Modeling the dynamical interaction between epidemics on overlay networks

Epidemics seldom occur as isolated phenomena. Typically, two or more viral agents spread within the same host population and may interact dynamically with each other. We present a general model where two viral agents interact via an immunity mechanism as they propagate simultaneously on two networks connecting the same set of nodes. Exploiting a correspondence between the propagation dynamics and a dynamical process performing progressive network generation, we develop an analytic approach that accurately captures the dynamical interaction between epidemics on overlay networks. The formalism allows for overlay networks with arbitrary joint degree distribution and overlap. To illustrate the versatility of our approach, we consider a hypothetical delayed intervention scenario in which an immunizing agent is disseminated in a host population to hinder the propagation of an undesirable agent (e.g. the spread of preventive information in the context of an emerging infectious disease).Comment: Accepted for publication in Phys. Rev. E. 15 pages, 7 figure

Brownian Dynamics of a Sphere Between Parallel Walls

We describe direct imaging measurements of a colloidal sphere's diffusion between two parallel surfaces. The dynamics of this deceptively simple hydrodynamically coupled system have proved difficult to analyze. Comparison with approximate formulations of a confined sphere's hydrodynamic mobility reveals good agreement with both a leading-order superposition approximation as well as a more general all-images stokeslet analysis.Comment: 4 pages, 3 figures, REVTeX with PostScript figure

Percolation on random networks with arbitrary k-core structure

The k-core decomposition of a network has thus far mainly served as a powerful tool for the empirical study of complex networks. We now propose its explicit integration in a theoretical model. We introduce a Hard-core Random Network model that generates maximally random networks with arbitrary degree distribution and arbitrary k-core structure. We then solve exactly the bond percolation problem on the HRN model and produce fast and precise analytical estimates for the corresponding real networks. Extensive comparison with selected databases reveals that our approach performs better than existing models, while requiring less input information.Comment: 9 pages, 5 figure

Designing Effective Questions for Classroom Response System Teaching

Classroom response systems (CRSs) can be potent tools for teaching physics. Their efficacy, however, depends strongly on the quality of the questions used. Creating effective questions is difficult, and differs from creating exam and homework problems. Every CRS question should have an explicit pedagogic purpose consisting of a content goal, a process goal, and a metacognitive goal. Questions can be engineered to fulfil their purpose through four complementary mechanisms: directing students' attention, stimulating specific cognitive processes, communicating information to instructor and students via CRS-tabulated answer counts, and facilitating the articulation and confrontation of ideas. We identify several tactics that help in the design of potent questions, and present four "makeovers" showing how these tactics can be used to convert traditional physics questions into more powerful CRS questions.Comment: 11 pages, including 6 figures and 2 tables. Submitted (and mostly approved) to the American Journal of Physics. Based on invited talk BL05 at the 2005 Winter Meeting of the American Association of Physics Teachers (Albuquerque, NM

Growing networks of overlapping communities with internal structure

We introduce an intuitive model that describes both the emergence of community structure and the evolution of the internal structure of communities in growing social networks. The model comprises two complementary mechanisms: One mechanism accounts for the evolution of the internal link structure of a single community, and the second mechanism coordinates the growth of multiple overlapping communities. The first mechanism is based on the assumption that each node establishes links with its neighbors and introduces new nodes to the community at different rates. We demonstrate that this simple mechanism gives rise to an effective maximal degree within communities. This observation is related to the anthropological theory known as Dunbar's number, i.e., the empirical observation of a maximal number of ties which an average individual can sustain within its social groups. The second mechanism is based on a recently proposed generalization of preferential attachment to community structure, appropriately called structural preferential attachment (SPA). The combination of these two mechanisms into a single model (SPA+) allows us to reproduce a number of the global statistics of real networks: The distribution of community sizes, of node memberships and of degrees. The SPA+ model also predicts (a) three qualitative regimes for the degree distribution within overlapping communities and (b) strong correlations between the number of communities to which a node belongs and its number of connections within each community. We present empirical evidence that support our findings in real complex networks.Comment: 14 pages, 8 figures, 2 table

Separating invariants for arbitrary linear actions of the additive group

We consider an arbitrary representation of the additive group G_a over a field of characteristic zero and give an explicit description of a finite separating set in the corresponding ring of invariants

The Cohen-Macaulay property of separating invariants of finite groups

In the case of finite groups, a separating algebra is a subalgebra of the ring of invariants which separates the orbits. Although separating algebras are often better behaved than the ring of invariants, we show that many of the criteria which imply the ring of invariants is non Cohen-Macaulay actually imply that no graded separating algebra is Cohen-Macaulay. For example, we show that, over a field of positive characteristic p, given sufficiently many copies of a faithful modular representation, no graded sep- arating algebra is Cohen-Macaulay. Furthermore, we show that, for a p-group, the existence of a Cohen-Macaulay graded separat- ing algebra implies the group is generated by bireflections. Ad- ditionally, we give an example which shows that Cohen-Macaulay separating algebras can occur when the ring of invariants is not Cohen-Macaulay