General Equilibrium Analysis. A Century after Walras

2010 marks the hundredth anniversary of the death of Léon Walras, the brilliant originator and first formaliser of general equilibrium theory - one of the pillars of modern economic theory. In advancing much derided practical solutions Walras also displayed more concern for the problems of living in a second best world than is common in modern pure theories of the invisible hand, efficient market hypothesis, DSGE macroeconomics or the thinking of some contemporary free market admirers all based on general equilibrium theory. This book brings contributions from the likes of Kenneth Arrow, Alan Kirman, Richard Posner, Amartya Sen and Robert Solow to share their thoughts and reflections on the theoretical heritage of Léon Walras. Some authors reminisce on the part they played in the development of modern general economics theory; others reflect on the crucial part played by general equilibrium in the development of macroeconomics, microeconomics, growth theory, welfare economics and the theory of justice; others still complain about the wrong path economic theory took under the influence of post 1945 developments in general equilibrium theory.

The Effects of High Steady State Auxin Levels on Root Cell Elongation in Brachypodium.

The long-standing Acid Growth Theory of plant cell elongation posits that auxin promotes cell elongation by stimulating cell wall acidification and thus expansin action. To date, the paucity of pertinent genetic materials has precluded thorough analysis of the importance of this concept in roots. The recent isolation of mutants of the model grass species Brachypodium distachyon with dramatically enhanced root cell elongation due to increased cellular auxin levels has allowed us to address this question. We found that the primary transcriptomic effect associated with elevated steady state auxin concentration in elongating root cells is upregulation of cell wall remodeling factors, notably expansins, while plant hormone signaling pathways maintain remarkable homeostasis. These changes are specifically accompanied by reduced cell wall arabinogalactan complexity but not by increased proton excretion. On the contrary, we observed a tendency for decreased rather than increased proton extrusion from root elongation zones with higher cellular auxin levels. Moreover, similar to Brachypodium, root cell elongation is, in general, robustly buffered against external pH fluctuation in Arabidopsis thaliana However, forced acidification through artificial proton pump activation inhibits root cell elongation. Thus, the interplay between auxin, proton pump activation, and expansin action may be more flexible in roots than in shoots.

Unpacking the cognitive map: the parallel map theory of hippocampal function

In the parallel map theory, the hippocampus encodes space with 2 mapping systems. The bearing map is constructed primarily in the dentate gyrus from directional cues such as stimulus gradients. The sketch map is constructed within the hippocampus proper from positional cues. The integrated map emerges when data from the bearing and sketch maps are combined. Because the component maps work in parallel, the impairment of one can reveal residual learning by the other. Such parallel function may explain paradoxes of spatial learning, such as learning after partial hippocampal lesions, taxonomic and sex differences in spatial learning, and the function of hippocampal neurogenesis. By integrating evidence from physiology to phylogeny, the parallel map theory offers a unified explanation for hippocampal function.

Parts, places, and perspectives : a theory of spatial relations based an mereotopology and convexity

This thesis suggests to carry on the philosophical work begun in Casati's and Varzi's seminal book Parts and Places, by extending their general reflections on the basic formal structure of spatial representation beyond mereotopology and absolute location to the question of perspectives and perspective-dependent spatial relations. We show how, on the basis of a conceptual analysis of such notions as perspective and direction, a mereotopological theory with convexity can express perspectival spatial relations in a strictly qualitative framework. We start by introducing a particular mereotopological theory, AKGEMT, and argue that it constitutes an adequate core for a theory of spatial relations. Two features of AKGEMT are of particular importance: AKGEMT is an extensional mereotopology, implying that sameness of proper parts is a sufficient and necessary condition for identity, and it allows for (lower- dimensional) boundary elements in its domain of quantification. We then discuss an extension of AKGEMT, AKGEMTS, which results from the addition of a binary segment operator whose interpretation is that of a straight line segment between mereotopological points. Based on existing axiom systems in standard point-set topology, we propose an axiomatic characterisation of the segment operator and show that it is strong enough to sustain complex properties of a convexity predicate and a convex hull operator. We compare our segment-based characterisation of the convex hull to Cohn et al.'s axioms for the convex hull operator, arguing that our notion of convexity is significantly stronger. The discussion of AKGEMTS defines the background theory of spatial representation on which the developments in the second part of this thesis are built. The second part deals with perspectival spatial relations in two-dimensional space, i.e., such relations as those expressed by 'in front of, 'behind', 'to the left/right of, etc., and develops a qualitative formalism for perspectival relations within the framework of AKGEMTS. Two main claims are defended in part 2: That perspectival relations in two-dimensional space are four- place relations of the kind R(x, y, z, w), to be read as x is i?-related to y as z looks at w; and that these four-place structures can be satisfactorily expressed within the qualitative theory AKGEMTS. To defend these two claims, we start by arguing for a unified account of perspectival relations, thus rejecting the traditional distinction between 'relative' and 'intrinsic' perspectival relations. We present a formal theory of perspectival relations in the framework of AKGEMTS, deploying the idea that perspectival relations in two-dimensional space are four-place relations, having a locational and a perspectival part and show how this four-place structure leads to a unified framework of perspectival relations. Finally, we present a philosophical motivation to the idea that perspectival relations are four-place, cashing out the thesis that perspectives are vectorial properties and argue that vectorial properties are relations between spatial entities. Using Fine's notion of "qua objects" for an analysis of points of view, we show at last how our four-place approach to perspectival relations compares to more traditional understandings.

