M Santos Tomás

Norm derivatives and characterizations of inner product spaces

Norm Derivatives Characterizations of Inner Product Spaces Orthogonality Relations Norm Derivatives and Heights Perpendicular Bisectors in Real Normed Spaces Bisectrices in Real Normed Spaces Areas of Triangles in Normed Real Spaces.

Assessment of the sampling performance of multiple-copy dynamics versus a unique trajectory

The goal of the present study was to ascertain the differential performance of a long molecular dynamics trajectory versus several shorter ones starting from different points in the phase space and covering the same sampling time. For this purpose, we selected the 16-mer peptide Bak16BH3 as a model for study and carried out several samplings in explicit solvent. These samplings included an 8 μs trajectory (sampling S1); two 4 μs trajectories (sampling S2); four 2 μs trajectories (sampling S3); eight 1 μs trajectories (sampling S4); 16 0.5 μs trajectories (sampling S5), and 80 0.1 μs trajectories (sampling S6). Moreover, the 8 μs trajectory was further extended to 16 μs to have reference values of the diverse properties measured. The diverse samplings were compared qualitatively and quantitatively. Among the former, we carried out a comparison of the conformational profiles of the peptide using cluster analysis. Moreover, we also gained insight into the interchange among these structures along the sampling process. Among the latter, we computed the number of new conformational patterns sampled with time using strings defined from the conformations attained by each of the residues in the peptide. We also compared the locations and depths of the obtained minima on the free energy surface using principal component analysis. Finally, we also compared the helical profiles per residue at the end of the sampling process. The results suggest that a few short molecular dynamics trajectories may provide better sampling than one unique trajectory. Moreover, this procedure can also be advantageous to avoid getting trapped in a local minimum. However, caution should be exercised since short trajectories need to be long enough to overcome local barriers surrounding the starting point and the required sampling time depends on the number of degrees of freedom of the system under study. An effective way to gain insight into the minimum MD trajectory length is to monitor the convergence of different structural features, as shown in the present work.

RED: A Set of Molecular Descriptors Based on Renyi Entropy

New molecular descriptors, RED (Renyi entropy descriptors), based on the generalized entropies introduced by Renyi are presented. Topological descriptors based on molecular features have proven to be useful for describing molecular profiles. Renyi entropy is used as a variability measure to contract a feature-pair distribution composing the descriptor vector. The performance of RED descriptors was tested for the analysis of different sets of molecular distances, virtual screening, and pharmacological profiling. A free parameter of the Renyi entropy has been optimized for all the considered applications.

Pseudometrics from three-positive semidefinite similarities

We prove that when some transformations are applied to three-positive semidefinite similarities we obtain a pseudometric. In addition, we demonstrate that some similarity coefficients usually employed in diversity studies fulfil this condition.

Effect of the solvent on the conformational behavior of the alanine dipeptide deduced from MD simulations

In general, peptides do not exhibit a well-defined conformational profile in solution. However, despite the experimental blurred picture associated with their structure, compelling spectroscopic evidence shows that peptides exhibit local order. The conformational profile of a peptide is the result of a balance between intramolecular interactions between different atoms of the molecule and intermolecular interactions between atoms of the molecule and the solvent. Accordingly, the conformational profile of a peptide will change upon the properties of the solvent it is soaked. To get insight into the balance between intra- and intermolecular interactions on the conformational preferences of the peptide backbone we have studied the conformational profile of the alanine dipeptide in diverse solvents using molecular dynamics as sampling technique. Solvents studied include chloroform, methanol, dimethyl sulfoxide, water and N-methylacetamide. Different treatments of the solvent have been studied in the present work including explicit solvent molecules, a generalized Born model and using the bulk dielectric constant of the solvent. The diverse calculations identify four major conformations with different populations in the diverse solvents: the C7eq only sampled in chloroform; the C5 or extended conformation; the polyproline (PII) conformation and the right-handed α-helix conformation (αR). The results of present calculations permit to analyze how the balance between intra- and intermolecular interactions explains the populations of the diverse conformations observed.

A benchmark calculation for the fuzzy c-means clustering algorithm: initial memberships

We report a benchmark calculation for the fuzzy c-means clustering algorithm that can be used as a reference in theoretical and practical studies related to classification methodologies. A full exploration of the hard-initialization space is done for all possible different groupings on a simple fifteen-pattern system to describe their stationary points. Numerical problems associated with the stopping criteria are discussed in relation with the calculation of some validity indexes. All necessary information to assure an easy reproduction of the obtained results is clearly reported.

A note on logical connectives with weak duality

We study the weak duality \(S(x,N(x))=N(T(x,N(x)))\) where \(S\) is a continuous t-conorm, \(T\) is a continuous t-norm and \(N\) is a strong negation. We characterize completely the strict cases and show that in all other cases there is no direct relation between generators of \(T\) and \(S\) or between their possible Archimedean components in ordinal sums.