Stochastic differential equations with random coefficients

In this paper we establish the existence and uniqueness of a solution for different types of stochastic differential equation with random initial conditions and random coefficients. The stochastic integral is interpreted as a generalized Stratonovich integral, and the techniques used to derive these results are mainly based on the path properties of the Brownian motion, and the definition of the Stratonovich integral.

Tecnologias da informação e da comunicação e a polêmica sobre direito autoral: o caso Google Book Search

Anotamos, neste trabalho, reflexões sobre as conseqüências das Tecnologias da Informação e da Comunicação (TICs) para o direito autoral e sobre os atores do processo informativo. Partimos da lei do direito autoral vigente no Brasil, perguntando-nos como tais normas protegem as obras intelectuais no contexto digital e até que ponto há legalidade e legitimidade na digitalização de livros protegidos, disponibilizados on-line, tomando como exemplo o caso "Google Book Search". Constatamos que a lei atual pouco defende os direitos dos autores e dos leitores, pois se volta para a proteção dos interesses privados comerciais, e que a sociedade civil encontra formas de ampliar o fluxo comunicativo em decorrência da facilidade de reprodução e distribuição de cópias de obras intelectuais proporcionada pelas TICs.

Linear random knots and their scaling behavior

We present here a nonbiased probabilistic method that allows us to consistently analyze knottedness of linear random walks with up to several hundred noncorrelated steps. The method consists of analyzing the spectrum of knots formed by multiple closures of the same open walk through random points on a sphere enclosing the walk. Knottedness of individual "frozen" configurations of linear chains is therefore defined by a characteristic spectrum of realizable knots. We show that in the great majority of cases this method clearly defines the dominant knot type of a walk, i.e., the strongest component of the spectrum. In such cases, direct end-to-end closure creates a knot that usually coincides with the knot type that dominates the random closure spectrum. Interestingly, in a very small proportion of linear random walks, the knot type is not clearly defined. Such walks can be considered as residing in a border zone of the configuration space of two or more knot types. We also characterize the scaling behavior of linear random knots.

Test result-based sampling: an efficient design for estimating the accuracy of patient safety indicators.

OBJECTIVE: Accuracy studies of Patient Safety Indicators (PSIs) are critical but limited by the large samples required due to low occurrence of most events. We tested a sampling design based on test results (verification-biased sampling [VBS]) that minimizes the number of subjects to be verified. METHODS: We considered 3 real PSIs, whose rates were calculated using 3 years of discharge data from a university hospital and a hypothetical screen of very rare events. Sample size estimates, based on the expected sensitivity and precision, were compared across 4 study designs: random and VBS, with and without constraints on the size of the population to be screened. RESULTS: Over sensitivities ranging from 0.3 to 0.7 and PSI prevalence levels ranging from 0.02 to 0.2, the optimal VBS strategy makes it possible to reduce sample size by up to 60% in comparison with simple random sampling. For PSI prevalence levels below 1%, the minimal sample size required was still over 5000. CONCLUSIONS: Verification-biased sampling permits substantial savings in the required sample size for PSI validation studies. However, sample sizes still need to be very large for many of the rarer PSIs.

Stochastic models and numerical algorithms for a class of regulatory gene networks.

Regulatory gene networks contain generic modules, like those involving feedback loops, which are essential for the regulation of many biological functions (Guido et al. in Nature 439:856-860, 2006). We consider a class of self-regulated genes which are the building blocks of many regulatory gene networks, and study the steady-state distribution of the associated Gillespie algorithm by providing efficient numerical algorithms. We also study a regulatory gene network of interest in gene therapy, using mean-field models with time delays. Convergence of the related time-nonhomogeneous Markov chain is established for a class of linear catalytic networks with feedback loops.

Random assignment of intervention points in two phase single-case designs: data-division-specific distributions

The present study explores the statistical properties of a randomization test based on the random assignment of the intervention point in a two-phase (AB) single-case design. The focus is on randomization distributions constructed with the values of the test statistic for all possible random assignments and used to obtain p-values. The shape of those distributions is investigated for each specific data division defined by the moment in which the intervention is introduced. Another aim of the study consisted in testing the detection of inexistent effects (i.e., production of false alarms) in autocorrelated data series, in which the assumption of exchangeability between observations may be untenable. In this way, it was possible to compare nominal and empirical Type I error rates in order to obtain evidence on the statistical validity of the randomization test for each individual data division. The results suggest that when either of the two phases has considerably less measurement times, Type I errors may be too probable and, hence, the decision making process to be carried out by applied researchers may be jeopardized.

Systematic review of delayed postoperative hemorrhage after pancreatic resection.

