Generalized sampling in U-invariant subspaces

In this work we carry out some results in sampling theory for U-invariant subspaces of a separable Hilbert space H, also called atomic subspaces. These spaces are a generalization of the well-known shift- invariant subspaces in L2 (R); here the space L2 (R) is replaced by H, and the shift operator by U. Having as data the samples of some related operators, we derive frame expansions allowing the recovery of the elements in Aa. Moreover, we include a frame perturbation-type result whenever the samples are affected with a jitter error.

Sampling strategies using the "accumulation chamber" for monitoring geological storage of CO2

Fundación Ciudad de la Energía (CIUDEN) is carrying out a project of geological storage of CO2, where CO2 injection tests are planned in saline aquifers at a depth of 1500 m for scientific objectives and project demonstration. Before any CO2 is stored, it is necessary to determine the baseline flux of CO2 in order to detect potential leakage during injection and post-injection monitoring. In November 2009 diffuse flux measurements of CO2 using an accumulation chamber were made in the area selected by CIUDEN for geological storage, located in Hontomin province of Burgos (Spain). This paper presents the tests carried out in order to establish the optimum sampling methodology and the geostatistical analyses performed to determine the range, with which future field campaigns will be planned.

On-road visual vehicle tracking using Markov chain Monte Carlo with metropolis sampling

In this study, a method for vehicle tracking through video analysis based on Markov chain Monte Carlo (MCMC) particle filtering with metropolis sampling is proposed. The method handles multiple targets with low computational requirements and is, therefore, ideally suited for advanced-driver assistance systems that involve real-time operation. The method exploits the removed perspective domain given by inverse perspective mapping (IPM) to define a fast and efficient likelihood model. Additionally, the method encompasses an interaction model using Markov Random Fields (MRF) that allows treatment of dependencies between the motions of targets. The proposed method is tested in highway sequences and compared to state-of-the-art methods for vehicle tracking, i.e., independent target tracking with Kalman filtering (KF) and joint tracking with particle filtering. The results showed fewer tracking failures using the proposed method.

Spatial sampling methods for improved communication for wireless relay robots

Having reliable wireless communication in a network of mobile robots is an ongoing challenge, especially when the mobile robots are given tasks in hostile or harmful environments such as radiation environments in scientific facilities, tunnels with large metallic components and complicated geometries as found at CERN. In this paper, we propose a decentralised method for improving the wireless network throughput by optimizing the wireless relay robot position to receive the best wireless signal strength using implicit spatial diversity concepts and gradient-search algorithms. We experimentally demonstrate the effectiveness of the proposed solutions with a KUKA Youbot omni-directional mobile robot. The performance of the algorithms is compared under various scenarios in an underground scientific facility at CERN.

El análogo natural de almacenamiento y escape de Co2 de la cuenca de Gañuelas-Mazarrón : implicaciones para el comportamiento y la seguridad de un almacenamiento de Co2 en estaso supercrítico

