String field theory: From high energy to cosmology

We review recent achievements and open questions in string field theory. We comment on the history of the construction of the covariant gauge-invariant string field formulation and briefly consider possible applications of string field theory in D-brane physics and cosmology.     

Arguing about social evaluations: From theory to experimentation

In open multiagent systems, agents depend on reputation and trust mechanisms to evaluate the behavior of potential partners. Often these evaluations are associated with a measure of reliability that the source agent computes. However, due to the subjectivity of reputation-related information, this can lead to serious problems when considering communicated social evaluations. In this paper, instead of considering only reliability measures computed from the sources, we provide a mechanism that allows the recipient decide whether the piece of information is reliable according to its own knowledge. We do it by allowing the agents engage in an argumentation-based dialog specifically designed for the exchange of social evaluations. We evaluate our framework through simulations. The results show that in most of the checked conditions, agents that use our dialog framework significantly improve (statistically) the accuracy of the evaluations, over the agents that do not use it. In particular, the simulations reveal that when there is a heterogeneity set of agents (not all the agents have the same goals) and agents base part of their inferences on third-party information, it is worth using our dialog protocol.     

Mathematics for Independence: From Spanish Liberal Exile to the Young American Republics

This paper studies one period in the history of mathematical relationships between Spain and Latin America, when right after the first liberating movements at the beginning of the 19th century, the Spanish-exiled liberals in London produced a peculiar kind of mathematical textbook for the new republics, the catechisms. Copyright 1999 Academic Press.Este trabajo estudia un periodo de la historia de los intercambios matemáticos entre España y Latinoamérica inmediatamente posterior a los movimientos liberadores de principios del siglo XIX, cuando los liberales españoles exiliados en Londres produjeron un tipo muy peculiar de textos matemáticos para las nuevas repúblicas americanas, los catecismos. Copyright 1999 Academic Press.AMS 1991 subject classifications: 00A05, 01A55, 01A80.     

From infinite ergodic theory to number theory (and possibly back)

Some basic facts of infinite ergodic theory are reviewed in a form suitable to be applied to interval maps with number theoretic significance such as the Farey map. This is an enlarged version of the lecture notes accompanying a short course on Infinite Ergodic Theory at the First meeting of the (mostly) young italian hyperbolicians (Corinaldo, Italy, June 8-12, 2009).     

From decision theory to decision aiding methodology

The paper presents the author’s partial and personal historical reconstruction of how decision theory is evolving to a decision aiding methodology. The presentation shows mainly how “alternative” approaches to classic decision theory evolved. In the paper it is claimed that all such decision “theories” share a common methodological feature, which is the use of formal and abstract languages as well as of a model of rationality. Different decision aiding approaches can thus be defined, depending on the origin of the model of rationality used in the decision aiding process. The concept of decision aiding process is then introduced and analysed. The paper’s ultimate claim is that all such decision aiding approaches can be seen as part of a decision aiding methodology.     

从一道数学竞赛题谈起

第四届 ( 1 992年 )北京市大学生数学竞赛 (非数学专业 )有这样一道试题 :若函数 f ( x)对一切 u≠ v均有f( u) - f( v)u- v =αf′( u) + βf′( v) , ( 1 )其中 α,β>0且 α+ β=1 ,试求 f( x)的表达式 .本题有多种解法 ,现介绍两种不同于 [1 ]的解法 .解法一　 1°若 f′( x)≡ k( k为常数 ) ,则 f( x)为一次函数 ,问题已经解决 .2°若 f′( x)不恒为常数 ,则至少存在两点 x1与 x2 使 f′( x1)≠ f′( x2 ) ,在 ( 1 )式中分别令 u=x1,v=x2 及 u=x2 ,v=x1,可得f ( x1) - f ( x2 )x1- x2=αf′( x1) + βf′( x2 ) , ( 2 )f ( x2 ) - f ( …     

From singularity theory to finiteness of Walrasian equilibria

The main result of this paper states that there exists a residual subset of the set of critical economies whose associated equilibria are finite in number. We also show that this subset does not contain any open set and therefore the result is the best possible for our choice of topology (compact-open topology). The proof rests on results and concepts from singularity theory.     

Model theory of partial differential fields: From commuting to noncommuting derivations

McGrail (2000) has shown the existence of a model completion for the universal theory of fields on which a finite number of commuting derivations act and, independently, Yaffe (2001) has shown the existence of a model completion for the univeral theory of fields on which a fixed Lie algebra acts as derivations. We show how to derive the second result from the first.

     

Nonsymmetrical distance between probability distributions,entropy and the theorem of pythagoras

The Kullback-Leibler information I[Q¦p¦ for discrimination in favor of the probability distribution Q against P is considered as a nonsymmetrical analog of one half of the square of the distance between the points Q and P. For the n-dimensional planes we take the exponential families. We shall prove a nonsymmetrical analogue of the theorem of Pythagoras in the formulation: The squared length of an oblique line equals the sum of the squared lengths of the perpendicular and the projection of the oblique line, and also an analog of the cosine theorem and the like.Translated from Matematicheskie Zametki, Vol. 4, No. 3, pp. 323–332, September, 1968.