Описание вращений в трёхмерном пространстве с помощью методов геометрической алгебры с реализацией на языке Python

This paper provides a brief overview of the basic theoretical information from geometric algebra and modules for Python, in particular the clifford module. During the presentation of the theoretical material, much attention was paid to the mathematical apparatus of geometric algebra. Classical methods of rotations on the plane and in space were studied: complex numbers, matrices and quaternions. Geometric algebra is based on the concept of a multivector and a geometric product. With the help of a special kind of multivector, rotations in spaces of any dimension are described in a uniform way. The mathematical apparatus of geometric algebra is relatively simple to master and therefore has gained great popularity in various applied fields. One of these areas is computer graphics. The fact is that with the help of a special kind of multivector, it becomes possible to uniformly describe rotations and reflections in spaces of any dimension. Potentially, this method of describing rotations can displace the method based on quaternions and biquaternions, since it is algorithmically not more complicated, but allows for a much clearer geometric interpretation. The paper provides an overview of a number of Python programming language libraries: libraries implementing algebraic operations, quaternions, libraries for visualization and libraries for geometric algebra. There are also a number of examples of using multivectors to describe rotations and reflections and their implementation using the Python Clifford module. Programs were written that implement rotations on the plane in various ways, they were also visualized in 2D and in 3D.В данной работе даётся краткий обзор основных теоретических сведений из геометрической алгебры и модулей для языка Python, в частности модуля clifford. В ходе изложения теоретического материала большое внимание было уделено математическому аппарату геометрической алгебры. Были изучены классические методы поворотов на плоскости и в пространстве: комплексные числа, матрицы и кватернионы. Геометрическая алгебра основывается на понятии мультивектора и геометрического произведения. С помощью мультивектора специального вида описываются вращения в пространствах любой размерности единообразным способом. Математический аппарат геометрической алгебры сравнительно прост для освоения и поэтому обрёл большую популярность в различных прикладных областях. Одной из таких областей является компьютерная графика. Дело в том, что с помощью мультивектора специального вида становится возможным единообразно описать вращения и отражения в пространствах любой размерности. Потенциально этот способ описания вращений может вытеснить способ, основанный на кватернионах и бикватернионах, так как алгоритмически не сложнее, но допускает намного более ясную геометрическую интерпретацию. В работе дан обзор ряда библиотек языка программирования Python: библиотеки, реализующие алгебраические операции, кватернионы, библиотеки для визуализации и библиотеки для геометрической алгебры. Также приводится ряд примеров использования мультивекторов для описания вращений и отражений и их реализация с помощью модуля Clifford языка Python. Были написаны программы, реализующие повороты на плоскости различными способами, также они были визуализированы в 2D и в 3D

The MAOA and COMT Gene Polymorphisms in Patients with Schizophrenia Committed Homicide

Numerous studies have indicated that aggression and homicide are more frequent among people with schizophrenia than in the general population. There is considerable evidence that schizophrenia involves a dysbalance between subcortical and cortical dopaminergic systems. The major pathways for catecholamine degradation are oxidative deamination through the action of monoamine oxidase A (MAOA) and by methylation through the action of catechol-O-methyltransferase (COMT). Activity of both enzymes is encoded by the corresponding genes—MAOA and COMT. The aim of our study was to analyze the association between the COMT-Val158Met and MAOA-uVNTR polymorphisms and the risk of committing homicide by patients with schizophrenia. Methods: The study included 50 Caucasian male patients with paranoid schizophrenia (PS). All patients were divided into two groups: Group 1 consisted of 26 PS patients who have committed homicide; Group 2 consisted of 24 PS patients who did not have a history of socially violent behavior. The control group comprised 23 apparently healthy Caucasian men of the same age. All patients underwent clinical-psychopathological and clinical-anamnestic examinations. Molecular genetic studies were performed in the Shared Research Facility Center "High Technologies" at SFedU. Results: Our study revealed no direct correlation between the COMT-Val158Met and MAOA-uVNTR polymorphisms and risk of committing homicide by patients with schizophrenia. At the same time, we detected an association between high-activity gene variants, viz., the MAOA-4R allele and the COMT-158Met/158Met genotype, and the schizoid and unstable premorbid accentuation in patients who had committed murder, whereas the schizoid and unstable accentuation correlated with homicide behavior in patients with schizophrenia. Conclusion: The obtained findings suggest that genetic variation affects the homicidal behavior indirectly, through the various types of premorbid accentuation and confirm the validity of the well-known concept of "syndrome-person-situation," traced back to the mid-20th century, which explains the commission of serious offenses by patients with schizophrenia