Exact and efficient calculation of Lagrange multipliers in constrained biological polymers: Proteins and nucleic acids as example cases

In order to accelerate molecular dynamics simulations, it is very common to impose holonomic constraints on their hardest degrees of freedom. In this way, the time step used to integrate the equations of motion can be increased, thus allowing, in principle, to reach longer total simulation times. The imposition of such constraints results in an aditional set of Nc equations (the equations of constraint) and unknowns (their associated Lagrange multipliers), that must be solved in one way or another at each time step of the dynamics. In this work it is shown that, due to the essentially linear structure of typical biological polymers, such as nucleic acids or proteins, the algebraic equations that need to be solved involve a matrix which is banded if the constraints are indexed in a clever way. This allows to obtain the Lagrange multipliers through a non-iterative procedure, which can be considered exact up to machine precision, and which takes O(Nc) operations, instead of the usual O(Nc3) for generic molecular systems. We develop the formalism, and describe the appropriate indexing for a number of model molecules and also for alkanes, proteins and DNA. Finally, we provide a numerical example of the technique in a series of polyalanine peptides of different lengths using the AMBER molecular dynamics package.Comment: 29 pages, 10 figures, 1 tabl

Efficient model chemistries for peptides. I. Split-valence Gaussian basis sets and the heterolevel approximation in RHF and MP2

We present an exhaustive study of more than 250 ab initio potential energy surfaces (PESs) of the model dipeptide HCO-L-Ala-NH2. The model chemistries (MCs) used are constructed as homo- and heterolevels involving possibly different RHF and MP2 calculations for the geometry and the energy. The basis sets used belong to a sample of 39 selected representants from Pople's split-valence families, ranging from the small 3-21G to the large 6-311++G(2df,2pd). The reference PES to which the rest are compared is the MP2/6-311++G(2df,2pd) homolevel, which, as far as we are aware, is the more accurate PES of a dipeptide in the literature. The aim of the study presented is twofold: On the one hand, the evaluation of the influence of polarization and diffuse functions in the basis set, distinguishing between those placed at 1st-row atoms and those placed at hydrogens, as well as the effect of different contraction and valence splitting schemes. On the other hand, the investigation of the heterolevel assumption, which is defined here to be that which states that heterolevel MCs are more efficient than homolevel MCs. The heterolevel approximation is very commonly used in the literature, but it is seldom checked. As far as we know, the only tests for peptides or related systems, have been performed using a small number of conformers, and this is the first time that this potentially very economical approximation is tested in full PESs. In order to achieve these goals, all data sets have been compared and analyzed in a way which captures the nearness concept in the space of MCs.Comment: 54 pages, 16 figures, LaTeX, AMSTeX, Submitted to J. Comp. Che

Between Planning and Heritage: Cultural Parks and National Heritage Areas

The number of cultural parks and heritage areas is increasing in Europe and the United States. Those are spreading over other areas where the economic sectors related to tourism and leisure gain weight. Heritage areas or parks are heterogeneous initiatives that place cultural heritage at the heart of spatial planning policy and economic development, aiming at the reinvention of large territories and local community participation in planning. Their relevance stems from their potential influence on the territorial configuration of broad regions and their impact upon the articulation of traditional protected areas. Notwithstanding this, they have attracted scant academic attention so far

Effects of constraints in general branched molecules: A quantitative ab initio study in HCO-L-Ala-NH2

A general approach to the design of accurate classical potentials for protein folding is described. It includes the introduction of a meaningful statistical measure of the differences between approximations of the same potential energy, the definition of a set of Systematic and Approximately Separable and Modular Internal Coordinates (SASMIC), much convenient for the simulation of general branched molecules, and the imposition of constraints on the most rapidly oscillating degrees of freedom. All these tools are used to study the effects of constraints in the Conformational Equilibrium Distribution (CED) of the model dipeptide HCO-L-Ala-NH2. We use ab initio Quantum Mechanics calculations including electron correlation at the MP2 level to describe the system, and we measure the conformational dependence of the correcting terms to the naive CED based in the Potential Energy Surface (PES) without any simplifying assumption. These terms are related to mass-metric tensors determinants and also occur in the Fixman's compensating potential. We show that some of the corrections are non-negligible if one is interested in the whole Ramachandran space. On the other hand, if only the energetically lower region, containing the principal secondary structure elements, is assumed to be relevant, then, all correcting terms may be neglected up to peptides of considerable length. This is the first time, as far as we know, that the analysis of the conformational dependence of these correcting terms is performed in a relevant biomolecule with a realistic potential energy function.Comment: 8 pages, 1 figure, LaTeX, aipproc style (included

Profile identification via weighted related metric scaling : an application to dependent Spanish children

Disability and dependency (lack of autonomy in performing common everyday actions) affect health status and quality of life, therefore they are significant public health issues. The main purpose of this study is to establish the existing relationship among different variables (continuous, categorical and binary) referred to children between 3 and 6 years old and their functional dependence in basic activities of daily living. We combine different types of information via weighted related metric scaling to obtain homogeneous profiles for dependent Spanish children. The redundant information between groups of variables is modeled with an interaction parameter that can be optimized according to several criteria. In this paper, the goal is to obtain maximum explained variability in an Euclidean configuration. Data comes from the Survey about Disabilities, Personal Autonomy and Dependence Situations, EDAD 2008, (Spanish National Institute of Statistics, 2008)ADL, Disability, Mixed-type data, Public health, Related metric scaling

