Random perturbations of stochastic processes with unbounded variable length memory

We consider binary infinite order stochastic chains perturbed by a random noise. This means that at each time step, the value assumed by the chain can be randomly and independently flipped with a small fixed probability. We show that the transition probabilities of the perturbed chain are uniformly close to the corresponding transition probabilities of the original chain. As a consequence, in the case of stochastic chains with unbounded but otherwise finite variable length memory, we show that it is possible to recover the context tree of the original chain, using a suitable version of the algorithm Context, provided that the noise is small enough.

Super-resolution of remotely sensed images with variable-pixel linear reconstruction

This paper describes the development and applications of a super-resolution method, known as Super-Resolution Variable-Pixel Linear Reconstruction. The algorithm works combining different lower resolution images in order to obtain, as a result, a higher resolution image. We show that it can make significant spatial resolution improvements to satellite images of the Earth¿s surface allowing recognition of objects with size approaching the limiting spatial resolution of the lower resolution images. The algorithm is based on the Variable-Pixel Linear Reconstruction algorithm developed by Fruchter and Hook, a well-known method in astronomy but never used for Earth remote sensing purposes. The algorithm preserves photometry, can weight input images according to the statistical significance of each pixel, and removes the effect of geometric distortion on both image shape and photometry. In this paper, we describe its development for remote sensing purposes, show the usefulness of the algorithm working with images as different to the astronomical images as the remote sensing ones, and show applications to: 1) a set of simulated multispectral images obtained from a real Quickbird image; and 2) a set of multispectral real Landsat Enhanced Thematic Mapper Plus (ETM+) images. These examples show that the algorithm provides a substantial improvement in limiting spatial resolution for both simulated and real data sets without significantly altering the multispectral content of the input low-resolution images, without amplifying the noise, and with very few artifacts.

Partially Observed Markov Random Fields Are Variable Neighborhood Random Fields

The present paper has two goals. First to present a natural example of a new class of random fields which are the variable neighborhood random fields. The example we consider is a partially observed nearest neighbor binary Markov random field. The second goal is to establish sufficient conditions ensuring that the variable neighborhoods are almost surely finite. We discuss the relationship between the almost sure finiteness of the interaction neighborhoods and the presence/absence of phase transition of the underlying Markov random field. In the case where the underlying random field has no phase transition we show that the finiteness of neighborhoods depends on a specific relation between the noise level and the minimum values of the one-point specification of the Markov random field. The case in which there is phase transition is addressed in the frame of the ferromagnetic Ising model. We prove that the existence of infinite interaction neighborhoods depends on the phase.

An empirical evaluation of the Random Forests classifier models for variable selection in a large-scale lung cancer case-control study

Random Forests™ is reported to be one of the most accurate classification algorithms in complex data analysis. It shows excellent performance even when most predictors are noisy and the number of variables is much larger than the number of observations. In this thesis Random Forests was applied to a large-scale lung cancer case-control study. A novel way of automatically selecting prognostic factors was proposed. Also, synthetic positive control was used to validate Random Forests method. Throughout this study we showed that Random Forests can deal with large number of weak input variables without overfitting. It can account for non-additive interactions between these input variables. Random Forests can also be used for variable selection without being adversely affected by collinearities. ^ Random Forests can deal with the large-scale data sets without rigorous data preprocessing. It has robust variable importance ranking measure. Proposed is a novel variable selection method in context of Random Forests that uses the data noise level as the cut-off value to determine the subset of the important predictors. This new approach enhanced the ability of the Random Forests algorithm to automatically identify important predictors for complex data. The cut-off value can also be adjusted based on the results of the synthetic positive control experiments. ^ When the data set had high variables to observations ratio, Random Forests complemented the established logistic regression. This study suggested that Random Forests is recommended for such high dimensionality data. One can use Random Forests to select the important variables and then use logistic regression or Random Forests itself to estimate the effect size of the predictors and to classify new observations. ^ We also found that the mean decrease of accuracy is a more reliable variable ranking measurement than mean decrease of Gini. ^

Variable threshold algorithm for division of labor analyzed as a dynamical system

Division of labor is a widely studied aspect of colony behavior of social insects. Division of labor models indicate how individuals distribute themselves in order to perform different tasks simultaneously. However, models that study division of labor from a dynamical system point of view cannot be found in the literature. In this paper, we define a division of labor model as a discrete-time dynamical system, in order to study the equilibrium points and their properties related to convergence and stability. By making use of this analytical model, an adaptive algorithm based on division of labor can be designed to satisfy dynamic criteria. In this way, we have designed and tested an algorithm that varies the response thresholds in order to modify the dynamic behavior of the system. This behavior modification allows the system to adapt to specific environmental and collective situations, making the algorithm a good candidate for distributed control applications. The variable threshold algorithm is based on specialization mechanisms. It is able to achieve an asymptotically stable behavior of the system in different environments and independently of the number of individuals. The algorithm has been successfully tested under several initial conditions and number of individuals.

