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University of Illinois at Urbana-Champaign |
Wednesdays, 12:00 -- 12:50pm, 136 LLP (Loomis Laboratory of Physics)
It is uncertain to what extent competitive interactions affect the composition of communities. Null model tests have been used to address this question in ecology, but they are non-robust and hence yield unreliable conclusions. Here, I develop a robust, graph-theoretic test. Upon application to seven large data sets, this test does not suggest effects of competitive interactions in most cases. Although simplistic, the tested null model accounts remarkably well for much of the variability in community composition (median R^2 > 0.99). Hence, in addition to being useful for testing for the effects of competitive interactions, the model appears to be a step towards providing a simple, general theory of ecological community assembly. The model also appears useful in understanding the assembly of communities in other fields.
It has been shown that both Random Boolean Networks (RBN) and Random Threshold Networks (RTN) exhibit a transition from ordered to chaotic dynamics at a critical average connectivity K_c in the thermodynamical limit. We go beyond this extensively studied mean-field approximation and study the scaling properties of damage size distributions as a function of system size N and initial perturbation size d(t=0) in the sparse percolation (SP) limit. We present evidence that another characteristic point, K_s exists for finite system sizes, where the expectation value of damage spreading in the network is independent of N. Similarly, we find deviations of K_c(N) from the mean-field prediction, even for large N. Our results suggest that, for finite size RBN and RTN, phase space structure is very complex and may not exhibit a sharp order-disorder transition. Finally, we discuss the implications of our findings for evolutionary processes and learning applied to networks which solve specific computational tasks.
Geographers have for many years searched for a way to construct cartograms, maps in which the sizes of geographic regions such as countries or provinces appear in proportion to their population. Such maps are invaluable for the representation of census results, election returns, disease incidence, and many other kinds of human data. Unfortunately, to scale regions and still have them fit together, one is normally forced to distort the regions' shapes, potentially resulting in maps that are difficult to read. Many methods for making cartograms have been proposed, some of them are extremely complex, but all suffer either from this lack of readability or from other pathologies, like overlapping regions or strong dependence on the choice of coordinate axes. Here, we present a technique based on ideas borrowed from elementary physics that suffers none of these drawbacks. We illustrate the method with applications to U.S. election results, lung cancer cases in the State of New York, and the optimal geographical distribution of service facilities in the lower 48 states.
Related Seminars:
Applied/Interdisciplinary Mathematics Seminar
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University of Illinois at Urbana-Champaign |