Topological data analysis of contagion maps for examining spreading processes on networks

Social and biological contagions are influenced by the spatial embeddedness of networks. Historically, many epidemics spread as a wave across part of the Earth's surface; however, in modern contagions long-range edges -- for example, due to airline transportation or communication media -- allow clusters of a contagion to appear in distant locations. Here we study the spread of contagions on networks through a methodology grounded in topological data analysis and nonlinear dimension reduction. We construct "contagion maps" that use multiple contagions on a network to map the nodes as a point cloud. By analyzing the topology, geometry, and dimensionality of manifold structure in such point clouds, we reveal insights to aid in the modeling, forecast, and control of spreading processes. Our approach highlights contagion maps also as a viable tool for inferring low-dimensional structure in networks.Comment: Main Text and Supplementary Informatio

Characterizing Granular Networks Using Topological Metrics

We carry out a direct comparison of experimental and numerical realizations of the exact same granular system as it undergoes shear jamming. We adjust the numerical methods used to optimally represent the experimental settings and outcomes up to microscopic contact force dynamics. Measures presented here range form microscopic, through mesoscopic to system-wide characteristics of the system. Topological properties of the mesoscopic force networks provide a key link between micro and macro scales. We report two main findings: the number of particles in the packing that have at least two contacts is a good predictor for the mechanical state of the system, regardless of strain history and packing density. All measures explored in both experiments and numerics, including stress tensor derived measures and contact numbers depend in a universal manner on the fraction of non-rattler particles, $f_{NR}$. The force network topology also tends to show this universality, yet the shape of the master curve depends much more on the details of the numerical simulations. In particular we show that adding force noise to the numerical data set can significantly alter the topological features in the data. We conclude that both $f_{NR}$ and topological metrics are useful measures to consider when quantifying the state of a granular system.Comment: 8 pages, 8 figure

Educational work as a method of implementation of plans for the development of a training group in medical universities

The article deals with the principles of educational work, with the help of which it is possible to implement the program of group development, training and formation of a qualified specialist, which is the main goal of the work of teachers of higher educational institutions. Preliminary planning and high-quality organization of educational work can help students to acquire professional knowledge and form the necessary qualities for the physician such as morality, intelligence, compassion for the neighbor, teamwork, responsibility, and others. The article emphasizes the need for cooperation in the educational work of various staff and units of the university: from the lecturer of the department, administration of the faculty and the university to public organizations and associations. The authors emphasize the continuity of educational work, the necessity of conducting it both in classrooms in classes, and in extracurricular time

Augusta Ada Byron

Augusta Ada Byron was born 10 December 1815 as the only child of the poet Lord Byron and his wife Anne Isabella Byron. Byron did not have a relationship with his daughter.Ada was often ill, beginning in early childhood. At the age of eight, she experienced headaches that obscured her vision. In June 1829, she was paralyzed after a bout of measles. She was subjected to continuous bed rest for nearly a year. By 1831, she was able to walk with crutches. Despite being ill Ada developed her mathematical and technological skills. At age 12, this future "Lady Fairy", as Charles Babbage affectionately called her, decided she wanted to fly. Ada went about the project methodically, thoughtfully, with imagination and passio

Augusta Ada Byron

Augusta Ada Byron was born 10 December 1815 as the only child of the poet Lord Byron and his wife Anne Isabella Byron. Byron did not have a relationship with his daughter.Ada was often ill, beginning in early childhood. At the age of eight, she experienced headaches that obscured her vision. In June 1829, she was paralyzed after a bout of measles. She was subjected to continuous bed rest for nearly a year. By 1831, she was able to walk with crutches. Despite being ill Ada developed her mathematical and technological skills. At age 12, this future "Lady Fairy", as Charles Babbage affectionately called her, decided she wanted to fly. Ada went about the project methodically, thoughtfully, with imagination and passio