A homogenization theorem for Langevin systems with an application to Hamiltonian dynamics

This paper studies homogenization of stochastic differential systems. The standard example of this phenomenon is the small mass limit of Hamiltonian systems. We consider this case first from the heuristic point of view, stressing the role of detailed balance and presenting the heuristics based on a multiscale expansion. This is used to propose a physical interpretation of recent results by the authors, as well as to motivate a new theorem proven here. Its main content is a sufficient condition, expressed in terms of solvability of an associated partial differential equation ("the cell problem"), under which the homogenization limit of an SDE is calculated explicitly. The general theorem is applied to a class of systems, satisfying a generalized detailed balance condition with a position-dependent temperature.Comment: 32 page

Secure pseudo-random linear binary sequences generators based on arithmetic polynoms

We present a new approach to constructing of pseudo-random binary sequences (PRS) generators for the purpose of cryptographic data protection, secured from the perpetrator's attacks, caused by generation of masses of hardware errors and faults. The new method is based on use of linear polynomial arithmetic for the realization of systems of boolean characteristic functions of PRS' generators. "Arithmetizatio" of systems of logic formulas has allowed to apply mathematical apparatus of residue systems for multisequencing of the process of PRS generation and organizing control of computing errors, caused by hardware faults. This has guaranteed high security of PRS generator's functioning and, consequently, security of tools for cryptographic data protection based on those PRSs

A Framework for Generalising the Newton Method and Other Iterative Methods from Euclidean Space to Manifolds

The Newton iteration is a popular method for minimising a cost function on Euclidean space. Various generalisations to cost functions defined on manifolds appear in the literature. In each case, the convergence rate of the generalised Newton iteration needed establishing from first principles. The present paper presents a framework for generalising iterative methods from Euclidean space to manifolds that ensures local convergence rates are preserved. It applies to any (memoryless) iterative method computing a coordinate independent property of a function (such as a zero or a local minimum). All possible Newton methods on manifolds are believed to come under this framework. Changes of coordinates, and not any Riemannian structure, are shown to play a natural role in lifting the Newton method to a manifold. The framework also gives new insight into the design of Newton methods in general.Comment: 36 page

INTERVENCIÓN DE ENFERMERÍA ANTE LA AGITACIÓN DE UNA PERSONA DISCAPACITADA INTELECTUAL INSTITUCIONALIZADA

In this article, basic facts are shown regarding the treatment of the psychologically impaired and persons with disturbed behaviour by the nursing personnel. All supported by a nursing care plan. Objectives Educate and Inform nursing professionals in order to assess and intervene in each case in an efficient manner in reference to institutionalized psychologically impaired patients. Methodology Bibliographic examination of the topic and exhibition of the common ways to assist the process. Starting with the use of verbal methods and, if not enough, using chemical measures and as a last resource applying movement restrictions with suitable devices for each subject. Results Presentation of a performance protocol in regards to an institutionalized psychologically impaired patient. Conclusion Nursing professionals need to be educated in order to recognize and understand the manifestations of aggressive impulses when planning more efficient direct care, in this way better adjusting to the needs of the patient. At the same time, inform them about the motivations, the conflicts and the basic impulses of this kind of patients, so that they can better understand the patients’ behavior and feelings.En el presente trabajo se muestran los elementos básicos para el abordaje de un individuo con discapacidad intelectual agitado por parte del personal de enfermería. Todo ello, respaldado por un plan de cuidados de enfermería. Objetivos Formar e informar a los profesionales de enfermería para valorar e intervenir de forma eficiente en cada caso ante un discapacitado intelectual institucionalizado. Metodología Revisión bibliográfica sobre el tema y exposición de las técnicas propias para atender el proceso: primero, con técnicas verbales, y si éstas no son suficientes, medidas de contención química, y por último mediante la restricción de movimientos con elementos adecuados para tal efecto. Resultados Presentación de un protocolo de actuación ante el paciente discapacitado intelectual institucionalizado Conclusiones Es necesario formar al profesional de enfermería para reconocer y comprender las manifestaciones de impulsos agresivos, a la hora de planificar el cuidado directo más eficiente y que se ajuste mejor a las necesidades del paciente. De igual modo instruirles sobre la motivación, el conflicto y los impulsos básicos de este tipo de pacientes, a fin de entender mejor su conducta y los sentimientos que manifiestan

