Multidimensional integration through Markovian sampling under steered function morphing: a physical guise from statistical mechanics

We present a computational strategy for the evaluation of multidimensional integrals on hyper-rectangles based on Markovian stochastic exploration of the integration domain while the integrand is being morphed by starting from an initial appropriate profile. Thanks to an abstract reformulation of Jarzynski's equality applied in stochastic thermodynamics to evaluate the free-energy profiles along selected reaction coordinates via non-equilibrium transformations, it is possible to cast the original integral into the exponential average of the distribution of the pseudo-work (that we may term "computational work") involved in doing the function morphing, which is straightforwardly solved. Several tests illustrate the basic implementation of the idea, and show its performance in terms of computational time, accuracy and precision. The formulation for integrand functions with zeros and possible sign changes is also presented. It will be stressed that our usage of Jarzynski's equality shares similarities with a practice already known in statistics as Annealed Importance Sampling (AIS), when applied to computation of the normalizing constants of distributions. In a sense, here we dress the AIS with its "physical" counterpart borrowed from statistical mechanics.Comment: 3 figures Supplementary Material (pdf file named "JEMDI_SI.pdf"

Hydrodynamic fluctuations in the presence of one parameter Mittag-Leffler friction

The effects of hydrodynamic fluctuations on the subdiffusive motion of a particle subject to one parameter Mittag-Leffler friction are examined by means of the fractional Langevin equation. The particle experiences an overall additive colored noise formed by, on the one hand, the hydrodynamic back flow effects and, on the other hand, an additional contribution predicted by fluctuation dissipation relation. Particle motion may or may not be subject to a restoring force. All possible combinations of forces exerted on the test particle are being studied, and for each of them the generalized response function in terms of multinomial Mittag-Leffler functions is provided. Mean square displacement, normalized velocity and position auto-correlation functions are furnished as special cases of the generalized response function, and their short and long time limits are analytically given. In addition, for the same measures analytical expressions valid for time windows much broader than the usual asymptotic limit are provided, and can be used to fit real life data. We demonstrate that normalized velocity and position auto-correlation functions are the main sources providing information on the effect of hydrodynamic fluctuations on particle motion. Actually, they oppose to friction and to restoring force, and smooth out the anti-persistent character of the motion

Daughter Coloured Noises: The Legacy of Their Mother White Noises Drawn from Different Probability Distributions

White noise is fundamentally linked to many processes; it has a flat power spectral density and a delta-correlated autocorrelation. Operators acting on white noise can result in coloured noise, whether they operate in the time domain, like fractional calculus, or in the frequency domain, like spectral processing. We investigate whether any of the white noise properties remain in the coloured noises produced by the action of an operator. For a coloured noise, which drives a physical system, we provide evidence to pinpoint the mother process from which it came. We demonstrate the existence of two indices, that is, kurtosis and codifference, whose values can categorise coloured noises according to their mother process. Four different mother processes are used in this study: Gaussian, Laplace, Cauchy, and Uniform white noise distributions. The mother process determines the kurtosis value of the coloured noises that are produced. It maintains its value for Gaussian, never converges for Cauchy, and takes values for Laplace and Uniform that are within a range of its white noise value. In addition, the codifference function maintains its value for zero lag-time essentially constant around the value of the corresponding white noise

Differential Dynamics at Glycosidic Linkages of an Oligosaccharide as Revealed by 13C NMR Spin Relaxation and Stochastic Modeling

Among biomolecules, carbohydrates are unique in that not only can linkages be formed through different positions but the structures may also be branched. The trisaccharide \uf062-D-Glcp-(1\uf0ae3)[\uf062-D-Glcp-(1\uf0ae2)]-\uf061-D-Manp-OMe represents a model of a branched vicinally disubstituted structure. A 13C site-specific isotopologue with labeling in each of the two terminal glucosyl residues enabled acquisition of high-quality 13C NMR relaxation parameters T1, T2 and heteronuclear NOE, with standard deviations of \uf0a3 0.5%. For interpretation of the experimental NMR data a diffusive chain model was used in which the dynamics of the glycosidic linkages is coupled to the global reorientation motion of the trisaccharide. Brownian dynamics simulations relying on the potential of mean force at the glycosidic linkages were employed to evaluate spectral densities of the spin probes. Calculated NMR relaxation parameters showed very good agreement with experimental data, deviating < 3%. The resulting dynamics is described by correlation times of 196 ps and 174 ps for the \uf062-(1\uf0ae2)- and \uf062-(1\uf0ae3)-linked glucosyl residues, respectively, i.e., different and linkage dependent. Notably, the devised computational protocol was performed without any fitting of parameters

The roto-conformational diffusion tensor as a tool to interpret molecular flexibility

Stochastic modeling approaches can be used to rationalize complex molecular dynamical behaviours in solution, helping to interpret the coupling mechanisms among internal and external degrees of freedom, providing insight into reaction mechanisms and extracting structural and dynamical data from spectroscopic observables. However, the definition of comprehensive models is usually limited by (i) the difficulty in defining – without resorting to phenomenological assumptions – a representative reduced ensemble of molecular coordinates able to capture essential dynamical properties and (ii) the complexity of numerical or approximate treatments of the resulting equations. In this paper, we address the first of these two issues. Building on a previously defined systematic approach to construct rigorous stochastic models of flexible molecules in solutions from basic principles, we define a manageable diffusive framework leading to a Smoluchowski equation determined by one main tensorial parameter, namely the scaled roto-conformational diffusion tensor, which accounts for the influence of both conservative and dissipative forces and describes the molecular mobility via a precise definition of internal–external and internal–internal couplings. We then show the usefulness of the roto-conformational scaled diffusion tensor as an efficient gauge of molecular flexibility through the analysis of a set of molecular systems of increasing complexity ranging from dimethylformamide to a protein domain

