A non-extensive maximum entropy based regulations method for bad conditioned inverse problems

A regularization method based on the non-extensive maximum entropy principle is devised. Special emphasis is given to the q=1/2 case. We show that, when the residual principle is considered as constraint, the q=1/2 generalized distribution of Tsallis yields a regularized solution for bad-conditioned problems. The so devised regularized distribution is endowed with a component which corresponds to the well known regularized solution of Tikhonov (1977).

Frames: a maximum entropy statistical estimate of the inverse problem

A maximum entropy statistical treatment of an inverse problem concerning frame theory is presented. The problem arises from the fact that a frame is an overcomplete set of vectors that defines a mapping with no unique inverse. Although any vector in the concomitant space can be expressed as a linear combination of frame elements, the coefficients of the expansion are not unique. Frame theory guarantees the existence of a set of coefficients which is “optimal” in a minimum norm sense. We show here that these coefficients are also “optimal” from a maximum entropy viewpoint.

Statistical modelling of CSP solving algorithms performance

The goal of this work is to try to create a statistical model, based only on easily computable parameters from the CSP problem to predict runtime behaviour of the solving algorithms, and let us choose the best algorithm to solve the problem. Although it seems that the obvious choice should be MAC, experimental results obtained so far show, that with big numbers of variables, other algorithms perfom much better, specially for hard problems in the transition phase.

Application of Information Statistical Theory to the Description of the Effect of Heat Conduction on the Chemical Reaction Rate in Gases

The effect of the heat flux on the rate of chemical reaction in dilute gases is shown to be important for reactions characterized by high activation energies and in the presence of very large temperature gradients. This effect, obtained from the second-order terms in the distribution function (similar to those obtained in the Burnett approximation to the solution of the Boltzmann equation), is derived on the basis of information theory. It is shown that the analytical results describing the effect are simpler if the kinetic definition for the nonequilibrium temperature is introduced than if the thermodynamic definition is introduced. The numerical results are nearly the same for both definitions

Statistical Reviewers Improve Reporting in Biomedical Articles: a Randomized Trial.

Background. Although peer review is widely considered to be the most credible way of selecting manuscripts and improving the quality of accepted papers in scientific journals, there is little evidence to support its use. Our aim was to estimate the effects on manuscript quality of either adding a statistical peer reviewer or suggesting the use of checklists such as CONSORT or STARD to clinical reviewers or both. Methodology and Principal Findings. Interventions were defined as 1) the addition of a statistical reviewer to the clinical peer review process, and 2) suggesting reporting guidelines to reviewers; with"no statistical expert" and"no checklist" as controls. The two interventions were crossed in a 262 balanced factorial design including original research articles consecutively selected, between May 2004 and March 2005, by the Medicina Clinica (Barc) editorial committee. We randomized manuscripts to minimize differences in terms of baseline quality and type of study (intervention, longitudinal, cross-sectional, others). Sample-size calculations indicated that 100 papers provide an 80% power to test a 55% standardized difference. We specified the main outcome as the increment in quality of papers as measured on the Goodman Scale. Two blinded evaluators rated the quality of manuscripts at initial submission and final post peer review version. Of the 327 manuscripts submitted to the journal, 131 were accepted for further review, and 129 were randomized. Of those, 14 that were lost to follow-up showed no differences in initial quality to the followed-up papers. Hence, 115 were included in the main analysis, with 16 rejected for publication after peer review. 21 (18.3%) of the 115 included papers were interventions, 46 (40.0%) were longitudinal designs, 28 (24.3%) cross-sectional and 20 (17.4%) others. The 16 (13.9%) rejected papers had a significantly lower initial score on the overall Goodman scale than accepted papers (difference 15.0, 95% CI: 4.6- 24.4). The effect of suggesting a guideline to the reviewers had no effect on change in overall quality as measured by the Goodman scale (0.9, 95% CI: 20.3+2.1). The estimated effect of adding a statistical reviewer was 5.5 (95% CI: 4.3-6.7), showing a significant improvement in quality. Conclusions and Significance. This prospective randomized study shows the positive effect of adding a statistical reviewer to the field-expert peers in improving manuscript quality. We did not find a statistically significant positive effect by suggesting reviewers use reporting guidelines.

REGSTATTOOLS: freeware statistical tools for the analysis of disease population databases used in health and social studies

Background: The repertoire of statistical methods dealing with the descriptive analysis of the burden of a disease has been expanded and implemented in statistical software packages during the last years. The purpose of this paper is to present a web-based tool, REGSTATTOOLS http://regstattools.net intended to provide analysis for the burden of cancer, or other group of disease registry data. Three software applications are included in REGSTATTOOLS: SART (analysis of disease"s rates and its time trends), RiskDiff (analysis of percent changes in the rates due to demographic factors and risk of developing or dying from a disease) and WAERS (relative survival analysis). Results: We show a real-data application through the assessment of the burden of tobacco-related cancer incidence in two Spanish regions in the period 1995-2004. Making use of SART we show that lung cancer is the most common cancer among those cancers, with rising trends in incidence among women. We compared 2000-2004 data with that of 1995-1999 to assess percent changes in the number of cases as well as relative survival using RiskDiff and WAERS, respectively. We show that the net change increase in lung cancer cases among women was mainly attributable to an increased risk of developing lung cancer, whereas in men it is attributable to the increase in population size. Among men, lung cancer relative survival was higher in 2000-2004 than in 1995-1999, whereas it was similar among women when these time periods were compared. Conclusions: Unlike other similar applications, REGSTATTOOLS does not require local software installation and it is simple to use, fast and easy to interpret. It is a set of web-based statistical tools intended for automated calculation of population indicators that any professional in health or social sciences may require.

