907 resultados para Discrete supported Rail


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The paper studies the influence of rail weld dip on wheel-rail contact dynamics, with particular reference to freight trains where it is important to increase the operating speed and also the load transported. This has produced a very precise model, albeit simple and cost-effective, which has enabled train-track dynamic interactions over rail welds to be studied to make it possible to quantify the influence on dynamic forces and displacements of the welding geometry; of the position of the weld relative to the sleeper; of the vehicle's speed; and of the axle load and wheelset unsprung mass. It is a vertical model on the spatial domain and is drawn up in a simple fashion from vertical track receptances. For the type of track and vehicle used, the results obtained enable the quantification of increases in wheel-rail contact forces due to the new speed and load conditions.

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Trabalho Final de Mestrado para a obtenção do grau de Mestre em Engenharia Civil, na Área de Especialização de Vias de Comunicação e Transportes

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The response of high-speed bridges at resonance, particularly under flexural vibrations, constitutes a subject of research for many scientists and engineers at the moment. The topic is of great interest because, as a matter of fact, such kind of behaviour is not unlikely to happen due to the elevated operating speeds of modern rains, which in many cases are equal to or even exceed 300 km/h ( [1,2]). The present paper addresses the subject of the evolution of the wheel-rail contact forces during resonance situations in simply supported bridges. Based on a dimensionless formulation of the equations of motion presented in [4], very similar to the one introduced by Klasztorny and Langer in [3], a parametric study is conducted and the contact forces in realistic situations analysed in detail. The effects of rail and wheel irregularities are not included in the model. The bridge is idealised as an Euler-Bernoulli beam, while the train is simulated by a system consisting of rigid bodies, springs and dampers. The situations such that a severe reduction of the contact force could take place are identified and compared with typical situations in actual bridges. To this end, the simply supported bridge is excited at resonace by means of a theoretical train consisting of 15 equidistant axles. The mechanical characteristics of all axles (unsprung mass, semi-sprung mass, and primary suspension system) are identical. This theoretical train permits the identification of the key parameters having an influence on the wheel-rail contact forces. In addition, a real case of a 17.5 m bridges traversed by the Eurostar train is analysed and checked against the theoretical results. The influence of three fundamental parameters is investigated in great detail: a) the ratio of the fundamental frequency of the bridge and natural frequency of the primary suspension of the vehicle; b) the ratio of the total mass of the bridge and the semi-sprung mass of the vehicle and c) the ratio between the length of the bridge and the characteristic distance between consecutive axles. The main conclusions derived from the investigation are: The wheel-rail contact forces undergo oscillations during the passage of the axles over the bridge. During resonance, these oscillations are more severe for the rear wheels than for the front ones. If denotes the span of a simply supported bridge, and the characteristic distance between consecutive groups of loads, the lower the value of , the greater the oscillations of the contact forces at resonance. For or greater, no likelihood of loss of wheel-rail contact has been detected. The ratio between the frequency of the primary suspension of the vehicle and the fundamental frequency of the bridge is denoted by (frequency ratio), and the ratio of the semi-sprung mass of the vehicle (mass of the bogie) and the total mass of the bridge is denoted by (mass ratio). For any given frequency ratio, the greater the mass ratio, the greater the oscillations of the contact forces at resonance. The oscillations of the contact forces at resonance, and therefore the likelihood of loss of wheel-rail contact, present a minimum for approximately between 0.5 and 1. For lower or higher values of the frequency ratio the oscillations of the contact forces increase. Neglecting the possible effects of torsional vibrations, the metal or composite bridges with a low linear mass have been found to be the ones where the contact forces may suffer the most severe oscillations. If single-track, simply supported, composite or metal bridges were used in high-speed lines, and damping ratios below 1% were expected, the minimum contact forces at resonance could drop to dangerous values. Nevertheless, this kind of structures is very unusual in modern high-speed railway lines.

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We investigate the mobility of nonlinear localized modes in a generalized discrete Ginzburg-Landau-type model, describing a one-dimensional waveguide array in an active Kerr medium with intrinsic, saturable gain and damping. It is shown that exponentially localized, traveling discrete dissipative breather-solitons may exist as stable attractors supported only by intrinsic properties of the medium, i.e., in the absence of any external field or symmetry-breaking perturbations. Through an interplay by the gain and damping effects, the moving soliton may overcome the Peierls-Nabarro barrier, present in the corresponding conservative system, by self-induced time-periodic oscillations of its power (norm) and energy (Hamiltonian), yielding exponential decays to zero with different rates in the forward and backward directions. In certain parameter windows, bistability appears between fast modes with small oscillations and slower, large-oscillation modes. The velocities and the oscillation periods are typically related by lattice commensurability and exhibit period-doubling bifurcations to chaotically "walking" modes under parameter variations. If the model is augmented by intersite Kerr nonlinearity, thereby reducing the Peierls-Nabarro barrier of the conservative system, the existence regime for moving solitons increases considerably, and a richer scenario appears including Hopf bifurcations to incommensurately moving solutions and phase-locking intervals. Stable moving breathers also survive in the presence of weak disorder. © 2014 American Physical Society.

