Convergence to equilibrium for many particle systems

The goal of this paper is to give a short review of recent results of the authors concerning classical Hamiltonian many particle systems. We hope that these results support the new possible formulation of Boltzmann's ergodicity hypothesis which sounds as follows. For almost all potentials, the minimal contact with external world, through only one particle of $N$, is sufficient for ergodicity. But only if this contact has no memory. Also new results for quantum case are presented

Analysis of the backward bending modes in damped rotating beams

[EN] This article presents a study of the backward bending mode of a simply supported rotating Rayleigh beam with internal damping. The study analyses the natural frequency behaviour of the backward mode according to the internal viscous damping ratio, the slenderness of the beam and its spin speed. To date, the behaviour of the natural frequency of the backward mode is known to be a monotonically decreasing function with spin speed due to gyroscopic effects. In this article, however, it is shown that this behaviour of the natural frequency may not hold for certain damping and slenderness conditions, and reaches a minimum value (concave function) from which it begins to increase. Accordingly, the analytical expression of the spin speed for which the natural frequency of the backward mode attains the minimum value has been obtained. In addition, the internal damping ratio and slenderness intervals associated with such behaviour have been also provided.The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The authors gratefully acknowledge the financial support of Ministerio de Ciencia, Innovacion y Universidades Agencia Estatal de Investigacion and the European Regional Development Fund (project TRA2017-84701-R), as well as Generalitat Valenciana (project Prometeo/2016/007) and European Commission through the project 'RUN2Rail - Innovative RUNning gear soluTiOns for new dependable, sustainable, intelligent and comfortable RAIL vehicles' (Horizon 2020 Shift2Rail JU call 2017, grant number 777564)Martínez Casas, J.; Denia Guzmán, FD.; Fayos Sancho, J.; Nadal, E.; Giner Navarro, J. (2019). Analysis of the backward bending modes in damped rotating beams. Advances in Mechanical Engineering. 11(4):1-13. https://doi.org/10.1177/1687814019840474S113114Zorzi, E. S., & Nelson, H. D. (1977). Finite Element Simulation of Rotor-Bearing Systems With Internal Damping. Journal of Engineering for Power, 99(1), 71-76. doi:10.1115/1.3446254Ku, D.-M. (1998). FINITE ELEMENT ANALYSIS OF WHIRL SPEEDS FOR ROTOR-BEARING SYSTEMS WITH INTERNAL DAMPING. Mechanical Systems and Signal Processing, 12(5), 599-610. doi:10.1006/mssp.1998.0159Dimentberg, M. F. (2005). Vibration of a rotating shaft with randomly varying internal damping. Journal of Sound and Vibration, 285(3), 759-765. doi:10.1016/j.jsv.2004.11.025Vatta, F., & Vigliani, A. (2008). Internal damping in rotating shafts. Mechanism and Machine Theory, 43(11), 1376-1384. doi:10.1016/j.mechmachtheory.2007.12.009Rosales, M. B., & Filipich, C. P. (1993). Dynamic Stability of a Spinning Beam Carrying an Axial Dead Load. Journal of Sound and Vibration, 163(2), 283-294. doi:10.1006/jsvi.1993.1165Mazzei, A. J., & Scott, R. A. (2003). Effects of internal viscous damping on the stability of a rotating shaft driven through a universal joint. Journal of Sound and Vibration, 265(4), 863-885. doi:10.1016/s0022-460x(02)01256-7Ehrich, F. F. (1964). Shaft Whirl Induced by Rotor Internal Damping. Journal of Applied Mechanics, 31(2), 279-282. doi:10.1115/1.3629598Vance, J. M., & Lee, J. (1974). Stability of High Speed Rotors With Internal Friction. Journal of Engineering for Industry, 96(3), 960-968. doi:10.1115/1.3438468Vila, P., Baeza, L., Martínez-Casas, J., & Carballeira, J. (2014). Rail corrugation growth accounting for the flexibility and rotation of the wheel set and the non-Hertzian and non-steady-state effects at contact patch. Vehicle System Dynamics, 52(sup1), 92-108. doi:10.1080/00423114.2014.881513Glocker, C., Cataldi-Spinola, E., & Leine, R. I. (2009). Curve squealing of trains: Measurement, modelling and simulation. Journal of Sound and Vibration, 324(1-2), 365-386. doi:10.1016/j.jsv.2009.01.048Bauer, H. F. (1980). Vibration of a rotating uniform beam, part I: Orientation in the axis of rotation. Journal of Sound and Vibration, 72(2), 177-189. doi:10.1016/0022-460x(80)90651-3Shiau, T. N., & Hwang, J. L. (1993). Generalized Polynomial Expansion Method for the Dynamic Analysis of Rotor-Bearing Systems. Journal of Engineering for Gas Turbines and Power, 115(2), 209-217. doi:10.1115/1.2906696Hili, M. A., Fakhfakh, T., & Haddar, M. (2006). Vibration analysis of a rotating flexible shaft–disk system. Journal of Engineering Mathematics, 57(4), 351-363. doi:10.1007/s10665-006-9060-3Young, T. H., Shiau, T. N., & Kuo, Z. H. (2007). Dynamic stability of rotor-bearing systems subjected to random axial forces. Journal of Sound and Vibration, 305(3), 467-480. doi:10.1016/j.jsv.2007.04.016Wang, J., Hurskainen, V.-V., Matikainen, M. K., Sopanen, J., & Mikkola, A. (2017). On the dynamic analysis of rotating shafts using nonlinear superelement and absolute nodal coordinate formulations. Advances in Mechanical Engineering, 9(11), 168781401773267. doi:10.1177/1687814017732672Lee, C.-W. (1993). Vibration Analysis of Rotors. Solid Mechanics and Its Applications. doi:10.1007/978-94-015-8173-8Genta, G. (1999). Vibration of Structures and Machines. doi:10.1007/978-1-4612-1450-2Cheng, C. C., & Lin, J. K. (2003). Modelling a rotating shaft subjected to a high-speed moving force. Journal of Sound and Vibration, 261(5), 955-965. doi:10.1016/s0022-460x(02)01374-