Privacy-Preserving Patient Similarity Learning in a Federated Environment: Development and Analysis

Background: There is an urgent need for the development of global analytic frameworks that can perform analyses in a privacy-preserving federated environment across multiple institutions without privacy leakage. A few studies on the topic of federated medical analysis have been conducted recently with the focus on several algorithms. However, none of them have solved similar patient matching, which is useful for applications such as cohort construction for cross-institution observational studies, disease surveillance, and clinical trials recruitment. Objective: The aim of this study was to present a privacy-preserving platform in a federated setting for patient similarity learning across institutions. Without sharing patient-level information, our model can find similar patients from one hospital to another. Methods: We proposed a federated patient hashing framework and developed a novel algorithm to learn context-specific hash codes to represent patients across institutions. The similarities between patients can be efficiently computed using the resulting hash codes of corresponding patients. To avoid security attack from reverse engineering on the model, we applied homomorphic encryption to patient similarity search in a federated setting. Results: We used sequential medical events extracted from the Multiparameter Intelligent Monitoring in Intensive Care-III database to evaluate the proposed algorithm in predicting the incidence of five diseases independently. Our algorithm achieved averaged area under the curves of 0.9154 and 0.8012 with balanced and imbalanced data, respectively, in ??-nearest neighbor with ??=3. We also confirmed privacy preservation in similarity search by using homomorphic encryption. Conclusions: The proposed algorithm can help search similar patients across institutions effectively to support federated data analysis in a privacy-preserving manner

The Sound of Topology in the AdS/CFT Correspondence

Using the gauge/gravity correspondence, we study the properties of 2-point correlation functions of finite-temperature strongly coupled gauge field theories, defined on a curved space of general spatial topology with a dual black hole description. We derive approximate asymptotic expressions for the correlation functions and their poles, supported by exact numerical calculations, and study their dependence on the dimension of spacetime and the spatial topology. The asymptotic structure of the correlation functions depends on the relation between the spatial curvature and the temperature, and is noticeable when they are of the same order. In the case of a hyperbolic topology, a specific temperature is identified for which exact analytical solutions exist for all types of perturbations. The asymptotic structure of the correlation functions poles is found to behave in a non-smooth manner when approaching this temperature.Comment: 65 pages, LaTeX, 21 figures, 1 table; fixed a small error in subsection 3.

Alkylphenols and polycyclic aromatic hydrocarbons in eastern Mediterranean Spanish coastal marine bivalves