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Transportation plays a major role in the gross domestic product of various nations. There are, however, many obstacles hindering the transportation sector. Cost-efficiency along with proper delivery times, high frequency and reliability are not a straightforward task. Furthermore, environmental friendliness has increased the importance of the whole transportation sector. This development will change roles inside the transportation sector. Even now, but especially in the future, decisions regarding the transportation sector will be partly based on emission levels and other externalities originating from transportation in addition to pure transportation costs. There are different factors, which could have an impact on the transportation sector. IMO’s sulphur regulation is estimated to increase the costs of short sea shipping in the Baltic Sea. Price development of energy could change the roles of different transport modes. Higher awareness of the environmental impacts originating from transportation could also have an impact on the price level of more polluting transport modes. According to earlier research, increased inland transportation, modal shift and slowsteaming can be possible results of these changes in the transportation sector. Possible changes in the transportation sector and ways to settle potential obstacles are studied in this dissertation. Furthermore, means to improve cost-efficiency and to decrease environmental impacts originating from transportation are researched. Hypothetical Finnish dry port network and Rail Baltica transport corridor are studied in this dissertation. Benefits and disadvantages are studied with different methodologies. These include gravitational models, which were optimized with linear integer programming, discrete-event and system dynamics simulation, an interview study and a case study. Geographical focus is on the Baltic Sea Region, but the results can be adapted to other geographical locations with discretion. Results indicate that the dry port concept has benefits, but optimization regarding the location and the amount of dry ports plays an important role. In addition, the utilization of dry ports for freight transportation should be carefully operated, since only a certain amount of total freight volume can be cost-efficiently transported through dry ports. If dry ports are created and located without proper planning, they could actually increase transportation costs and delivery times of the whole transportation system. With an optimized dry port network, transportation costs can be lowered in Finland with three to five dry ports. Environmental impacts can be lowered with up to nine dry ports. If more dry ports are added to the system, the benefits become very minor, i.e. payback time of investments becomes extremely long. Furthermore, dry port network could support major transport corridors such as Rail Baltica. Based on an analysis of statistics and interview study, there could be enough freight volume available for Rail Baltica, especially, if North-West Russia is part of the Northern end of the corridor. Transit traffic to and from Russia (especially through the Baltic States) plays a large role. It could be possible to increase transit traffic through Finland by connecting the potential Finnish dry port network and the studied transport corridor. Additionally, sulphur emission regulation is assumed to increase the attractiveness of Rail Baltica in the year 2015. Part of the transit traffic could be rerouted along Rail Baltica instead of the Baltic Sea, since the price level of sea transport could increase due to the sulphur regulation. Both, the hypothetical Finnish dry port network and Rail Baltica transport corridor could benefit each other. The dry port network could gain more market share from Russia, but also from Central Europe, which is the other end of Rail Baltica. In addition, further Eastern countries could also be connected to achieve higher potential freight volume by rail.

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This work is supported by Brazilian agencies Fapesp, CAPES and CNPq

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Until few years ago, 3D modelling was a topic confined into a professional environment. Nowadays technological innovations, the 3D printer among all, have attracted novice users to this application field. This sudden breakthrough was not supported by adequate software solutions. The 3D editing tools currently available do not assist the non-expert user during the various stages of generation, interaction and manipulation of 3D virtual models. This is mainly due to the current paradigm that is largely supported by two-dimensional input/output devices and strongly affected by obvious geometrical constraints. We have identified three main phases that characterize the creation and management of 3D virtual models. We investigated these directions evaluating and simplifying the classic editing techniques in order to propose more natural and intuitive tools in a pure 3D modelling environment. In particular, we focused on freehand sketch-based modelling to create 3D virtual models, interaction and navigation in a 3D modelling environment and advanced editing tools for free-form deformation and objects composition. To pursuing these goals we wondered how new gesture-based interaction technologies can be successfully employed in a 3D modelling environments, how we could improve the depth perception and the interaction in 3D environments and which operations could be developed to simplify the classical virtual models editing paradigm. Our main aims were to propose a set of solutions with which a common user can realize an idea in a 3D virtual model, drawing in the air just as he would on paper. Moreover, we tried to use gestures and mid-air movements to explore and interact in 3D virtual environment, and we studied simple and effective 3D form transformations. The work was carried out adopting the discrete representation of the models, thanks to its intuitiveness, but especially because it is full of open challenges.

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Intestinal dendritic cells (DCs) are believed to sample and present commensal bacteria to the gut-associated immune system to maintain immune homeostasis. How antigen sampling pathways handle intestinal pathogens remains elusive. We present a murine colitogenic Salmonella infection model that is highly dependent on DCs. Conditional DC depletion experiments revealed that intestinal virulence of S. Typhimurium SL1344 DeltainvG mutant lacking a functional type 3 secretion system-1 (DeltainvG)critically required DCs for invasion across the epithelium. The DC-dependency was limited to the early phase of infection when bacteria colocalized with CD11c(+)CX3CR1(+) mucosal DCs. At later stages, the bacteria became associated with other (CD11c(-)CX3CR1(-)) lamina propria cells, DC depletion no longer attenuated the pathology, and a MyD88-dependent mucosal inflammation was initiated. Using bone marrow chimeric mice, we showed that the MyD88 signaling within hematopoietic cells, which are distinct from DCs, was required and sufficient for induction of the colitis. Moreover, MyD88-deficient DCs supported transepithelial uptake of the bacteria and the induction of MyD88-dependent colitis. These results establish that pathogen sampling by DCs is a discrete, and MyD88-independent, step during the initiation of a mucosal innate immune response to bacterial infection in vivo.

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This work presents a method for the analysis of timber composite beams which considers the slip in the connection system, based on assembling the flexibility matrix of the whole structure. This method is based on one proposed by Tommola and Jutila (2001). This paper extends the method to the case of a gap between two pieces with an arbitrary location at the first connector, which notably broadens its practical application. The addition of the gap makes it possible to model a cracked zone in concrete topping, as well as the case in which forming produces the gap. The consideration of induced stresses due to changes in temperature and moisture content is also described, while the concept of equivalent eccentricity is generalized. This method has important advantages in connection with the current European Standard EN 1995-1-1: 2004, as it is able to deal with any type of load, variable section, discrete and non-regular connection systems, a gap between the two pieces, and variations in temperature and moisture content. Although it could be applied to any structural system, it is specially suited for the case of simple supported and continuous beams. Working examples are presented at the end, showing that the arrangement of the connection notably modifies shear force distribution. A first interpretation of the results is made on the basis of the strut and tie theory. The examples prove that the use of EC-5 is unsafe when, as a rule of thumb, the strut or compression field between the support and the first connector is at an angle with the axis of the beam of less than 60º.

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Urban areas benefit from significant improvements in accessibility when a new high speed rail (HSR) project is built. These improvements, which are due mainly to a rise in efficiency, produce locational advantagesand increase the attractiveness of these cities, thereby possibly enhancing their competitivenessand economic growth. However, there may be equity issues at stake, as the main accessibility benefits are primarily concentrated in urban areas with a HSR station, whereas other locations obtain only limited benefits. HSR extensions may contribute to an increase in spatial imbalance and lead to more polarized patterns of spatial development. Procedures for assessing the spatial impacts of HSR must therefore follow a twofold approach which addresses issues of both efficiency and equity. This analysis can be made by jointly assessing both the magnitude and distribution of the accessibility improvements deriving from a HSR project. This paper describes an assessment methodology for HSR projects which follows this twofold approach. The procedure uses spatial impact analysis techniques and is based on the computation of accessibility indicators, supported by a Geographical Information System (GIS). Efficiency impacts are assessed in terms of the improvements in accessibility resulting from the HSR project, with a focus on major urban areas; and spatial equity implications are derived from changes in the distribution of accessibility values among these urban agglomerations.

