918 resultados para time dependant cost function


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Nous considérons des processus de diffusion, définis par des équations différentielles stochastiques, et puis nous nous intéressons à des problèmes de premier passage pour les chaînes de Markov en temps discret correspon- dant à ces processus de diffusion. Comme il est connu dans la littérature, ces chaînes convergent en loi vers la solution des équations différentielles stochas- tiques considérées. Notre contribution consiste à trouver des formules expli- cites pour la probabilité de premier passage et la durée de la partie pour ces chaînes de Markov à temps discret. Nous montrons aussi que les résultats ob- tenus convergent selon la métrique euclidienne (i.e topologie euclidienne) vers les quantités correspondantes pour les processus de diffusion. En dernier lieu, nous étudions un problème de commande optimale pour des chaînes de Markov en temps discret. L’objectif est de trouver la valeur qui mi- nimise l’espérance mathématique d’une certaine fonction de coût. Contraire- ment au cas continu, il n’existe pas de formule explicite pour cette valeur op- timale dans le cas discret. Ainsi, nous avons étudié dans cette thèse quelques cas particuliers pour lesquels nous avons trouvé cette valeur optimale.

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Cette thèse est divisée en deux grands chapitres, dont le premier porte sur des problèmes de commande optimale en dimension un et le deuxième sur des problèmes en dimension deux ou plus. Notons bien que, dans cette thèse, nous avons supposé que le facteur temps n'intervient pas. Dans le premier chapitre, nous calculons, au début, l'équation de programmation dynamique pour la valeur minimale F de l'espérance mathématique de la fonction de coût considérée. Ensuite, nous utilisons le théorème de Whittle qui est applicable seulement si une condition entre le bruit blanc v et les termes b et q associés à la commande est satisfaite. Sinon, nous procédons autrement. En effet, un changement de variable transforme notre équation en une équation de Riccati en G= F', mais sans conditions initiales. Dans certains cas, à partir de la symétrie des paramètres infinitésimaux et de q, nous pouvons en déduire le point x' où G(x')=0. Si ce n'est pas le cas, nous nous limitons à des bonnes approximations. Cette même démarche est toujours possible si nous sommes dans des situations particulières, par exemple, lorsque nous avons une seule barrière. Dans le deuxième chapitre, nous traitons les problèmes en dimension deux ou plus. Puisque la condition de Whittle est difficile à satisfaire dans ce cas, nous essayons de généraliser les résultats du premier chapitre. Nous utilisons alors dans quelques exemples la méthode des similitudes, qui permet de transformer le problème en dimension un. Ensuite, nous proposons une nouvelle méthode de résolution. Cette dernière linéarise l'équation de programmation dynamique qui est une équation aux dérivées partielles non linéaire. Il reste à la fin à trouver les conditions initiales pour la nouvelle fonction et aussi à vérifier que les n expressions obtenues pour F sont équivalentes.