This paper reports the first results on alkylphenol pollution in edible bivalves from the Spanish coast. Two sampling campaigns (July 2006 and July 2007) were carried out to determine the concentration of nonylphenol (NP), octylphenol (OP), and eight polycyclic aromatic hydrocarbons (PAHs) in wild mussels (Mytilus galloprovincialys) and clams (Donax trunculus) at 14 sampling sites along the eastern Mediterranean Spanish coast. The results show that NP is the predominant alkylphenol, being the port of Valencia the most polluted area (up to 147 mu g/kg wet weight in clams). Moving away from the ports the concentration of NP in bivalves decreased. OP concentration was below its detection limit in most of the studied areas and its maximum concentration (6 mu g/kg w/w) was measured in clams from the port of Sagunto. The presence of low levels of PAHs was observed in most of the studied areas. The total PAHs concentration (i.e., sum of the eight measured PAHs) achieved a maximum value of 10.09 mu g/kg w/w in the north coast of Valencia city. The distribution pattern of the individual PAHs showed that both pollution sources petrogenic and pyrolytic were present in the sampled areas. Fluoranthene was the most abundant PAH in mussels while benzo(b)fluoranthene in clams. The maximum concentration of 10 mu g/kg w/w for benzo(a)pyrene established by the European Commission was never reached, indeed sampled bivalves showed concentrations 10 times lower than this reference value. Thus, they can be considered safe for human consumption. Despite the low contamination levels, the results show an overall pollution of bivalves by alkylphenol and PAHs as well as an increment in the number of polluted areas from 2006 to 2007. Thus, periodical sampling campaigns should be carried out to monitor the long-term tendency of these toxic and persistent pollutants. © 2010 Springer Science+Business Media B.V.Financial support from Conselleria de Medio Ambiente, Agua, Urbanismo y Vivienda de la Generalitat Valenciana (Application of Water Framework Directive 2000/60/EC on endocrine disruptors and priority substances in coastal areas in the Comunidad Valenciana) is gratefully acknowledged.Bouzas Blanco, A.; Aguado García, D.; Martí Ortega, N.; Pastor, J.; Herraez, R.; Campins, P.; Seco Torrecillas, A. (2011). Alkylphenols and polycyclic aromatic hydrocarbons in eastern Mediterranean Spanish coastal marine bivalves. Environmental Monitoring and Assessment. 176(1-4):169-181. doi:10.1007/s10661-010-1574-5S1691811761-4Antizar-Ladislao, B. (2009). Polycyclic aromatic hydrocarbons, polycholirnated biphenyls, phthalates and organotins in northern Atlantic Spain’s coastal marine sediments. 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Distribution of polycyclic aromatic hydrocarbons (PAHs) and phenolic endocrine disrupting chemicals in South and Southeast Asian mussels. Environmental Monitoring Assessment, 135, 423–440.Jackson, J. E. (2003). A user’s guide to principal components. NJ: Wiley.Khairy, M. A., Kolb, M., Mostafa, A. R., EL-Fiky, A., & Bahadir, M. (2009). Risk assessment of polycyclic aromatic hydrocarbons in a Mediterranean semienclosed basin affected by human activities (Abu Qui Bay, Egypt). Journal of Hazardous Material. doi: 10.1016/j.jhazmat.2009.04.084 .Koh, C. H., Khim, J. S., Kannan, K., Villeneuve, D. L., Senthil Kumar, K., & Giesy, J. P. (2004). Polychlorinated dibenzo-p-dioxins (PCDDs), dibenzofurans (PCDFs), biphenyls (PCBs), and polycyclic aromatic hydrocarbons (PAHs) and 2,3,7,8-TCDD equivalents (TEQs) in sediment from the Hyeongsan River, Korea. Environmental Pollution, 132, 489–501.Law, R. J., Kelly, C. A., Baker, K. L., Langford, K. H., & Bartlett, T. (2002). 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Numerical approximations of second-order matrix differential equations using higher-degree splines