This review assesses the presentation, management, and outcome of delayed postpancreatectomy hemorrhage (PPH) and suggests a novel algorithm as possible standard of care.An electronic search of Medline and Embase databases from January 1990 to February 2010 was undertaken. A random-effect meta-analysis for success rate and mortality of laparotomy vs. interventional radiology after delayed PPH was performed.Fifteen studies comprising of 248 patients with delayed PPH were included. Its incidence was of 3.3%. A sentinel bleed heralding a delayed PPH was observed in 45% of cases. Pancreatic leaks or intraabdominal abscesses were found in 62%. Interventional radiology was attempted in 41%, and laparotomy was undertaken in 49%. On meta-analysis comparing laparotomy vs. interventional radiology, no significant difference could be found in terms of complete hemostasis (76% vs. 80%; P = 0.35). A statistically significant difference favored interventional radiology vs. laparotomy in term of mortality (22% vs. 47%; P = 0.02).Proper management of postoperative complications, such as pancreatic leak and intraabdominal abscess, minimizes the risk of delayed PPH. Sentinel bleeding needs to be thoroughly investigated. If a pseudoaneurysm is detected, it has to be treated by interventional angiography, in order to prevent a further delayed PPH. Early angiography and embolization or stenting is safe and should be the procedure of choice. Surgery remains a therapeutic option if no interventional radiology is available, or patients cannot be resuscitated for an interventional treatment.

Effects of cognitive abilities on metapopulation connectivity

Connectivity among demes in a metapopulation depends on both the landscape's and the focal organism's properties (including its mobility and cognitive abilities). Using individual-based simulations, we contrast the consequences of three different cognitive strategies on several measures of metapopulation connectivity. Model animals search suitable habitat patches while dispersing through a model landscape made of cells varying in size, shape, attractiveness and friction. In the blind strategy, the next cell is chosen randomly among the adjacent ones. In the near-sighted strategy, the choice depends on the relative attractiveness of these adjacent cells. In the far-sighted strategy, animals may additionally target suitable patches that appear within their perceptual range. Simulations show that the blind strategy provides the best overall connectivity, and results in balanced dispersal. The near-sighted strategy traps animals into corridors that reduce the number of potential targets, thereby fragmenting metapopulations in several local clusters of demes, and inducing sink-source dynamics. This sort of local trapping is somewhat prevented in the far-sighted strategy. The colonization success of strategies depends highly on initial energy reserves: blind does best when energy is high, near-sighted wins at intermediate levels, and far-sighted outcompetes its rivals at low energy reserves. We also expect strong effects in terms of metapopulation genetics: the blind strategy generates a migrant-pool mode of dispersal that should erase local structures. By contrast, near- and far-sighted strategies generate a propagule-pool mode of dispersal and source-sink behavior that should boost structures (high genetic variance among- and low variance within local clusters of demes), particularly if metapopulation dynamics is also affected by extinction-colonization processes. Our results thus point to important effects of the cognitive ability of dispersers on the connectivity, dynamics and genetics of metapopulations.

The co-evolution of culturally inherited altruistic helping and cultural transmission under random group formation.

Limited migration results in kin selective pressure on helping behaviors under a wide range of ecological, demographic and life-history situations. However, such genetically determined altruistic helping can evolve only when migration is not too strong and group size is not too large. Cultural inheritance of helping behaviors may allow altruistic helping to evolve in groups of larger size because cultural transmission has the potential to markedly decrease the variance within groups and augment the variance between groups. Here, we study the co-evolution of culturally inherited altruistic helping behaviors and two alternative cultural transmission rules for such behaviors. We find that conformist transmission, where individuals within groups tend to copy prevalent cultural variants (e.g., beliefs or values), has a strong adverse effect on the evolution of culturally inherited helping traits. This finding is at variance with the commonly held view that conformist transmission is a crucial factor favoring the evolution of altruistic helping in humans. By contrast, we find that under one-to-many transmission, where individuals within groups tend to copy a "leader" (or teacher), altruistic helping can evolve in groups of any size, although the cultural transmission rule itself hitchhikes rather weakly with a selected helping trait. Our results suggest that culturally determined helping behaviors are more likely to be driven by "leaders" than by popularity, but the emergence and stability of the cultural transmission rules themselves should be driven by some extrinsic factors.

Measuring potentially avoidable hospital readmissions.

The objectives of this study were to develop a computerized method to screen for potentially avoidable hospital readmissions using routinely collected data and a prediction model to adjust rates for case mix. We studied hospital information system data of a random sample of 3,474 inpatients discharged alive in 1997 from a university hospital and medical records of those (1,115) readmitted within 1 year. The gold standard was set on the basis of the hospital data and medical records: all readmissions were classified as foreseen readmissions, unforeseen readmissions for a new affection, or unforeseen readmissions for a previously known affection. The latter category was submitted to a systematic medical record review to identify the main cause of readmission. Potentially avoidable readmissions were defined as a subgroup of unforeseen readmissions for a previously known affection occurring within an appropriate interval, set to maximize the chance of detecting avoidable readmissions. The computerized screening algorithm was strictly based on routine statistics: diagnosis and procedures coding and admission mode. The prediction was based on a Poisson regression model. There were 454 (13.1%) unforeseen readmissions for a previously known affection within 1 year. Fifty-nine readmissions (1.7%) were judged avoidable, most of them occurring within 1 month, which was the interval used to define potentially avoidable readmissions (n = 174, 5.0%). The intra-sample sensitivity and specificity of the screening algorithm both reached approximately 96%. Higher risk for potentially avoidable readmission was associated with previous hospitalizations, high comorbidity index, and long length of stay; lower risk was associated with surgery and delivery. The model offers satisfactory predictive performance and a good medical plausibility. The proposed measure could be used as an indicator of inpatient care outcome. However, the instrument should be validated using other sets of data from various hospitals.