A group topology on the free abelian group of cardinality c that makes its square countably compact

Under p = c, we prove that it is possible to endow the free abelian group of cardinality c with a group topology that makes its square countably compact. This answers a question posed by Madariaga-Garcia and Tomita and by Tkachenko. We also prove that there exists a Wallace semigroup (i.e., a countably compact both-sided cancellative topological semigroup which is not a topological group) whose square is countably compact. This answers a question posed by Grant.

Abelian torsion groups with a countably compact group topology

Comfort and Remus [W.W. Comfort, D. Remus, Abelian torsion groups with a pseudo-compact group topology, Forum Math. 6 (3) (1994) 323-337] characterized algebraically the Abelian torsion groups that admit a pseudocompact group topology using the Ulm-Kaplansky invariants. We show, under a condition weaker than the Generalized Continuum Hypothesis, that an Abelian torsion group (of any cardinality) admits a pseudocompact group topology if and only if it admits a countably compact group topology. Dikranjan and Tkachenko [D. Dikranjan. M. Tkachenko, Algebraic structure of small countably compact Abelian groups, Forum Math. 15 (6) (2003) 811-837], and Dikranjan and Shakhmatov [D. Dikranjan. D. Shakhmatov, Forcing hereditarily separable compact-like group topologies on Abelian groups, Topology Appl. 151 (1-3) (2005) 2-54] showed this equivalence for groups of cardinality not greater than 2(c). We also show, from the existence of a selective ultrafilter, that there are countably compact groups without non-trivial convergent sequences of cardinality kappa(omega), for any infinite cardinal kappa. In particular, it is consistent that for every cardinal kappa there are countably compact groups without non-trivial convergent sequences whose weight lambda has countable cofinality and lambda > kappa. (C) 2009 Elsevier B.V. All rights reserved.

Vacuum effects on massive spinor fields: S-1 x R-3 topology

The aim of this work was to investigate the role played by an external field on the Casimir energy density for massive fermions under S-1 x R-3 topology. Both twisted- and untwisted-spin connections are considered and the calculation in a closed form is performed using an alternative approach based on the combination of the analytic regularization method and the Euler-Maclaurin summation formula. It is shown that no mass scale appears in the final result and, therefore, Casimir effect arises only from the boundary conditions and vacuum fluctuations induced by the coupling with the external field.

Low voltage four-quadrant current multiplier: An improved topology for n-well CMOS process

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Low voltage four-quadrant current multiplier: an improved topology for n-well CMOS process

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

In silico network topology-based prediction of gene essentiality

The identification of genes essential for survival is important for the understanding of the minimal requirements for cellular life and for drug design. As experimental studies with the purpose of building a catalog of essential genes for a given organism are time-consuming and laborious, a computational approach which could predict gene essentiality with high accuracy would be of great value. We present here a novel computational approach, called NTPGE (Network Topology-based Prediction of Gene Essentiality), that relies on the network topology features of a gene to estimate its essentiality. The first step of NTPGE is to construct the integrated molecular network for a given organism comprising protein physical, metabolic and transcriptional regulation interactions. The second step consists in training a decision-tree-based machine-learning algorithm on known essential and non-essential genes of the organism of interest, considering as learning attributes the network topology information for each of these genes. Finally, the decision-tree classifier generated is applied to the set of genes of this organism to estimate essentiality for each gene. We applied the NTPGE approach for discovering the essential genes in Escherichia coli and then assessed its performance. (C) 2007 Elsevier B.V. All rights reserved.

Towards the prediction of essential genes by integration of network topology, cellular localization and biological process information

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

The size of excavators within a polymorphic termite species governs tunnel topology

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)