Many studies of mechanical systems in engineering are based on second-order matrix models. This work discusses the second-order generalization of previous research on matrix differential equations dealing with the construction of approximate solutions for non-stiff initial problems Y 00(x) = f(x, Y (x), Y 0 (x)) using higher-degree matrix splines without any dimensional increase. An estimation of the approximation error for some illustrative examples are presented by using Mathematica. Several MatLab functions have also been developed, comparing, under equal conditions, accuracy and execution times with built-in MatLab functions. Experimental results show the advantages of solving the above initial problem by using the implemented MatLab functions.The authors wish to thank for financial support by the Universidad Politecnica de Valencia [grant number PAID-06-11-2020].Defez Candel, E.; Tung ., MM.; Solis Lozano, FJ.; Ibáñez González, JJ. (2015). Numerical approximations of second-order matrix differential equations using higher-degree splines. Linear and Multilinear Algebra. 63(3):472-489. https://doi.org/10.1080/03081087.2013.873427S472489633Loscalzo, F. R., & Talbot, T. D. (1967). Spline Function Approximations for Solutions of Ordinary Differential Equations. SIAM Journal on Numerical Analysis, 4(3), 433-445. doi:10.1137/0704038Al-Said, E. A. (2001). The use of cubic splines in the numerical solution of a system of second-order boundary value problems. Computers & Mathematics with Applications, 42(6-7), 861-869. doi:10.1016/s0898-1221(01)00204-8Al-Said, E. A., & Noor, M. A. (2003). Cubic splines method for a system of third-order boundary value problems. Applied Mathematics and Computation, 142(2-3), 195-204. doi:10.1016/s0096-3003(02)00294-1Kadalbajoo, M. K., & Patidar, K. C. (2002). Numerical solution of singularly perturbed two-point boundary value problems by spline in tension. Applied Mathematics and Computation, 131(2-3), 299-320. doi:10.1016/s0096-3003(01)00146-1Micula, G., & Revnic, A. (2000). An implicit numerical spline method for systems for ODEs. Applied Mathematics and Computation, 111(1), 121-132. doi:10.1016/s0096-3003(98)10111-xDefez, E., Soler, L., Hervás, A., & Santamaría, C. (2005). Numerical solution ofmatrix differential models using cubic matrix splines. Computers & Mathematics with Applications, 50(5-6), 693-699. doi:10.1016/j.camwa.2005.04.012Defez, E., Hervás, A., Soler, L., & Tung, M. M. (2007). Numerical solutions of matrix differential models using cubic matrix splines II. Mathematical and Computer Modelling, 46(5-6), 657-669. doi:10.1016/j.mcm.2006.11.027Ascher, U., Pruess, S., & Russell, R. D. (1983). On Spline Basis Selection for Solving Differential Equations. SIAM Journal on Numerical Analysis, 20(1), 121-142. doi:10.1137/0720009Brunner, H. (2004). On the Divergence of Collocation Solutions in Smooth Piecewise Polynomial Spaces for Volterra Integral Equations. BIT Numerical Mathematics, 44(4), 631-650. doi:10.1007/s10543-004-3828-5Tung, M. M., Defez, E., & Sastre, J. (2008). Numerical solutions of second-order matrix models using cubic-matrix splines. Computers & Mathematics with Applications, 56(10), 2561-2571. doi:10.1016/j.camwa.2008.05.022Defez, E., Tung, M. M., Ibáñez, J. J., & Sastre, J. (2012). Approximating and computing nonlinear matrix differential models. Mathematical and Computer Modelling, 55(7-8), 2012-2022. doi:10.1016/j.mcm.2011.11.060Claeyssen, J. R., Canahualpa, G., & Jung, C. (1999). A direct approach to second-order matrix non-classical vibrating equations. Applied Numerical Mathematics, 30(1), 65-78. doi:10.1016/s0168-9274(98)00085-3Froese, C. (1963). NUMERICAL SOLUTION OF THE HARTREE–FOCK EQUATIONS. Canadian Journal of Physics, 41(11), 1895-1910. doi:10.1139/p63-189Marzulli, P. (1991). Global error estimates for the standard parallel shooting method. Journal of Computational and Applied Mathematics, 34(2), 233-241. doi:10.1016/0377-0427(91)90045-lShore, B. W. (1973). Comparison of matrix methods applied to the radial Schrödinger eigenvalue equation: The Morse potential. The Journal of Chemical Physics, 59(12), 6450-6463. doi:10.1063/1.1680025ZHANG, J. F. (2002). OPTIMAL CONTROL FOR MECHANICAL VIBRATION SYSTEMS BASED ON SECOND-ORDER MATRIX EQUATIONS. Mechanical Systems and Signal Processing, 16(1), 61-67. doi:10.1006/mssp.2001.1441Flett, T. M. (1980). Differential Analysis. doi:10.1017/cbo978051189719

Structured squaring down and zero assignment

The problem of zero assignment by squaring down is considered for a system of p-inputs, n-outputs and n-states (m > p), where not all outputs are free variables for design. We consider the case where a k-subset of outputs is preserved in the new output set, and the rest are recombined to produce a total new set of p-outputs. New invariants for the problem are introduced which include a new class of fixed zeros and the methodology of the global linearization, developed originally for the output feedback pole assignment problem, is applied to this restricted form of the squaring down problem. It is shown that the problem can be solved generically if (p − k)(m − p) > δ*, where k (k < p) is the number of fixed outputs and δ* is a system and compensation scheme invariant, which is defined as the restricted Forney degree