Regular Infinite Economies

The main contribution of this paper is to place smooth infinite economies in the setting of the equilibrium manifold and the natural projection map à la Balasko. We show that smooth infinite economies have an equilibrium set that has the structure of a Banach manifold and that the natural projection map is smooth. We define regular and critical economies, and regular and critical prices, and we show that the set of regular economies coincides with the set of economies whose excess demand function has only regular prices. Generic determinacy of equilibria follows as a by-product.General equilibrium, Infinite economies, Intertemporal choice, Uncertainty.

Necessary and sufficient conditions for global uniqueness of equilibria

We study the problem of finding necessary and sufficient conditions that guarantee global uniqueness of equilibria in a pure exchange economy. We show that for every economy to have a unique equilibrium it is necessary and sufficient that (i) there are no critical economies and (ii) a compact set of economies has a compact set of equilibria.general equilibrium, invertibility, global uniqueness, critical economy, regular economy, equilibrium manifold, natural projection, diffeomorphism, Jacobian

The Number of Equilibria of Smooth Infinite Economies

We construct an index theorem for smooth infinite economies that shows that generically the number of equilibria is odd. As a corollary, this gives a new proof of existence and gives conditions that guarantee global uniqueness of equilibria.Uniqueness; determinacy; equilibria; infinite economy; Fredholm map; equilibrium manifold; index theorem; Z-Rothe vector field.

The Equilibrium Set of Economies with a Continuous Consumption Space

We study global properties of the equilibrium set of economies with a continuous consumption space. This framework is important in intertemporal allocation problems (continuous or infinite time), financial markets with uncertainty (continuous states of nature) and commodity differentiation. We show that the equilibrium set is contractible which implies that (i) there is a continuous economic policy linking any two equilibrium states, and (ii) any two such economic policies can be continuously deformed one into the other. We also give three equivalent formulations of the problem of global uniqueness of equilibria in terms of the projection map from the equilibrium set to the space of parameters. We finally study the local and global effects that the existence of critical economies has on the equilibrium set.General equilibrium, infinite economies, intertemporal choice, uncertainty.

The number of equilibria of smooth infinite economies with separable utilities

We construct an index theorem for smooth infinite economies with separable utilities that shows that generically the number of equilbria is odd. As a corollary, this gives a new proof of existence and gives conditions that guarantee global uniqueness of equilibria.Uniqueness; determinacy; equilibria; infinite economy; Fredholm map; equilibrium manifold; Banach manifold; index theorem; vector field; Rothe

Determinacy of equilibria of smooth infinite economies

This paper deals with generic determinacy of equilibria for infinite dimensional consumption spaces. Our work could be seen as an infinite-dimensional analogue of Dierker and Dierker (1972), by characterising equilibria of an economy as a zero of the aggregate excess demand, and studying its transversality. In this case, we can use extensions of the transversality density theorem. Assuming separable utilities, we give a new proof of generic determinacy of equilibria. We define regular price systems in this setting and show that an economy is regular if and only if its associated excess demand function only has regular equilibrium prices. We also define the infinite equilibrium manifold and show that it has the structure of a Banach manifold.Determinacy, equilibria, infinite economies, Fredholm maps, equilibrium manifold, Banach manifolds

The how and why of lncRNA function: An innate immune perspective.

Next-generation sequencing has provided a more complete picture of the composition of the human transcriptome indicating that much of the "blueprint" is a vastness of poorly understood non-protein-coding transcripts. This includes a newly identified class of genes called long noncoding RNAs (lncRNAs). The lack of sequence conservation for lncRNAs across species meant that their biological importance was initially met with some skepticism. LncRNAs mediate their functions through interactions with proteins, RNA, DNA, or a combination of these. Their functions can often be dictated by their localization, sequence, and/or secondary structure. Here we provide a review of the approaches typically adopted to study the complexity of these genes with an emphasis on recent discoveries within the innate immune field. Finally, we discuss the challenges, as well as the emergence of new technologies that will continue to move this field forward and provide greater insight into the biological importance of this class of genes. This article is part of a Special Issue entitled: ncRNA in control of gene expression edited by Kotb Abdelmohsen

El Carácter Relativo de la Objetividad Científica

Las formas y contenidos de los objetos reales sean estos naturales o sociales, depende más de la concepción ontológica del sujeto que del ser en sí, por lo que al existir múltiples racionalidades científicas, existen o pueden existir múltiples maneras de pensar y concebir teóricamente los objetos reales. La construcción de criterios suprateóricos capaces de comprender la racionalidad interna de una teoría, inevitablemente conlleva el problema de provenir de una racionalidad científica determinada o de una metateoría con sustrato filosófico, lo que conduce a poner en duda la objetividad del conocimiento científico y la del conocimiento construido desde las metarracionalidades teóricas. Los hechos son creados por la teoría y no existen con independencia de ella. Algunos hechos son percibidos por los científicos por medio de referentes ateóricos y otros son formulados y producidos por la teoría. Pero aquellos hechos que son percibidos con referentes acientíficos no son incorporados tal cual a la ciencia sino por medio de una traducción a la teoría que predomina en la conciencia del científico. De cualquier forma, se ha partido del supuesto de la existencia exterior de los hechos con independencia de los contenidos de la conciencia, lo cual es absolutamente falso. El conocimiento científico es objetivo o puede serlo si sale bien librado de las pruebas verificatorias de la teoría desde la cual se construyó; el conocimiento metarracional es objetivo si sus enunciados corresponden a la lógica implicada en la racionalidad de la teoría de pertenencia porque, de no ser así, los enunciados confrontados a racionalidades contrapuestas aparecen como metafísica. Pero, la lógica de una racionalidad científica o de una metarracionalidad no es aplicable a enunciados cognitivos construidos desde otra racionalidad, a menos que se trate de racionalidades científicas o metarracionalidades basadas en la misma concepción ontológica