El aumento de la temperatura media de la Tierra durante el pasado siglo en casi 1 ºC; la subida del nivel medio del mar; la disminución del volumen de hielo y nieve terrestres; la fuerte variabilidad del clima y los episodios climáticos extremos que se vienen sucediendo durante las ultimas décadas; y el aumento de las epidemias y enfermedades infecciosas son solo algunas de las evidencias del cambio climático actual, causado, principalmente, por la acumulación de gases de efecto invernadero en la atmósfera por actividades antropogénicas. La problemática y preocupación creciente surgida a raíz de estos fenómenos, motivo que, en 1997, se adoptara el denominado “Protocolo de Kyoto” (Japón), por el que los países firmantes adoptaron diferentes medidas destinadas a controlar y reducir las emisiones de los citados gases. Entre estas medidas cabe destacar las tecnologías CAC, enfocadas a la captura, transporte y almacenamiento de CO2. En este contexto se aprobó, en octubre de 2008, el Proyecto Singular Estratégico “Tecnologías avanzadas de generación, captura y almacenamiento de CO2” (PSE-120000-2008-6), cofinanciado por el Ministerio de Ciencia e Innovación y el FEDER, el cual abordaba, en su Subproyecto “Almacenamiento Geológico de CO2” (PSS-120000-2008-31), el estudio detallado, entre otros, del Análogo Natural de Almacenamiento y Escape de CO2 de la cuenca de Ganuelas-Mazarrón (Murcia). Es precisamente en el marco de dicho Proyecto en el que se ha realizado este trabajo, cuyo objetivo final ha sido el de predecir el comportamiento y evaluar la seguridad, a corto, medio y largo plazo, de un Almacenamiento Geológico Profundo de CO2 (AGP-CO2), mediante el estudio integral del citado análogo natural. Este estudio ha comprendido: i) la contextualización geológica e hidrogeológica de la cuenca, así como la investigación geofísica de la misma; ii) la toma de muestras de aguas de algunos acuíferos seleccionados con el fin de realizar su estudio hidrogeoquímico e isotópico; iii) la caracterización mineralógica, petrográfica, geoquímica e isotópica de los travertinos precipitados a partir de las aguas de algunos de los sondeos de la cuenca; y iv) la medida y caracterización química e isotópica de los gases libres y disueltos detectados en la cuenca, con especial atención al CO2 y 222Rn. Esta información, desarrollada en capítulos independientes, ha permitido realizar un modelo conceptual de funcionamiento del sistema natural que constituye la cuenca de Ganuelas-Mazarrón, así como establecer las analogías entre este y un AGP-CO2, con posibles escapes naturales y/o antropogénicos. La aplicación de toda esta información ha servido, por un lado, para predecir el comportamiento y evaluar la seguridad, a corto, medio y largo plazo, de un AGP-CO2 y, por otro, proponer una metodología general aplicable al estudio de posibles emplazamientos de AGP-CO2 desde la perspectiva de los reservorios naturales de CO2. Los resultados más importantes indican que la cuenca de Ganuelas-Mazarrón se trata de una cubeta o fosa tectónica delimitada por fallas normales, con importantes saltos verticales, que hunden al substrato rocoso (Complejo Nevado-Filabride), y rellenas, generalmente, por materiales volcánicos-subvolcánicos ácidos. Además, esta cuenca se encuentra rellena por formaciones menos resistivas que son, de muro a techo, las margas miocenas, predominantes y casi exclusivas de la cuenca, y los conglomerados y gravas pliocuaternarias. El acuífero salino profundo y enriquecido en CO2, puesto de manifiesto por la xx exploración geotérmica realizada en dicha cuenca durante la década de los 80 y objeto principal de este estudio, se encuentra a techo de los materiales del Complejo Nevado-Filabride, a una profundidad que podría superar los 800 m, según los datos de la investigación mediante sondeos y geofísica. Por ello, no se descarta la posibilidad de que el CO2 se encuentre en estado supe critico, por lo que la citada cuenca reuniría las características principales de un almacenamiento geológico natural y profundo de CO2, o análogo natural de un AGP-CO2 en un acuífero salino profundo. La sobreexplotación de los acuíferos mas someros de la cuenca, con fines agrícolas, origino, por el descenso de sus niveles piezométricos y de la presión hidrostática, el ascenso de las aguas profundas, salinas y enriquecidas en CO2, las cuales son las responsables de la contaminación de dichos acuíferos. El estudio hidrogeoquímico de las aguas de los acuíferos investigados muestra una gran variedad de hidrofacies, incluso en aquellos de litología similar. La alta salinidad de estas aguas las hace inservibles tanto para el consumo humano como para fines agrícolas. Además, el carácter ligeramente ácido de la mayoría de estas aguas determina que tengan gran capacidad para disolver y transportar, hacia la superficie, elementos pesados y/o tóxicos, entre los que destaca el U, elemento abundante en las rocas