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Esta tesis doctoral se centra principalmente en técnicas de ataque y contramedidas relacionadas con ataques de canal lateral (SCA por sus siglas en inglés), que han sido propuestas dentro del campo de investigación académica desde hace 17 años. Las investigaciones relacionadas han experimentado un notable crecimiento en las últimas décadas, mientras que los diseños enfocados en la protección sólida y eficaz contra dichos ataques aún se mantienen como un tema de investigación abierto, en el que se necesitan iniciativas más confiables para la protección de la información persona de empresa y de datos nacionales. El primer uso documentado de codificación secreta se remonta a alrededor de 1700 B.C., cuando los jeroglíficos del antiguo Egipto eran descritos en las inscripciones. La seguridad de la información siempre ha supuesto un factor clave en la transmisión de datos relacionados con inteligencia diplomática o militar. Debido a la evolución rápida de las técnicas modernas de comunicación, soluciones de cifrado se incorporaron por primera vez para garantizar la seguridad, integridad y confidencialidad de los contextos de transmisión a través de cables sin seguridad o medios inalámbricos. Debido a las restricciones de potencia de cálculo antes de la era del ordenador, la técnica de cifrado simple era un método más que suficiente para ocultar la información. Sin embargo, algunas vulnerabilidades algorítmicas pueden ser explotadas para restaurar la regla de codificación sin mucho esfuerzo. Esto ha motivado nuevas investigaciones en el área de la criptografía, con el fin de proteger el sistema de información ante sofisticados algoritmos. Con la invención de los ordenadores se ha acelerado en gran medida la implementación de criptografía segura, que ofrece resistencia eficiente encaminada a obtener mayores capacidades de computación altamente reforzadas. Igualmente, sofisticados cripto-análisis han impulsado las tecnologías de computación. Hoy en día, el mundo de la información ha estado involucrado con el campo de la criptografía, enfocada a proteger cualquier campo a través de diversas soluciones de cifrado. Estos enfoques se han fortalecido debido a la unificación optimizada de teorías matemáticas modernas y prácticas eficaces de hardware, siendo posible su implementación en varias plataformas (microprocesador, ASIC, FPGA, etc.). Las necesidades y requisitos de seguridad en la industria son las principales métricas de conducción en el diseño electrónico, con el objetivo de promover la fabricación de productos de gran alcance sin sacrificar la seguridad de los clientes. Sin embargo, una vulnerabilidad en la implementación práctica encontrada por el Prof. Paul Kocher, et al en 1996 implica que un circuito digital es inherentemente vulnerable a un ataque no convencional, lo cual fue nombrado posteriormente como ataque de canal lateral, debido a su fuente de análisis. Sin embargo, algunas críticas sobre los algoritmos criptográficos teóricamente seguros surgieron casi inmediatamente después de este descubrimiento. En este sentido, los circuitos digitales consisten típicamente en un gran número de celdas lógicas fundamentales (como MOS - Metal Oxide Semiconductor), construido sobre un sustrato de silicio durante la fabricación. La lógica de los circuitos se realiza en función de las innumerables conmutaciones de estas células. Este mecanismo provoca inevitablemente cierta emanación física especial que puede ser medida y correlacionada con el comportamiento interno del circuito. SCA se puede utilizar para revelar datos confidenciales (por ejemplo, la criptografía de claves), analizar la arquitectura lógica, el tiempo e incluso inyectar fallos malintencionados a los circuitos que se implementan en sistemas embebidos, como FPGAs, ASICs, o tarjetas inteligentes. Mediante el uso de la comparación de correlación entre la cantidad de fuga estimada y las fugas medidas de forma real, información confidencial puede ser reconstruida en mucho menos tiempo y computación. Para ser precisos, SCA básicamente cubre una amplia gama de tipos de ataques, como los análisis de consumo de energía y radiación ElectroMagnética (EM). Ambos se basan en análisis estadístico y, por lo tanto, requieren numerosas muestras. Los algoritmos de cifrado no están intrínsecamente preparados para ser resistentes ante SCA. Es por ello que se hace necesario durante la implementación de circuitos integrar medidas que permitan camuflar las fugas a través de "canales laterales". Las medidas contra SCA están evolucionando junto con el desarrollo de nuevas técnicas de ataque, así como la continua mejora de los dispositivos electrónicos. Las características físicas requieren contramedidas sobre la capa física, que generalmente se pueden clasificar en soluciones intrínsecas y extrínsecas. Contramedidas extrínsecas se ejecutan para confundir la fuente de ataque mediante la integración de ruido o mala alineación de la actividad interna. Comparativamente, las contramedidas intrínsecas están integradas en el propio algoritmo, para modificar la aplicación con el fin de minimizar las fugas medibles, o incluso hacer que dichas fugas no puedan ser medibles. Ocultación y Enmascaramiento son dos técnicas típicas incluidas en esta categoría. Concretamente, el enmascaramiento se aplica a nivel algorítmico, para alterar los datos intermedios sensibles con una máscara de manera reversible. A diferencia del enmascaramiento lineal, las operaciones no lineales que ampliamente existen en criptografías modernas son difíciles de enmascarar. Dicho método de ocultación, que ha sido verificado como una solución efectiva, comprende principalmente la codificación en doble carril, que está ideado especialmente para aplanar o eliminar la fuga dependiente de dato en potencia o en EM. En esta tesis doctoral, además de la descripción de las metodologías de ataque, se han dedicado grandes esfuerzos sobre la estructura del prototipo de la lógica propuesta, con el fin de realizar investigaciones enfocadas a la seguridad sobre contramedidas de arquitectura a nivel lógico. Una característica de SCA reside en el formato de las fuentes de fugas. Un típico ataque de canal lateral se refiere al análisis basado en la potencia, donde la capacidad fundamental del transistor MOS y otras capacidades parásitas son las fuentes esenciales de fugas. Por lo tanto, una lógica robusta resistente a SCA debe eliminar o mitigar las fugas de estas micro-unidades, como las puertas lógicas básicas, los puertos I/O y las rutas. Las herramientas EDA proporcionadas por los vendedores manipulan la lógica desde un nivel más alto, en lugar de realizarlo desde el nivel de puerta, donde las fugas de canal lateral se manifiestan. Por lo tanto, las implementaciones clásicas apenas satisfacen estas necesidades e inevitablemente atrofian el prototipo. Por todo ello, la implementación de un esquema de diseño personalizado y flexible ha de ser tomado en cuenta. En esta tesis se presenta el diseño y la implementación de una lógica innovadora para contrarrestar SCA, en la que se abordan 3 aspectos fundamentales: I. Se basa en ocultar la estrategia sobre el circuito en doble carril a nivel de puerta para obtener dinámicamente el equilibrio de las fugas en las capas inferiores; II. Esta lógica explota las características de la arquitectura de las FPGAs, para reducir al mínimo el gasto de recursos en la implementación; III. Se apoya en un conjunto de herramientas asistentes personalizadas, incorporadas al flujo genérico de diseño sobre FPGAs, con el fin de manipular los circuitos de forma automática. El kit de herramientas de diseño automático es compatible con la lógica de doble carril propuesta, para facilitar la aplicación práctica sobre la familia