Diminishing Return for Increased Mappability with Longer Sequencing Reads: Implications of the k-mer Distributions in the Human Genome

The amount of non-unique sequence (non-singletons) in a genome directly affects the difficulty of read alignment to a reference assembly for high throughput-sequencing data. Although a greater length increases the chance for reads being uniquely mapped to the reference genome, a quantitative analysis of the influence of read lengths on mappability has been lacking. To address this question, we evaluate the k-mer distribution of the human reference genome. The k-mer frequency is determined for k ranging from 20 to 1000 basepairs. We use the proportion of non-singleton k-mers to evaluate the mappability of reads for a corresponding read length. We observe that the proportion of non-singletons decreases slowly with increasing k, and can be fitted by piecewise power-law functions with different exponents at different k ranges. A faster decay at smaller values for k indicates more limited gains for read lengths > 200 basepairs. The frequency distributions of k-mers exhibit long tails in a power-law-like trend, and rank frequency plots exhibit a concave Zipf's curve. The location of the most frequent 1000-mers comprises 172 kilobase-ranged regions, including four large stretches on chromosomes 1 and X, containing genes with biomedical implications. Even the read length 1000 would be insufficient to reliably sequence these specific regions.Comment: 5 figure

The activation frequency self-organizing map

In the self-organizing map (SOM), the best matching units (BMUs) affect neurons as a function of distance and the learning parameter. Here we study the effects in SOM when a new parameter in the learning rule, the activation frequency, is included. This parameter is based on the relative frequency by which each neuron is included in each BMU's neighborhood, so there is an individual memory (synapse strength) of the activation received from each neuron. The parameter leads to non-radial influence areas for BMUs, what is a more realistic feature observed in the brain cortex which modifies the map formation dynamics, including the fact that the weight vector for BMU may not be the closest one to the input stimulus after weight adaptation. Also, two error measures are lower for the maps trained with this model than those obtained with SOM, as shown in several experiments with six data sets

Beyond Zipf's Law: The Lavalette Rank Function and its Properties

Although Zipf's law is widespread in natural and social data, one often encounters situations where one or both ends of the ranked data deviate from the power-law function. Previously we proposed the Beta rank function to improve the fitting of data which does not follow a perfect Zipf's law. Here we show that when the two parameters in the Beta rank function have the same value, the Lavalette rank function, the probability density function can be derived analytically. We also show both computationally and analytically that Lavalette distribution is approximately equal, though not identical, to the lognormal distribution. We illustrate the utility of Lavalette rank function in several datasets. We also address three analysis issues on the statistical testing of Lavalette fitting function, comparison between Zipf's law and lognormal distribution through Lavalette function, and comparison between lognormal distribution and Lavalette distribution.Comment: 15 pages, 4 figure

Global Stability Results in a SVIR Epidemic Model with Immunity Loss Rate Depending on the Vaccine-Age

We formulate a susceptible-vaccinated-infected-recovered (SVIR) model by incorporating the vaccination of newborns, vaccine-age, and mortality induced by the disease into the SIR epidemic model. It is assumed that the period of immunity induced by vaccines varies depending on the vaccine-age. Using the direct Lyapunov method with Volterra-type Lyapunov function, we show the global asymptotic stability of the infection-free and endemic steady states

The activation frequency self-organizing map

In the self-organizing map (SOM), the best matching units (BMUs) affect neurons as a function of distance and the learning parameter. Here we study the effects in SOM when a new parameter in the learning rule, the activation frequency, is included. This parameter is based on the relative frequency by which each neuron is included in each BMU's neighborhood, so there is an individual memory (synapse strength) of the activation received from each neuron. The parameter leads to non-radial influence areas for BMUs, what is a more realistic feature observed in the brain cortex which modifies the map formation dynamics, including the fact that the weight vector for BMU may not be the closest one to the input stimulus after weight adaptation. Also, two error measures are lower for the maps trained with this model than those obtained with SOM, as shown in several experiments with six data sets

Kuhn’s philosophical revolution

En este artículo postulamos que el trabajo de Kuhn es una revolución filosófica para la filosofía de la ciencia. La búsqueda de revoluciones filosóficas es una extensión de las ideas de Kuhn acerca de las revoluciones científicas. Las revoluciones filosóficas se distinguen de las revoluciones científicas en algunos aspectos que discutimos en este trabajo. Defendemos que la revolución kuhniana consiste en la naturalización de la filosofía de la ciencia que se desprende de sus trabajos y discutimos la analogía biológica que Kuhn empleó como un ejemplo ilustrativo.In this paper we propose that Kuhn's work constitutes a philosophical revolution in the Philosophy of Science. The search for philosophical revolutions is an extension of Kuhn's ideas about scientific revolutions severed from the scientific field. Revolutions in Philosophy are different from those in Science due to some relevant aspects which we briefly discuss in this work. We argue that the Kuhnian philosophical revolution consists in the naturalization of the Philosophy of Science which we find in his writings, finally we discuss Kuhn's biological analogy as an illustrative instance

Dynamics of High-Risk Nonvaccine Human Papillomavirus Types after Actual Vaccination Scheme

Human papillomavirus (HPV) has been identified as the main etiological factor in the developing of cervical cancer (CC). This finding has propitiated the development of vaccines that help to prevent the HPVs 16 and 18 infection. Both genotypes are associated with 70% of CC worldwide. In the present study, we aimed to determine the emergence of high-risk nonvaccine HPV after actual vaccination scheme to estimate the impact of the current HPV vaccines. A SIR-type model was used to study the HPV dynamics after vaccination. According to the results, our model indicates that the application of the vaccine reduces infection by target or vaccine genotypes as expected. However, numerical simulations of the model suggest the presence of the phenomenon called vaccine—induced pathogen strain replacement. Here, we report the following replacement mechanism: if the effectiveness of cross-protective immunity is not larger than the effectiveness of the vaccine, then the high-risk nonvaccine genotypes emerge. In this scenario, further studies of infection dispersion by HPV are necessary to ascertain the real impact of the current vaccines, primarily because of the different high-risk HPV types that are found in CC