association between the TGFBR1*6A variant and colorectal cancer: a family-based association study on non-syndromic family members from Australia and Spain.

Genome-wide linkage studies have identified the 9q22 chromosomal region as linked with colorectal cancer (CRC) predisposition. A candidate gene in this region is transforming growth factor beta receptor 1 (TGFBR1). Investigation of TGFBR1 has focused on the common genetic variant rs11466445, a short exonic deletion of nine base pairs which results in truncation of a stretch of nine alanine residues to six alanine residues in the gene product. While the six alanine (*6A) allele has been reported to be associated with increased risk of CRC in some population based study groups this association remains the subject of robust debate. To date, reports have been limited to population-based case-control association studies, or case-control studies of CRC families selecting one affected individual per family. No study has yet taken advantage of all the genetic information provided by multiplex CRC families. Methods: We have tested for an association between rs11466445 and risk of CRC using several family-based statistical tests in a new study group comprising members of non-syndromic high risk CRC families sourced from three familial cancer centres, two in Australia and one in Spain. Results: We report a finding of a nominally significant result using the pedigree-based association test approach (PBAT; p = 0.028), while other family-based tests were non-significant, but with a p-value < 0.10 in each instance. These other tests included the Generalised Disequilibrium Test (GDT; p = 0.085), parent of origin GDT Generalised Disequilibrium Test (GDT-PO; p = 0.081) and empirical Family-Based Association Test (FBAT; p = 0.096, additive model). Related-person case-control testing using the 'More Powerful' Quasi-Likelihood Score Test did not provide any evidence for association (M-QL5; p = 0.41). Conclusions: After conservatively taking into account considerations for multiple hypothesis testing, we find little evidence for an association between the TGFBR1*6A allele and CRC risk in these families. The weak support for an increase in risk in CRC predisposed families is in agreement with recent meta-analyses of case-control studies, which estimate only a modest increase in sporadic CRC risk among 6*A allele carriers.