de FPGA del fabricante Xilinx. En este sentido, la metodología y las herramientas son flexibles para ser extendido a una amplia gama de aplicaciones en las que se desean obtener restricciones mucho más rígidas y sofisticadas a nivel de puerta o rutado. En esta tesis se realiza un gran esfuerzo para facilitar el proceso de implementación y reparación de lógica de doble carril genérica. La viabilidad de las soluciones propuestas es validada mediante la selección de algoritmos criptográficos ampliamente utilizados, y su evaluación exhaustiva en comparación con soluciones anteriores. Todas las propuestas están respaldadas eficazmente a través de ataques experimentales con el fin de validar las ventajas de seguridad del sistema. El presente trabajo de investigación tiene la intención de cerrar la brecha entre las barreras de implementación y la aplicación efectiva de lógica de doble carril. En esencia, a lo largo de esta tesis se describirá un conjunto de herramientas de implementación para FPGAs que se han desarrollado para trabajar junto con el flujo de diseño genérico de las mismas, con el fin de lograr crear de forma innovadora la lógica de doble carril. Un nuevo enfoque en el ámbito de la seguridad en el cifrado se propone para obtener personalización, automatización y flexibilidad en el prototipo de circuito de bajo nivel con granularidad fina. Las principales contribuciones del presente trabajo de investigación se resumen brevemente a continuación: Lógica de Precharge Absorbed-DPL logic: El uso de la conversión de netlist para reservar LUTs libres para ejecutar la señal de precharge y Ex en una lógica DPL. Posicionamiento entrelazado Row-crossed con pares idénticos de rutado en redes de doble carril, lo que ayuda a aumentar la resistencia frente a la medición EM selectiva y mitigar los impactos de las variaciones de proceso. Ejecución personalizada y herramientas de conversión automática para la generación de redes idénticas para la lógica de doble carril propuesta. (a) Para detectar y reparar conflictos en las conexiones; (b) Detectar y reparar las rutas asimétricas. (c) Para ser utilizado en otras lógicas donde se requiere un control estricto de las interconexiones en aplicaciones basadas en Xilinx. Plataforma CPA de pruebas personalizadas para el análisis de EM y potencia, incluyendo la construcción de dicha plataforma, el método de medición y análisis de los ataques. Análisis de tiempos para cuantificar los niveles de seguridad. División de Seguridad en la conversión parcial de un sistema de cifrado complejo para reducir los costes de la protección. Prueba de concepto de un sistema de calefacción auto-adaptativo para mitigar los impactos eléctricos debido a la variación del proceso de silicio de manera dinámica. La presente tesis doctoral se encuentra organizada tal y como se detalla a continuación: En el capítulo 1 se abordan los fundamentos de los ataques de canal lateral, que abarca desde conceptos básicos de teoría de modelos de análisis, además de la implementación de la plataforma y la ejecución de los ataques. En el capítulo 2 se incluyen las estrategias de resistencia SCA contra los ataques de potencia diferencial y de EM. Además de ello, en este capítulo se propone una lógica en doble carril compacta y segura como contribución de gran relevancia, así como también se presentará la transformación lógica basada en un diseño a nivel de puerta. Por otra parte, en el Capítulo 3 se abordan los desafíos relacionados con la implementación de lógica en doble carril genérica. Así mismo, se describirá un flujo de diseño personalizado para resolver los problemas de aplicación junto con una herramienta de desarrollo automático de aplicaciones propuesta, para mitigar las barreras de diseño y facilitar los procesos. En el capítulo 4 se describe de forma detallada la elaboración e implementación de las herramientas propuestas. Por otra parte, la verificación y validaciones de seguridad de la lógica propuesta, así como un sofisticado experimento de verificación de la seguridad del rutado, se describen en el capítulo 5. Por último, un resumen de las conclusiones de la tesis y las perspectivas como líneas futuras se incluyen en el capítulo 6. Con el fin de profundizar en el contenido de la tesis doctoral, cada capítulo se describe de forma más detallada a continuación: En el capítulo 1 se introduce plataforma de implementación hardware además las teorías básicas de ataque de canal lateral, y contiene principalmente: (a) La arquitectura genérica y las características de la FPGA a utilizar, en particular la Xilinx Virtex-5; (b) El algoritmo de cifrado seleccionado (un módulo comercial Advanced Encryption Standard (AES)); (c) Los elementos esenciales de los métodos de canal lateral, que permiten revelar las fugas de disipación correlacionadas con los comportamientos internos; y el método para recuperar esta relación entre las fluctuaciones físicas en los rastros de canal lateral y los datos internos procesados; (d) Las configuraciones de las plataformas de pruebas de potencia / EM abarcadas dentro de la presente tesis. El contenido de esta tesis se amplia y profundiza a partir del capítulo 2, en el cual se abordan varios aspectos claves. En primer lugar, el principio de protección de la compensación dinámica de la lógica genérica de precarga de doble carril (Dual-rail Precharge Logic-DPL) se explica mediante la descripción de los elementos compensados a nivel de puerta. En segundo lugar, la lógica PA-DPL es propuesta como aportación original, detallando el protocolo de la lógica y un caso de aplicación. En tercer lugar, dos flujos de diseño personalizados se muestran para realizar la conversión de doble carril. Junto con ello, se aclaran las definiciones técnicas relacionadas con la manipulación por encima de la netlist a nivel de LUT. Finalmente, una breve discusión sobre el proceso global se aborda en la parte final del capítulo. El Capítulo 3 estudia los principales retos durante la implementación de DPLs en FPGAs. El nivel de seguridad de las soluciones de resistencia a SCA encontradas en el estado del arte se ha degenerado debido a las barreras de implantación a través de herramientas EDA convencionales. En el escenario de la arquitectura FPGA estudiada, se discuten los problemas de los formatos de doble carril, impactos parásitos, sesgo tecnológico y la viabilidad de implementación. De acuerdo con estas elaboraciones, se plantean dos problemas: Cómo implementar la lógica propuesta sin penalizar los niveles de seguridad, y cómo manipular un gran número de celdas y automatizar el proceso. El PA-DPL propuesto en el capítulo 2 se valida con una serie de iniciativas, desde características estructurales como doble carril entrelazado o redes de rutado clonadas, hasta los métodos de aplicación tales como las herramientas de personalización y automatización de EDA. Por otra parte, un sistema de calefacción auto-adaptativo es representado y aplicado a una lógica de doble núcleo, con el fin de ajustar alternativamente la temperatura local para equilibrar los impactos negativos de la variación del proceso durante la operación en tiempo real. El capítulo 4 se centra en los detalles de la implementación del kit de herramientas. Desarrollado sobre una API third-party, el kit de herramientas personalizado es capaz de manipular los elementos de la lógica de circuito post P&R ncd (una versión binaria ilegible del xdl) convertido al formato XDL Xilinx. El mecanismo y razón de ser del conjunto de instrumentos propuestos son cuidadosamente descritos, que cubre la detección de enrutamiento y los enfoques para la reparación. El conjunto de herramientas desarrollado tiene como objetivo lograr redes de enrutamiento estrictamente idénticos para la lógica de doble carril, tanto para posicionamiento