Outlier Mining Methods Based on Graph Structure Analysis

Outlier detection in high-dimensional datasets is a fundamental and challenging problem across disciplines that has also practical implications, as removing outliers from the training set improves the performance of machine learning algorithms. While many outlier mining algorithms have been proposed in the literature, they tend to be valid or efficient for specific types of datasets (time series, images, videos, etc.). Here we propose two methods that can be applied to generic datasets, as long as there is a meaningful measure of distance between pairs of elements of the dataset. Both methods start by defining a graph, where the nodes are the elements of the dataset, and the links have associated weights that are the distances between the nodes. Then, the first method assigns an outlier score based on the percolation (i.e., the fragmentation) of the graph. The second method uses the popular IsoMap non-linear dimensionality reduction algorithm, and assigns an outlier score by comparing the geodesic distances with the distances in the reduced space. We test these algorithms on real and synthetic datasets and show that they either outperform, or perform on par with other popular outlier detection methods. A main advantage of the percolation method is that is parameter free and therefore, it does not require any training; on the other hand, the IsoMap method has two integer number parameters, and when they are appropriately selected, the method performs similar to or better than all the other methods tested.Peer ReviewedPostprint (published version

La Arqueología Industrial de León. Reflexiones a partir de la investigación en el Val de San Lorenzo

La Arqueología Industrial es una disciplina relativamente joven cuyas bases teóricas y prácticas se encuentran en continua discusión y renovación. Con el presente artículo tratamos de hacer alguna aportación al debate y mostrar, a la vez que reivindicar, la deficitaria situación de la provincia de León en cuanto al cuidado de este Patrimonio y la realización de estudios arqueológicos. Partimos del trabajo realizado en el Val de San Lorenzo, un pueblo que vivió un gran auge de su industria textil y ahora se enfrenta a la decadencia.Peer reviewe

Relexiones en torno a la Arqueología Industrial: el caso del Val de San Lorenzo

El presente artículo pretende mostrar, por un lado, un posible acercamiento al patrimonio histórico industrial desde un punto de vista arqueológico. Por otro, exponer una serie de relexiones derivadas y ampliadas de nuestra experiencia. Convencidos del valor de esta disciplina para el estudio y salvaguarda de un patrimonio del que cada vez queda menos, para ponerla al servicio de una sociedad que no duda en caliicarse de posmoderna. Este carácter posmoderno, escudriñando desde las alturas, mira a su pasado y se ve a sí mismo como una culminación de la historia. Desde ese punto de observación privilegiado busca conocer y conservar todos y cada uno de los peldaños que le llevaron a ese ocaso. Es lo que Nietzsche llamaría una sociedad con un “exceso de historia”. Gran Bretaña sería un ejemplo particularmente claro; el resto de las naciones europeas siguen, de uno u otro modo, su camino.Peer reviewe

Implicit Legal Principles and Coherence

El presente trabajo presenta una concepción de los principios jurídicos implícitos compatible con la tesis juspositivista de las fuentes sociales del derecho, a través de tres funciones de la coherencia jurídica: una descriptiva y dos normativas. En la función descriptiva, los principios «describen» (o «explican») las relaciones de coherencia del sistema de normas. En la primera función normativa, los principios se utilizan para resolver algún caso difícil (i. e. lagunas normativas). En la segunda función normativa, los principios se utilizan para detectar incoherencias y, eventualmente, «derrotarlas». Los principios implícitos son inducidos/abducidos a partir de las normas positivas. Se parte de la concepción de las normas y de los sistemas normativos de Alchourrón y Bulygin, y de la distinción de MacCormick entre consistencia y coherencia.The present work presents a conception of implicit legal principles, compatible with the Social Sources Thesis of Legal Positivism, through three functions of legal coherence: a descriptive one and two normative ones. In the descriptive function, the principles «describe» (or «explain») the coherence relations of a system of norms. In the first of the normative functions, principles are used to solve a hard case (i. e. legal gaps). In the second normative function, principles are used to detect incoherencies and, eventually, «defeat» them. Implicit principles are induced/abduced from positive norms of the system. The present work takes as a starting point Alchourrón and Bulygin’s conceptions of norms and normative systems, and the distinction, traced by MacCormick between consistency and coherence

Immigration and crime in Spain, 1999-2006

Crime in Spain is not high, by European standards, but together with immigration, crime rates have increased significantly in the last decade. The goals of this paper are (i) to evaluate empirically the extent to which there is either a negative or a positive correlation between crime and immigration and, (ii) to provide a preliminary assessment of the extent to which a causal mechanism can be identified. We find that both immigrants and natives have contributed to the increase in the crime rate. However, the contribution of immigrants seems to be relatively higher. This result is partly explained by the fact that immigration has contributed to the main increase of the collective of males aged 20 to 50, which are responsible for most offences, and by differences in socioeconomic opportunities between migrants and natives. After controlling for such differences, being an immigrant still plays a significant role, but its estimated effect is diminished and the gradual decrease in the crime rates for each nationality appears to indicate a lower propensity to commit criminal offences among the newly-arrived immigrants. We find significant differences in the behavior of immigrants towards crime by their nationality of origin. The crime gap between immigrants and natives is moderate, and can be largely explained by a higher propensity of immigrants to commit minor offences. This type of crimes, although being the less serious, generates a strong perception of insecurity among native population, but its number has decreased in recent years