Random error in willingness to pay measurement: A multiple indicators, latent variable approach to the reliability of contingent values

The reliability of measurement refers to unsystematic error in observed responses. Investigations of the prevalence of random error in stated estimates of willingness to pay (WTP) are important to an understanding of why tests of validity in CV can fail. However, published reliability studies have tended to adopt empirical methods that have practical and conceptual limitations when applied to WTP responses. This contention is supported in a review of contingent valuation reliability studies that demonstrate important limitations of existing approaches to WTP reliability. It is argued that empirical assessments of the reliability of contingent values may be better dealt with by using multiple indicators to measure the latent WTP distribution. This latent variable approach is demonstrated with data obtained from a WTP study for stormwater pollution abatement. Attitude variables were employed as a way of assessing the reliability of open-ended WTP (with benchmarked payment cards) for stormwater pollution abatement. The results indicated that participants' decisions to pay were reliably measured, but not the magnitude of the WTP bids. This finding highlights the need to better discern what is actually being measured in VVTP studies, (C) 2003 Elsevier B.V. All rights reserved.

Threshold behaviour and final outcome of an epidemic on a random network with household structure

This paper considers a stochastic SIR (susceptible-infective-removed) epidemic model in which individuals may make infectious contacts in two ways, both within 'households' (which for ease of exposition are assumed to have equal size) and along the edges of a random graph describing additional social contacts. Heuristically-motivated branching process approximations are described, which lead to a threshold parameter for the model and methods for calculating the probability of a major outbreak, given few initial infectives, and the expected proportion of the population who are ultimately infected by such a major outbreak. These approximate results are shown to be exact as the number of households tends to infinity by proving associated limit theorems. Moreover, simulation studies indicate that these asymptotic results provide good approximations for modestly-sized finite populations. The extension to unequal sized households is discussed briefly.

Chemical evolution models for spiral disks: the Milky Way, M31, and M33

Context. The distribution of chemical abundances and their variation with time are important tools for understanding the chemical evolution of galaxies. In particular, the study of chemical evolution models can improve our understanding of the basic assumptions made when modelling our Galaxy and other spirals. Aims. We test a standard chemical evolution model for spiral disks in the Local Universe and study the influence of a threshold gas density and different efficiencies in the star formation rate (SFR) law on radial gradients of abundance, gas, and SFR. The model is then applied to specific galaxies. Methods. We adopt a one-infall chemical evolution model where the Galactic disk forms inside-out by means of infall of gas, and we test different thresholds and efficiencies in the SFR. The model is scaled to the disk properties of three Local Group galaxies (the Milky Way, M31 and M33) by varying its dependence on the star formation efficiency and the timescale for the infall of gas onto the disk. Results. Using this simple model, we are able to reproduce most of the observed constraints available in the literature for the studied galaxies. The radial oxygen abundance gradients and their time evolution are studied in detail. The present day abundance gradients are more sensitive to the threshold than to other parameters, while their temporal evolutions are more dependent on the chosen SFR efficiency. A variable efficiency along the galaxy radius can reproduce the present day gas distribution in the disk of spirals with prominent arms. The steepness in the distribution of stellar surface density differs from massive to lower mass disks, owing to the different star formation histories. Conclusions. The most massive disks seem to have evolved faster (i.e., with more efficient star formation) than the less massive ones, thus suggesting a downsizing in star formation for spirals. The threshold and the efficiency of star formation play a very important role in the chemical evolution of spiral disks. For instance, an efficiency varying with radius can be used to regulate the star formation. The oxygen abundance gradient can steepen or flatten in time depending on the choice of this parameter.

