Structure Theorems for Basic Algebras

A basic finite dimensional algebra over an algebraically closed field $k$ is isomorphic to a quotient of a tensor algebra by an admissible ideal. The category of left modules over the algebra is isomorphic to the category of representations of a finite quiver with relations. In this article we will remove the assumption that $k$ is algebraically closed to look at both perfect and non-perfect fields. We will introduce the notion of species with relations to describe the category of left modules over such algebras. If the field is not perfect, then the algebra is isomorphic to a quotient of a tensor algebra by an ideal that is no longer admissible in general. This gives hereditary algebras isomorphic to a quotient of a tensor algebra by a non-zero ideal. We will show that these non-zero ideals correspond to cyclic subgraphs of the graph associated to the species of the algebra. This will lead to the ideal being zero in the case when the underlying graph of the algebra is a tree

On the basic computational structure of gene regulatory networks

Gene regulatory networks constitute the first layer of the cellular computation for cell adaptation and surveillance. In these webs, a set of causal relations is built up from thousands of interactions between transcription factors and their target genes. The large size of these webs and their entangled nature make difficult to achieve a global view of their internal organisation. Here, this problem has been addressed through a comparative study for {\em Escherichia coli}, {\em Bacillus subtilis} and {\em Saccharomyces cerevisiae} gene regulatory networks. We extract the minimal core of causal relations, uncovering the hierarchical and modular organisation from a novel dynamical/causal perspective. Our results reveal a marked top-down hierarchy containing several small dynamical modules for \textit{E. coli} and \textit{B. subtilis}. Conversely, the yeast network displays a single but large dynamical module in the middle of a bow-tie structure. We found that these dynamical modules capture the relevant wiring among both common and organism-specific biological functions such as transcription initiation, metabolic control, signal transduction, response to stress, sporulation and cell cycle. Functional and topological results suggest that two fundamentally different forms of logic organisation may have evolved in bacteria and yeast.Comment: This article is published at Molecular Biosystems, Please cite as: Carlos Rodriguez-Caso, Bernat Corominas-Murtra and Ricard V. Sole. Mol. BioSyst., 2009, 5 pp 1617--171

Cohen's Equivocal Attack on Rawls's Basic Structure Restriction

G.A. Cohen is famous for his critique of John Rawls’s view that principles of justice are restricted in scope to institutional structures. In recent work, however, Cohen has suggested that Rawlsians get more than just the scope of justice wrong: they get the concept wrong too. He claims that justice is a fundamental value, i.e. a moral input in our deliberations about the content of action-guiding regulatory principles, rather than the output. I argue here that Cohen’s arguments for extending the scope of justice equivocate across his distinction between fundamental principles of justice, i.e. principles that tell us what justice is; and regulatory principles of justice, i.e. principles that tell us what is required of us, all things – including justice – considered. Though Cohen initially had the regulatory sense of the word ‘justice’ in mind when critiquing the basic structure restriction, his replies to the problem of demandingness presuppose his own, fundamental sense of the word ‘justice’. The upshot is that he escapes demandingness at the cost of sacrificing regulatory justice’s capacity to provide clear guidance. I conclude by considering Peter Singer’s efforts to deal with demandingness in his own work on global poverty. Since Singer manages to deal with demandingness without giving up clarity, his work is a good a place to start in the search for regulatory principles that are suitable for the context of personal choice

On the Structure of Equilibria in Basic Network Formation

We study network connection games where the nodes of a network perform edge swaps in order to improve their communication costs. For the model proposed by Alon et al. (2010), in which the selfish cost of a node is the sum of all shortest path distances to the other nodes, we use the probabilistic method to provide a new, structural characterization of equilibrium graphs. We show how to use this characterization in order to prove upper bounds on the diameter of equilibrium graphs in terms of the size of the largest $k$-vicinity (defined as the the set of vertices within distance $k$ from a vertex), for any $k \geq 1$ and in terms of the number of edges, thus settling positively a conjecture of Alon et al. in the cases of graphs of large $k$-vicinity size (including graphs of large maximum degree) and of graphs which are dense enough. Next, we present a new swap-based network creation game, in which selfish costs depend on the immediate neighborhood of each node; in particular, the profit of a node is defined as the sum of the degrees of its neighbors. We prove that, in contrast to the previous model, this network creation game admits an exact potential, and also that any equilibrium graph contains an induced star. The existence of the potential function is exploited in order to show that an equilibrium can be reached in expected polynomial time even in the case where nodes can only acquire limited knowledge concerning non-neighboring nodes.Comment: 11 pages, 4 figure

Topological Semantics and Decidability

It is well-known that the basic modal logic of all topological spaces is $S4$. However, the structure of basic modal and hybrid logics of classes of spaces satisfying various separation axioms was until present unclear. We prove that modal logics of $T_0$, $T_1$ and $T_2$ topological spaces coincide and are S4$. We also examine basic hybrid logics of these classes and prove their decidability; as part of this, we find out that the hybrid logics of$T_1$and T_2$ spaces coincide.Comment: presentation changes, results about concrete structure adde

The Basic Structure as Object: Institutions and Humanitarian Concern (draft)

[FIRST PARAGRAPHS] One third of the human species is infested with worms. The World Health Organization estimates that worms account for 40 percent of the global disease burden from tropical diseases excluding malaria. Worms cause a lot of misery. In this article I will focus on one particular type of infestation, which is hookworm. Approximately 740 million people suffer from hookworm infection in areas of rural poverty: more than one human in ten, a total greater than 23 times the population of Canada or twice the population of the United States. The greatest numbers of cases occur in China, Southeast Asia and Sub-Saharan Africa—that is, mostly in the places in the world where poverty is most severe