A BROADER CONTEXT FOR MONOTONICALLY MONOLITHIC SPACES

This is a sequel of the work done on (strongly) monotonically monolithic spaces and their generalizations. We introduce the notion of monotonically kappa-monolithic space for any infinite cardinal kappa and present the relevant results. We show, among other things, that any sigma-product of monotonically kappa-monolithic spaces is monotonically kappa-monolithic for any infinite cardinal kappa; besides, it is consistent that any strongly monotonically omega-monolithic space with caliber omega(1) is second countable. We also study (strong) monotone kappa-monolithicity in linearly ordered spaces and subspaces of ordinals.

NONSTATIONARY MIXING AND THE UNIQUE ERGODICITY OF ADIC TRANSFORMATIONS

We define topological and measure-theoretic mixing for nonstationary dynamical systems and prove that for a nonstationary subshift of finite type, topological mixing implies the minimality of any adic transformation defined on the edge space, while if the Parry measure sequence is mixing, the adic transformation is uniquely ergodic. We also show this measure theoretic mixing is equivalent to weak ergodicity of the edge matrices in the sense of inhomogeneous Markov chain theory.

NATURAL TOPOLOGIES ON COLOMBEAU ALGEBRAS

We define intrinsic, natural and metrizable topologies T(Omega), T, T(s,Omega) and T(s) in G(Omega), (K) over bar, G(s)(Omega) and (K) over bar (s) respectively. The topology T(Omega) induces T, T(s,Omega) and T(s). The topologies T(s,Omega) and T(s) coincide with the Scarpalezos sharp topologies.

Equivariant Nielsen root theory for G-maps

Let X be a compact Hausdorff space, Y be a connected topological manifold, f : X -> Y be a map between closed manifolds and a is an element of Y. The vanishing of the Nielsen root number N(f; a) implies that f is homotopic to a root free map h, i.e., h similar to f and h(-1) (a) = empty set. In this paper, we prove an equivariant analog of this result for G-maps between G-spaces where G is a finite group. (C) 2010 Elsevier B.V. All rights reserved.

GENERICITY OF NONDEGENERATE GEODESICS WITH GENERAL BOUNDARY CONDITIONS

Let M be a possibly noncompact manifold. We prove, generically in the C(k)-topology (2 <= k <= infinity), that semi-Riemannian metrics of a given index on M do not possess any degenerate geodesics satisfying suitable boundary conditions. This extends a result of L. Biliotti, M. A. Javaloyes and P. Piccione [6] for geodesics with fixed endpoints to the case where endpoints lie on a compact submanifold P subset of M x M that satisfies an admissibility condition. Such condition holds, for example, when P is transversal to the diagonal Delta subset of M x M. Further aspects of these boundary conditions are discussed and general conditions under which metrics without degenerate geodesics are C(k)-generic are given.

Examples from trees, related to discrete subsets, pseudo-radiality and omega-boundedness

We construct some examples using trees. Some of them are consistent counterexamples for the discrete reflection of certain topological properties. All the properties dealt with here were already known to be non-discretely reflexive if we assume CH and we show that the same is true assuming the existence of a Suslin tree. In some cases we actually get some ZFC results. We construct also, using a Suslin tree, a compact space that is pseudo-radial but it is not discretely generated. With a similar construction, but using an Aronszajn tree, we present a ZFC space that is first countable, omega-bounded but is not strongly w-bounded, answering a question of Peter Nyikos. (C) 2008 Elsevier B.V. All rights reserved.

Designing Novel Antitrypanosomal Agents from a Mixed Graph-Theoretical Substructural Approach

Chagas disease is nowadays the most serious parasitic health problem. This disease is caused by Trypanosoma cruzi. The great number of deaths and the insufficient effectiveness of drugs against this parasite have alarmed the scientific community worldwide. In an attempt to overcome this problem, a model for the design and prediction of new antitrypanosomal agents was obtained. This used a mixed approach, containing simple descriptors based on fragments and topological substructural molecular design descriptors. A data set was made up of 188 compounds, 99 of them characterized an antitrypanosomal activity and 88 compounds that belong to other pharmaceutical categories. The model showed sensitivity, specificity and accuracy values above 85%. Quantitative fragmental contributions were also calculated. Then, and to confirm the quality of the model, 15 structures of molecules tested as antitrypanosomal compounds (that we did not include in this study) were predicted, taking into account the information on the abovementioned calculated fragmental contributions. The model showed an accuracy of 100% which means that the ""in silico"" methodology developed by our team is promising for the rational design of new antitrypanosomal drugs. (C) 2009 Wiley Periodicals, Inc. J Comput Chem 31: 882-894. 2010

Design of novel antituberculosis compounds using graph-theoretical and substructural approaches

The increasing resistance of Mycobacterium tuberculosis to the existing drugs has alarmed the worldwide scientific community. In an attempt to overcome this problem, two models for the design and prediction of new antituberculosis agents were obtained. The first used a mixed approach, containing descriptors based on fragments and the topological substructural molecular design approach (TOPS-MODE) descriptors. The other model used a combination of two-dimensional (2D) and three-dimensional (3D) descriptors. A data set of 167 compounds with great structural variability, 72 of them antituberculosis agents and 95 compounds belonging to other pharmaceutical categories, was analyzed. The first model showed sensitivity, specificity, and accuracy values above 80% and the second one showed values higher than 75% for these statistical indices. Subsequently, 12 structures of imidazoles not included in this study were designed, taking into account the two models. In both cases accuracy was 100%, showing that the methodology in silico developed by us is promising for the rational design of antituberculosis drugs.

A chemometric study of the 5-HT1A receptor affinities presented by arylpiperazine compounds

Arylpiperazine compounds are promising 5-HT1A receptor ligands that can contribute for accelerating the onset of therapeutic effect of selective serotonin reuptake inhibitors. In the present work, the chemometric methods HCA, PCA, KNN, SIMCA and PLS were employed in order to obtain SAR and QSAR models relating the structures of arylpiperazine compounds to their 5-HT1A receptor affinities. A training set of 52 compounds was used to construct the models and the best ones were obtained with nine topological descriptors. The classification and regression models were externally validated by means of predictions for a test set of 14 compounds and have presented good quality, as verified by the correctness of classifications, in the case of pattern recognition studies, and b, the high correlation coefficients (q(2) = 0.76, r(2) = 0.83) and small prediction errors for the PLS regression. Since the results are in good agreement with previous SAR studies, we can suggest that these findings can help in the search for 5-HT1A receptor ligands that are able to improve antidepressant treatment. (c) 2007 Elsevier Masson SAS. All rights reserved.