Universal correlations in random matrices: quantum chaos, the 1/r21/r^2 integrable model, and quantum gravity

Random matrix theory (RMT) provides a common mathematical formulation of distinct physical questions in three different areas: quantum chaos, the 1-d integrable model with the $1/r^2$ interaction (the Calogero-Sutherland-Moser system), and 2-d quantum gravity. We review the connection of RMT with these areas. We also discuss the method of loop equations for determining correlation functions in RMT, and smoothed global eigenvalue correlators in the 2-matrix model for gaussian orthogonal, unitary and symplectic ensembles.Comment: 26 pages, LaTe

Emergence and Growth of Complex Networks in Adaptive Systems

We consider the population dynamics of a set of species whose network of catalytic interactions is described by a directed graph. The relationship between the attractors of this dynamics and the underlying graph theoretic structures like cycles and autocatalytic sets is discussed. It is shown that when the population dynamics is suitably coupled to a slow dynamics of the graph itself, the network evolves towards increasing complexity driven by autocatalytic sets. Some quantitative measures of network complexity are described.Comment: 10 pages (including figures), 3 Postscript figure

Autocatalytic Sets and the Growth of Complexity in an Evolutionary Model

A model of $s$ interacting species is considered with two types of dynamical variables. The fast variables are the populations of the species and slow variables the links of a directed graph that defines the catalytic interactions among them. The graph evolves via mutations of the least fit species. Starting from a sparse random graph, we find that an autocatalytic set (ACS) inevitably appears and triggers a cascade of exponentially increasing connectivity until it spans the whole graph. The connectivity subsequently saturates in a statistical steady state. The time scales for the appearance of an ACS in the graph and its growth have a power law dependence on $s$ and the catalytic probability. At the end of the growth period the network is highly non-random, being localized on an exponentially small region of graph space for large $s$.Comment: 13 pages REVTEX (including figures), 4 Postscript figure

An Analysis of the Impact of Social Factors on Purchase Behavior

Consumers purchase conspicuous goods to satisfy not just material needs but also social needs such as prestige. In an attempt to meet these social needs, marketing managers of conspicuous goods like cars, perfumes, and watches employ several strategies to highlight the exclusivity of their products. These strategies include using exclusive distribution, charging high prices, and limiting production. Further, marketing textbooks suggest that the demand curve for prestige goods could be upward sloping and therefore firms should not set prices which are ``too low''. In this paper we examine whether the desire for exclusivity can lead to an upward-sloping demand curve. We also investigate how social factors such as the desire for exclusivity and conformity affect prices and firms' profits. To analyze these issues, we develop a model of conspicuous consumption using the rational expectations framework. We consider two different market structures: monopoly and duopoly. Our results shows that the desire for exclusivity can lead to an upward-sloping demand curve when there is a segment of consumers who are (weakly) conformists. The impact of exclusivity and conformity on prices and profits varies with the market structure. Interestingly, an increase in perceived functional differentiation of products consumed by snobs could decrease firms' profits and prices. In the laboratory, we observe an upward sloping demand curve for snobs, in both the monopoly and duopoly setting. We also track consumer's expectations, and find on average that subjects' beliefs are consistent with the observed outcome and the rational expectations equilibrium solution.Game Theory, Experimental Economics, Consumer Behavior, Rational Expectations, Prestige Pricing,

Public Opinion and the Dynamics of Reform

Why do economic reforms that are proceeding successfully often run aground? A number of observers have expressed surprise that public opinion regarding the continuation of a reform process often runs directly counter to the performance of the reform itself. This is especially surprising if one thinks of voters as forward-looking. If anything, a reform that is proceeding successfully might be expected to see burgeoning political support, as voters learn something about the underlying reform, or about the incumbent government's ability to implement it smoothly. In this paper we show that there might arise circumstances where the initial success of reform might result in it running into a political impasse. We suggest that the key might lie in the effect that the reform process has on the balance of political power. In particular, if initially successful reforms change the balance of political power in such a way as to make future redistribution less likely, then public opinion may turn against reform. Thus, in some sense, an initially successful reform may well end up sowing the seeds of its own destruction.political economy, economic reform, public opinion, redistribution, compensation

Feedbacks from the metabolic network to the genetic network reveal regulatory modules in E. coli and B. subtilis

The genetic regulatory network (GRN) plays a key role in controlling the response of the cell to changes in the environment. Although the structure of GRNs has been the subject of many studies, their large scale structure in the light of feedbacks from the metabolic network (MN) has received relatively little attention. Here we study the causal structure of the GRNs, namely the chain of influence of one component on the other, taking into account feedback from the MN. First we consider the GRNs of E. coli and B. subtilis without feedback from MN and illustrate their causal structure. Next we augment the GRNs with feedback from their respective MNs by including (a) links from genes coding for enzymes to metabolites produced or consumed in reactions catalyzed by those enzymes and (b) links from metabolites to genes coding for transcription factors whose transcriptional activity the metabolites alter by binding to them. We find that the inclusion of feedback from MN into GRN significantly affects its causal structure, in particular the number of levels and relative positions of nodes in the hierarchy, and the number and size of the strongly connected components (SCCs). We then study the functional significance of the SCCs. For this we identify condition specific feedbacks from the MN into the GRN by retaining only those enzymes that are essential for growth in specific environmental conditions simulated via the technique of flux balance analysis (FBA). We find that the SCCs of the GRN augmented by these feedbacks can be ascribed specific functional roles in the organism. Our algorithmic approach thus reveals relatively autonomous subsystems with specific functionality, or regulatory modules in the organism. This automated approach could be useful in identifying biologically relevant modules in other organisms for which network data is available, but whose biology is less well studied.Comment: 15 figure

Testing the consistency between cosmological measurements of distance and age

We present a model independent method to test the consistency between cosmological measurements of distance and age, assuming the distance duality relation. We use type Ia supernovae, baryon acoustic oscillations, and observational Hubble data, to reconstruct the luminosity distance D_L(z), the angle averaged distance D_V(z) and the Hubble rate H(z), using Gaussian processes regression technique. We obtain estimate of the distance duality relation in the redshift range 0.1<z<0.73 and we find no evidence for inconsistency between the data sets used.Comment: 5 pages, 1 pdf figure, minor revision, accepted for publication in Physics Letters