On finite-dimensional Hopf algebras

This is a survey on the state-of-the-art of the classification of finite-dimensional complex Hopf algebras. This general question is addressed through the consideration of different classes of such Hopf algebras. Pointed Hopf algebras constitute the class best understood; the classification of those with abelian group is expected to be completed soon and there is substantial progress in the non-abelian case.Comment: 25 pages. To be presented at the algebra session of ICM 2014. Submitted versio

Machines must be wrong

Making mistakes is an intrinsic human feature. But far to be an unwelcome feature, it is useful. For instance it bears us to learn, to review our beliefs and to support our decisions among others. This capability of using mistakes in our reasonings is already represented by Logic by means of the inference rule of “reduction ad absurdum”, which can be seen as a “supervised kind of mistake”. However in Computer Sciences, apart from the theoretical tools of “reductio ad absurdum” and methods obtained from it (as SLD resolution [1]), contradictions and mistakes are considered features that must be avoided. In some situations this behavior is understandable (e.g. the control of a train or a medical device) but in others, it represents a considerable limitation (e.g. in learning or optimization). Thus, considering knowledge systems involved in wrong information is not only an option for the scientific community, but a necessity. In this talk we explain how wrongness can be represented as a fuzzy notion and why con- tradictory information must be considered as an important piece of information nowadays. Moreover, the consideration of inconsistent knowledge systems is motivated to show how we can retrieve informations from wrongness. We refer to readers interested in more information to [2, 3].Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

The implicit equation of a multigraded hypersurface

In this article we analyze the implicitization problem of the image of a rational map $\phi: X --> P^n$, with $T$ a toric variety of dimension $n-1$ defined by its Cox ring $R$. Let $I:=(f_0,...,f_n)$ be $n+1$ homogeneous elements of $R$. We blow-up the base locus of $\phi$, $V(I)$, and we approximate the Rees algebra $Rees_R(I)$ of this blow-up by the symmetric algebra $Sym_R(I)$. We provide under suitable assumptions, resolutions $\Z.$ for $Sym_R(I)$ graded by the torus-invariant divisor group of $X$, $Cl(X)$, such that the determinant of a graded strand, $\det((\Z.)_\mu)$, gives a multiple of the implicit equation, for suitable $\mu\in Cl(X)$. Indeed, we compute a region in $Cl(X)$ which depends on the regularity of $Sym_R(I)$ where to choose $\mu$. We also give a geometrical interpretation of the possible other factors appearing in $\det((\Z.)_\mu)$. A very detailed description is given when $X$ is a multiprojective space.Comment: 19 pages, 2 figures. To appear in Journal of Algebr

A Historical Perspective on the Development of an Ethnic Minority Consciousness in the Spanish-Language Press of the Southwest

Various scholars have treated ethnic newspapers in the United States as if they all have evolved from an immigrant press.(i) While one may accept their analysis of the functions of the ethnic press, there is a substantial and qualitative difference between newspapers that were built on an immigration base and those that developed from the experience of colonialism and racial oppression. Hispanics were subjected to racialization (ii) for more than a century through such doctrines as the Spanish Black Legend and Manifest Destiny during the nineteenth and early twentieth century. They were conquered and incorporated into the United States and then treated as colonial subjects as is the case of Mexicans in the Southwest and the Puerto Ricans in the Caribbean. Some were incorporated through territorial purchase as was the case of the Hispanics in Florida and Louisiana. (I would also make a case that, in many ways, Cubans and Dominicans also developed under United States domination in the twentieth century.) The subsequent migration and immigration of these peoples to the United States was often directly related to the domination of their homelands by the United States. Their immigration and subsequent cultural perspective on life in the United States, of course, has been substantially different from that of European immigrant groups. Hispanic native or ethnic minority perspective has manifested itself in the political realm, often as an attitude of entitlement to civil and political rights

A graph semantics for a variant of the ambient calculus more adequate for modeling SOC

In this paper we present a graph semantics of a variant of the well known ambient calculus. The main change of our variant is to extract the mobility commands of the original calculus from the ambient topology. Similar to a previous work of ours, we prove that our encoding have good properties. We strongly believe that this variant would allow us to integrate our graph semantics of our mobile calculus with previous work of us in service oriented computing (SOC). Basically, our work on SOC develops a new graph transformation system which we call temporal symbolic graphs. This new graph formalism is used to give semantics to a design language for SOC developed in an european project, but it could also be used in connection with other approaches for modeling or specifying service systems.Postprint (published version