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Im Rahmen dieser Arbeit wird eine gemeinsame Optimierung der Hybrid-Betriebsstrategie und des Verhaltens des Verbrennungsmotors vorgestellt. Die Übernahme von den im Steuergerät verwendeten Funktionsmodulen in die Simulationsumgebung für Fahrzeuglängsdynamik stellt eine effiziente Applikationsmöglichkeit der Originalparametrierung dar. Gleichzeitig ist es notwendig, das Verhalten des Verbrennungsmotors derart nachzubilden, dass das stationäre und das dynamische Verhalten, inklusive aller relevanten Einflussmöglichkeiten, wiedergegeben werden kann. Das entwickelte Werkzeug zur Übertragung der in Ascet definierten Steurgerätefunktionen in die Simulink-Simulationsumgebung ermöglicht nicht nur die Simulation der relevanten Funktionsmodule, sondern es erfüllt auch weitere wichtige Eigenschaften. Eine erhöhte Flexibilität bezüglich der Daten- und Funktionsstandänderungen, sowie die Parametrierbarkeit der Funktionsmodule sind Verbesserungen die an dieser Stelle zu nennen sind. Bei der Modellierung des stationären Systemverhaltens des Verbrennungsmotors erfolgt der Einsatz von künstlichen neuronalen Netzen. Die Auswahl der optimalen Neuronenanzahl erfolgt durch die Betrachtung des SSE für die Trainings- und die Verifikationsdaten. Falls notwendig, wird zur Sicherstellung der angestrebten Modellqualität, das Interpolationsverhalten durch Hinzunahme von Gauß-Prozess-Modellen verbessert. Mit den Gauß-Prozess-Modellen werden hierbei zusätzliche Stützpunkte erzeugt und mit einer verminderten Priorität in die Modellierung eingebunden. Für die Modellierung des dynamischen Systemverhaltens werden lineare Übertragungsfunktionen verwendet. Bei der Minimierung der Abweichung zwischen dem Modellausgang und den Messergebnissen wird zusätzlich zum SSE das 2σ-Intervall der relativen Fehlerverteilung betrachtet. Die Implementierung der Steuergerätefunktionsmodule und der erstellten Steller-Sensor-Streckenmodelle in der Simulationsumgebung für Fahrzeuglängsdynamik führt zum Anstieg der Simulationszeit und einer Vergrößerung des Parameterraums. Das aus Regelungstechnik bekannte Verfahren der Gütevektoroptimierung trägt entscheidend zu einer systematischen Betrachtung und Optimierung der Zielgrößen bei. Das Ergebnis des Verfahrens ist durch das Optimum der Paretofront der einzelnen Entwurfsspezifikationen gekennzeichnet. Die steigenden Simulationszeiten benachteiligen Minimumsuchverfahren, die eine Vielzahl an Iterationen benötigen. Um die Verwendung einer Zufallsvariablen, die maßgeblich zur Steigerung der Iterationanzahl beiträgt, zu vermeiden und gleichzeitig eine Globalisierung der Suche im Parameterraum zu ermöglichen wird die entwickelte Methode DelaunaySearch eingesetzt. Im Gegensatz zu den bekannten Algorithmen, wie die Partikelschwarmoptimierung oder die evolutionären Algorithmen, setzt die neu entwickelte Methode bei der Suche nach dem Minimum einer Kostenfunktion auf eine systematische Analyse der durchgeführten Simulationsergebnisse. Mit Hilfe der bei der Analyse gewonnenen Informationen werden Bereiche mit den bestmöglichen Voraussetzungen für ein Minimum identifiziert. Somit verzichtet das iterative Verfahren bei der Bestimmung des nächsten Iterationsschrittes auf die Verwendung einer Zufallsvariable. Als Ergebnis der Berechnungen steht ein gut gewählter Startwert für eine lokale Optimierung zur Verfügung. Aufbauend auf der Simulation der Fahrzeuglängsdynamik, der Steuergerätefunktionen und der Steller-Sensor-Streckenmodelle in einer Simulationsumgebung wird die Hybrid-Betriebsstrategie gemeinsam mit der Steuerung des Verbrennungsmotors optimiert. Mit der Entwicklung und Implementierung einer neuen Funktion wird weiterhin die Verbindung zwischen der Betriebsstrategie und der Motorsteuerung erweitert. Die vorgestellten Werkzeuge ermöglichten hierbei nicht nur einen Test der neuen Funktionalitäten, sondern auch eine Abschätzung der Verbesserungspotentiale beim Verbrauch und Abgasemissionen. Insgesamt konnte eine effiziente Testumgebung für eine gemeinsame Optimierung der Betriebsstrategie und des Verbrennungsmotorverhaltens eines Hybridfahrzeugs realisiert werden.

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This work extends a previously developed research concerning about the use of local model predictive control in differential driven mobile robots. Hence, experimental results are presented as a way to improve the methodology by considering aspects as trajectory accuracy and time performance. In this sense, the cost function and the prediction horizon are important aspects to be considered. The aim of the present work is to test the control method by measuring trajectory tracking accuracy and time performance. Moreover, strategies for the integration with perception system and path planning are briefly introduced. In this sense, monocular image data can be used to plan safety trajectories by using goal attraction potential fields