volcánicas ácidas de la cuenca, con contenidos de hasta 14 ppm, y en forma de uraninita submicroscópica. El estudio isotópico ha permitido discernir el origen, entre otros, del C del DIC de las aguas (δ13C-DIC), explicándose como una mezcla de dos componentes principales: uno, procedente de la descomposición térmica de las calizas y mármoles del substrato y, otro, de origen edáfico, sin descartar una aportación menor de C de origen mantélico. El estudio de los travertinos que se están formando a la salida de las aguas de algunos sondeos, por la desgasificación rápida de CO2 y el consiguiente aumento de pH, ha permitido destacar este fenómeno, por analogía, como alerta de escapes de CO2 desde un AGP-CO2. El análisis de los gases disueltos y libres, con especial atención al CO2 y al 222Rn asociado, indican que el C del CO2, tanto disuelto como en fase libre, tiene un origen similar al del DIC, confirmándose la menor contribución de CO2 de origen mantélico, dada la relación R/Ra del He existente en estos gases. El 222Rn sería el generado por el decaimiento radiactivo del U, particularmente abundante en las rocas volcánicas de la cuenca, y/o por el 226Ra procedente del U o del existente en los yesos mesinienses de la cuenca. Además, el CO2 actúa como carrier del 222Rn, hecho evidenciado en las anomalías positivas de ambos gases a ~ 1 m de profundidad y relacionadas principalmente con perturbaciones naturales (fallas y contactos) y antropogénicas (sondeos). La signatura isotópica del C a partir del DIC, de los carbonatos (travertinos), y del CO2 disuelto y libre, sugiere que esta señal puede usarse como un excelente trazador de los escapes de CO2 desde un AGPCO2, en el cual se inyectara un CO2 procedente, generalmente, de la combustión de combustibles fósiles, con un δ13C(V-PDB) de ~ -30 ‰. Estos resultados han permitido construir un modelo conceptual de funcionamiento del sistema natural de la cuenca de Ganuelas-Mazarrón como análogo natural de un AGP-CO2, y establecer las relaciones entre ambos. Así, las analogías mas importantes, en cuanto a los elementos del sistema, serian la existencia de: i) un acuífero salino profundo enriquecido en CO2, que seria análoga a la formación almacén de un AGPxxi CO2; ii) una formación sedimentaria margosa que, con una potencia superior a 500 m, se correspondería con la formación sello de un AGP-CO2; y iii) acuíferos mas someros con aguas dulces y aptas para el consumo humano, rocas volcánicas ricas en U y fallas que se encuentran selladas por yesos y/o margas; elementos que también podrían concurrir en un emplazamiento de un AGP-CO2. Por otro lado, los procesos análogos mas importantes identificados serian: i) la inyección ascendente del CO2, que seria análoga a la inyección de CO2 de origen antropogénico, pero este con una signatura isotópica δ13C(V-PDB) de ~ -30 ‰; ii) la disolución de CO2 y 222Rn en las aguas del acuífero profundo, lo que seria análogo a la disolución de dichos gases en la formación almacén de un AGP-CO2; iii) la contaminación de los acuíferos mas someros por el ascenso de las aguas sobresaturadas en CO2, proceso que seria análogo a la contaminación que se produciría en los acuíferos existentes por encima de un AGP-CO2, siempre que este se perturbara natural (reactivación de fallas) o artificialmente (sondeos); iv) la desgasificación (CO2 y gases asociados, entre los que destaca el 222Rn) del acuífero salino profundo a través de sondeos, proceso análogo al que pudiera ocurrir en un AGP-CO2 perturbado; y v) la formación rápida de travertinos, proceso análogo indicativo de que el AGP-CO2 ha perdido su estanqueidad. La identificación de las analogías más importantes ha permitido, además, analizar y evaluar, de manera aproximada, el comportamiento y la seguridad, a corto, medio y largo plazo, de un AGP-CO2 emplazado en un contexto geológico similar al sistema natural estudiado. Para ello se ha seguido la metodología basada en el análisis e identificación de los FEPs (Features, Events and Processes), los cuales se han combinado entre sí para generar y analizar diferentes escenarios de evolución del sistema (scenario analysis). Estos escenarios de evolución identificados en el sistema natural perturbado, relacionados con la perforación de sondeos, sobreexplotación de acuíferos, precipitación rápida de travertinos, etc., serian análogos a los que podrían ocurrir en un AGP-CO2 que también fuera perturbado antropogénicamente, por lo que resulta totalmente necesario evitar la perturbación artificial de la formación sello del AGPCO2. Por último, con toda la información obtenida se ha propuesto una metodología de estudio que pueda aplicarse al estudio de posibles emplazamientos de un AGP-CO2 desde la perspectiva de los reservorios naturales de CO2, sean estancos o no. Esta metodología comprende varias fases de estudio, que comprendería la caracterización geológico-estructural del sitio y de sus componentes (agua, roca