separado como para el entrelazado. Este capítulo particularmente especifica las bases técnicas para apoyar las implementaciones en los dispositivos de Xilinx y su flexibilidad para ser utilizado sobre otras aplicaciones. El capítulo 5 se enfoca en la aplicación de los casos de estudio para la validación de los grados de seguridad de la lógica propuesta. Se discuten los problemas técnicos detallados durante la ejecución y algunas nuevas técnicas de implementación. (a) Se discute el impacto en el proceso de posicionamiento de la lógica utilizando el kit de herramientas propuesto. Diferentes esquemas de implementación, tomando en cuenta la optimización global en seguridad y coste, se verifican con los experimentos con el fin de encontrar los planes de posicionamiento y reparación optimizados; (b) las validaciones de seguridad se realizan con los métodos de correlación y análisis de tiempo; (c) Una táctica asintótica se aplica a un núcleo AES sobre BCDL estructurado para validar de forma sofisticada el impacto de enrutamiento sobre métricas de seguridad; (d) Los resultados preliminares utilizando el sistema de calefacción auto-adaptativa sobre la variación del proceso son mostrados; (e) Se introduce una aplicación práctica de las herramientas para un diseño de cifrado completa. Capítulo 6 incluye el resumen general del trabajo presentado dentro de esta tesis doctoral. Por último, una breve perspectiva del trabajo futuro se expone, lo que puede ampliar el potencial de utilización de las contribuciones de esta tesis a un alcance más allá de los dominios de la criptografía en FPGAs. ABSTRACT This PhD thesis mainly concentrates on countermeasure techniques related to the Side Channel Attack (SCA), which has been put forward to academic exploitations since 17 years ago. The related research has seen a remarkable growth in the past decades, while the design of solid and efficient protection still curiously remain as an open research topic where more reliable initiatives are required for personal information privacy, enterprise and national data protections. The earliest documented usage of secret code can be traced back to around 1700 B.C., when the hieroglyphs in ancient Egypt are scribed in inscriptions. Information security always gained serious attention from diplomatic or military intelligence transmission. Due to the rapid evolvement of modern communication technique, crypto solution was first incorporated by electronic signal to ensure the confidentiality, integrity, availability, authenticity and non-repudiation of the transmitted contexts over unsecure cable or wireless channels. Restricted to the computation power before computer era, simple encryption tricks were practically sufficient to conceal information. However, algorithmic vulnerabilities can be excavated to restore the encoding rules with affordable efforts. This fact motivated the development of modern cryptography, aiming at guarding information system by complex and advanced algorithms. The appearance of computers has greatly pushed forward the invention of robust cryptographies, which efficiently offers resistance relying on highly strengthened computing capabilities. Likewise, advanced cryptanalysis has greatly driven the computing technologies in turn. Nowadays, the information world has been involved into a crypto world, protecting any fields by pervasive crypto solutions. These approaches are strong because of the optimized mergence between modern mathematical theories and effective hardware practices, being capable of implement crypto theories into various platforms (microprocessor, ASIC, FPGA, etc). Security needs from industries are actually the major driving metrics in electronic design, aiming at promoting the construction of systems with high performance without sacrificing security. Yet a vulnerability in practical implementation found by Prof. Paul Kocher, et al in 1996 implies that modern digital circuits are inherently vulnerable to an unconventional attack approach, which was named as side-channel attack since then from its analysis source. Critical suspicions to theoretically sound modern crypto algorithms surfaced almost immediately after this discovery. To be specifically, digital circuits typically consist of a great number of essential logic elements (as MOS - Metal Oxide Semiconductor), built upon a silicon substrate during the fabrication. Circuit logic is realized relying on the countless switch actions of these cells. This mechanism inevitably results in featured physical emanation that can be properly measured and correlated with internal circuit behaviors. SCAs can be used to reveal the confidential data (e.g. crypto-key), analyze the logic architecture, timing and even inject malicious faults to the circuits that are implemented in hardware system, like FPGA, ASIC, smart Card. Using various comparison solutions between the predicted leakage quantity and the measured leakage, secrets can be reconstructed at much less expense of time and computation. To be precisely, SCA basically encloses a wide range of attack types, typically as the analyses of power consumption or electromagnetic (EM) radiation. Both of them rely on statistical analyses, and hence require a number of samples. The crypto algorithms are not intrinsically fortified with SCA-resistance. Because of the severity, much attention has to be taken into the implementation so as to assemble countermeasures to camouflage the leakages via "side channels". Countermeasures against SCA are evolving along with the development of attack techniques. The physical characteristics requires countermeasures over physical layer, which can be generally classified into intrinsic and extrinsic vectors. Extrinsic countermeasures are executed to confuse the attacker by integrating noise, misalignment to the intra activities. Comparatively, intrinsic countermeasures are built into the algorithm itself, to modify the implementation for minimizing the measurable leakage, or making them not sensitive any more. Hiding and Masking are two typical techniques in this category. Concretely, masking applies to the algorithmic level, to alter the sensitive intermediate values with a mask in reversible ways. Unlike the linear masking, non-linear operations that widely exist in modern cryptographies are difficult to be masked. Approved to be an effective counter solution, hiding method mainly mentions dual-rail logic, which is specially devised for flattening or removing the data-dependent leakage in power or EM signatures. In this thesis, apart from the context describing the attack methodologies, efforts have also been dedicated to logic prototype, to mount extensive security investigations to countermeasures on logic-level. A characteristic of SCA resides on the format of leak sources. Typical side-channel attack concerns the power based analysis, where the fundamental capacitance from MOS transistors and other parasitic capacitances are the essential leak sources. Hence, a robust SCA-resistant logic must eliminate or mitigate the leakages from these micro units, such as basic logic gates, I/O ports and routings. The vendor provided EDA tools manipulate the logic from a higher behavioral-level, rather than the lower gate-level where side-channel leakage is generated. So, the classical implementations barely satisfy these needs and inevitably stunt the prototype. In this case, a customized and flexible design scheme is appealing to be devised. This thesis profiles an innovative logic style to counter SCA, which mainly addresses three major aspects: I. The proposed logic is based on the hiding strategy over gate-level dual-rail style to dynamically overbalance side-channel leakage from lower circuit layer; II. This logic exploits architectural features of modern