Identification of disease-causing genes using microarray data mining and gene ontology

Background: One of the best and most accurate methods for identifying disease-causing genes is monitoring gene expression values in different samples using microarray technology. One of the shortcomings of microarray data is that they provide a small quantity of samples with respect to the number of genes. This problem reduces the classification accuracy of the methods, so gene selection is essential to improve the predictive accuracy and to identify potential marker genes for a disease. Among numerous existing methods for gene selection, support vector machine-based recursive feature elimination (SVMRFE) has become one of the leading methods, but its performance can be reduced because of the small sample size, noisy data and the fact that the method does not remove redundant genes. Methods: We propose a novel framework for gene selection which uses the advantageous features of conventional methods and addresses their weaknesses. In fact, we have combined the Fisher method and SVMRFE to utilize the advantages of a filtering method as well as an embedded method. Furthermore, we have added a redundancy reduction stage to address the weakness of the Fisher method and SVMRFE. In addition to gene expression values, the proposed method uses Gene Ontology which is a reliable source of information on genes. The use of Gene Ontology can compensate, in part, for the limitations of microarrays, such as having a small number of samples and erroneous measurement results. Results: The proposed method has been applied to colon, Diffuse Large B-Cell Lymphoma (DLBCL) and prostate cancer datasets. The empirical results show that our method has improved classification performance in terms of accuracy, sensitivity and specificity. In addition, the study of the molecular function of selected genes strengthened the hypothesis that these genes are involved in the process of cancer growth. Conclusions: The proposed method addresses the weakness of conventional methods by adding a redundancy reduction stage and utilizing Gene Ontology information. It predicts marker genes for colon, DLBCL and prostate cancer with a high accuracy. The predictions made in this study can serve as a list of candidates for subsequent wet-lab verification and might help in the search for a cure for cancers