Permanent Magnet Heater for a Precise Control of Temperature in Aluminum Billets before Extrusion

Abstract Aluminum billets are heated at a prescribed temperature before hot working in gas or induction or resistance furnaces. Temperature distribution variable along the billet axis, or 'taper profile' with the initial section hotter than the final part of the billet, improves the extrusion process (isothermal extrusion). Taper temperature distribution is typically realized in induction heater thanks to the accurate control that this technology allows in thermal processing. Permanent Magnet Heaters, PMH, have been recently proposed as a high efficiency solution for the heating of electrically conductive materials. The optimal design of a Permanent Magnet Heater is presented with reference to a real industrial case. The design has been carried out by means of transient magnetic and thermal 2D and 3D Finite Element Models coupled with multiobjective optimization algorithms

Incorporation of Molecular Nanoparticles Inside Proteins: The Trojan Horse Approach in Theranostics

CONSPECTUS: Molecular nanoparticles, MNPs, characterized by well-defined chemical formulas, structures, and sizes can interact with a variety of proteins. Fullerenes, carboranes, and gold nanoclusters well represent the diversity of MNPs properties available in nanoscience. They can have diameters smaller than 1.5 nm, be hydrophilic or hydrophobic, and can use a paraphernalia of means to establish local and global interactions with the amino acidic residues of proteins. Proteins, endowed as they are with an assortment of pockets, crevices, and gaps are natural supramolecular hosts to incorporate/hide/transport MNPs directly in water with a facile and "green" approach.This Account identifies and discusses the rules that govern the interactions and binding between MNPs and proteins. Fullerenes are composed solely by carbon atoms arranged to form hollow polyhedra. Hydrophobic interactions occur between aliphatic residues and the fullerene surface. The amino acids most effectively interacting with fullerenes are aromatic residues that establish p-p stacking interactions with the cage. Amphiphilic and charged residues produce also cation-p, anion-p, and surfactant-like interactions with the cages.Carboranes are composed of boron, carbon, and hydrogen atoms, also arranged to form cages. They are hydrophobic with unusual properties originating from the presence of boron atoms. Hydride-like hydrogens bound to the boron atoms govern carborane chemistry. These negatively charged hydrogens do not participate in classic hydrogen bonding with water and promote hydrophobic interactions with proteins. On the contrary, the electronegativity of these hydrogens drives the formation of unconventional dihydrogen bonds with the acidic hydrogen atoms of positively charged amino acid. Carboranes also establish C-H center dot center dot center dot p and B-H center dot center dot center dot p interactions with aromatic residues.Gold nanoclusters, AuNCs, are synthesizable with atomically precise stoichiometry. Amino acid residues with sulfur atoms or with nitrogen-containing heterocycles are the strongest Au binders. The proteins can act as supramolecular hosts but also as templates for the synthesis of AuNCs directly inside the protein core. Of the pristine amino acids, tryptophan, tyrosine, phenylalanine, and aspartic acid are the most efficient reducing groups. In a peptide sequence, the best Au-reducing moieties are obtained by nitrogencontaining residue such as glutamine, asparagine, arginine, and lysine. The investigation of the interactions between AuNCs and proteins therefore adds further complexity with respect to that of fullerenes and carboranes. The selection of the host proteins should consider that they will have to contain active sites for metal ion accumulation and ion reduction where AuNC can form and stabilize. This Account further discusses the hybridization of MNPs with proteins in view of creating innovative multifunctional theranostic platforms where the role of proteins is akin to that of "Trojan Horses" since they can (i) hide the MNPs, (ii) control their cellular uptake, (iii) drive their crossing of physiological barriers, and (iv) ultimately govern their biological fate

Implementação do Alojamento Conjunto: dificuldades enfrentadas na percepção de uma equipe de enfermagem

O alojamento conjunto (AC) consiste em um sistema de internação hospitalar em que mãe e recém-nascido sadio permanecem juntos por 24 horas. Estudo descritivo-analítico, de abordagem qualitativa, que objetivou identificar por meio da perspectiva da equipe de enfermagem, as dificuldades encontradas para implementação do Alojamento Conjunto em uma maternidade do interior de São Paulo, bem como analisar se o sistema respeita as normas básicas para o AC, preconizadas pelo Ministério da Saúde. Os dados foram coletados em 2008, por meio de entrevista semi-estruturada, observação livre e submetidos à análise de conteúdo temática. Emergiram quatro categorias temáticas: AC – espaço de relações e de cuidados; dificuldades da equipe de enfermagem ao cuidar das mães; condições limitadoras de trabalho ao desenvolvimento das atividades de enfermagem e infraestrutura do AC - recursos materiais, físicos e humanos. Os resultados apontaram que as maiores dificuldades dos profissionais de enfermagem envolveram a execução de suas atribuições devido às instalações físicas inadequadas, redução de recursos humanos e materiais e ao processo educacional e técnico durante a orientação às mães, principalmente quanto à amamentação e cuidados com o coto umbilical. Concluiu-se que o AC necessita ser revisto, considerando as recomendações advindas do Ministério da Saúde