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The aim of this thesis is to narrow the gap between two different control techniques: the continuous control and the discrete event control techniques DES. This gap can be reduced by the study of Hybrid systems, and by interpreting as Hybrid systems the majority of large-scale systems. In particular, when looking deeply into a process, it is often possible to identify interaction between discrete and continuous signals. Hybrid systems are systems that have both continuous, and discrete signals. Continuous signals are generally supposed continuous and differentiable in time, since discrete signals are neither continuous nor differentiable in time due to their abrupt changes in time. Continuous signals often represent the measure of natural physical magnitudes such as temperature, pressure etc. The discrete signals are normally artificial signals, operated by human artefacts as current, voltage, light etc. Typical processes modelled as Hybrid systems are production systems, chemical process, or continuos production when time and continuous measures interacts with the transport, and stock inventory system. Complex systems as manufacturing lines are hybrid in a global sense. They can be decomposed into several subsystems, and their links. Another motivation for the study of Hybrid systems is the tools developed by other research domains. These tools benefit from the use of temporal logic for the analysis of several properties of Hybrid systems model, and use it to design systems and controllers, which satisfies physical or imposed restrictions. This thesis is focused in particular types of systems with discrete and continuous signals in interaction. That can be modelled hard non-linealities, such as hysteresis, jumps in the state, limit cycles, etc. and their possible non-deterministic future behaviour expressed by an interpretable model description. The Hybrid systems treated in this work are systems with several discrete states, always less than thirty states (it can arrive to NP hard problem), and continuous dynamics evolving with expression: with Ki ¡ Rn constant vectors or matrices for X components vector. In several states the continuous evolution can be several of them Ki = 0. In this formulation, the mathematics can express Time invariant linear system. By the use of this expression for a local part, the combination of several local linear models is possible to represent non-linear systems. And with the interaction with discrete events of the system the model can compose non-linear Hybrid systems. Especially multistage processes with high continuous dynamics are well represented by the proposed methodology. Sate vectors with more than two components, as third order models or higher is well approximated by the proposed approximation. Flexible belt transmission, chemical reactions with initial start-up and mobile robots with important friction are several physical systems, which profits from the benefits of proposed methodology (accuracy). The motivation of this thesis is to obtain a solution that can control and drive the Hybrid systems from the origin or starting point to the goal. How to obtain this solution, and which is the best solution in terms of one cost function subject to the physical restrictions and control actions is analysed. Hybrid systems that have several possible states, different ways to drive the system to the goal and different continuous control signals are problems that motivate this research. The requirements of the system on which we work is: a model that can represent the behaviour of the non-linear systems, and that possibilities the prediction of possible future behaviour for the model, in order to apply an supervisor which decides the optimal and secure action to drive the system toward the goal. Specific problems can be determined by the use of this kind of hybrid models are: - The unity of order. - Control the system along a reachable path. - Control the system in a safe path. - Optimise the cost function. - Modularity of control The proposed model solves the specified problems in the switching models problem, the initial condition calculus and the unity of the order models. Continuous and discrete phenomena are represented in Linear hybrid models, defined with defined eighth-tuple parameters to model different types of hybrid phenomena. Applying a transformation over the state vector : for LTI system we obtain from a two-dimensional SS a single parameter, alpha, which still maintains the dynamical information. Combining this parameter with the system output, a complete description of the system is obtained in a form of a graph in polar representation. Using Tagaki-Sugeno type III is a fuzzy model which include linear time invariant LTI models for each local model, the fuzzyfication of different LTI local model gives as a result a non-linear time invariant model. In our case the output and the alpha measure govern the membership function. Hybrid systems control is a huge task, the processes need to be guided from the Starting point to the desired End point, passing a through of different specific states and points in the trajectory. The system can be structured in different levels of abstraction and the control in three layers for the Hybrid systems from planning the process to produce the actions, these are the planning, the process and control layer. In this case the algorithms will be applied to robotics ¡V a domain where improvements are well accepted ¡V it is expected to find a simple repetitive processes for which the extra effort in complexity can be compensated by some cost reductions. It may be also interesting to implement some control optimisation to processes such as fuel injection, DC-DC converters etc. In order to apply the RW theory of discrete event systems on a Hybrid system, we must abstract the continuous signals and to project the events generated for these signals, to obtain new sets of observable and controllable events. Ramadge & Wonham¡¦s theory along with the TCT software give a Controllable Sublanguage of the legal language generated for a Discrete Event System (DES). Continuous abstraction transforms predicates over continuous variables into controllable or uncontrollable events, and modifies the set of uncontrollable, controllable observable and unobservable events. Continuous signals produce into the system virtual events, when this crosses the bound limits. If this event is deterministic, they can be projected. It is necessary to determine the controllability of this event, in order to assign this to the corresponding set, , controllable, uncontrollable, observable and unobservable set of events. Find optimal trajectories in order to minimise some cost function is the goal of the modelling procedure. Mathematical model for the system allows the user to apply mathematical techniques over this expression. These possibilities are, to minimise a specific cost function, to obtain optimal controllers and to approximate a specific trajectory. The combination of the Dynamic Programming with Bellman Principle of optimality, give us the procedure to solve the minimum time trajectory for Hybrid systems. The problem is greater when there exists interaction between adjacent states. In Hybrid systems the problem is to determine the partial set points to be applied at the local models. Optimal controller can be implemented in each local model in order to assure the minimisation of the local costs. The solution of this problem needs to give us the trajectory to follow the system. Trajectory marked by a set of set points to force the system to passing over them. Several ways are possible to drive the system from the Starting point Xi to the End point Xf. Different ways are interesting in: dynamic sense, minimum states, approximation at set points, etc. These ways need to be safe and viable and RchW. And only one of them must to be applied, normally the best, which minimises the proposed cost function. A Reachable Way, this means the controllable way and safe, will be evaluated in order to obtain which one minimises the cost function. Contribution of this work is a complete framework to work with the majority Hybrid systems, the procedures to model, control and supervise are defined and explained and its use is demonstrated. Also explained is the procedure to model the systems to be analysed for automatic verification. Great improvements were obtained by using this methodology in comparison to using other piecewise linear approximations. It is demonstrated in particular cases this methodology can provide best approximation. The most important contribution of this work, is the Alpha approximation for non-linear systems with high dynamics While this kind of process is not typical, but in this case the Alpha approximation is the best linear approximation to use, and give a compact representation.