y gases), la identificación de las analogías entre un sistema natural de almacenamiento de CO2 y un modelo conceptual de un AGP-CO2, y el establecimiento de las implicaciones para el comportamiento y la seguridad de un AGP-CO2. ABSTRACT The accumulation of the anthropogenic greenhouse gases in the atmosphere is the main responsible for: i) the increase in the average temperature of the Earth over the past century by almost 1 °C; ii) the rise in the mean sea level; iii) the drop of the ice volume and terrestrial snow; iv) the strong climate variability and extreme weather events that have been happening over the last decades; and v) the spread of epidemics and infectious diseases. All of these events are just some of the evidence of current climate change. The problems and growing concern related to these phenomena, prompted the adoption of the so-called "Kyoto Protocol" (Japan) in 1997, in which the signatory countries established different measurements to control and reduce the emissions of the greenhouse gases. These measurements include the CCS technologies, focused on the capture, transport and storage of CO2. Within this context, it was approved, in October 2008, the Strategic Singular Project "Tecnologías avanzadas de generación, captura y almacenamiento de CO2" (PSE-120000-2008-6), supported by the Ministry of Science and Innovation and the FEDER funds. This Project, by means of the Subproject "Geological Storage of CO2" (PSS- 120000-2008-31), was focused on the detailed study of the Natural Analogue of CO2 Storage and Leakage located in the Ganuelas-Mazarron Tertiary basin (Murcia), among other Spanish Natural Analogues. This research work has been performed in the framework of this Subproject, being its final objective to predict the behaviour and evaluate the safety, at short, medium and long-term, of a CO2 Deep Geological Storage (CO2-DGS) by means of a comprehensive study of the abovementioned Natural Analogue. This study comprises: i) the geological and hydrogeological context of the basin and its geophysical research; ii) the water sampling of the selected aquifers to establish their hydrogeochemical and isotopic features; iii) the mineralogical, petrographic, geochemical and isotopic characterisation of the travertines formed from upwelling groundwater of several hydrogeological and geothermal wells; and iv) the measurement of the free and dissolved gases detected in the basin, as well as their chemical and isotopic characterisation, mainly regarding CO2 and 222Rn. This information, summarised in separate chapters in the text, has enabled to build a conceptual model of the studied natural system and to establish the analogies between both the studied natural system and a CO2-DGS, with possible natural and/or anthropogenic escapes. All this information has served, firstly, to predict the behaviour and to evaluate the safety, at short, medium and long-term, of a CO2-DGS and, secondly, to propose a general methodology to study suitable sites for a CO2-DGS, taking into account the lessons learned from this CO2 natural reservoir. The main results indicate that the Ganuelas-Mazarron basin is a graben bounded by normal faults with significant vertical movements, which move down the metamorphic substrate (Nevado-Filabride Complex), and filled with acid volcanic-subvolcanic rocks. Furthermore, this basin is filled with two sedimentary formations: i) the Miocene marls, which are predominant and almost exclusive in the basin; xxiv and ii) the Plio-Quaternary conglomerates and gravels. A deep saline CO2-rich aquifer was evidenced in this basin as a result of the geothermal exploration wells performed during the 80s, located just at the top of the Nevado-Filabride Complex and at a depth that could exceed 800 m, according to the geophysical exploration performed. This saline CO2-rich aquifer is precisely the main object of this study. Therefore, it is not discarded the possibility that the CO2 in this aquifer be in supercritical state. Consequently, the aforementioned basin gathers the main characteristics of a natural and deep CO2 geological storage, or natural analogue of a CO2-DGS in a deep saline aquifer. The overexploitation of the shallow aquifers in this basin for agriculture purposes caused the drop of the groundwater levels and hydrostatic pressures, and, as a result, the ascent of the deep saline and CO2-rich groundwater, which is the responsible for the contamination of the shallow and fresh aquifers. The hydrogeochemical features of groundwater from the investigated aquifers show the presence of very different hydrofacies, even in those with similar lithology. The high salinity of this groundwater prevents the human and agricultural uses. In addition, the slightly acidic character of most of these waters determines their capacity to dissolve and transport towards the surface heavy and/or toxic elements, among which U is highlighted. This