271 research outputs found
Steven Strogatz Wired 2012
No full textThe Beauty and Delight of Mathematics: Q&A with Steven Strogatz -- Steven Strogatz story.pdfThe work(s) contained within this record have been analyzed and cataloged by members of the University Libraries' Resource Management Division.Alan Alda Center for Communicating Scienc
Nonlinear dynamics and chaos: Lab demonstrations
No full textThis video shows six laboratory demonstrations of chaos and
nonlinear phenomena, intended for use in a first course on nonlinear
dynamics. Steven Strogatz explains the principles being illustrated and
why they are important. The demonstrations are: (1) A tabletop
waterwheel that is an exact mechanical analog of the Lorenz equations, one
of the most famous chaotic systems; (2) A double pendulum, a paradigm of
chaos in conservative systems; (3) Airplane wing vibrations and
aeroelastic instabilities, as exemplars of Hopf bifurcations; (4)
Self-sustained oscillations in a chemical reaction; (5) Using synchronized
chaos to send secret messages; and (6) Composing musical variations with a
chaotic mapping. Strogatz is joined by his colleagues Howard Stone, John
Dugundji, Irving Epstein, Kevin Cuomo, and Diana Dabby.1_i3adhmw
Sync the emerging science of spontaneous order
No full text"At once elegant and riveting, SYNC tells the story of the dawn of a new science. As one of its pioneers, Steven Strogatz, a leading mathematician in the fields of chaos and complexity theory, it explains how enormous systems can synchronize themselves, from the electrons in a superconductor to the pacemaker cells in our hearts. He shows that although these phenomena might seem unrelated on the surface, at a deeper level there is a connection, forged by the unifying power of mathematics." "Along with vivid explanations of cutting-edge theory, Strogatz provides an intimate and highly personal narrative filled with often humerous anecdotes about some of the visionary thinkers of our time. He also describes the startling applications of this new knowledge, such as the harnessing of synchronized electrons to create the world's most sensitive detectors, able to locate oil buried deep underground and to pinpoint diseased tissues associated with epilepsy and heart arrhythmias."--BOOK JACKET
Introducing Steven Strogatz
No full textHe is the author of several best-selling books like The Joy of X: A Guided Tour of Math, From One to Infinity. He writes frequently for the New York Times, and appears regularly on National Public Radio in the US.
The purpose of this short review is to alert readers to Steven Strogatz’s work (http://www.stevenstrogatz.com) in general, and to draw special attention to 15 pieces, under the broad heading of ‘Elements of Maths,' that he wrote for the New York Times from January 2010 to May 2010(http://www.stevenstrogatz.com/essays/tag=Elements+of+Math)
Toward the Darwinian transition: Switching between distributed and speciated states in a simple model of early life
No full textIt has been hypothesized that in the era just before the last universal common ancestor emerged, life on earth was fundamentally collective. Ancient life forms shared their genetic material freely through massive horizontal gene transfer (HGT). At a certain point, however, life made a transition to the modern era of individuality and vertical descent. Here we present a minimal model for stochastic processes potentially contributing to this hypothesized “Darwinian transition.” The model suggests that HGT-dominated dynamics may have been intermittently interrupted by selection-driven processes during which genotypes became fitter and decreased their inclination toward HGT. Stochastic switching in the population dynamics with three-point (hypernetwork) interactions may have destabilized the HGT-dominated collective state and essentially contributed to the emergence of vertical descent and the first well-defined species in early evolution. A systematic nonlinear analysis of the stochastic model dynamics covering key features of evolutionary processes (such as selection, mutation, drift and HGT) supports this view. Our findings thus suggest a viable direction out of early collective evolution, potentially enabling the start of individuality and vertical Darwinian evolution
Analysis of Watts-Strogatz Networks
No full textAbstract This report implements an algorithm to generate random Watts-Strogatz networks based on a modified (unbiased) rewiring procedure. The small-world properties of the generated networks are verified with various rewiring probability β. A Matlab and a R package are also included to visualize Watts-Strogatz networks
Review of The Joy of x: A Guided Tour of Math, from One to Infinity by Steven Strogatz
No full textStrogatz, Steven. The Joy of x: A Guided Tour of Math, from One to Infinity, (New York, NY, Houghton Mifflin Harcourt, 2012). 316 pp. ISBN 978-0-547-51765-0
The Joy of x: A Guided Tour of Math, from One to Infinity, by Steven Strogatz, is an engaging and example-filled argument for mathematics as a valuable and enjoyable activity. The thirty chapters are divided into six parts, entitled Numbers, Relationships, Shapes, Change, Data, and Frontiers. The discussion ranges from intuitive explanations of basic concepts such as place value, the four arithmetic operations, percentage increase and decrease, and solving equations, to “higher” levels of mathematics such as calculus, probability and statistics, group theory, and the nature of infinity. As in John Allen Paulos’ work, Beyond Numeracy, the chapters are short and punchy, and they can be read independently. While the book is not specifically devoted to numeracy, several chapters, especially those in Part Five on Data, address ideas and examples relevant to quantitative literacy