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The correlated k-distribution (CKD) method is widely used in the radiative transfer schemes of atmospheric models and involves dividing the spectrum into a number of bands and then reordering the gaseous absorption coefficients within each one. The fluxes and heating rates for each band may then be computed by discretizing the reordered spectrum into of order 10 quadrature points per major gas and performing a monochromatic radiation calculation for each point. In this presentation it is shown that for clear-sky longwave calculations, sufficient accuracy for most applications can be achieved without the need for bands: reordering may be performed on the entire longwave spectrum. The resulting full-spectrum correlated k (FSCK) method requires significantly fewer monochromatic calculations than standard CKD to achieve a given accuracy. The concept is first demonstrated by comparing with line-by-line calculations for an atmosphere containing only water vapor, in which it is shown that the accuracy of heating-rate calculations improves approximately in proportion to the square of the number of quadrature points. For more than around 20 points, the root-mean-squared error flattens out at around 0.015 K/day due to the imperfect rank correlation of absorption spectra at different pressures in the profile. The spectral overlap of m different gases is treated by considering an m-dimensional hypercube where each axis corresponds to the reordered spectrum of one of the gases. This hypercube is then divided up into a number of volumes, each approximated by a single quadrature point, such that the total number of quadrature points is slightly fewer than the sum of the number that would be required to treat each of the gases separately. The gaseous absorptions for each quadrature point are optimized such that they minimize a cost function expressing the deviation of the heating rates and fluxes calculated by the FSCK method from line-by-line calculations for a number of training profiles. This approach is validated for atmospheres containing water vapor, carbon dioxide, and ozone, in which it is found that in the troposphere and most of the stratosphere, heating-rate errors of less than 0.2 K/day can be achieved using a total of 23 quadrature points, decreasing to less than 0.1 K/day for 32 quadrature points. It would be relatively straightforward to extend the method to include other gases.