On the resilience of long cycles in random graphs

In this paper we determine the local and global resilience of random graphs G(n,p) (p >> n(-1)) with respect to the property of containing a cycle of length at least (1 - alpha)n. Roughly speaking, given alpha > 0, we determine the smallest r(g) (G, alpha) with the property that almost surely every subgraph of G = G(n,p) having more than r(g) (G, alpha)vertical bar E(G)vertical bar edges contains a cycle of length at least (1 - alpha)n (global resilience). We also obtain, for alpha < 1/2, the smallest r(l) (G, alpha) such that any H subset of G having deg(H) (v) larger than r(l) (G, alpha) deg(G) (v) for all v is an element of V(G) contains a cycle of length at least (1 - alpha)n (local resilience). The results above are in fact proved in the more general setting of pseudorandom graphs.

TESTING STATISTICAL HYPOTHESIS ON RANDOM TREES AND APPLICATIONS TO THE PROTEIN CLASSIFICATION PROBLEM

Efficient automatic protein classification is of central importance in genomic annotation. As an independent way to check the reliability of the classification, we propose a statistical approach to test if two sets of protein domain sequences coming from two families of the Pfam database are significantly different. We model protein sequences as realizations of Variable Length Markov Chains (VLMC) and we use the context trees as a signature of each protein family. Our approach is based on a Kolmogorov-Smirnov-type goodness-of-fit test proposed by Balding et at. [Limit theorems for sequences of random trees (2008), DOI: 10.1007/s11749-008-0092-z]. The test statistic is a supremum over the space of trees of a function of the two samples; its computation grows, in principle, exponentially fast with the maximal number of nodes of the potential trees. We show how to transform this problem into a max-flow over a related graph which can be solved using a Ford-Fulkerson algorithm in polynomial time on that number. We apply the test to 10 randomly chosen protein domain families from the seed of Pfam-A database (high quality, manually curated families). The test shows that the distributions of context trees coming from different families are significantly different. We emphasize that this is a novel mathematical approach to validate the automatic clustering of sequences in any context. We also study the performance of the test via simulations on Galton-Watson related processes.

Constant-random practice and the adaptive process in motor learning with varying amounts of constant practice

The adaptive process in motor learning was examined in terms of effects of varying amounts of constant practice performed before random practice. Participants pressed five response keys sequentially, the last one coincident with the lighting of a final visual stimulus provided by a complex coincident timing apparatus. Different visual stimulus speeds were used during the random practice. 33 children (M age=11.6 yr.) were randomly assigned to one of three experimental groups: constant-random, constant-random 33%, and constant-random 66%. The constant-random group practiced constantly until they reached a criterion of performance stabilization three consecutive trials within 50 msec. of error. The other two groups had additional constant practice of 33 and 66%, respectively, of the number of trials needed to achieve the stabilization criterion. All three groups performed 36 trials under random practice; in the adaptation phase, they practiced at a different visual stimulus speed adopted in the stabilization phase. Global performance measures were absolute, constant, and variable errors, and movement pattern was analyzed by relative timing and overall movement time. There was no group difference in relation to global performance measures and overall movement time. However, differences between the groups were observed on movement pattern, since constant-random 66% group changed its relative timing performance in the adaptation phase.

Impact of Atypical Retardation Patterns on Detection of Glaucoma Progression using the GDx with Variable Corneal Compensation

PURPOSE: To evaluate the impact of atypical retardation patterns (ARP) on detection of progressive retinal nerve fiber layer (RNFL) loss using scanning laser polarimetry with variable corneal compensation (VCC). DESIGN: Observational cohort study. METHODS: The study included 377 eyes of 221 patients with a median follow-up of 4.0 years. Images were obtained annually with the GDx VCC (Carl Zeiss Med, itec Inc, Dublin, California, USA), along with optic disc stereophotographs and standard automated perimetry (SAP) visual fields. Progression was determined by the Guided Progression Analysis software for SAP and by masked assessment of stereophotographs by expert graders. The typical scan score (TSS) was used to quantify the presence of ARPs on GDx VCC images. Random coefficients models were used to evaluate the relationship between ARP and RNFL thickness measurements over time. RESULTS: Thirty-eight eyes (10%) showed progression over time on visual fields, stereophotographs, or both. Changes in TSS scores from baseline were significantly associated with changes in RNFL thickness measurements in both progressing and nonprogressing eyes. Each I unit increase in TSS score was associated with a 0.19-mu m decrease in RNFL thickness measurement (P < .001) over time. CONCLUSIONS: ARPs had a significant effect on detection of progressive RNFL loss with the GDx VCC. Eyes with large amounts of atypical patterns, great fluctuations on these patterns over time, or both may show changes in measurements that can appear falsely as glaucomatous progression or can mask true changes in the RNFL. (Am J Ophthalmol 2009;148:155-163. (C) 2009 by Elsevier Inc. All rights reserved.)

