Search results for "topological"
showing 10 items of 420 documents
Bounded geometry, growth and topology
2010
We characterize functions which are growth types of Riemannian manifolds of bounded geometry.
Finite-temperature geometric properties of the Kitaev honeycomb model
2018
We study finite temperature topological phase transitions of the Kitaev's spin honeycomb model in the vortex-free sector with the use of the recently introduced mean Uhlmann curvature. We employ an appropriate Fermionisation procedure to study the system as a two-band p-wave superconductor described by a BdG Hamiltonian. This allows to study relevant quantities such as Berry and mean Uhlmann curvatures in a simple setting. More specifically, we consider the spin honeycomb in the presence of an external magnetic field breaking time reversal symmetry. The introduction of such an external perturbation opens a gap in the phase of the system characterised by non-Abelian statistics, and makes the…
New applications of extremely regular function spaces
2017
Let $L$ be an infinite locally compact Hausdorff topological space. We show that extremely regular subspaces of $C_0(L)$ have very strong diameter $2$ properties and, for every real number $\varepsilon$ with $0<\varepsilon<1$, contain an $\varepsilon$-isometric copy of $c_0$. If $L$ does not contain isolated points they even have the Daugavet property, and thus contain an asymptotically isometric copy of $\ell_1$.
Asplund Operators on Locally Convex Spaces
2000
We study the relationship between the local Radon-Nikodým property, introduced by Defant [4] as a generalization of the Radon-Nikodým property to duals of locally convex spaces, and the Asplund operators, introduced by Robertson [7]. We also give a characterization of Asplund symmetric tensor products of Banach spaces in terms of Asplund maps.
Graph Topology Learning and Signal Recovery Via Bayesian Inference
2019
The estimation of a meaningful affinity graph has become a crucial task for representation of data, since the underlying structure is not readily available in many applications. In this paper, a topology inference framework, called Bayesian Topology Learning, is proposed to estimate the underlying graph topology from a given set of noisy measurements of signals. It is assumed that the graph signals are generated from Gaussian Markov Random Field processes. First, using a factor analysis model, the noisy measured data is represented in a latent space and its posterior probability density function is found. Thereafter, by utilizing the minimum mean square error estimator and the Expectation M…
TOMOCOMD-CARDD descriptors-based virtual screening of tyrosinase inhibitors: evaluation of different classification model combinations using bond-bas…
2006
Abstract A new set of bond-level molecular descriptors (bond-based linear indices) are used here in QSAR (quantitative structure–activity relationship) studies of tyrosinase inhibitors, for finding functions that discriminate between the tyrosinase inhibitor compounds and inactive ones. A database of 246 compounds was collected for this study; all organic chemicals were reported as tyrosinase inhibitors; they had great structural diversity. This dataset can be considered as a helpful tool, not only for theoretical chemists but also for other researchers in this area. The set used as inactive has 412 drugs with other clinical uses. Twelve LDA-based QSAR models were obtained, the first six us…
Non-stochastic quadratic fingerprints and LDA-based QSAR models in hit and lead generation through virtual screening: theoretical and experimental as…
2005
In order to explore the ability of non-stochastic quadratic indices to encode chemical information in antimalarials, four quantitative models for the discrimination of compounds having this property were generated and statistically compared. Accuracies of 90.2% and 83.3% for the training and test sets, respectively, were observed for the best of all the models, which included non-stochastic quadratic fingerprints weighted with Pauling electronegativities. With a comparative purpose and as a second validation experiment, an exercise of virtual screening of 65 already-reported antimalarials was carried out. Finally, 17 new compounds were classified as either active/inactive ones and experimen…
Self-assembly of semiflexible polymers confined to thin spherical shells
2018
Confinement effects are critical for stiff macromolecules in biological cells, vesicles, and other systems in soft matter. For these molecules, the competition between the packing entropy and the enthalpic cost of bending is further shaped by strong confinement effects. Through coarse-grained molecular dynamics simulations, we explore the self-assembly of semiflexible polymers confined in thin spherical shells for various chain lengths, chain stiffnesses, and shell thicknesses. Here, we focus on the case where the contour and persistence length of the polymers are comparable to the radius of the confining cavity. The range of ordered structures is analyzed using several order parameters to …
Chemistry Explained by Topology: An Alternative Approach
2011
Molecular topology can be considered an application of graph theory in which the molecular structure is characterized through a set of graph-theoretical descriptors called topological indices. Molecular topology has found applications in many different fields, particularly in biology, chemistry, and pharmacology. The first topological index was introduced by H. Wiener in 1947 [1]. Although its very first application was the prediction of the boiling points of the alkanes, the Wiener index has demonstrated since then a predictive capability far beyond that. Along with the Wiener index, in this paper we focus on a few pioneering topological indices, just to illustrate the connection between p…
Quasi *-Algebras of Operators in Rigged Hilbert Spaces
2002
In this chapter, we will study families of operators acting on a rigged Hilbert space, with a particular interest in their partial algebraic structure. In Section 10.1 the notion of rigged Hilbert space D[t] ↪ H ↪ D × [t ×] is introduced and some examples are presented. In Section 10.2, we consider the space.L(D, D ×) of all continuous linear maps from D[t] into D × [t ×] and look for conditions under which (L(D, D ×), L +(D)) is a (topological) quasi *-algebra. Moreover the general problem of introducing in L(D, D ×) a partial multiplication is considered. In Section 10.3 representations of abstract quasi *-algebras into quasi*-algebras of operators are studied and the GNS-construction is …