Derivation of Context-free Stochastic L-Grammar Rules for Promoter Sequence Modeling Using Support Vector Machine

Formal grammars can used for describing complex repeatable structures such as DNA sequences. In this paper, we describe the structural composition of DNA sequences using a context-free stochastic L-grammar. L-grammars are a special class of parallel grammars that can model the growth of living organisms, e.g. plant development, and model the morphology of a variety of organisms. We believe that parallel grammars also can be used for modeling genetic mechanisms and sequences such as promoters. Promoters are short regulatory DNA sequences located upstream of a gene. Detection of promoters in DNA sequences is important for successful gene prediction. Promoters can be recognized by certain patterns that are conserved within a species, but there are many exceptions which makes the promoter recognition a complex problem. We replace the problem of promoter recognition by induction of context-free stochastic L-grammar rules, which are later used for the structural analysis of promoter sequences. L-grammar rules are derived automatically from the drosophila and vertebrate promoter datasets using a genetic programming technique and their fitness is evaluated using a Support Vector Machine (SVM) classifier. The artificial promoter sequences generated using the derived L- grammar rules are analyzed and compared with natural promoter sequences.

On the Equivalence of the Riemann-Liouville and the Caputo Fractional Order Derivatives in Modeling of Linear Viscoelastic Materials

Mathematics Subject Classification: 26A33

Modeling Optical Response of Thin Films: Choice of the Refractive Index Dispersion Law

Determination of the so-called optical constants (complex refractive index N, which is usually a function of the wavelength, and physical thickness D) of thin films from experimental data is a typical inverse non-linear problem. It is still a challenge to the scientific community because of the complexity of the problem and its basic and technological significance in optics. Usually, solutions are looked for models with 3-10 parameters. Best estimates of these parameters are obtained by minimization procedures. Herein, we discuss the choice of orthogonal polynomials for the dispersion law of the thin film refractive index. We show the advantage of their use, compared to the Selmeier, Lorentz or Cauchy models.

Training a Linear Neural Network with a Stable LSP Solution for Jamming Cancellation

Two jamming cancellation algorithms are developed based on a stable solution of least squares problem (LSP) provided by regularization. They are based on filtered singular value decomposition (SVD) and modifications of the Greville formula. Both algorithms allow an efficient hardware implementation. Testing results on artificial data modeling difficult real-world situations are also provided.

Applied Aspects of Mathematical Modeling and Optimization of Dynamics of Charged Beams

The complex of questions connected with the analysis, estimation and structural-parametrical optimization of dynamic system is considered in this article. Connection of such problems with tasks of control by beams of trajectories is emphasized. The special attention is concentrated on the review and analysis of spent scientific researches, the attention is stressed to their constructability and applied directedness. Efficiency of the developed algorithmic and software is demonstrated on the tasks of modeling and optimization of output beam characteristics in linear resonance accelerators.

Method of Linear Programming as an Idea for High School Curriculum

2010 Mathematics Subject Classification: 97D40, 97M10, 97M40, 97N60, 97N80, 97R80

Parameterized Link Functions in Generalized Linear Random Effect Models: a Case Study on Breast Cancer Treatment

In non-linear random effects some attention has been very recently devoted to the analysis ofsuitable transformation of the response variables separately (Taylor 1996) or not (Oberg and Davidian 2000) from the transformations of the covariates and, as far as we know, no investigation has been carried out on the choice of link function in such models. In our study we consider the use of a random effect model when a parameterized family of links (Aranda-Ordaz 1981, Prentice 1996, Pregibon 1980, Stukel 1988 and Czado 1997) is introduced. We point out the advantages and the drawbacks associated with the choice of this data-driven kind of modeling. Difficulties in the interpretation of regression parameters, and therefore in understanding the influence of covariates, as well as problems related to loss of efficiency of estimates and overfitting, are discussed. A case study on radiotherapy usage in breast cancer treatment is discussed.

Mathematical Modeling, Music Literacy and Their Transmission in Fine Arts Education

Report published in the Proceedings of the National Conference on "Education and Research in the Information Society", Plovdiv, May, 2014