Social Balance on Networks: The Dynamics of Friendship and Enmity

How do social networks evolve when both friendly and unfriendly relations exist? Here we propose a simple dynamics for social networks in which the sense of a relationship can change so as to eliminate imbalanced triads--relationship triangles that contains 1 or 3 unfriendly links. In this dynamics, a friendly link changes to unfriendly or vice versa in an imbalanced triad to make the triad balanced. Such networks undergo a dynamic phase transition from a steady state to "utopia"--all friendly links--as the amount of network friendliness is changed. Basic features of the long-time dynamics and the phase transition are discussed.Comment: 16 pages, 11 figures, paper based on an invited talk at Dyonet06, Dynamics on Complex Networks and Applications, Dresden, Germany, Feburary 200

Long-Wavelength Instability in Surface-Tension-Driven Benard Convection

Laboratory studies reveal a deformational instability that leads to a drained region (dry spot) in an initially flat liquid layer (with a free upper surface) heated uniformly from below. This long-wavelength instability supplants hexagonal convection cells as the primary instability in viscous liquid layers that are sufficiently thin or are in microgravity. The instability occurs at a temperature gradient 34% smaller than predicted by linear stability theory. Numerical simulations show a drained region qualitatively similar to that seen in the experiment.Comment: 4 pages. The RevTeX file has a macro allowing various styles. The appropriate style is "mypprint" which is the defaul

Quantum saturation and condensation of excitons in Cu2_2O: a theoretical study

Recent experiments on high density excitons in Cu$_2$O provide evidence for degenerate quantum statistics and Bose-Einstein condensation of this nearly ideal gas. We model the time dependence of this bosonic system including exciton decay mechanisms, energy exchange with phonons, and interconversion between ortho (triplet-state) and para (singlet-state) excitons, using parameters for the excitonic decay, the coupling to acoustic and low-lying optical phonons, Auger recombination, and ortho-para interconversion derived from experiment. The single adjustable parameter in our model is the optical-phonon cooling rate for Auger and laser-produced hot excitons. We show that the orthoexcitons move along the phase boundary without crossing it (i.e., exhibit a ``quantum saturation''), as a consequence of the balance of entropy changes due to cooling of excitons by phonons and heating by the non-radiative Auger two-exciton recombination process. The Auger annihilation rate for para-para collisions is much smaller than that for ortho-para and ortho-ortho collisions, explaining why, under the given experimental conditions, the paraexcitons condense while the orthoexcitons fail to do so.Comment: Revised to improve clarity and physical content 18 pages, revtex, figures available from G. Kavoulakis, Physics Department, University of Illinois, Urban

The History of Galaxy Formation in Groups: An Observational Perspective

We present a pedagogical review on the formation and evolution of galaxies in groups, utilizing observational information from the Local Group to galaxies at z~6. The majority of galaxies in the nearby universe are found in groups, and galaxies at all redshifts up to z~6 tend to cluster on the scale of nearby groups (~1 Mpc). This suggests that the group environment may play a role in the formation of most galaxies. The Local Group, and other nearby groups, display a diversity in star formation and morphological properties that puts limits on how, and when, galaxies in groups formed. Effects that depend on an intragroup medium, such as ram-pressure and strangulation, are likely not major mechanisms driving group galaxy evolution. Simple dynamical friction arguments however show that galaxy mergers should be common, and a dominant process for driving evolution. While mergers between L_* galaxies are observed to be rare at z < 1, they are much more common at earlier times. This is due to the increased density of the universe, and to the fact that high mass galaxies are highly clustered on the scale of groups. We furthermore discus why the local number density environment of galaxies strongly correlates with galaxy properties, and why the group environment may be the preferred method for establishing the relationship between properties of galaxies and their local density.Comment: Invited review, 16 pages, to be published in ESO Astrophysics Symposia: "Groups of Galaxies in the Nearby Universe", eds. I. Saviane, V. Ivanov, J. Borissov

