Non-existence of competitive equilibria with dynamically inconsistent preferences

This paper shows the robust non-existence of competitive equilibria even in a simple three period representative agent economy with dynamically inconsistent preferences. We distinguish between a sophisticated and naive representative agent. Even when underlying preferences are monotone and convex, at given prices, we show by example that the induced preference of the sophisticated representative agent over choices in first-period markets is both non-convex and satiated. Even allowing for negative prices, the market-clearing allocation is not contained in the convex hull of demand. Finally, with a naive representative agent, we show that perfect foresight is incompatible with market clearing and individual optimization at given prices.

Estimation of optimal gravity wave parameters for climate models using data assimilation

There is a current need to constrain the parameters of gravity wave drag (GWD) schemes in climate models using observational information instead of tuning them subjectively. In this work, an inverse technique is developed using data assimilation principles to estimate gravity wave parameters. Because mostGWDschemes assume instantaneous vertical propagation of gravity waves within a column, observations in a single column can be used to formulate a one-dimensional assimilation problem to estimate the unknown parameters. We define a cost function that measures the differences between the unresolved drag inferred from observations (referred to here as the ‘observed’ GWD) and the GWD calculated with a parametrisation scheme. The geometry of the cost function presents some difficulties, including multiple minima and ill-conditioning because of the non-independence of the gravity wave parameters. To overcome these difficulties we propose a genetic algorithm to minimize the cost function, which provides a robust parameter estimation over a broad range of prescribed ‘true’ parameters. When real experiments using an independent estimate of the ‘observed’ GWD are performed, physically unrealistic values of the parameters can result due to the non-independence of the parameters. However, by constraining one of the parameters to lie within a physically realistic range, this degeneracy is broken and the other parameters are also found to lie within physically realistic ranges. This argues for the essential physical self-consistency of the gravity wave scheme. A much better fit to the observed GWD at high latitudes is obtained when the parameters are allowed to vary with latitude. However, a close fit can be obtained either in the upper or the lower part of the profiles, but not in both at the same time. This result is a consequence of assuming an isotropic launch spectrum. The changes of sign in theGWDfound in the tropical lower stratosphere, which are associated with part of the quasi-biennial oscillation forcing, cannot be captured by the parametrisation with optimal parameters.

On the existence of two-dimensional Euler flows satisfying energy-Casimir stability criteria

The energy-Casimir stability method, also known as the Arnold stability method, has been widely used in fluid dynamical applications to derive sufficient conditions for nonlinear stability. The most commonly studied system is two-dimensional Euler flow. It is shown that the set of two-dimensional Euler flows satisfying the energy-Casimir stability criteria is empty for two important cases: (i) domains having the topology of the sphere, and (ii) simply-connected bounded domains with zero net vorticity. The results apply to both the first and the second of Arnold’s stability theorems. In the spirit of Andrews’ theorem, this puts a further limitation on the applicability of the method. © 2000 American Institute of Physics.

On the application of optimal wavelet filter banks for ECG signal classification

This paper discusses ECG signal classification after parametrizing the ECG waveforms in the wavelet domain. Signal decomposition using perfect reconstruction quadrature mirror filter banks can provide a very parsimonious representation of ECG signals. In the current work, the filter parameters are adjusted by a numerical optimization algorithm in order to minimize a cost function associated to the filter cut-off sharpness. The goal consists of achieving a better compromise between frequency selectivity and time resolution at each decomposition level than standard orthogonal filter banks such as those of the Daubechies and Coiflet families. Our aim is to optimally decompose the signals in the wavelet domain so that they can be subsequently used as inputs for training to a neural network classifier.

Transreal proof of the existence of universal possible worlds

Transreal arithmetic is total, in the sense that the fundamental operations of addition, subtraction, multiplication and division can be applied to any transreal numbers with the result being a transreal number [1]. In particular division by zero is allowed. It is proved, in [3], that transreal arithmetic is consistent and contains real arithmetic. The entire set of transreal numbers is a total semantics that models all of the semantic values, that is truth values, commonly used in logics, such as the classical, dialetheaic, fuzzy and gap values [2]. By virtue of the totality of transreal arithmetic, these logics can be implemented using total, arithmetical functions, specifically operators, whose domain and counterdomain is the entire set of transreal numbers

Quasi-sure existence of Gaussian rough paths and large deviation principles for capacities

We construct a quasi-sure version (in the sense of Malliavin) of geometric rough paths associated with a Gaussian process with long-time memory. As an application we establish a large deviation principle (LDP) for capacities for such Gaussian rough paths. Together with Lyons' universal limit theorem, our results yield immediately the corresponding results for pathwise solutions to stochastic differential equations driven by such Gaussian process in the sense of rough paths. Moreover, our LDP result implies the result of Yoshida on the LDP for capacities over the abstract Wiener space associated with such Gaussian process.

