Solving the Levins' paradox in the logistic model to the population growth

We introduce a new method to improve Markov maps by means of a Bayesian approach. The method starts from an initial map model, wherefrom a likelihood function is defined which is regulated by a temperature-like parameter. Then, the new constraints are added by the use of Bayes rule in the prior distribution. We applied the method to the logistic map of population growth of a single species. We show that the population size is limited for all ranges of parameters, allowing thus to overcome difficulties in interpretation of the concept of carrying capacity known as the Levins paradox. © Published under licence by IOP Publishing Ltd.

Relaxation to Fixed Points in the Logistic and Cubic Maps: Analytical and Numerical Investigation

Convergence to a period one fixed point is investigated for both logistic and cubic maps. For the logistic map the relaxation to the fixed point is considered near a transcritical bifurcation while for the cubic map it is near a pitchfork bifurcation. We confirmed that the convergence to the fixed point in both logistic and cubic maps for a region close to the fixed point goes exponentially fast to the fixed point and with a relaxation time described by a power law of exponent -1. At the bifurcation point, the exponent is not universal and depends on the type of the bifurcation as well as on the nonlinearity of the map.

Dimensões fractais para certos sistemas dinâmicos discretos

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Relaxação e decaimento para pontos de equilíbrio em mapeamentos não lineares unidimensionais

We investigate in this work the behaviour of the decay to the fixed points, in particular along the bifurcations, for a family of one-dimensional logistic-like discrete mappings. We start with the logistic map focusing in the transcritical bifurcation. Next we investigate the convergence to the stationary state at the cubic map. At the end we generalise the procedure for a mapping of the logistic-like type. Near the fixed point, the dynamical variable varies slowly. This property allows us to approximate/rewrite the equation of differences, hence natural from discrete mappings, into an ordinary differential equation. We then solve such equation which furnishes the evolution towards the stationary state. Our numerical simulations confirm the theoretical results validating the above mentioned approximation

Comparison of logistic and neural network models to fit to the egg production curve of White Leghorn hens

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

MAP Kinase Phosphatase-1 Protects against Inflammatory Bone Loss

The mitogen-activated protein (MAP) kinase phosphatase (MKP) family plays an important function in regulating the pro-inflammatory cytokines by deactivating MAP kinases. MKP-1 is essential for the dephosphorylation of p38 MAP kinase that regulates expression of IL-6, TNF-alpha, and IL-1 beta. We hypothesized that MKP-1 regulates inflammatory bone loss in experimental periodontitis. Wild-type and Mkp-1(-/-) mice received A. actinomycetemcomitans LPS injection in the palatal region or PBS control 3 times/wk for 30 days. Mice were killed, and maxillae were assessed by microcomputed tomography, histological analysis, and TRAP staining for measurement of bone loss, extent of inflammation, and degree of osteoclastogenesis. Results indicated that, in LPS-injected Mkp-1(-/-) mice, significantly greater bone loss occurred with more inflammatory infiltrate and a significant increase in osteoclastogenesis compared with Mkp-1(-/-) control sites or either wild-type group. Analysis of these data indicates that MKP-1 plays a key role in the regulation of inflammatory bone loss.

Logistic regression analysis of potential prognostic factors for pulmonary thromboembolism