FPGAs, to minimize the implementation expenses; III. It is supported by a set of assistant custom tools, incorporated by the generic FPGA design flow, to have circuit manipulations in an automatic manner. The automatic design toolkit supports the proposed dual-rail logic, facilitating the practical implementation on Xilinx FPGA families. While the methodologies and the tools are flexible to be expanded to a wide range of applications where rigid and sophisticated gate- or routing- constraints are desired. In this thesis a great effort is done to streamline the implementation workflow of generic dual-rail logic. The feasibility of the proposed solutions is validated by selected and widely used crypto algorithm, for thorough and fair evaluation w.r.t. prior solutions. All the proposals are effectively verified by security experiments. The presented research work attempts to solve the implementation troubles. The essence that will be formalized along this thesis is that a customized execution toolkit for modern FPGA systems is developed to work together with the generic FPGA design flow for creating innovative dual-rail logic. A method in crypto security area is constructed to obtain customization, automation and flexibility in low-level circuit prototype with fine-granularity in intractable routings. Main contributions of the presented work are summarized next: Precharge Absorbed-DPL logic: Using the netlist conversion to reserve free LUT inputs to execute the Precharge and Ex signal in a dual-rail logic style. A row-crossed interleaved placement method with identical routing pairs in dual-rail networks, which helps to increase the resistance against selective EM measurement and mitigate the impacts from process variations. Customized execution and automatic transformation tools for producing identical networks for the proposed dual-rail logic. (a) To detect and repair the conflict nets; (b) To detect and repair the asymmetric nets. (c) To be used in other logics where strict network control is required in Xilinx scenario. Customized correlation analysis testbed for EM and power attacks, including the platform construction, measurement method and attack analysis. A timing analysis based method for quantifying the security grades. A methodology of security partitions of complex crypto systems for reducing the protection cost. A proof-of-concept self-adaptive heating system to mitigate electrical impacts over process variations in dynamic dual-rail compensation manner. The thesis chapters are organized as follows: Chapter 1 discusses the side-channel attack fundamentals, which covers from theoretic basics to analysis models, and further to platform setup and attack execution. Chapter 2 centers to SCA-resistant strategies against generic power and EM attacks. In this chapter, a major contribution, a compact and secure dual-rail logic style, will be originally proposed. The logic transformation based on bottom-layer design will be presented. Chapter 3 is scheduled to elaborate the implementation challenges of generic dual-rail styles. A customized design flow to solve the implementation problems will be described along with a self-developed automatic implementation toolkit, for mitigating the design barriers and facilitating the processes. Chapter 4 will originally elaborate the tool specifics and construction details. The implementation case studies and security validations for the proposed logic style, as well as a sophisticated routing verification experiment, will be described in Chapter 5. Finally, a summary of thesis conclusions and perspectives for future work are included in Chapter 5. To better exhibit the thesis contents, each chapter is further described next: Chapter 1 provides the introduction of hardware implementation testbed and side-channel attack fundamentals, and mainly contains: (a) The FPGA generic architecture and device features, particularly of Virtex-5 FPGA; (b) The selected crypto algorithm - a commercially and extensively used Advanced Encryption Standard (AES) module - is detailed; (c) The essentials of Side-Channel methods are profiled. It reveals the correlated dissipation leakage to the internal behaviors, and the method to recover this relationship between the physical fluctuations in side-channel traces and the intra processed data; (d) The setups of the power/EM testing platforms enclosed inside the thesis work are given. The content of this thesis is expanded and deepened from chapter 2, which is divided into several aspects. First, the protection principle of dynamic compensation of the generic dual-rail precharge logic is explained by describing the compensated gate-level elements. Second, the novel DPL is originally proposed by detailing the logic protocol and an implementation case study. Third, a couple of custom workflows are shown next for realizing the rail conversion. Meanwhile, the technical definitions that are about to be manipulated above LUT-level netlist are clarified. A brief discussion about the batched process is given in the final part. Chapter 3 studies the implementation challenges of DPLs in FPGAs. The security level of state-of-the-art SCA-resistant solutions are decreased due to the implementation barriers using conventional EDA tools. In the studied FPGA scenario, problems are discussed from dual-rail format, parasitic impact, technological bias and implementation feasibility. According to these elaborations, two problems arise: How to implement the proposed logic without crippling the security level; and How to manipulate a large number of cells and automate the transformation. The proposed PA-DPL in chapter 2 is legalized with a series of initiatives, from structures to implementation methods. Furthermore, a self-adaptive heating system is depicted and implemented to a dual-core logic, assumed to alternatively adjust local temperature for balancing the negative impacts from silicon technological biases on real-time. Chapter 4 centers to the toolkit system. Built upon a third-party Application Program Interface (API) library, the customized toolkit is able to manipulate the logic elements from post P&R circuit (an unreadable binary version of the xdl one) converted to Xilinx xdl format. The mechanism and rationale of the proposed toolkit are carefully convoyed, covering the routing detection and repairing approaches. The developed toolkit aims to achieve very strictly identical routing networks for dual-rail logic both for separate and interleaved placement. This chapter particularly specifies the technical essentials to support the implementations in Xilinx devices and the flexibility to be expanded to other applications. Chapter 5 focuses on the implementation of the case studies for validating the security grades of the proposed logic style from the proposed toolkit. Comprehensive implementation techniques are discussed. (a) The placement impacts using the proposed toolkit are discussed. Different execution schemes, considering the global optimization in security and cost, are verified with experiments so as to find the optimized placement and repair schemes; (b) Security validations are realized with correlation, timing methods; (c) A systematic method is applied to a BCDL structured module to validate the routing impact over security metric; (d) The preliminary results using the self-adaptive heating system over process variation is given; (e) A practical implementation of the proposed toolkit to a large design is introduced. Chapter 6 includes the general summary of the complete work presented inside this thesis. Finally, a brief perspective for the future work is drawn which might expand the potential utilization of the thesis contributions to a wider range of implementation domains beyond cryptography on FPGAs.

