540 research outputs found
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, . 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
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
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