Mathematical machine usage in medical information systems

Biosystem of the human body is viewed as a whole. First of all adequate mathematical machine selection and class of biosystems needs to be assigned for creation of mathematical model of biological system. Biosystem has two types of appoach. One of them is supposed to be a simple approach, the other is likely to be very complex – indexed approach. Different biosystems with determination properties are usually described by differential and integral equations, linear and nonlinear algebra. In some cases, algebraic polynoms with timed argument are used for presenting determined biosystem dynamics. Adequate mathematical modeling machine, probability theory, Markov and random processes theory and the laws are applied for the description of likely characterized biosystems. Key words: biosystem, biocybernetic issues, differential and integral equations, mathematical model, Markov chains, Bayes method, artifical neural networks

Nonlinear Algebra and Applications

<p style='text-indent:20px;'>We showcase applications of nonlinear algebra in the sciences and engineering. Our review is organized into eight themes: polynomial optimization, partial differential equations, algebraic statistics, integrable systems, configuration spaces of frameworks, biochemical reaction networks, algebraic vision, and tensor decompositions. Conversely, developments on these topics inspire new questions and algorithms for algebraic geometry.</p>

Cooperativity, absolute interaction, and algebraic optimization

We consider a measure of cooperativity based on the minimal interaction required to generate an observed titration behavior. We describe the corresponding algebraic optimization problem and show how it can be solved using the nonlinear algebra tool . Moreover, we compute the minimal interactions and minimal molecules for several binding polynomials that describe the oxygen binding of various hemoglobins under different conditions. We compare their minimal interaction with the maximal slope of the Hill plot, and discuss similarities and discrepancies with a view towards the shapes of the binding curves.

EXTENDED CONFORMAL GROUP AND DSR VELOCITIES ON THE PHYSICAL SURFACE

The relation between conformal generators and Magueijo–Smolin Doubly Special Relativity term, is achieved. Through a dimensional reduction procedure, it is demonstrated that a massless relativistic particle living in a d-dimensional space, is isomorphic to the one living in a d+2 space with pure Lorentz invariance and to a particle living in a AdS d+1 space. To accomplish these identifications, the conformal group is extended and a nonlinear algebra is obtained. Finally, because the relation between momenta and velocities is known through the dimensional reduction procedure, the problem of position space dynamics is solved.

Two-Dimensional Extended Poincaré Gravity with Nontrivial Potential

We consider two-dimensional gravity models invariant under the local action of the extended Poincaré group, whose Lagrangian contains a nontrivial potential. After eliminating some degrees of freedom, one can write down an effective theory whose symmetries are described in general by a nonlinear algebra.