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There is a current need to constrain the parameters of gravity wave drag (GWD) schemes in climate models using observational information instead of tuning them subjectively. In this work, an inverse technique is developed using data assimilation principles to estimate gravity wave parameters. Because mostGWDschemes assume instantaneous vertical propagation of gravity waves within a column, observations in a single column can be used to formulate a one-dimensional assimilation problem to estimate the unknown parameters. We define a cost function that measures the differences between the unresolved drag inferred from observations (referred to here as the ‘observed’ GWD) and the GWD calculated with a parametrisation scheme. The geometry of the cost function presents some difficulties, including multiple minima and ill-conditioning because of the non-independence of the gravity wave parameters. To overcome these difficulties we propose a genetic algorithm to minimize the cost function, which provides a robust parameter estimation over a broad range of prescribed ‘true’ parameters. When real experiments using an independent estimate of the ‘observed’ GWD are performed, physically unrealistic values of the parameters can result due to the non-independence of the parameters. However, by constraining one of the parameters to lie within a physically realistic range, this degeneracy is broken and the other parameters are also found to lie within physically realistic ranges. This argues for the essential physical self-consistency of the gravity wave scheme. A much better fit to the observed GWD at high latitudes is obtained when the parameters are allowed to vary with latitude. However, a close fit can be obtained either in the upper or the lower part of the profiles, but not in both at the same time. This result is a consequence of assuming an isotropic launch spectrum. The changes of sign in theGWDfound in the tropical lower stratosphere, which are associated with part of the quasi-biennial oscillation forcing, cannot be captured by the parametrisation with optimal parameters.

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Toward the ultimate goal of replacing field-based evaluation of seasonal growth habit, we describe the design and validation of a multiplex polymerase chain reaction assay diagnostic for allelic status at the barley (Hordeum vulgare ssp. vulgare L.) vernalization locus, VRN-H1 By assaying for the presence of all known insertion–deletion polymorphisms thought to be responsible for the difference between spring and winter alleles, this assay directly tests for the presence of functional polymorphism at VRN-H1 Four of the nine previously recognized VRN-H1 haplotypes (including both winter alleles) give unique profiles using this assay. The remaining five spring haplotypes share a single profile, indicative of function-altering deletions spanning, or adjacent to, the putative “vernalization critical” region of intron 1. When used in conjunction with a previously published PCR-based assay diagnostic for alleles at VRN-H2, it was possible to predict growth habit in all the 100 contemporary UK spring and winter lines analyzed in this study. This assay is likely to find application in instances when seasonal growth habit needs to be determined without the time and cost of phenotypic assessment and during marker-assisted selection using conventional and multicross population analysis.

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We propose a new sparse model construction method aimed at maximizing a model’s generalisation capability for a large class of linear-in-the-parameters models. The coordinate descent optimization algorithm is employed with a modified l1- penalized least squares cost function in order to estimate a single parameter and its regularization parameter simultaneously based on the leave one out mean square error (LOOMSE). Our original contribution is to derive a closed form of optimal LOOMSE regularization parameter for a single term model, for which we show that the LOOMSE can be analytically computed without actually splitting the data set leading to a very simple parameter estimation method. We then integrate the new results within the coordinate descent optimization algorithm to update model parameters one at the time for linear-in-the-parameters models. Consequently a fully automated procedure is achieved without resort to any other validation data set for iterative model evaluation. Illustrative examples are included to demonstrate the effectiveness of the new approaches.

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This paper discusses ECG signal classification after parametrizing the ECG waveforms in the wavelet domain. Signal decomposition using perfect reconstruction quadrature mirror filter banks can provide a very parsimonious representation of ECG signals. In the current work, the filter parameters are adjusted by a numerical optimization algorithm in order to minimize a cost function associated to the filter cut-off sharpness. The goal consists of achieving a better compromise between frequency selectivity and time resolution at each decomposition level than standard orthogonal filter banks such as those of the Daubechies and Coiflet families. Our aim is to optimally decompose the signals in the wavelet domain so that they can be subsequently used as inputs for training to a neural network classifier.

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Accurate and reliable rain rate estimates are important for various hydrometeorological applications. Consequently, rain sensors of different types have been deployed in many regions. In this work, measurements from different instruments, namely, rain gauge, weather radar, and microwave link, are combined for the first time to estimate with greater accuracy the spatial distribution and intensity of rainfall. The objective is to retrieve the rain rate that is consistent with all these measurements while incorporating the uncertainty associated with the different sources of information. Assuming the problem is not strongly nonlinear, a variational approach is implemented and the Gauss–Newton method is used to minimize the cost function containing proper error estimates from all sensors. Furthermore, the method can be flexibly adapted to additional data sources. The proposed approach is tested using data from 14 rain gauges and 14 operational microwave links located in the Zürich area (Switzerland) to correct the prior rain rate provided by the operational radar rain product from the Swiss meteorological service (MeteoSwiss). A cross-validation approach demonstrates the improvement of rain rate estimates when assimilating rain gauge and microwave link information.