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This article presents a new and computationally efficient method of analysis of a railway track modelled as a continuous beam of 2N spans supported by elastic vertical springs. The main feature of this method is its important reduction in computational effort with respect to standard matrix methods of structural analysis. In this article, the whole structure is considered to be a repetition of a single one. The analysis presented is applied to a simple railway track model, i.e. to a repetitive beam supported on vertical springs (sleepers). The proposed method of analysis is based on the general theory of spatially periodic structures. The main feature of this theory is the possibility to apply Discrete Fourier Transform (DFT) in order to reduce a large system of q(2N + 1) linear stiffness equilibrium equations to a set of 2N + 1 uncoupled systems of q equations each. In this way, a dramatic reduction of the computational effort of solving the large system of equations is achieved. This fact is particularly important in the analysis of railway track structures, in which N is a very large number (around several thousands), and q = 2, the vertical displacement and rotation, is very small. The proposed method allows us to easily obtain the exact solution given by Samartín [1], i.e. the continuous beam railway track response. The comparison between the proposed method and other methods of analysis of railway tracks, such as Lorente de Nó and Zimmermann-Timoshenko, clearly shows the accuracy of the obtained results for the proposed method, even for low values of N. In addition, identical results between the proposed and the Lorente methods have been found, although the proposed method seems to be of simpler application and computationally more efficient than the Lorente one. Small but significative differences occur between these two methods and the one developed by Zimmermann-Timoshenko. This article also presents a detailed sensitivity analysis of the vertical displacement of the sleepers. Although standard matrix methods of structural analysis can handle this railway model, one of the objectives of this article is to show the efficiency of DFT method with respect to standard matrix structural analysis. A comparative analysis between standard matrix structural analysis and the proposed method (DFT), in terms of computational time, input, output and also software programming, will be carried out. Finally, a URL link to a MatLab computer program list, based on the proposed method, is given

