New solutions to the complex Ginzburg-Landau equations.

The various regimes observed in the one-dimensional complex Ginzburg-Landau equation result from the interaction of a very small number of elementary patterns such as pulses, fronts, shocks, holes, and sinks. Here we provide three exact such patterns observed in numerical calculations but never found analytically. One is a quintic case localized homoclinic defect, observed by Popp et al. [S. Popp et al., Phys. Rev. Lett. 70, 3880 (1993)10.1103/PhysRevLett.70.3880], and the two others are bound states of two quintic dark solitons, observed by Afanasyev et al. [V. V. Afanasyev et al., Phys. Rev. E 57, 1088 (1998)10.1103/PhysRevE.57.1088].

A New Transmission Route for the Propagation of the SARS-CoV-2 Coronavirus.

BACKGROUND: Starting late 2019, a novel coronavirus spread from the capital of the Hubei province in China to the rest of the country, then to most of the world. To anticipate future trends in the development of the pandemic, we explore here, based on public records of infected persons, how variation in the virus tropism could end up in different patterns, warranting a specific strategy to handle the epidemic. METHODS: We use a compartmental model to describe the evolution of an individual through several possible states: susceptible, infected, alternative infection, detected, and removed. We fit the parameters of the model to the existing data, taking into account significant quarantine changes where necessary. RESULTS: The model indicates that Wuhan quarantine measures were effective, but that alternative virus forms and a second propagation route are compatible with available data. For the Hong Kong, Singapore, and Shenzhen regions, the secondary route does not seem to be active. CONCLUSIONS: Hypotheses of an alternative infection tropism (the gut tropism) and a secondary propagation route are discussed using a model fitted by the available data. Corresponding prevention measures that take into account both routes should be implemented to the benefit of epidemic control.

CpG/CpNpG motifs in the coding region are preferred sites for mutagenesis in the breast cancer susceptibility genes.

The range of BRCA1/BRCA2 gene mutations is diverse and the mechanism accounting for this heterogeneity is obscure. To gain insight into the endogenous mutational mechanisms involved, we evaluated the association of specific sequences (i.e. CpG/CpNpG motifs, homonucleotides, short repeats) and mutations within the genes. We classified 1337 published mutations in BRCA1 (1765 BRCA2 mutations) for each specific sequence, and employed computer simulation combined with mathematical calculations to estimate the true underlying tendency of mutation occurrence. Interestingly, we found no mutational bias to homonucleotides and repeats in deletions/insertions and substitutions but striking bias to CpG/CpNpG in substitutions in both genes. This suggests that methylation-dependent DNA alterations would be a major mechanism for mutagenesis.

A double epidemic model for the SARS propagation.

BACKGROUND: An epidemic of a Severe Acute Respiratory Syndrome (SARS) caused by a new coronavirus has spread from the Guangdong province to the rest of China and to the world, with a puzzling contagion behavior. It is important both for predicting the future of the present outbreak and for implementing effective prophylactic measures, to identify the causes of this behavior. RESULTS: In this report, we show first that the standard Susceptible-Infected-Removed (SIR) model cannot account for the patterns observed in various regions where the disease spread. We develop a model involving two superimposed epidemics to study the recent spread of the SARS in Hong Kong and in the region. We explore the situation where these epidemics may be caused either by a virus and one or several mutants that changed its tropism, or by two unrelated viruses. This has important consequences for the future: the innocuous epidemic might still be there and generate, from time to time, variants that would have properties similar to those of SARS. CONCLUSION: We find that, in order to reconcile the existing data and the spread of the disease, it is convenient to suggest that a first milder outbreak protected against the SARS. Regions that had not seen the first epidemic, or that were affected simultaneously with the SARS suffered much more, with a very high percentage of persons affected. We also find regions where the data appear to be inconsistent, suggesting that they are incomplete or do not reflect an appropriate identification of SARS patients. Finally, we could, within the framework of the model, fix limits to the future development of the epidemic, allowing us to identify landmarks that may be useful to set up a monitoring system to follow the evolution of the epidemic. The model also suggests that there might exist a SARS precursor in a large reservoir, prompting for implementation of precautionary measures when the weather cools down.

A weighted local least squares imputation method for missing value estimation in microarray gene expression data.

Many clustering techniques and classification methods for analysing microarray data require a complete dataset. However, very often gene expression datasets contain missing values due to various reasons. In this paper, we first propose to use vector angle as a measurement for the similarity between genes. We then propose the Weighted Local Least Square Imputation (WLLSI) method for missing values estimation. Numerical results on both synthetic data and real microarray data indicate that WLLSI method is more robust. The imputation methods are then applied to a breast cancer dataset and interesting results are obtained.

A parasite vector-host epidemic model for TSE propagation.

BACKGROUND: Transmissible spongiform encephalopathies (TSEs) are a family of diseases that infect mammals. They are explained by cross-contamination through an unknown route or from infection of food contaminated with prion proteins (PrPs), natural proteins that take an infectious form contributing to the slow destruction of the animal brain. While the extreme resistance of PrPs to denaturation and proteolysis accounts for a route from the mouth to the brain, the possible role of another route of contamination is explored here. Many diseases are spread by vectors, as seen in plague, typhus, malaria, or dengue. The situation where PrPs would be transmitted by a vector and, from the characteristics of outbreaks, proposed hypotheses about the biological nature of such vectors are explored. MATERIAL/METHODS: The nontrivial situation where contamination by the vector prevents infection by making the host immune to further vector contamination was analyzed. To investigate the nature of a possible vector, the spread of a disease in a closed population of hosts and vectors where the number of hosts is constant and the vectors multiply in the host was modeled mathematically. In this model, the disease is caused by an infective agent and is spread by a vector, while direct host-to-host spread is not permitted. RESULTS: Concrete values of the parameters of the model were computed from simulation of the BSE outbreak in the UK as a possible example of the process. CONCLUSIONS: Microbial vector-borne diseases might play an unexpected role in the spread of epidemics, warranting further exploration.