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A novel technique for selecting the poles of orthonormal basis functions (OBF) in Volterra models of any order is presented. It is well-known that the usual large number of parameters required to describe the Volterra kernels can be significantly reduced by representing each kernel using an appropriate basis of orthonormal functions. Such a representation results in the so-called OBF Volterra model, which has a Wiener structure consisting of a linear dynamic generated by the orthonormal basis followed by a nonlinear static mapping given by the Volterra polynomial series. Aiming at optimizing the poles that fully parameterize the orthonormal bases, the exact gradients of the outputs of the orthonormal filters with respect to their poles are computed analytically by using a back-propagation-through-time technique. The expressions relative to the Kautz basis and to generalized orthonormal bases of functions (GOBF) are addressed; the ones related to the Laguerre basis follow straightforwardly as a particular case. The main innovation here is that the dynamic nature of the OBF filters is fully considered in the gradient computations. These gradients provide exact search directions for optimizing the poles of a given orthonormal basis. Such search directions can, in turn, be used as part of an optimization procedure to locate the minimum of a cost-function that takes into account the error of estimation of the system output. The Levenberg-Marquardt algorithm is adopted here as the optimization procedure. Unlike previous related work, the proposed approach relies solely on input-output data measured from the system to be modeled, i.e., no information about the Volterra kernels is required. Examples are presented to illustrate the application of this approach to the modeling of dynamic systems, including a real magnetic levitation system with nonlinear oscillatory behavior.

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In this paper we examine the geometrically constrained optimization approach to localization with hybrid bearing (angle of arrival, AOA) and time difference of  arrival (TDOA) sensors. In particular, we formulate a constraint on the measurement errors which is then used along with constraint-based optimization tools in order to estimate the maximum likelihood values of the errors given an appropriate cost function. In particular we focus on deriving a localization algorithm for stationary target localization in the so-called adverse localization geometries where the relative positioning of the sensors and the target do not readily permit accurate or convergent localization using traditional approaches. We illustrate this point via simulation and we compare our approach to a number of different techniques that are discussed in the literature.

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Shed feathers obtained by noninvasive genetic sampling (NGS) are a valuable source of DNA for genetic studies of birds. They can be collected across a large geographical range and facilitate research on species that would otherwise be extremely difficult to study. A limitation of this approach is uncertainty concerning the quality of the extracted DNA. Here we investigate the relationship between feather type, feather condition and DNA quality (amplification success) in order to provide a simple, cost-effective method for screening samples prior to genetic analysis. We obtained 637 shed feathers of the powerful owl ( Ninox strenua) from across its range in southeastern Australia. The extracted DNA was amplified using polymerase chain reaction for a range of markers including mitochondrial DNA, ND3 and nuclear DNA, a simple sequence repeat (Nst02) and a portion of the CHD-1 gene (P2/P8). We found that feather condition significantly influenced the amplification success of all three loci, with feathers characterized as ‘good’ having greater success. Feather type was found to be of lower importance, with good quality feathers of all types consistently producing high success for all three loci. We also found that the successful amplification of multilocus genotypes was dependant on the condition of the starting material and was highly correlated with successful amplification of the sex-linked CHD-1 locus. Samples with low DNA quality have a higher probability of amplification failure and are more likely to produce incorrect genotypes; therefore, identifying samples with high DNA quality can save substantial time and cost associated with the genetic analysis of NGS. As a result, we propose a method for screening shed feathers in order to provide a subset of samples which will have a greater probability of containing high quality DNA suitable for the amplification of multilocus genotypes.

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The next generation of wireless networks is envisioned as convergence of heterogeneous radio access networks. Since technologies are becoming more collaborative, a possible integration between IEEE 802.16 based network and previous generation of telecommunication systems (2G, ..., 3G) must be considered. A novel quality function based vertical handoff (VHO) algorithm, based on proposed velocity and average receive power estimation algorithms is discussed in this paper. The short-time Fourier analysis of received signal strength (RSS) is employed to obtain mobile speed and average received power estimates. Performance of quality function based VHO algorithm is evaluated by means of measure of quality of service (QoS). Simulation results show that proposed quality function, brings significant gains in QoS and more efficient use of resources can be achieved.