The Apparent Madness of Crowds: Irrational collective behavior emerging from interactions among rational agents

Standard economic theory assumes that agents in markets behave rationally. However, the observation of extremely large fluctuations in the price of financial assets that are not correlated to changes in their fundamental value, as well as the extreme instance of financial bubbles and crashes, imply that markets (at least occasionally) do display irrational behavior. In this paper, we briefly outline our recent work demonstrating that a market with interacting agents having bounded rationality can display price fluctuations that are {\em quantitatively} similar to those seen in real markets.Comment: 4 pages, 1 figure, to appear in Proceedings of International Workshop on "Econophysics of Stock Markets and Minority Games" (Econophys-Kolkata II), Feb 14-17, 200

On Spatial Consensus Formation: Is the Sznajd Model Different from a Voter Model?

In this paper, we investigate the so-called ``Sznajd Model'' (SM) in one dimension, which is a simple cellular automata approach to consensus formation among two opposite opinions (described by spin up or down). To elucidate the SM dynamics, we first provide results of computer simulations for the spatio-temporal evolution of the opinion distribution $L(t)$, the evolution of magnetization $m(t)$, the distribution of decision times $P(\tau)$ and relaxation times $P(\mu)$. In the main part of the paper, it is shown that the SM can be completely reformulated in terms of a linear VM, where the transition rates towards a given opinion are directly proportional to frequency of the respective opinion of the second-nearest neighbors (no matter what the nearest neighbors are). So, the SM dynamics can be reduced to one rule, ``Just follow your second-nearest neighbor''. The equivalence is demonstrated by extensive computer simulations that show the same behavior between SM and VM in terms of $L(t)$, $m(t)$, $P(\tau)$, $P(\mu)$, and the final attractor statistics. The reformulation of the SM in terms of a VM involves a new parameter $\sigma$, to bias between anti- and ferromagnetic decisions in the case of frustration. We show that $\sigma$ plays a crucial role in explaining the phase transition observed in SM. We further explore the role of synchronous versus asynchronous update rules on the intermediate dynamics and the final attractors. Compared to the original SM, we find three additional attractors, two of them related to an asymmetric coexistence between the opposite opinions.Comment: 22 pages, 20 figures. For related publications see http://www.ais.fraunhofer.de/~fran

A local families index formula for d-bar operators on punctured Riemann surfaces

Using heat kernel methods developed by Vaillant, a local index formula is obtained for families of d-bar operators on the Teichmuller universal curve of Riemann surfaces of genus g with n punctures. The formula also holds on the moduli space M{g,n} in the sense of orbifolds where it can be written in terms of Mumford-Morita-Miller classes. The degree two part of the formula gives the curvature of the corresponding determinant line bundle equipped with the Quillen connection, a result originally obtained by Takhtajan and Zograf.Comment: 47 page

On the infimum attained by a reflected L\'evy process

This paper considers a L\'evy-driven queue (i.e., a L\'evy process reflected at 0), and focuses on the distribution of $M(t)$, that is, the minimal value attained in an interval of length $t$ (where it is assumed that the queue is in stationarity at the beginning of the interval). The first contribution is an explicit characterization of this distribution, in terms of Laplace transforms, for spectrally one-sided L\'evy processes (i.e., either only positive jumps or only negative jumps). The second contribution concerns the asymptotics of \prob{M(T_u)> u} (for different classes of functions $T_u$ and $u$ large); here we have to distinguish between heavy-tailed and light-tailed scenarios

