Machine Learning Clifford Invariants of ADE Coxeter Elements

There has been recent interest in novel Clifford geometric invariants of linear transformations. This motivates the investigation of such invariants for a certain type of geometric transformation of interest in the context of root systems, reflection groups, Lie groups and Lie algebras: the Coxeter transformations. We perform exhaustive calculations of all Coxeter transformations for A8, D8 and E8 for a choice of basis of simple roots and compute their invariants, using high-performance computing. This computational algebra paradigm generates a dataset that can then be mined using techniques from data science such as supervised and unsupervised machine learning. In this paper we focus on neural network classification and principal component analysis. Since the output—the invariants—is fully determined by the choice of simple roots and the permutation order of the corresponding reflections in the Coxeter element, we expect huge degeneracy in the mapping. This provides the perfect setup for machine learning, and indeed we see that the datasets can be machine learned to very high accuracy. This paper is a pump-priming study in experimental mathematics using Clifford algebras, showing that such Clifford algebraic datasets are amenable to machine learning, and shedding light on relationships between these novel and other well-known geometric invariants and also giving rise to analytic results

Somatometric Method to Assess the Level of High Schoolers' Physical Development

Раціональна організація фізичного виховання учнівської молоді неможлива без об’єктивного оцінювання її фізичного розвитку. Своєчасно проведене відповідне тестування – запорука запобіганню фізичних перенапружень, порушенням стану здоров’я. Метою дослідження була розробка таблиць для оцінювання рівня фізичного розвитку учнів на основі взаємодії тотальних розмірів тіла. Матеріалом дослідження були показники довжини тіла, маси тіла та обхвату грудної клітки хлопців (n=1111 осіб) і дівчат (n=1133 особи) 7-17 років загальноосвітніх шкіл. Для обчислення взаємодії показників тотальних розмірів тіла вперше застосовувалася множинна кореляція, а для розробки статево-вікових стандартів фізичного розвитку учнів – множинна регресія.Aim: To develop tables to assess the physical development of high schoolers based on the interaction of total physical dimensions. Materials and Methods: To achieve this goal, we studied the indicators of body length, body weight and chest circumference of 7-17 years old boys (n=1 111) and girls (n=l 133) of secondary schools in Kyiv (Ukraine). Multiple correlation was used to calculate the interaction of indicators of total physical dimensions, and multiple regression was used to develop gender and age standards of physical development of high schoolers. Results: The tables to assess physical development of high schoolers ofa certain gender and age have been developed. The tables contain body length in vertical direction and body weight or chest circumference in horizontal direction, depending on what is needed for determination: the proper values of CC or body weight. The guantitative characteristics of high schoolers with good, excessive, below average and low levels of physical development are presented. Conclusions: Rational organization of physical training of high schoolers is impossible without objective testing ofthe level of their physical development. Timely corresponding testing is a guarantee in preventing physical strains and health problems

Prostate cancer evolution from multilineage primary to single lineage metastases with implications for liquid biopsy

From Springer Nature via Jisc Publications RouterHistory: received 2020-01-21, accepted 2020-09-01, registration 2020-09-18, online 2020-10-08, pub-electronic 2020-10-08, collection 2020-12Publication status: PublishedAbstract: The evolutionary progression from primary to metastatic prostate cancer is largely uncharted, and the implications for liquid biopsy are unexplored. We infer detailed reconstructions of tumor phylogenies in ten prostate cancer patients with fatal disease, and investigate them in conjunction with histopathology and tumor DNA extracted from blood and cerebrospinal fluid. Substantial evolution occurs within the prostate, resulting in branching into multiple spatially intermixed lineages. One dominant lineage emerges that initiates and drives systemic metastasis, where polyclonal seeding between sites is common. Routes to metastasis differ between patients, and likely genetic drivers of metastasis distinguish the metastatic lineage from the lineage that remains confined to the prostate within each patient. Body fluids capture features of the dominant lineage, and subclonal expansions that occur in the metastatic phase are non-uniformly represented. Cerebrospinal fluid analysis reveals lineages not detected in blood-borne DNA, suggesting possible clinical utility

The architecture of clonal expansions in morphologically normal tissue from cancerous and non-cancerous prostates