Objective: To identify potential prognostic factors for pulmonary thromboembolism (PTE), establishing a mathematical model to predict the risk for fatal PTE and nonfatal PTE.Method: the reports on 4,813 consecutive autopsies performed from 1979 to 1998 in a Brazilian tertiary referral medical school were reviewed for a retrospective study. From the medical records and autopsy reports of the 512 patients found with macroscopically and/or microscopically,documented PTE, data on demographics, underlying diseases, and probable PTE site of origin were gathered and studied by multiple logistic regression. Thereafter, the jackknife method, a statistical cross-validation technique that uses the original study patients to validate a clinical prediction rule, was performed.Results: the autopsy rate was 50.2%, and PTE prevalence was 10.6%. In 212 cases, PTE was the main cause of death (fatal PTE). The independent variables selected by the regression significance criteria that were more likely to be associated with fatal PTE were age (odds ratio [OR], 1.02; 95% confidence interval [CI], 1.00 to 1.03), trauma (OR, 8.5; 95% CI, 2.20 to 32.81), right-sided cardiac thrombi (OR, 1.96; 95% CI, 1.02 to 3.77), pelvic vein thrombi (OR, 3.46; 95% CI, 1.19 to 10.05); those most likely to be associated with nonfatal PTE were systemic arterial hypertension (OR, 0.51; 95% CI, 0.33 to 0.80), pneumonia (OR, 0.46; 95% CI, 0.30 to 0.71), and sepsis (OR, 0.16; 95% CI, 0.06 to 0.40). The results obtained from the application of the equation in the 512 cases studied using logistic regression analysis suggest the range in which logit p > 0.336 favors the occurrence of fatal PTE, logit p < - 1.142 favors nonfatal PTE, and logit P with intermediate values is not conclusive. The cross-validation prediction misclassification rate was 25.6%, meaning that the prediction equation correctly classified the majority of the cases (74.4%).Conclusions: Although the usefulness of this method in everyday medical practice needs to be confirmed by a prospective study, for the time being our results suggest that concerning prevention, diagnosis, and treatment of PTE, strict attention should be given to those patients presenting the variables that are significant in the logistic regression model.

Choosing between Cox proportional hazards and logistic models for interval-censored data via bootstrap

This work develops a new methodology in order to discriminate models for interval-censored data based on bootstrap residual simulation by observing the deviance difference from one model in relation to another, according to Hinde (1992). Generally, this sort of data can generate a large number of tied observations and, in this case, survival time can be regarded as discrete. Therefore, the Cox proportional hazards model for grouped data (Prentice & Gloeckler, 1978) and the logistic model (Lawless, 1982) can befitted by means of generalized linear models. Whitehead (1989) considered censoring to be an indicative variable with a binomial distribution and fitted the Cox proportional hazards model using complementary log-log as a link function. In addition, a logistic model can be fitted using logit as a link function. The proposed methodology arises as an alternative to the score tests developed by Colosimo et al. (2000), where such models can be obtained for discrete binary data as particular cases from the Aranda-Ordaz distribution asymmetric family. These tests are thus developed with a basis on link functions to generate such a fit. The example that motivates this study was the dataset from an experiment carried out on a flax cultivar planted on four substrata susceptible to the pathogen Fusarium oxysoprum. The response variable, which is the time until blighting, was observed in intervals during 52 days. The results were compared with the model fit and the AIC values.

Critical points in logistic growth curves and treatment comparisons

Several biological phenomena have a behavior over time mathematically characterized by a strong increasing function in the early stages of development, then by a less pronounced growth, sometimes showing stability. The separation between these phases is very important to the researcher, since the maintenance of a less productive phase results in uneconomical activity. In this report we present methods of determining critical points in logistic functions that separate the early stages of growth from the asymptotic phase, with the aim of establishing a stopping critical point in the growth and on this basis determine differences in treatments. The logistic growth model is fitted to experimental data of imbibition of arariba seeds (Centrolobium tomentosum). To determine stopping critical points the following methods were used: i) accelerating growth function, ii) tangent at the inflection point, iii) segmented regression; iv) modified segmented regression; v) non-significant difference; and vi) non-significant difference by simulation. The analysis of variance of the abscissas and ordinates of the breakpoints was performed with the objective of comparing treatments and methods used to determine the critical points. The methods of segmented regression and of the tangent at the inflection point lead to early stopping points, in comparison with other methods, with proportions ordinate/asymptote lower than 0.90. The non-significant difference method by simulation had higher values of abscissas for stopping point, with an average proportion ordinate/asymptote equal to 0.986. An intermediate proportion of 0.908 was observed for the acceleration function method.