Multi-domain Fourier-continuation/WENO hybrid solver for conservation laws

We introduce a multi-domain Fourier-continuation/WENO hybrid method (FC-WENO) that enables high-order and non-oscillatory solution of systems of nonlinear conservation laws, and which enjoys essentially dispersionless, spectral character away from discontinuities, as well as mild CFL constraints (comparable to those of finite difference methods). The hybrid scheme employs the expensive, shock-capturing WENO method in small regions containing discontinuities and the efficient FC method in the rest of the computational domain, yielding a highly effective overall scheme for applications with a mix of discontinuities and complex smooth structures. The smooth and discontinuous solution regions are distinguished using the multi-resolution procedure of Harten [J. Comput. Phys. 115 (1994) 319-338]. We consider WENO schemes of formal orders five and nine and a FC method of order five. The accuracy, stability and efficiency of the new hybrid method for conservation laws is investigated for problems with both smooth and non-smooth solutions. In the latter case, we solve the Euler equations for gas dynamics for the standard test case of a Mach three shock wave interacting with an entropy wave, as well as a shock wave (with Mach 1.25, three or six) interacting with a very small entropy wave and evaluate the efficiency of the hybrid FC-WENO method as compared to a purely WENO-based approach as well as alternative hybrid based techniques. We demonstrate considerable computational advantages of the new FC-based method, suggesting a potential of an order of magnitude acceleration over alternatives when extended to fully three-dimensional problems. (C) 2011 Elsevier Inc. All rights reserved

The application of ecologically intensive principles to the systemic redesign of livestock farms on native grasslands: A case of co-innovation in Rocha, Uruguay

CONTEXT: Family-run cow-calf farms based on native grasslands exhibit low economic and social sustainability, as reflected in low family incomes and high workloads. Experimental results have shown that pasture–herd interaction management could improve native grasslands and animal productivity OBJECTIVE: This paper analyzes the extent to which the sustainability of family-run livestock farms based on native grasslands could be enhanced by a systemic redesign informed by ecological intensification practices. The research questions address the initial state of farm sustainability, key bottlenecks to improving farm sustainability, and changes in sustainability criteria achieved over three years of farm redesign. METHODS: The study was executed as part of a multi-level co-innovation project in Uruguay in which a team of scientist-practitioners and seven farm families participated in farm characterization, diagnosis, and redesign. The farm characterization took the form of indicators to describe the farms’ management and bio-physical subsystems. Redesign plans were negotiated between the research team and the farmers. Frequent monitoring and evaluation cycles enabled finetuning across the years of implementation. RESULTS AND CONCLUSION: Improvements were observed in the economic indicators gross margin (+55%), return to labor (+71%), and family income (+53%) and in the social indicator workload ( 22%), and the environmental indicators bird diversity and ecosystem integrity index were maintained or increased slightly. These changes were explained by the uptake of coherent sets of ecological intensification practices causing changes in forage height (+30%), forage allowance (+69%), pregnancy (+22), weight of weaning calf per mating cow (+32%), and presence of tussocks (+65%). Ecological intensification principles resulted in synergistic positive effects between productivity–biodiversity tradeoffs and the scope for enhanced farm resilience and stability. SIGNIFICANCE: Cow-calf family-run farms can be transformed to produce positive environmental and social effects and viable economic results. The implementation of projects in a co-innovation context may be taken as a guide to scaling up and scaling out the ecological intensification of livestock production on native grasslands, contributing to an extension system at the national level with the aim of improving cow-calf systems sustainability.Estación Experimental Agropecuaria BarilocheFil: Ruggia, Andrea. Instituto Nacional de Investigacion Agropecuaria (INIA). Programa Nacional de Investigacion en Produccion Familiar. Estacion Experimental INIA Las Brujas; UruguayFil: Dogliotti, Santiago. Universidad de la República. Facultad de Agronomía. Departamento de Produccion Vegetal; UruguayFil: Aguerre, Maria Veronica. Instituto Nacional de Investigacion Agropecuaria (INIA). Programa Nacional de Investigacion en Produccion Familiar. Estacion Experimental INIA Las Brujas; UruguayFil: Albicette, Maria Marta. Instituto Nacional de Investigacion Agropecuaria (INIA). Programa Nacional de Investigacion en Produccion Familiar. Estacion Experimental INIA Las Brujas; UruguayFil: Blumetto, Oscar. Instituto Nacional de Investigacion Agropecuaria (INIA). Programa Nacional de Investigacion en Produccion Familiar. Estacion Experimental INIA Las Brujas; UruguayFil: Cardozo, Geronimo. Instituto Nacional de Investigacion Agropecuaria (INIA). Programa Nacional de Investigacion en Pasturas y Forrajes. Estacion Experimental INIA Treinta y Tres; UruguayFil: Leoni, Carolina. Instituto Nacional de Investigacion Agropecuaria (INIA). Programa Nacional de Investigacion en Produccion Familiar. Estacion Experimental INIA Las Brujas; UruguayFil: Quintans, Graciela. Instituto Nacional de Investigacion Agropecuaria (INIA). Programa Nacional de Investigacion en Carne y Lana. Estacion Experimental INIA Treinta y Tres; UruguayFil: Scarlato, Santiago. nstituto Nacional de Investigacion Agropecuaria (INIA). Programa Nacional de Investigacion en Produccion Familiar. Estacion Experimental INIA Las Brujas; UruguayFil: Tittonell, Pablo Adrian. Instituto Nacional de Tecnología Agropecuaria (INTA). Estación Experimental Agropecuaria Bariloche; ArgentinaFil: Tittonell, Pablo Adrian. Consejo Nacional de Investigaciones Cientificas y Tecnicas. Instituto de Investigaciones Forestales y Agropecuarias Bariloche; ArgentinaFil: Rossing, Walter A.H. Wageningen University and Research. Farming Systems Ecology, Plant Sciences Group; Holand