Sync: the emerging science of spontaneous order
No full textAt the heart of the universe is a steady, insistent beat, the sound of cycles in sync. Along the tidal rivers of Malaysia, thousands of fireflies congregate and flash in unison; the moon spins in perfect resonance with its orbit around the earth; our hearts depend on the synchronous firing of ten thousand pacemaker cells. While the forces that synchronize the flashing of fireflies may seem to have nothing to do with our heart cells, there is in fact a deep connection. Synchrony is a science in its infancy, and Strogatz is a pioneer in this new frontier in which mathematicians and physicists attempt to pinpoint just how spontaneous order emerges from chaos. From underground caves in Texas where a French scientist spent six months alone tracking his sleep-wake cycle, to the home of a Dutch physicist who in 1665 discovered two of his pendulum clocks swinging in perfect time, this fascinating book spans disciplines, continents, and centuries. Engagingly written for readers of books such as Chaos and The Elegant Universe, Sync is a tour-de-force of nonfiction writing
Unified mathematical treatment of complex cascaded bipartite networks: The case of collections of journal papers
No full textIn this study, a mathematical treatment is proposed for analysis of entities and relations among entities in
complex networks consisting of cascaded bipartite networks. This treatment is applied to the case of
collections of journal papers. In this case, entities are distinguishable objects and concepts, such as papers,
references, paper authors, reference authors, paper journals, reference journals, institutions, terms, and term
definitions. Relations are associations between entity-types such as papers and the references they cite, or
paper authors and the papers they write. An entity-relationship model is introduced that explicitly shows
direct links between entity-types and possible useful indirect relations. From this a matrix formulation and
generalized matrix arithmetic are introduced that allow easy expression of relations between entities and
calculation of weights of indirect links and co-occurrence links. Occurrence matrices, equivalence
matrices, membership matrices and co-occurrence matrices are described. A dynamic model of growth
describes recursive relations in occurrence and co-occurrence matrices as papers are added to the paper
collection. Graph theoretic matrices are introduced to allow information flow studies of networks of papers
linked by their citations. Similarity calculations and similarity fusion are explained. Derivation of feature
vectors for pattern recognition techniques is presented. The relation of the proposed mathematical
treatment to seriation, clustering, multidimensional scaling, and visualization techniques is discussed. It is
shown that most existing bibliometric analysis techniques for dealing with collections of journal papers are
easily expressed in terms of the proposed mathematical treatment: co-citation analysis, bibliographic
coupling analysis, author co-citation analysis, journal co-citation analysis, Braam-Moed-vanRaan (BMV)
co-citation/co-word analysis, latent semantic analysis, hubs and authorities, and multidimensional scaling.
This report discusses an extensive software toolkit that was developed for this research for analyzing and
visualizing entities and links in a collection of journal papers. Additionally, an extensive case study is
presented, analyzing and visualizing 60 years of anthrax research through a collection of journal papers.
When dealing with complex networks that consist of cascaded bipartite networks, the treatment presented
here provides a general mathematical framework for all aspects of analysis of static network structure and
network dynamic growth. As such, it provides a basic paradigm for thinking about and modeling such
networks: computing direct and indirect links, expressing and analyzing statistical distributions of network
characteristics, describing network growth, deriving feature vectors, clustering, and visualizing network
structure and growth
Dynamics on Expanding Spaces: Modeling the Emergence of Novelties
No full textNovelties are part of our daily lives. We constantly adopt new technologies, conceive new ideas, meet new people, and experiment with new situations. Occasionally, we as individual, in a complicated cognitive and sometimes fortuitous process, come up with something that is not only new to us, but to our entire society so that what is a personal novelty can turn into an innovation at a global level. Innovations occur throughout social, biological, and technological systems and, though we perceive them as a very natural ingredient of our human experience, little is known about the processes determining their emergence. Still the statistical occurrence of innovations shows striking regularities that represent a starting point to get a deeper insight in the whole phenomenology. This paper represents a small step in that direction, focusing on reviewing the scientific attempts to effectively model the emergence of the new and its regularities, with an emphasis on more recent contributions: from the plain Simon?s model tracing back to the 1950s, to the newest model of Polya?s urn with triggering of one novelty by another. What seems to be key in the successful modeling schemes proposed so far is the idea of looking at evolution as a path in a complex space, physical, conceptual, biological, and technological, whose structure and topology get continuously reshaped and expanded by the occurrence of the new. Mathematically, it is very interesting to look at the consequences of the interplay between the ?actual? and the ?possible? and this is the aim of this short review
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