Statistical learning theory for geospatial data. Case study: Aral sea

In recent years there has been an explosive growth in the development of adaptive and data driven methods. One of the efficient and data-driven approaches is based on statistical learning theory (Vapnik 1998). The theory is based on Structural Risk Minimisation (SRM) principle and has a solid statistical background. When applying SRM we are trying not only to reduce training error ? to fit the available data with a model, but also to reduce the complexity of the model and to reduce generalisation error. Many nonlinear learning procedures recently developed in neural networks and statistics can be understood and interpreted in terms of the structural risk minimisation inductive principle. A recent methodology based on SRM is called Support Vector Machines (SVM). At present SLT is still under intensive development and SVM find new areas of application (www.kernel-machines.org). SVM develop robust and non linear data models with excellent generalisation abilities that is very important both for monitoring and forecasting. SVM are extremely good when input space is high dimensional and training data set i not big enough to develop corresponding nonlinear model. Moreover, SVM use only support vectors to derive decision boundaries. It opens a way to sampling optimization, estimation of noise in data, quantification of data redundancy etc. Presentation of SVM for spatially distributed data is given in (Kanevski and Maignan 2004).

Optimal growth strategies when mortality and production rates are size-dependent

Pontryagin's maximum principle from optimal control theory is used to find the optimal allocation of energy between growth and reproduction when lifespan may be finite and the trade-off between growth and reproduction is linear. Analyses of the optimal allocation problem to date have generally yielded bang-bang solutions, i.e. determinate growth: life-histories in which growth is followed by reproduction, with no intermediate phase of simultaneous reproduction and growth. Here we show that an intermediate strategy (indeterminate growth) can be selected for if the rates of production and mortality either both increase or both decrease with increasing body size, this arises as a singular solution to the problem. Our conclusion is that indeterminate growth is optimal in more cases than was previously realized. The relevance of our results to natural situations is discussed.

Extreme prematurity and intra uterine growth restriction effects in brain network topology at school age

Higher risk for long-term behavioral and emotional sequelae, with attentional problems (with or without hyperactivity) is now becoming one of the hallmarks of extreme premature (EP) birth and birth after pregancy conditions leading to poor intra uterine growth restriction (IUGR) [1,2]. However, little is know so far about the neurostructural basis of these complexe brain functional abnormalities that seem to have their origins in early critical periods of brain development. The development of cortical axonal pathways happens in a series of sequential events. The preterm phase (24-36 post conecptional weeks PCW) is known for being crucial for growth of the thalamocortical fiber bundles as well as for the development of long projectional, commisural and projectional fibers [3]. Is it logical to expect, thus, that being exposed to altered intrauterine environment (altered nutrition) or to extrauterine environment earlier that expected, lead to alterations in the structural organization and, consequently, alter the underlying white matter (WM) structure. Understanding rate and variability of normal brain development, and detect differences from typical development may offer insight into the neurodevelopmental anomalies that can be imaged at later stages. Due to its unique ability to non-invasively visualize and quantify in vivo white matter tracts in the brain, in this study we used diffusion MRI (dMRI) tractography to derive brain graphs [4,5,6]. This relatively simple way of modeling the brain enable us to use graph theory to study topological properties of brain graphs in order to study the effects of EP and IUGR on childrens brain connectivity at age 6 years old.