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Los sistemas transaccionales tales como los programas informáticos para la planificación de recursos empresariales (ERP software) se han implementado ampliamente mientras que los sistemas analíticos para la gestión de la cadena de suministro (SCM software) no han tenido el éxito deseado por la industria de tecnología de información (TI). Aunque se documentan beneficios importantes derivados de las implantaciones de SCM software, las empresas industriales son reacias a invertir en este tipo de sistemas. Por una parte esto es debido a la falta de métodos que son capaces de detectar los beneficios por emplear esos sistemas, y por otra parte porque el coste asociado no está identificado, detallado y cuantificado suficientemente. Los esquemas de coordinación basados únicamente en sistemas ERP son alternativas válidas en la práctica industrial siempre que la relación coste-beneficio esta favorable. Por lo tanto, la evaluación de formas organizativas teniendo en cuenta explícitamente el coste debido a procesos administrativos, en particular por ciclos iterativos, es de gran interés para la toma de decisiones en el ámbito de inversiones en TI. Con el fin de cerrar la brecha, el propósito de esta investigación es proporcionar métodos de evaluación que permitan la comparación de diferentes formas de organización y niveles de soporte por sistemas informáticos. La tesis proporciona una amplia introducción, analizando los retos a los que se enfrenta la industria. Concluye con las necesidades de la industria de SCM software: unas herramientas que facilitan la evaluación integral de diferentes propuestas de organización. A continuación, la terminología clave se detalla centrándose en la teoría de la organización, las peculiaridades de inversión en TI y la tipología de software de gestión de la cadena de suministro. La revisión de la literatura clasifica las contribuciones recientes sobre la gestión de la cadena de suministro, tratando ambos conceptos, el diseño de la organización y su soporte por las TI. La clasificación incluye criterios relacionados con la metodología de la investigación y su contenido. Los estudios empíricos en el ámbito de la administración de empresas se centran en tipologías de redes industriales. Nuevos algoritmos de planificación y esquemas de coordinación innovadoras se desarrollan principalmente en el campo de la investigación de operaciones con el fin de proponer nuevas funciones de software. Artículos procedentes del área de la gestión de la producción se centran en el análisis de coste y beneficio de las implantaciones de sistemas. La revisión de la literatura revela que el éxito de las TI para la coordinación de redes industriales depende en gran medida de características de tres dimensiones: la configuración de la red industrial, los esquemas de coordinación y las funcionalidades del software. La literatura disponible está enfocada sobre todo en los beneficios de las implantaciones de SCM software. Sin embargo, la coordinación de la cadena de suministro, basándose en el sistema ERP, sigue siendo la práctica industrial generalizada, pero el coste de coordinación asociado no ha sido abordado por los investigadores. Los fundamentos de diseño organizativo eficiente se explican en detalle en la medida necesaria para la comprensión de la síntesis de las diferentes formas de organización. Se han generado varios esquemas de coordinación variando los siguientes parámetros de diseño: la estructura organizativa, los mecanismos de coordinación y el soporte por TI. Las diferentes propuestas de organización desarrolladas son evaluadas por un método heurístico y otro basado en la simulación por eventos discretos. Para ambos métodos, se tienen en cuenta los principios de la teoría de la organización. La falta de rendimiento empresarial se debe a las dependencias entre actividades que no se gestionan adecuadamente. Dentro del método heurístico, se clasifican las dependencias y se mide su intensidad basándose en factores contextuales. A continuación, se valora la idoneidad de cada elemento de diseño organizativo para cada dependencia específica. Por último, cada forma de organización se evalúa basándose en la contribución de los elementos de diseño tanto al beneficio como al coste. El beneficio de coordinación se refiere a la mejora en el rendimiento logístico - este concepto es el objeto central en la mayoría de modelos de evaluación de la gestión de la cadena de suministro. Por el contrario, el coste de coordinación que se debe incurrir para lograr beneficios no se suele considerar en detalle. Procesos iterativos son costosos si se ejecutan manualmente. Este es el caso cuando SCM software no está implementada y el sistema ERP es el único instrumento de coordinación disponible. El modelo heurístico proporciona un procedimiento simplificado para la clasificación sistemática de las dependencias, la cuantificación de los factores de influencia y la identificación de configuraciones que indican el uso de formas organizativas y de soporte de TI más o menos complejas. La simulación de eventos discretos se aplica en el segundo modelo de evaluación utilizando el paquete de software ‘Plant Simulation’. Con respecto al rendimiento logístico, por un lado se mide el coste de fabricación, de inventario y de transporte y las penalizaciones por pérdida de ventas. Por otro lado, se cuantifica explícitamente el coste de la coordinación teniendo en cuenta los ciclos de coordinación iterativos. El método se aplica a una configuración de cadena de suministro ejemplar considerando diversos parámetros. Los resultados de la simulación confirman que, en la mayoría de los casos, el beneficio aumenta cuando se intensifica la coordinación. Sin embargo, en ciertas situaciones en las que se aplican ciclos de planificación manuales e iterativos el coste de coordinación adicional no siempre conduce a mejor rendimiento logístico. Estos resultados inesperados no se pueden atribuir a ningún parámetro particular. La investigación confirma la gran importancia de nuevas dimensiones hasta ahora ignoradas en la evaluación de propuestas organizativas y herramientas de TI. A través del método heurístico se puede comparar de forma rápida, pero sólo aproximada, la eficiencia de diferentes formas de organización. Por el contrario, el método de simulación es más complejo pero da resultados más detallados, teniendo en cuenta parámetros específicos del contexto del caso concreto y del diseño organizativo. ABSTRACT Transactional systems such as Enterprise Resource Planning (ERP) systems have been implemented widely while analytical software like Supply Chain Management (SCM) add-ons are adopted less by manufacturing companies. Although significant benefits are reported stemming from SCM software implementations, companies are reluctant to invest in such systems. On the one hand this is due to the lack of methods that are able to detect benefits from the use of SCM software and on the other hand associated costs are not identified, detailed and quantified sufficiently. Coordination schemes based only on ERP systems are valid alternatives in industrial practice because significant investment in IT can be avoided. Therefore, the evaluation of these coordination procedures, in particular the cost due to iterations, is of high managerial interest and corresponding methods are comprehensive tools for strategic IT decision making. The purpose of this research is to provide evaluation methods that allow the comparison of different organizational forms and software support levels. The research begins with a comprehensive introduction dealing with the business environment that industrial networks are facing and concludes highlighting the challenges for the supply chain software industry. Afterwards, the central terminology is addressed, focusing on organization theory, IT investment peculiarities and supply chain management software typology. The literature review classifies recent supply chain management research referring to organizational design and its software support. The classification encompasses criteria related to research methodology and content. Empirical studies from management science focus on network types and organizational fit. Novel planning algorithms and innovative coordination schemes are developed mostly in the field of operations research in order to propose new software features. Operations and production management researchers realize cost-benefit analysis of IT software implementations. The literature review reveals that the success of software solutions for network coordination depends strongly on the fit of three dimensions: network configuration, coordination scheme and software functionality. Reviewed literature is mostly centered on the benefits of SCM software implementations. However, ERP system based supply chain coordination is still widespread industrial practice but the associated coordination cost has not been addressed by researchers. Fundamentals of efficient organizational design are explained in detail as far as required for the understanding of the synthesis of different organizational forms. Several coordination schemes have been shaped through the variation of the following design parameters: organizational structuring, coordination mechanisms and software support. The different organizational proposals are evaluated using a heuristic approach and a simulation-based method. For both cases, the principles of organization theory are respected. A lack of performance is due to dependencies between activities which are not managed properly. Therefore, within the heuristic method, dependencies are classified and their intensity is measured based on contextual factors. Afterwards the suitability of each organizational design element for the management of a specific dependency is determined. Finally, each organizational form is evaluated based on the contribution of the sum of design elements to coordination benefit and to coordination cost. Coordination benefit refers to improvement in logistic performance – this is the core concept of most supply chain evaluation models. Unfortunately, coordination cost which must be incurred to achieve benefits is usually not considered in detail. Iterative processes are costly when manually executed. This is the case when SCM software is not implemented and the ERP system is the only available coordination instrument. The heuristic model provides a simplified procedure for the classification of dependencies, quantification of influence factors and systematic search for adequate organizational forms and IT support. Discrete event simulation is applied in the second evaluation model using the software package ‘Plant Simulation’. On the one hand logistic performance is measured by manufacturing, inventory and transportation cost and penalties for lost sales. On the other hand coordination cost is explicitly considered taking into account iterative coordination cycles. The method is applied to an exemplary supply chain configuration considering various parameter settings. The simulation results confirm that, in most cases, benefit increases when coordination is intensified. However, in some situations when manual, iterative planning cycles are applied, additional coordination cost does not always lead to improved logistic performance. These unexpected results cannot be attributed to any particular parameter. The research confirms the great importance of up to now disregarded dimensions when evaluating SCM concepts and IT tools. The heuristic method provides a quick, but only approximate comparison of coordination efficiency for different organizational forms. In contrast, the more complex simulation method delivers detailed results taking into consideration specific parameter settings of network context and organizational design.

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A MATLAB-based computer code has been developed for the simultaneous wavelet analysis and filtering of several environmental time series, particularly focused on the analyses of cave monitoring data. The continuous wavelet transform, the discrete wavelet transform and the discrete wavelet packet transform have been implemented to provide a fast and precise time–period examination of the time series at different period bands. Moreover, statistic methods to examine the relation between two signals have been included. Finally, the entropy of curves and splines based methods have also been developed for segmenting and modeling the analyzed time series. All these methods together provide a user-friendly and fast program for the environmental signal analysis, with useful, practical and understandable results.

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Population balances of polymer species in terms 'of discrete transforms with respect to counts of groups lead to tractable first order partial differential equations when ali rate constants are independent of chain length and loop formation is negligible [l]. Average molecular weights in the absence ofgelation are long known to be readily found through integration of an initial value problem. The extension to size distribution prediction is also feasible, but its performance is often lower to the one provided by methods based upon real chain length domain [2]. Moreover, the absence ofagood starting procedure and a higher numerical sensitivity hás decisively impaired its application to non-linear reversibly deactivated polymerizations, namely NMRP [3].