element is abundant in the acidic volcanic rocks of the basin, with concentrations up to 14 ppm, mainly as sub-microscopic uraninite crystals. The isotopic study of this groundwater, particularly the isotopic signature of C from DIC (δ13C-DIC), suggests that dissolved C can be explained considering a mixture of C from two main different sources: i) from the thermal decomposition of limestones and marbles forming the substrate; and ii) from edaphic origin. However, a minor contribution of C from mantle degassing cannot be discarded. The study of travertines being formed from upwelling groundwater of several hydrogeological and geothermal wells, as a result of the fast CO2 degassing and the pH increase, has allowed highlighting this phenomenon, by analogy, as an alert for the CO2 leakages from a CO2-DGS. The analysis of the dissolved and free gases, with special attention to CO2 and 222Rn, indicates that the C from the dissolved and free CO2 has a similar origin to that of the DIC. The R/Ra ratio of He corroborates the minor contribution of CO2 from the mantle degassing. Furthermore, 222Rn is generated by the radioactive decay of U, particularly abundant in the volcanic rocks of the basin, and/or by 226Ra from the U or from the Messinian gypsum in the basin. Moreover, CO2 acts as a carrier of the 222Rn, a fact evidenced by the positive anomalies of both gases at ~ 1 m depth and mainly related to natural (faults and contacts) and anthropogenic (wells) perturbations. The isotopic signature of C from DIC, carbonates (travertines), and dissolved and free CO2, suggests that this parameter can be used as an excellent tracer of CO2 escapes from a CO2-DGS, in which CO2 usually from the combustion of fossil fuels, with δ13C(V-PDB) of ~ -30 ‰, will be injected. All of these results have allowed to build a conceptual model of the behaviour of the natural system studied as a natural analogue of a CO2-DGS, as well as to establish the relationships between both natural xxv and artificial systems. Thus, the most important analogies, regarding the elements of the system, would be the presence of: i) a deep saline CO2-rich aquifer, which would be analogous to the storage formation of a CO2-DGS; ii) a marly sedimentary formation with a thickness greater than 500 m, which would correspond to the sealing formation of a CO2-DGS; and iii) shallow aquifers with fresh waters suitable for human consumption, U-rich volcanic rocks, and faults that are sealed by gypsums and/or marls; geological elements that could also be present in a CO2-DGS. On the other hand, the most important analogous processes identified are: i) the upward injection of CO2, which would be analogous to the downward injection of the anthropogenic CO2, this last with a δ13C(V-PDB) of ~ -30 ‰; ii) the dissolution of CO2 and 222Rn in groundwater of the deep aquifer, which would be analogous to the dissolution of these gases in the storage formation of a CO2-DGS; iii) the contamination of the shallow aquifers by the uprising of CO2-oversaturated groundwater, an analogous process to the contamination that would occur in shallow aquifers located above a CO2-DGS, whenever it was naturally (reactivation of faults) or artificially (wells) perturbed; iv) the degassing (CO2 and associated gases, among which 222Rn is remarkable) of the deep saline aquifer through wells, process which could be similar in a perturbed CO2- DGS; v) the rapid formation of travertines, indicating that the CO2-DGS has lost its seal capacity. The identification of the most important analogies has also allowed analysing and evaluating, approximately, the behaviour and safety in the short, medium and long term, of a CO2-DGS hosted in a similar geological context of the natural system studied. For that, it has been followed the methodology based on the analysis and identification of FEPs (Features, Events and Processes) that have been combined together in order to generate and analyse different scenarios of the system evolution (scenario analysis). These identified scenarios in the perturbed natural system, related to boreholes, overexploitation of aquifers, rapid precipitation of travertines, etc., would be similar to those that might occur in a CO2-DGS anthropogenically perturbed, so that it is absolutely necessary to avoid the artificial perturbation of the seal formation of a CO2-DGS. Finally, a useful methodology for the study of possible sites for a CO2-DGS is suggested based on the information obtained from this investigation, taking into account the lessons learned from this CO2 natural reservoir. This methodology comprises several phases of study, including the geological and structural characterisation of the site and its components (water, rock and gases), the identification of the analogies between a CO2 storage natural system and a conceptual model of a CO2-DGS, and the implications regarding the behaviour and safety of a CO2-DGS.