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.

Regression-based techniques for statistical decision making in single-case designs

The present study evaluates the performance of four methods for estimating regression coefficients used to make statistical decisions regarding intervention effectiveness in single-case designs. Ordinary least squares estimation is compared to two correction techniques dealing with general trend and one eliminating autocorrelation whenever it is present. Type I error rates and statistical power are studied for experimental conditions defined by the presence or absence of treatment effect (change in level or in slope), general trend, and serial dependence. The results show that empirical Type I error rates do not approximate the nominal ones in presence of autocorrelation or general trend when ordinary and generalized least squares are applied. The techniques controlling trend show lower false alarm rates, but prove to be insufficiently sensitive to existing treatment effects. Consequently, the use of the statistical significance of the regression coefficients for detecting treatment effects is not recommended for short data series.

Nature of the Epidemic Threshold for the Susceptible-Infected-Susceptible Dynamics in Networks

We develop an analytical approach to the susceptible-infected-susceptible epidemic model that allows us to unravel the true origin of the absence of an epidemic threshold in heterogeneous networks. We find that a delicate balance between the number of high degree nodes in the network and the topological distance between them dictates the existence or absence of such a threshold. In particular, small-world random networks with a degree distribution decaying slower than an exponential have a vanishing epidemic threshold in the thermodynamic limit.

Statistical mechanics of multi-edge networks

Statistical properties of binary complex networks are well understood and recently many attempts have been made to extend this knowledge to weighted ones. There are, however, subtle yet important considerations to be made regarding the nature of the weights used in this generalization. Weights can be either continuous or discrete magnitudes, and in the latter case, they can additionally have undistinguishable or distinguishable nature. This fact has not been addressed in the literature insofar and has deep implications on the network statistics. In this work we face this problem introducing multiedge networks as graphs where multiple (distinguishable) connections between nodes are considered. We develop a statistical mechanics framework where it is possible to get information about the most relevant observables given a large spectrum of linear and nonlinear constraints including those depending both on the number of multiedges per link and their binary projection. The latter case is particularly interesting as we show that binary projections can be understood from multiedge processes. The implications of these results are important as many real-agent-based problems mapped onto graphs require this treatment for a proper characterization of their collective behavior.

Persistent random walk model for transport trough thin slabs

We present a model for transport in multiply scattering media based on a three-dimensional generalization of the persistent random walk. The model assumes that photons move along directions that are parallel to the axes. Although this hypothesis is not realistic, it allows us to solve exactly the problem of multiple scattering propagation in a thin slab. Among other quantities, the transmission probability and the mean transmission time can be calculated exactly. Besides being completely solvable, the model could be used as a benchmark for approximation schemes to multiple light scattering.

The adequacy of different robust statistical tests in comparing two independent groups

In the current study, we evaluated various robust statistical methods for comparing two independent groups. Two scenarios for simulation were generated: one of equality and another of population mean differences. In each of the scenarios, 33 experimental conditions were used as a function of sample size, standard deviation and asymmetry. For each condition, 5000 replications per group were generated. The results obtained by this study show an adequate type error I rate but not a high power for the confidence intervals. In general, for the two scenarios studied (mean population differences and not mean population differences) in the different conditions analysed, the Mann-Whitney U-test demonstrated strong performance, and a little worse the t-test of Yuen-Welch.

Critical behavior in nonequilibrium phase transitions

The nonequilibrium phase transitions occurring in a fast-ionic-conductor model and in a reaction-diffusion Ising model are studied by Monte Carlo finite-size scaling to reveal nonclassical critical behavior; our results are compared with those in related models.

Critical behavior of a water monolayer under hydrophobic confinement

The properties of water can have a strong dependence on the confinement. Here, we consider a water monolayer nanoconfined between hydrophobic parallel walls under conditions that prevent its crystallization. We investigate, by simulations of a many-body coarse-grained water model, how the properties of the liquid are affected by the confinement. We show, by studying the response functions and the correlation length and by performing finite-size scaling of the appropriate order parameter, that at low temperature the monolayer undergoes a liquid-liquid phase transition ending in a critical point in the universality class of the two-dimensional (2D) Ising model. Surprisingly, by reducing the linear size L of the walls, keeping the walls separation h constant, we find a 2D-3D crossover for the universality class of the liquid-liquid critical point for L/h=~50, i.e. for a monolayer thickness that is small compared to its extension. This result is drastically different from what is reported for simple liquids, where the crossover occurs for , and is consistent with experimental results and atomistic simulations. We shed light on these findings showing that they are a consequence of the strong cooperativity and the low coordination number of the hydrogen bond network that characterizes water.