Branch Mode Selection during Early Lung Development

Many organs of higher organisms, such as the vascular system, lung, kidney, pancreas, liver and glands, are heavily branched structures. The branching process during lung development has been studied in great detail and is remarkably stereotyped. The branched tree is generated by the sequential, non-random use of three geometrically simple modes of branching (domain branching, planar and orthogonal bifurcation). While many regulatory components and local interactions have been defined an integrated understanding of the regulatory network that controls the branching process is lacking. We have developed a deterministic, spatio-temporal differential-equation based model of the core signaling network that governs lung branching morphogenesis. The model focuses on the two key signaling factors that have been identified in experiments, fibroblast growth factor (FGF10) and sonic hedgehog (SHH) as well as the SHH receptor patched (Ptc). We show that the reported biochemical interactions give rise to a Schnakenberg-type Turing patterning mechanisms that allows us to reproduce experimental observations in wildtype and mutant mice. The kinetic parameters as well as the domain shape are based on experimental data where available. The developed model is robust to small absolute and large relative changes in the parameter values. At the same time there is a strong regulatory potential in that the switching between branching modes can be achieved by targeted changes in the parameter values. We note that the sequence of different branching events may also be the result of different growth speeds: fast growth triggers lateral branching while slow growth favours bifurcations in our model. We conclude that the FGF10-SHH-Ptc1 module is sufficient to generate pattern that correspond to the observed branching modesComment: Initially published at PLoS Comput Bio

Localization of ultrasound in a three-dimensional elastic network

After exactly half a century of Anderson localization, the subject is more alive than ever. Direct observation of Anderson localization of electrons was always hampered by interactions and finite temperatures. Yet, many theoretical breakthroughs were made, highlighted by finite-size scaling, the self-consistent theory and the numerical solution of the Anderson tight-binding model. Theoretical understanding is based on simplified models or approximations and comparison with experiment is crucial. Despite a wealth of new experimental data, with microwaves, light, ultrasound and cold atoms, many questions remain, especially for three dimensions. Here we report the first observation of sound localization in a random three-dimensional elastic network. We study the time-dependent transmission below the mobility edge, and report ``transverse localization'' in three dimensions, which has never been observed previously with any wave. The data are well described by the self-consistent theory of localization. The transmission reveals non-Gaussian statistics, consistent with theoretical predictions.Comment: Final published version, 5 pages, 4 figure

Inner-sphere oxidation of ternary iminodiacetatochromium(III) complexes involving DL-valine and L-arginine as secondary ligands. Isokinetic relationship for the oxidation of ternary iminodiacetato-chromium(III) complexes by periodate

<p>Abstract</p> <p>Background</p> <p>In this paper, the kinetics of oxidation of [Cr^III(HIDA)(Val)(H₂O)₂]⁺and [Cr^III(HIDA)(Arg)(H₂O)₂]⁺(HIDA = iminodiacetic acid, Val = DL-valine and Arg = L-arginine) were studied. The choice of ternary complexes was attributed to two considerations. Firstly, in order to study the effect of the secondary ligands DL-valine and L-arginine on the stability of binary complex [Cr^III(HIDA)(IDA)(H₂O)] towards oxidation. Secondly, transition metal ternary complexes have received particular focus and have been employed in mapping protein surfaces as probes for biological redox centers and in protein capture for both purification and study.</p> <p>Results</p> <p>The results have shown that the reaction is first order with respect to both [IO₄^-] and the complex concentration, and the rate increases over the pH range 2.62 – 3.68 in both cases. The experimental rate law is consistent with a mechanism in which both the deprotonated forms of the complexes [Cr^III(IDA)(Val)(H₂O)₂] and [Cr^III(IDA)(Arg)(H₂O)₂] are significantly more reactive than the conjugate acids. The value of the intramolecular electron transfer rate constant for the oxidation of [Cr^III(HIDA)(Arg)(H₂O)₂]⁺, <it>k</it>₃(1.82 × 10^-3s^-1), is greater than the value of <it>k</it>₁(1.22 × 10^-3s^-1) for the oxidation of [Cr^III(HIDA)(Val)(H₂O)₂]⁺at 45.0°C and <it>I </it>= 0.20 mol dm^-3. It is proposed that electron transfer proceeds through an inner-sphere mechanism <it>via </it>coordination of IO₄^-to chromium(III).</p> <p>Conclusion</p> <p>The oxidation of [Cr^III(HIDA)(Val)(H₂O)₂]⁺and [Cr^III(HIDA)(Arg)(H₂O)₂]⁺by periodate may proceed through an inner-sphere mechanism via two electron transfer giving chromium(VI). The value of the intramolecular electron transfer rate constant for the oxidation of [Cr^III(HIDA)(Arg)(H₂O)₂]⁺, <it>k</it>₃, is greater than the value of <it>k</it>₁for the oxidation of [Cr^III(HIDA)(Val)(H₂O)₂]⁺. A common mechanism for the oxidation of ternary iminodiacetatochromium(III) complexes by periodate is proposed, and this is supported by an excellent isokinetic relationship between ΔH* and ΔS* values for these reactions.</p