Computation of the linear elastic properties of random porous materials with a wide variety of microstructure

A finite-element method is used to study the elastic properties of random three-dimensional porous materials with highly interconnected pores. We show that Young's modulus, E, is practically independent of Poisson's ratio of the solid phase, nu(s), over the entire solid fraction range, and Poisson's ratio, nu, becomes independent of nu(s) as the percolation threshold is approached. We represent this behaviour of nu in a flow diagram. This interesting but approximate behaviour is very similar to the exactly known behaviour in two-dimensional porous materials. In addition, the behaviour of nu versus nu(s) appears to imply that information in the dilute porosity limit can affect behaviour in the percolation threshold limit. We summarize the finite-element results in terms of simple structure-property relations, instead of tables of data, to make it easier to apply the computational results. Without using accurate numerical computations, one is limited to various effective medium theories and rigorous approximations like bounds and expansions. The accuracy of these equations is unknown for general porous media. To verify a particular theory it is important to check that it predicts both isotropic elastic moduli, i.e. prediction of Young's modulus alone is necessary but not sufficient. The subtleties of Poisson's ratio behaviour actually provide a very effective method for showing differences between the theories and demonstrating their ranges of validity. We find that for moderate- to high-porosity materials, none of the analytical theories is accurate and, at present, numerical techniques must be relied upon.

Usefulness of clinical risk markers and ischemic threshold to stratify risk in patients undergoing major noncardiac surgery

The risk of cardiac events in patients undergoing major noncardiac surgery is dependent on their clinical characteristics and the results of stress testing. The purpose of this study was to develop a composite approach to defining levels of risk and to examine whether different approaches to prophylaxis influenced this prediction of outcome. One hundred forty-five consecutive patients (aged 68 +/- 9 years, 79 men) with >1 clinical risk variable were studied with standard dobutamine-atropine stress echo before major noncardiac surgery. Risk levels were stratified according to the presence of ischemia (new or worsening wall motion abnormality), ischemic threshold (heart rate at development of ischemia), and number of clinical risk variables. Patients were followed for perioperative events (during hospital admission) and death or infarction over the subsequent 16 10 months. Ten perioperative events occurred in 105 patients who proceeded to surgery (10%, 95% confidence interval [CI] 5% to 17%), 40 being cancelled because of cardiac or other risk. No ischemia was identified in 56 patients, 1 of whom (1.8%) had a perioperative infarction. Of the 49 patients with ischemia, 22 (45%) had 1 or 2 clinical risk factors; 2 (9%, 95% CI 1% to 29%) had events. Another 15 patients had a high ischemic threshold and 3 or 4 risk factors; 3 (20%, 95% Cl 4% to 48%) had events. Twelve patients had a low ischemic threshold and 3 or 4 risk factors; 4 (33%, 95% CI 10% to 65%) had events. Preoperative myocardial revascularization was performed in only 3 patients, none of whom had events. Perioperative and long-term events occurred despite the use of beta blockers; 7 of 41 eta blocker-treated patients had a perioperative event (17%, 95% CI 7% to 32%); these treated patients were at higher anticipated risk than untreated patients (20 +/- 24% vs 10 +/- 19%, p = 0.02). The total event rate over late follow-up was 13%, and was predicted by dobutamine-atropine stress echo results and heart rate response. (C) 2002 by Excerpta Medica, Inc.

Lp-solutions to BSDEs with super-linear growth coefficient. Application to degenerate semilinear PDEs.

We consider multidimensional backward stochastic differential equations (BSDEs). We prove the existence and uniqueness of solutions when the coefficient grow super-linearly, and moreover, can be neither locally Lipschitz in the variable y nor in the variable z. This is done with super-linear growth coefficient and a p-integrable terminal condition (p & 1). As application, we establish the existence and uniqueness of solutions to degenerate semilinear PDEs with superlinear growth generator and an Lp-terminal data, p & 1. Our result cover, for instance, the case of PDEs with logarithmic nonlinearities.