Independent doubly Adaptive Rejection Metropolis Sampling

Adaptive Rejection Metropolis Sampling (ARMS) is a wellknown MCMC scheme for generating samples from onedimensional target distributions. ARMS is widely used within Gibbs sampling, where automatic and fast samplers are often needed to draw from univariate full-conditional densities. In this work, we propose an alternative adaptive algorithm (IA2RMS) that overcomes the main drawback of ARMS (an uncomplete adaptation of the proposal in some cases), speeding up the convergence of the chain to the target. Numerical results show that IA2RMS outperforms the standard ARMS, providing a correlation among samples close to zero.

Very intense pulse in the groundwater flow in fissurized-porous stratum

An asymptotic solution is obtained corresponding to a very intense pulse: a sudden strong increase and fast subsequent decrease of the water level at the boundary of semi-infinite fissurized-porous stratum. This flow is of practical interest: it gives a model of a groundwater flow after a high water period or after a failure of a dam around a collector of liquid waste. It is demonstrated that the fissures have a dramatic influence on the groundwater flow, increasing the penetration depth and speed of fluid penetration into the stratum. A characteristic property of the flow in fissurized-porous stratum is the rapid breakthrough of the fluid at the first stage deeply into the stratum via a system of cracks, feeding of porous blocks by the fluid in cracks, and at a later stage feeding of advancing fluid flow in fissures by the fluid, accumulated in porous blocks.

Effects of sampling standardization on estimates of Phanerozoic marine diversification

Global diversity curves reflect more than just the number of taxa that have existed through time: they also mirror variation in the nature of the fossil record and the way the record is reported. These sampling effects are best quantified by assembling and analyzing large numbers of locality-specific biotic inventories. Here, we introduce a new database of this kind for the Phanerozoic fossil record of marine invertebrates. We apply four substantially distinct analytical methods that estimate taxonomic diversity by quantifying and correcting for variation through time in the number and nature of inventories. Variation introduced by the use of two dramatically different counting protocols also is explored. We present sampling-standardized diversity estimates for two long intervals that sum to 300 Myr (Middle Ordovician-Carboniferous; Late Jurassic-Paleogene). Our new curves differ considerably from traditional, synoptic curves. For example, some of them imply unexpectedly low late Cretaceous and early Tertiary diversity levels. However, such factors as the current emphasis in the database on North America and Europe still obscure our view of the global history of marine biodiversity. These limitations will be addressed as the database and methods are refined.

