Density functional theory in the canonical ensemble I General formalism

Density functional theory stems from the Hohenberg-Kohn-Sham-Mermin (HKSM) theorem in the grand canonical ensemble (GCE). However, as recent work shows, although its extension to the canonical ensemble (CE) is not straightforward, work in nanopore systems could certainly benefit from a mesoscopic DFT in the CE. The stumbling block is the fixed $N$ constraint which is responsible for the failure in proving the interchangeability of density profiles and external potentials as independent variables. Here we prove that, if in the CE the correlation functions are stripped off of their asymptotic behaviour (which is not in the form of a properly irreducible $n$-body function), the HKSM theorem can be extended to the CE. In proving that, we generate a new {\it hierarchy} of $N$-modified distribution and correlation functions which have the same formal structure that the more conventional ones have (but with the proper irreducible $n$-body behaviour) and show that, if they are employed, either a modified external field or the density profiles can indistinctly be used as independent variables. We also write down the $N$-modified free energy functional and prove that the thermodynamic potential is minimized by the equilibrium values of the new hierarchy.Comment: 17 pages, IOP style, submitted to J. Phys. Condens. Matte

Tracking Event Model

This note presents the LHCb Tracking Event Model. It discusses the requirements and motivations and the subsequent choices that lead to the final implementation. The event model classes and tools as in software versions Brunel v30r17, LHCb v21r12, Lbcom v5r9 and Rec v3r14 are described; these versions were used for the physics production of the 2006 data challenge (DC06)

Variational Principle underlying Scale Invariant Social Systems

MaxEnt's variational principle, in conjunction with Shannon's logarithmic information measure, yields only exponential functional forms in straightforward fashion. In this communication we show how to overcome this limitation via the incorporation, into the variational process, of suitable dynamical information. As a consequence, we are able to formulate a somewhat generalized Shannonian Maximum Entropy approach which provides a unifying "thermodynamic-like" explanation for the scale-invariant phenomena observed in social contexts, as city-population distributions. We confirm the MaxEnt predictions by means of numerical experiments with random walkers, and compare them with some empirical data

Formaciones edáficas del tramo alto de la cuenca del río Lillas

En la cuenca del río Lillas podemos encontrar junto a suelos propios de áreas de montaña como regosoles y leptosoles, otros comunes en los valles fluviales: los fluvisoles. Los suelos se desarrollan a partir de materiales metamórficos: esquistos, pizarras y cuarcitas —siendo el material fluvial de la misma naturaleza—, bajo una vegetación de pastizal y melojar, en ocasiones sustituido por brezales y jarales. La presencia de permafrost y las subidas de la capa freática limitan el desarrollo de los suelos por lo que se hace muy recomendable su protección.The study about formation of unstable soils, formed from metamorphics rocks (slates, schists, quartzites) has been described in the bowl of Riaza river. The best represented groups of soils are: Leptosols, Regosols and Fluvisols. These soils are really limited and it is higly recomendable to protect them, specially the Fluvisols in recreative zone

Formaciones edáficas del tramo alto de la cuenca del río Riaza

The study about formation of unstable soils that has been developed in a low grade, formed from metamorphics rocks (slates, schists, quartzites) under beechs, oaks, heathers and meadows, in a warm-cold weather, with rains over 1.000 mm, in many diferents slopes, and between 1.300 m and 1.700 m. of highness. The best represented groups of soils are: Leptosols, Regosols, Podzols and Cambisols; with acid pH and, normally, unsatured. In these soils the main changeable cations are Ca2+ and Mg2+; they have sandly textures and high contents in organic matter. These soils are really limited,, it is higly recommendable to protect them.Se estudia la formación de suelos muy inestables, poco desarrollados, derivados de las rocas metamórficas de bajo grado (pizarras, esquistos y cuarcitas) bajo una vegetación de hayedo, melojar, brezal y pradera, y un clima templado frío, con precipitaciones que sobrepasan los 1.000 mm. En pendientes muy variables desde los 1.300 metros hasta los 1.700 metros de altitud. Los grupos de suelos mejor representados son: Leptosoles, Regosoles, Podsoles y Cambisoles, de naturaleza ácida, generalmente desaturados y con Ca2+ y Mg2+ como cationes de cambio mayoritarios, bastante arenosos y ricos en materia orgánica. Estos suelos presentan severas limitaciones por lo que es conveniente su protección

Flexible Bayesian Dynamic Modeling of Correlation and Covariance Matrices

Modeling correlation (and covariance) matrices can be challenging due to the positive-definiteness constraint and potential high-dimensionality. Our approach is to decompose the covariance matrix into the correlation and variance matrices and propose a novel Bayesian framework based on modeling the correlations as products of unit vectors. By specifying a wide range of distributions on a sphere (e.g. the squared-Dirichlet distribution), the proposed approach induces flexible prior distributions for covariance matrices (that go beyond the commonly used inverse-Wishart prior). For modeling real-life spatio-temporal processes with complex dependence structures, we extend our method to dynamic cases and introduce unit-vector Gaussian process priors in order to capture the evolution of correlation among components of a multivariate time series. To handle the intractability of the resulting posterior, we introduce the adaptive $\Delta$-Spherical Hamiltonian Monte Carlo. We demonstrate the validity and flexibility of our proposed framework in a simulation study of periodic processes and an analysis of rat's local field potential activity in a complex sequence memory task.Comment: 49 pages, 15 figure