Missed, not missing: phylogenomic evidence for the existence of Avian FoxP3

The Forkhead box transcription factor FoxP3 is pivotal to the development and function of regulatory T cells (Tregs), which make a major contribution to peripheral tolerance. FoxP3 is believed to perform a regulatory role in all the vertebrate species in which it has been detected. The prevailing view is that FoxP3 is absent in birds and that avian Tregs rely on alternative developmental and suppressive pathways. Prompted by the automated annotation of foxp3 in the ground tit (Parus humilis) genome, we have questioned this assumption. Our analysis of all available avian genomes has revealed that the foxp3 locus is missing, incomplete or of poor quality in the relevant genomic assemblies for nearly all avian species. Nevertheless, in two species, the peregrine falcon (Falco peregrinus) and the saker falcon (F. cherrug), there is compelling evidence for the existence of exons showing synteny with foxp3 in the ground tit. A broader phylogenomic analysis has shown that FoxP3 sequences from these three species are similar to crocodilian sequences, the closest living relatives of birds. In both birds and crocodilians, we have also identified a highly proline-enriched region at the N terminus of FoxP3, a region previously identified only in mammals.

Existence of pullback attractors for pullback asymptotically compact processes

This paper is concerned with the existence of pullback attractors for evolution processes. Our aim is to provide results that extend the following results for autonomous evolution processes (semigroups) (i) An autonomous evolution process which is bounded, dissipative and asymptotically compact has a global attractor. (ii) An autonomous evolution process which is bounded, point dissipative and asymptotically compact has a global attractor. The extension of such results requires the introduction of new concepts and brings up some important differences between the asymptotic properties of autonomous and non-autonomous evolution processes. An application to damped wave problem with non-autonomous damping is considered. (C) 2009 Elsevier Ltd. All rights reserved.

Existence of Solution for a Class of Quasilinear Systems

This paper proves the existence of nontrivial solution for a class of quasilinear systems oil bounded domains in R(N), N >= 2, whose nonlinearity has a double criticality. The proof is based oil a linking theorem without the Palais-Smale condition.

Existence of secondary bifurcations or isolas for PDEs

In this paper, we introduce a method to conclude about the existence of secondary bifurcations or isolas of steady state solutions for parameter dependent nonlinear partial differential equations. The technique combines the Global Bifurcation Theorem, knowledge about the non-existence of nontrivial steady state solutions at the zero parameter value and explicit information about the coexistence of multiple nontrivial steady states at a positive parameter value. We apply the method to the two-dimensional Swift-Hohenberg equation. (C) 2011 Elsevier Ltd. All rights reserved.

Existence of orthogonal geodesic chords on Riemannian manifolds with concave boundary and homeomorphic to the N-dimensional disk

In this paper we give a proof of the existence of an orthogonal geodesic chord on a Riemannian manifold homeomorphic to a closed disk and with concave boundary. This kind of study is motivated by the link (proved in Giambo et al. (2005) [8]) of the multiplicity problem with the famous Seifert conjecture (formulated in Seifert (1948) [1]) about multiple brake orbits for a class of Hamiltonian systems at a fixed energy level. (C) 2010 Elsevier Ltd. All rights reserved.

Beyond indifferent players: on the existence of prisoners dilemmas in games with amicable and adversarial preferences

Why don’t agents cooperate when they both stand to gain? This question ranks among the most fundamental in the social sciences. Explanations abound. Among the most compelling are various configurations of the prisoner’s dilemma (PD), or public goods problem. Payoffs in PD’s are specified in one of two ways: as primitive cardinal payoffs or as ordinal final utility. However, as final utility is objectively unobservable, only the primitive payoff games are ever observed. This paper explores mappings from primitive payoff to utility payoff games and demonstrates that though an observable game is a PD there are broad classes of utility functions for which there exists no associated utility PD. In particular we show that even small amounts of either altruism or enmity may disrupt the mapping from primitive payoff to utility PD. We then examine some implications of these results.