Effects of passage history and sampling bias on phylogenetic reconstruction of human influenza A evolution

In this paper we determine the extent to which host-mediated mutations and a known sampling bias affect evolutionary studies of human influenza A. Previous phylogenetic reconstruction of influenza A (H3N2) evolution using the hemagglutinin gene revealed an excess of nonsilent substitutions assigned to the terminal branches of the tree. We investigate two hypotheses to explain this observation. The first hypothesis is that the excess reflects mutations that were either not present or were at low frequency in the viral sample isolated from its human host, and that these mutations increased in frequency during passage of the virus in embryonated eggs. A set of 22 codons known to undergo such “host-mediated” mutations showed a significant excess of mutations assigned to branches attaching sequences from egg-cultured (as opposed to cell-cultured) isolates to the tree. Our second hypothesis is that the remaining excess results from sampling bias. Influenza surveillance is purposefully biased toward sequencing antigenically dissimilar strains in an effort to identify new variants that may signal the need to update the vaccine. This bias produces an excess of mutations assigned to terminal branches simply because an isolate with no close relatives is by definition attached to the tree by a relatively long branch. Simulations show that the magnitude of excess mutations we observed in the hemagglutinin tree is consistent with expectations based on our sampling protocol. Sampling bias does not affect inferences about evolution drawn from phylogenetic analyses. However, if possible, the excess caused by host-mediated mutations should be removed from studies of the evolution of influenza viruses as they replicate in their human hosts.

Enhanced conformational sampling in Monte Carlo simulations of proteins: application to a constrained peptide.

A Monte Carlo simulation method for globular proteins, called extended-scaled-collective-variable (ESCV) Monte Carlo, is proposed. This method combines two Monte Carlo algorithms known as entropy-sampling and scaled-collective-variable algorithms. Entropy-sampling Monte Carlo is able to sample a large configurational space even in a disordered system that has a large number of potential barriers. In contrast, scaled-collective-variable Monte Carlo provides an efficient sampling for a system whose dynamics is highly cooperative. Because a globular protein is a disordered system whose dynamics is characterized by collective motions, a combination of these two algorithms could provide an optimal Monte Carlo simulation for a globular protein. As a test case, we have carried out an ESCV Monte Carlo simulation for a cell adhesive Arg-Gly-Asp-containing peptide, Lys-Arg-Cys-Arg-Gly-Asp-Cys-Met-Asp, and determined the conformational distribution at 300 K. The peptide contains a disulfide bridge between the two cysteine residues. This bond mimics the strong geometrical constraints that result from a protein's globular nature and give rise to highly cooperative dynamics. Computation results show that the ESCV Monte Carlo was not trapped at any local minimum and that the canonical distribution was correctly determined.

A sampling problem in molecular dynamics simulations of macromolecules.

Correlations in low-frequency atomic displacements predicted by molecular dynamics simulations on the order of 1 ns are undersampled for the time scales currently accessible by the technique. This is shown with three different representations of the fluctuations in a macromolecule: the reciprocal space of crystallography using diffuse x-ray scattering data, real three-dimensional Cartesian space using covariance matrices of the atomic displacements, and the 3N-dimensional configuration space of the protein using dimensionally reduced projections to visualize the extent to which phase space is sampled.

Sampling Quantum Nonlocal Correlations with High Probability

It is well known that quantum correlations for bipartite dichotomic measurements are those of the form (Formula presented.), where the vectors ui and vj are in the unit ball of a real Hilbert space. In this work we study the probability of the nonlocal nature of these correlations as a function of (Formula presented.), where the previous vectors are sampled according to the Haar measure in the unit sphere of (Formula presented.). In particular, we prove the existence of an (Formula presented.) such that if (Formula presented.), (Formula presented.) is nonlocal with probability tending to 1 as (Formula presented.), while for (Formula presented.), (Formula presented.) is local with probability tending to 1 as (Formula presented.).