Coarse-Graining Auto-Encoders for Molecular Dynamics

Molecular dynamics simulations provide theoretical insight into the microscopic behavior of materials in condensed phase and, as a predictive tool, enable computational design of new compounds. However, because of the large temporal and spatial scales involved in thermodynamic and kinetic phenomena in materials, atomistic simulations are often computationally unfeasible. Coarse-graining methods allow simulating larger systems, by reducing the dimensionality of the simulation, and propagating longer timesteps, by averaging out fast motions. Coarse-graining involves two coupled learning problems; defining the mapping from an all-atom to a reduced representation, and the parametrization of a Hamiltonian over coarse-grained coordinates. Multiple statistical mechanics approaches have addressed the latter, but the former is generally a hand-tuned process based on chemical intuition. Here we present Autograin, an optimization framework based on auto-encoders to learn both tasks simultaneously. Autograin is trained to learn the optimal mapping between all-atom and reduced representation, using the reconstruction loss to facilitate the learning of coarse-grained variables. In addition, a force-matching method is applied to variationally determine the coarse-grained potential energy function. This procedure is tested on a number of model systems including single-molecule and bulk-phase periodic simulations.Comment: 8 pages, 6 figure

On turning waves for the inhomogeneous Muskat problem: a computer-assisted proof

We exhibit a family of graphs that develop turning singularities (i.e. their Lipschitz seminorm blows up and they cease to be a graph, passing from the stable to the unstable regime) for the inhomogeneous, two-phase Muskat problem where the permeability is given by a nonnegative step function. We study the influence of different choices of the permeability and different boundary conditions (both at infinity and considering finite/infinite depth) in the development or prevention of singularities for short time. In the general case (inhomogeneous, confined) we prove a bifurcation diagram concerning the appearance or not of singularities when the depth of the medium and the permeabilities change. The proofs are carried out using a combination of classical analysis techniques and computer-assisted verification.Comment: 30 pages, 6 figure

The importance of being mature: the effect of demographic maturation on global per-capita GDP

Given that savings behaviour and worker productivity have strong life-cycle components and given that demographic profiles vary across countries, population age structure should be linked to differences in levels of economic development. In this paper we measure the economic importance of age structure variation for the global economy. We find that even after adjusting for country-specific effects, demographic maturation has been associated with nearly half of the evolution of global per-capita GDP since 1960. We also find that age structure differences can account for just over half of the variation in worldwide per capita GDP (i.e. the lack of sigma convergence) observed since 1960. Taken as a whole, these results complement recent theoretical and empirical work on the importance of population size and economic development and reinforce empirical work linking mature demographic age structures with faster cross-country economic growth rates. JEL Classification: J13, J22, J24, O11, O40age structure, cross-country growth, life cycle savings model

Applying Constraint Databases in the Determination of Potential Minimal Conflicts to Polynomial Model-Based Diagnosis

Model-based Diagnosis allows the identification of the parts which fail in a system. The models are based on the knowledge of the system to diagnose, and may be represented by constraints associated to the components. The variables of these constraints can be observable or non-observable, depending on the situation of the sensors. In order to obtain the potential minimal diagnosis in a system, an important issue is related to finding out the potential minimal conflicts in an efficient way. We consider that Constraint Databases represent an excellent option in order to solve this problem in complex systems. In this work we have used a novel logical architecture of Constraint Databases which has allowed obtaining these potential conflicts by means of the corresponding queries. Moreover, we have considered Gröbner Bases as a projection operator to obtain the potential minimal conflicts of a system. The first results obtained on this work, which are shown in a heat exchangers example, have been very promising.Ministerio de Ciencia y Tecnología DPI2003-07146-C02-0

Developing a labelled object-relational constraint database architecture for the projection operator

Current relational databases have been developed in order to improve the handling of stored data, however, there are some types of information that have to be analysed for which no suitable tools are available. These new types of data can be represented and treated as constraints, allowing a set of data to be represented through equations, inequations and Boolean combinations of both. To this end, constraint databases were defined and some prototypes were developed. Since there are aspects that can be improved, we propose a new architecture called labelled object-relational constraint database (LORCDB). This provides more expressiveness, since the database is adapted in order to support more types of data, instead of the data having to be adapted to the database. In this paper, the projection operator of SQL is extended so that it works with linear and polynomial constraints and variables of constraints. In order to optimize query evaluation efficiency, some strategies and algorithms have been used to obtain an efficient query plan. Most work on constraint databases uses spatiotemporal data as case studies. However, this paper proposes model-based diagnosis since it is a highly potential research area, and model-based diagnosis permits more complicated queries than spatiotemporal examples. Our architecture permits the queries over constraints to be defined over different sets of variables by using symbolic substitution and elimination of variables.Ministerio de Ciencia y Tecnología DPI2006-15476-C02-0

NMUS: Structural Analysis for Improving the Derivation of All MUSes in Overconstrained Numeric CSPs

Models are used in science and engineering for experimentation, analysis, model-based diagnosis, design and planning/sheduling applications. Many of these models are overconstrained Numeric Constraint Satisfaction Problems (NCSP), where the numeric constraints could have linear or polynomial relations. In practical scenarios, it is very useful to know which parts of the overconstrained NCSP instances cause the unsolvability. Although there are algorithms to find all optimal solutions for this problem, they are computationally expensive, and hence may not be applicable to large and real-world problems. Our objective is to improve the performance of these algorithms for numeric domains using structural analysis. We provide experimental results showing that the use of the different strategies proposed leads to a substantially improved performance and it facilitates the application of solving larger and more realistic problems.Ministerio de Educación y Ciencia DIP2006-15476-C02-0

Monitoring water-soil dynamics and tree survival using soil sensors under a big data approach

ArticleThe high importance of green urban planning to ensure access to green areas requires modern and multi-source decision-support tools. The integration of remote sensing data and sensor developments can contribute to the improvement of decision-making in urban forestry. This study proposes a novel big data-based methodology that combines real-time information from soil sensors and climate data to monitor the establishment of a new urban forest in semi-arid conditions. Water-soil dynamics and their implication in tree survival were analyzed considering the application of di erent treatment restoration techniques oriented to facilitate the recovery of tree and shrub vegetation in the degraded area. The synchronized data-capturing scheme made it possible to evaluate hourly, daily, and seasonal changes in soil-water dynamics. The spatial variation of soil-water dynamics was captured by the sensors and it highly contributed to the explanation of the observed ground measurements on tree survival. The methodology showed how the e ciency of treatments varied depending on species selection and across the experimental design. The use of retainers for improving soil moisture content and adjusting tree-watering needs was, on average, the most successful restoration technique. The results and the applied calibration of the sensor technology highlighted the random behavior of water-soil dynamics despite the small-scale scope of the experiment. The results showed the potential of this methodology to assess watering needs and adjust watering resources to the vegetation status using real-time atmospheric and soil datainfo:eu-repo/semantics/publishedVersio

Impronta de religiosidad popular en Granada

En número dedicado a: Granad