Availability of data and materials: The datasets generated during the current study are available in the European Genome-Phenome Archive repository, https://ega-archive.org/datasets/EGAD00001000689 and https://ega-archive.org/datasets/EGAD00001004125. The variant calls generated are available from the corresponding author on reasonable request.Supplementary information is available online at https://molecular-cancer.biomedcentral.com/articles/10.1186/s12943-022-01644-3#Sec18 .Copyright © The Author(s) 2022. Background Up to 80% of cases of prostate cancer present with multifocal independent tumour lesions leading to the concept of a field effect present in the normal prostate predisposing to cancer development. In the present study we applied Whole Genome DNA Sequencing (WGS) to a group of morphologically normal tissue (n = 51), including benign prostatic hyperplasia (BPH) and non-BPH samples, from men with and men without prostate cancer. We assess whether the observed genetic changes in morphologically normal tissue are linked to the development of cancer in the prostate. Results Single nucleotide variants (P = 7.0 × 10–03, Wilcoxon rank sum test) and small insertions and deletions (indels, P = 8.7 × 10–06) were significantly higher in morphologically normal samples, including BPH, from men with prostate cancer compared to those without. The presence of subclonal expansions under selective pressure, supported by a high level of mutations, were significantly associated with samples from men with prostate cancer (P = 0.035, Fisher exact test). The clonal cell fraction of normal clones was always higher than the proportion of the prostate estimated as epithelial (P = 5.94 × 10–05, paired Wilcoxon signed rank test) which, along with analysis of primary fibroblasts prepared from BPH specimens, suggests a stromal origin. Constructed phylogenies revealed lineages associated with benign tissue that were completely distinct from adjacent tumour clones, but a common lineage between BPH and non-BPH morphologically normal tissues was often observed. Compared to tumours, normal samples have significantly less single nucleotide variants (P = 3.72 × 10–09, paired Wilcoxon signed rank test), have very few rearrangements and a complete lack of copy number alterations. Conclusions Cells within regions of morphologically normal tissue (both BPH and non-BPH) can expand under selective pressure by mechanisms that are distinct from those occurring in adjacent cancer, but that are allied to the presence of cancer. Expansions, which are probably stromal in origin, are characterised by lack of recurrent driver mutations, by almost complete absence of structural variants/copy number alterations, and mutational processes similar to malignant tissue. Our findings have implications for treatment (focal therapy) and early detection approaches.This project was funded by Cancer Research UK (C5047/A29626/A22530/A17528), the Dallaglio Foundation, and a Prostate Cancer UK Movember Training, Leadership & Development Award (TLD-S15-003). The funders played no role in the design of the study, collection, analysis, or interpretation of data

Національна доповідь про стан і перспективи розвитку освіти в Україні: монографія (До 30-річчя незалежності України)

The publication provides a comprehensive analysis of the state and development of national education over the 30 years of Ukraine’s independence, identifies current problems in education, ascertains the causes of their emergence, offers scientifically reasoned ways to modernise domestic education in the context of globalisation, European integration, innovative development, and national self-identification. Designed for legislators, state officials, education institutions leaders, teaching and academic staff, the general public, all those who seek to increase the competitiveness of Ukrainian education in the context of civilisation changes.У виданні здійснено всебічний аналіз стану і розвитку національної освіти за 30-річний період незалежності України, визначено актуальні проблеми освітньої сфери, виявлено причини їх виникнення, запропоновано науково обґрунтовані шляхи модернізації вітчизняної освіти в умовах глобалізації, європейської інтеграції, інноваційного розвитку та національної самоідентифікації. Розраховано на законодавців, державних управлінців, керівників закладів освіти, педагогічних і науково-педагогічних працівників, широку громадськість, усіх, хто прагне підвищення конкурентоспроможності української освіти в контексті цивілізаційних змін