UHECR as Decay Products of Heavy Relics? The Lifetime Problem

The essential features underlying the top-down scenarii for UHECR are discussed, namely, the stability (or lifetime) imposed to the heavy objects (particles) whatever they be: topological and non-topological solitons, X-particles, cosmic defects, microscopic black-holes, fundamental strings. We provide an unified formula for the quantum decay rate of all these objects as well as the particle decays in the standard model. The key point in the top-down scenarii is the necessity to adjust the lifetime of the heavy object to the age of the universe. This ad-hoc requirement needs a very high dimensional operator to govern its decay and/or an extremely small coupling constant. The natural lifetimes of such heavy objects are, however, microscopic times associated to the GUT energy scale (sim 10^{-28} sec. or shorter). It is at this energy scale (by the end of inflation) where they could have been abundantly formed in the early universe and it seems natural that they decayed shortly after being formed.Comment: 11 pages, LaTex, no figures, updated versio

Cropland can support high bird diversity in heterogeneous rural tropical landscapes

Land-use change for crop production is one of the key drivers of habitat loss and fragmentation and consequently biodiversity loss and change in tropical regions. This may impact biodiversity-regulated ecosystem services; birds are important to crop health regulating services (e.g. seed dispersal, pest control) and disservices (e.g. seed predation, grain herbivory). However, knowledge is limited on how birds use heterogeneous agricultural landscapes and the consequences for spatial distribution and flow of services and disservices. We studied crop and non-crop–habitat associations of birds in forest–agricultural landscapes of the Kilombero Valley, Tanzania. We focused on dietary preference as a key trait impacting bird responses to land-use change, services, and disservices to crops. We surveyed birds across four main habitat types using repeated point counts, recording a total of 148 species. We found that crop habitats supported higher species richness and larger communities of potentially beneficial species to crop health, whereby 34.5% of invertebrate-feeding species were recorded in cropland. We found that habitat heterogeneity within the landscape supports bird functional diversity and that each habitat type supported unique communities of species. Furthermore, the number of species unique to forest habitats increased with increasing forest canopy closure. Our findings suggest that management strategies for maintaining trees and shrubs, and enhancing tree cover within the crop production landscape, can be effective approaches for maintaining bird diversity and services. However, in-depth studies on trade-offs with disservices need further exploration to mitigate negative impacts of birds on crop yields

Low Complexity Regularization of Linear Inverse Problems

Inverse problems and regularization theory is a central theme in contemporary signal processing, where the goal is to reconstruct an unknown signal from partial indirect, and possibly noisy, measurements of it. A now standard method for recovering the unknown signal is to solve a convex optimization problem that enforces some prior knowledge about its structure. This has proved efficient in many problems routinely encountered in imaging sciences, statistics and machine learning. This chapter delivers a review of recent advances in the field where the regularization prior promotes solutions conforming to some notion of simplicity/low-complexity. These priors encompass as popular examples sparsity and group sparsity (to capture the compressibility of natural signals and images), total variation and analysis sparsity (to promote piecewise regularity), and low-rank (as natural extension of sparsity to matrix-valued data). Our aim is to provide a unified treatment of all these regularizations under a single umbrella, namely the theory of partial smoothness. This framework is very general and accommodates all low-complexity regularizers just mentioned, as well as many others. Partial smoothness turns out to be the canonical way to encode low-dimensional models that can be linear spaces or more general smooth manifolds. This review is intended to serve as a one stop shop toward the understanding of the theoretical properties of the so-regularized solutions. It covers a large spectrum including: (i) recovery guarantees and stability to noise, both in terms of $\ell^2$-stability and model (manifold) identification; (ii) sensitivity analysis to perturbations of the parameters involved (in particular the observations), with applications to unbiased risk estimation ; (iii) convergence properties of the forward-backward proximal splitting scheme, that is particularly well suited to solve the corresponding large-scale regularized optimization problem