A microsatellite-based, gene-rich linkage map for the AA genome of Arachis (Fabaceae)

Cultivated peanut (Arachis hypogaea) is an important crop, widely grown in tropical and subtropical regions of the world. It is highly susceptible to several biotic and abiotic stresses to which wild species are resistant. As a first step towards the introgression of these resistance genes into cultivated peanut, a linkage map based on microsatellite markers was constructed, using an F-2 population obtained from a cross between two diploid wild species with AA genome (A. duranensis and A. stenosperma). A total of 271 new microsatellite markers were developed in the present study from SSR-enriched genomic libraries, expressed sequence tags (ESTs), and by data-mining sequences available in GenBank. of these, 66 were polymorphic for cultivated peanut. The 271 new markers plus another 162 published for peanut were screened against both progenitors and 204 of these (47.1%) were polymorphic, with 170 codominant and 34 dominant markers. The 80 codominant markers segregating 1:2:1 (P < 0.05) were initially used to establish the linkage groups. Distorted and dominant markers were subsequently included in the map. The resulting linkage map consists of 11 linkage groups covering 1,230.89 cM of total map distance, with an average distance of 7.24 cM between markers. This is the first microsatellite-based map published for Arachis, and the first map based on sequences that are all currently publicly available. Because most markers used were derived from ESTs and genomic libraries made using methylation-sensitive restriction enzymes, about one-third of the mapped markers are genic. Linkage group ordering is being validated in other mapping populations, with the aim of constructing a transferable reference map for Arachis.

A linkage map for the B-genome of Arachis (Fabaceae) and its synteny to the A-genome

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Squamata, Elapidae, Micrurus surinamensis (Cuvier, 1817): new records and distribution map in the state of Mato Grosso, Brazil, with notes on diet and activity period.

We report six new records of M. surinamensis and present the map of distribution with known records for this species of semiaquatic coral snake in the state of Mato Grosso, Brazil.

A radiation hybrid map of river buffalo (Bubalus bubalis) chromosome 7 and comparative mapping to the cattle and human genomes

A preliminary radiation hybrid (RH) map containing 50 loci on chromosome 7 of the domestic river buffalo Bubalus bubalis (BBU; 2n = 50) was constructed based on a comparative mapping approach. The RH map of BBU7 includes thirty-seven gene markers and thirteen microsatellites. All loci have been previously assigned to Bos taurus (BTA) chromosome BTA6, which is known for its association with several economically important milk production traits in cattle. The map consists of two linkage groups spanning a total length of 627.9 cR(5,000). Comparative analysis of the BBU7 RH 5,000 map with BTA6 in cattle gave new evidence for strong similarity between the two chromosomes over their entire length and exposed minor differences in locus order. Comparison of the BBU7 RH 5,000 map with the Homo sapiens (HSA) genome revealed similarity with a large chromosome segment of HSA4. Comparative analysis of loci in both species revealed more variability than previously known in gene order and several chromosome rearrangements including centromere relocation. The data obtained in our study define the evolutionarily conserved segment on BBU7 and HSA4 to be between 3.5 megabases (Mb) and 115.8 Mb in the HSA4 (genome build 36) DNA sequence. Copyright (c) 2008 S. Karger AG, Basel.

A radiation hybrid map of river buffalo (Bubalus bubalis) chromosome 1 (BBU1)

The largest chromosome in the river buffalo karyotype, BBU1, is a submetacentric chromosome with reported homology between BBU1q and bovine chromosome 1 and between BBU1p and BTA27. We present the first radiation hybrid map of this chromosome containing 69 cattle derived markers including 48 coding genes, 17 microsatellites and four ESTs distributed in two linkage groups spanning a total length of 1330.1 cR(5000). The RH map was constructed based on analysis of a recently developed river buffalo-hamster whole genome radiation hybrid (BBURH5000) panel. The retention frequency of individual markers across the panel ranged from 17.8 to 52.2%. With few exceptions, the order of markers within linkage groups is identical to the order established for corresponding cattle RH maps. The BBU1 map provides a starting point for comparison of gene order rearrangements between river buffalo chromosome 1 and its bovine homologs. Copyright (C) 2007 S. Karger AG, Basel.