Machine Learning Clifford invariants of ADE Coxeter elements

There has been recent interest in novel Clifford geometric invariants of linear transformations. This motivates the investigation of such invariants for a certain type of geometric transformation of interest in the context of root systems, reflection groups, Lie groups and Lie algebras: the Coxeter transformations. We perform exhaustive calculations of all Coxeter transformations for A8, D8 and E8 for a choice of basis of simple roots and compute their invariants, using high-performance computing. This computational algebra paradigm generates a dataset that can then be mined using techniques from data science such as supervised and unsupervised machine learning. In this paper we focus on neural network classification and principal component analysis. Since the output – the invariants – is fully determined by the choice of simple roots and the permutation order of the corresponding reflections in the Coxeter element, we expect huge degeneracy in the mapping. This provides the perfect setup for machine learning, and indeed we see that the datasets can be machine learned to very high accuracy. This paper is a pump-priming study in experimental mathematics using Clifford algebras, showing that such Clifford algebraic datasets are amenable to machine learning, and shedding light on relationships between these novel and other well-known geometric invariants and also giving rise to analytic results

Prostate cancer evolution from multilineage primary to single lineage metastases with implications for liquid biopsy

The evolutionary progression from primary to metastatic prostate cancer is largely uncharted, and the implications for liquid biopsy are unexplored. We infer detailed reconstructions of tumor phylogenies in ten prostate cancer patients with fatal disease, and investigate them in conjunction with histopathology and tumor DNA extracted from blood and cerebrospinal fluid. Substantial evolution occurs within the prostate, resulting in branching into multiple spatially intermixed lineages. One dominant lineage emerges that initiates and drives systemic metastasis, where polyclonal seeding between sites is common. Routes to metastasis differ between patients, and likely genetic drivers of metastasis distinguish the metastatic lineage from the lineage that remains confined to the prostate within each patient. Body fluids capture features of the dominant lineage, and subclonal expansions that occur in the metastatic phase are non-uniformly represented. Cerebrospinal fluid analysis reveals lineages not detected in blood-borne DNA, suggesting possible clinical utility. The evolutionary progression from primary to metastatic prostate cancer is largely uncharted, and the implications for liquid biopsy are unexplored. Here, the authors use deep genomic sequencing and histopathological information to trace tumor evolution both within the prostate and during metastasis in ten men.Peer reviewe

Appropriate levels of physical capacities development in adolescents with different state of health

Мета: обґрунтувати відповідність рівня розвитку фізичних можливостей дівчаток 12-13 років з різним рівнем фізичного здоров'я. Матеріали і методи. У дослідженні взяли участь 101 учениця старших класів 12-13 років. Вибір старшокласниць цього віку зумовлений найбільшою варіативністю їх морфофункціонального стану. Оцінку фізичного здоров’я дівчат проводили за методикою Г. Л. Апанасенко. Фізичну підготовленість оцінювали за допомогою 13 рухових тестів, які визначають різні аспекти фізичних можливостей дівчат. Результати: Визначено відповідні нормативи фізичної підготовленості дівчаток 12-13 років з різним рівнем здоров'я та раціональні параметри рухової активності. Висновки. Виявлено, що основним принципом реалізації занять розвивально-оздоровчого спрямування з фізичного виховання підлітків є диференційоване використання навантажень та оцінка їхньої фізичної підготовленості. Розраховані за допомогою коефіцієнтів кореляції та рівнянь регресії відповідні значення показників фізичного розвитку у дівчаток 12-13 років з різним рівнем фізичного здоров’я дають змогу за допомогою відповідних вправ усунути відхилення в показниках їх здоров’я.The aim: To justify the appropriate levels of physical capabilities development in 12-13-years-old girls with different levels of physical health. Materials and methods: The research involved 101 12-13-years-old female high-school students. The choice of female high-school students of this age is due to the greatest variability of their morpho-functional state. The physical health of the girls was assessed according to the method of H. L. Apanasenko. Physical fitness was assessed with the help of 13 motor tests that determine different aspects of girls’ physical capabilities. Results: Appropriate normative standards of physical fitness for 12-13-years-old girls with different levels of health and rational parameters of physical activity were determined. It was established that a rational option for planning physical training for 12-13-years-old girls is: 26 % of time should be spent on strength development; speed and strength qualities and agility - by 22 %; endurance - 18 % and speed qualities - 12 %. Conclusions: It was found that the main principle of the implementation of developmental and health-oriented training sessions for the physical education of adolescents is the differentiated use of loads and assessment of their physical fitness. Calculated with the help of correlation coefficients and regression equations, the appropriate values of physical development in 12-13-years-old girls with different levels of physical health make it possible, using appropriate exercises, to eliminate deviations in their health indicators