Theorems on existence and global dynamics for the Einstein equations

This article is a guide to theorems on existence and global dynamics of solutions of the Einstein equations. It draws attention to open questions in the field. The local-in-time Cauchy problem, which is relatively well understood, is surveyed. Global results for solutions with various types of symmetry are discussed. A selection of results from Newtonian theory and special relativity that offer useful comparisons is presented. Treatments of global results in the case of small data and results on constructing spacetimes with prescribed singularity structure or late-time asymptotics are given. A conjectural picture of the asymptotic behaviour of general cosmological solutions of the Einstein equations is built up. Some miscellaneous topics connected with the main theme are collected in a separate section.Comment: Submitted to Living Reviews in Relativity, major update of Living Rev. Rel. 5 (2002)

The cost of mapping trachoma: data from the Global Trachoma Mapping Project

Background: The Global Trachoma Mapping Project (GTMP) was implemented with the aim of completing the baseline map of trachoma globally. Over 2.6 million people were examined in 1,546 districts across 29 countries between December 2012 and January 2016. The aim of the analysis was to estimate the unit cost and to identify the key cost drivers of trachoma prevalence surveys conducted as part of GTMP. Methodology and principal findings: In-country and global support costs were obtained using GTMP financial records. In-country expenditure was analysed for 1,164 districts across 17 countries. The mean survey cost was $13,113 per district [median:$11,675; IQR=$8,365-$14,618], $17,548 per evaluation unit [median:$15,839; IQR=$10,773-$19,915],$692 per cluster [median:$625; IQR=$452-$847] and $6.0 per person screened [median:$4.9; IQR=$3.7-$7.9]. Survey unit costs varied substantially across settings, and were driven by parameters such as geographic location, demographic characteristics, seasonal effects, and local operational constraints. Analysis by activities showed that fieldwork constituted the largest share of in-country survey costs (73.69%), followed by training of survey teams (11.01%). The main drivers of in-country survey costs were personnel (49.49%) and transportation (43.56%). Global support expenditure for all surveyed districts amounted to $5.1m, which included grant management, epidemiological support, and data stewardship. Conclusion: This study provides the most extensive analysis of the cost of conducting trachoma prevalence surveys to date. The findings can aid planning and budgeting for future trachoma surveys required to measure the impact of trachoma elimination activities. Furthermore, the results of this study can also be used as a cost basis for other disease mapping programmes, where disease or context-specific survey cost data are not available

A meta-analytic review of stand-alone interventions to improve body image

Objective Numerous stand-alone interventions to improve body image have been developed. The present review used meta-analysis to estimate the effectiveness of such interventions, and to identify the specific change techniques that lead to improvement in body image. Methods The inclusion criteria were that (a) the intervention was stand-alone (i.e., solely focused on improving body image), (b) a control group was used, (c) participants were randomly assigned to conditions, and (d) at least one pretest and one posttest measure of body image was taken. Effect sizes were meta-analysed and moderator analyses were conducted. A taxonomy of 48 change techniques used in interventions targeted at body image was developed; all interventions were coded using this taxonomy. Results The literature search identified 62 tests of interventions (N = 3,846). Interventions produced a small-to-medium improvement in body image (d+ = 0.38), a small-to-medium reduction in beauty ideal internalisation (d+ = -0.37), and a large reduction in social comparison tendencies (d+ = -0.72). However, the effect size for body image was inflated by bias both within and across studies, and was reliable but of small magnitude once corrections for bias were applied. Effect sizes for the other outcomes were no longer reliable once corrections for bias were applied. Several features of the sample, intervention, and methodology moderated intervention effects. Twelve change techniques were associated with improvements in body image, and three techniques were contra-indicated. Conclusions The findings show that interventions engender only small improvements in body image, and underline the need for large-scale, high-quality trials in this area. The review identifies effective techniques that could be deployed in future interventions