Implied volatility of basket options at extreme strikes

In the paper, we characterize the asymptotic behavior of the implied volatility of a basket call option at large and small strikes in a variety of settings with increasing generality. First, we obtain an asymptotic formula with an error bound for the left wing of the implied volatility, under the assumption that the dynamics of asset prices are described by the multidimensional Black-Scholes model. Next, we find the leading term of asymptotics of the implied volatility in the case where the asset prices follow the multidimensional Black-Scholes model with time change by an independent increasing stochastic process. Finally, we deal with a general situation in which the dependence between the assets is described by a given copula function. In this setting, we obtain a model-free tail-wing formula that links the implied volatility to a special characteristic of the copula called the weak lower tail dependence function

Partition functions and double-trace deformations in AdS/CFT

We study the effect of a relevant double-trace deformation on the partition function (and conformal anomaly) of a CFT at large N and its dual picture in AdS. Three complementary previous results are brought into full agreement with each other: bulk and boundary computations, as well as their formal identity. We show the exact equality between the dimensionally regularized partition functions or, equivalently, fluctuational determinants involved. A series of results then follows: (i) equality between the renormalized partition functions for all d; (ii) for all even d, correction to the conformal anomaly; (iii) for even d, the mapping entails a mixing of UV and IR effects on the same side (bulk) of the duality, with no precedent in the leading order computations; and finally, (iv) a subtle relation between overall coefficients, volume renormalization and IR-UV connection. All in all, we get a clean test of the AdS/CFT correspondence beyond the classical SUGRA approximation in the bulk and at subleading O(1) order in the large-N expansion on the boundary.Comment: 18 pages, uses JHEP3.cls. Published JHEP versio

Determinant and Weyl anomaly of Dirac operator: a holographic derivation

We present a holographic formula relating functional determinants: the fermion determinant in the one-loop effective action of bulk spinors in an asymptotically locally AdS background, and the determinant of the two-point function of the dual operator at the conformal boundary. The formula originates from AdS/CFT heuristics that map a quantum contribution in the bulk partition function to a subleading large-N contribution in the boundary partition function. We use this holographic picture to address questions in spectral theory and conformal geometry. As an instance, we compute the type-A Weyl anomaly and the determinant of the iterated Dirac operator on round spheres, express the latter in terms of Barnes' multiple gamma function and gain insight into a conjecture by B\"ar and Schopka.Comment: 11 pages; new comments and references added, typos correcte