941 resultados para Holder-type discrete functions


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Mathematics Subject Classification: 33C05, 33C10, 33C20, 33C60, 33E12, 33E20, 40A30

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The purpose of this study was to correct some mistakes in the literature and derive a necessary and sufficient condition for the MRL to follow the roller-coaster pattern of the corresponding failure rate function. It was also desired to find the conditions under which the discrete failure rate function has an upside-down bathtub shape if corresponding MRL function has a bathtub shape. The study showed that if discrete MRL has a bathtub shape, then under some conditions the corresponding failure rate function has an upside-down bathtub shape. Also the study corrected some mistakes in proofs of Tang, Lu and Chew (1999) and established a necessary and sufficient condition for the MRL to follow the roller-coaster pattern of the corresponding failure rate function. Similarly, some mistakes in Gupta and Gupta (2000) are corrected, with the ensuing results being expanded and proved thoroughly to establish the relationship between the crossing points of the failure rate and associated MRL functions. The new results derived in this study will be useful to model various lifetime data that occur in environmental studies, medical research, electronics engineering, and in many other areas of science and technology.

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Adjoint methods have proven to be an efficient way of calculating the gradient of an objective function with respect to a shape parameter for optimisation, with a computational cost nearly independent of the number of the design variables [1]. The approach in this paper links the adjoint surface sensitivities (gradient of objective function with respect to the surface movement) with the parametric design velocities (movement of the surface due to a CAD parameter perturbation) in order to compute the gradient of the objective function with respect to CAD variables.
For a successful implementation of shape optimization strategies in practical industrial cases, the choice of design variables or parameterisation scheme used for the model to be optimized plays a vital role. Where the goal is to base the optimization on a CAD model the choices are to use a NURBS geometry generated from CAD modelling software, where the position of the NURBS control points are the optimisation variables [2] or to use the feature based CAD model with all of the construction history to preserve the design intent [3]. The main advantage of using the feature based model is that the optimized model produced can be directly used for the downstream applications including manufacturing and process planning.
This paper presents an approach for optimization based on the feature based CAD model, which uses CAD parameters defining the features in the model geometry as the design variables. In order to capture the CAD surface movement with respect to the change in design variable, the “Parametric Design Velocity” is calculated, which is defined as the movement of the CAD model boundary in the normal direction due to a change in the parameter value.
The approach presented here for calculating the design velocities represents an advancement in terms of capability and robustness of that described by Robinson et al. [3]. The process can be easily integrated to most industrial optimisation workflows and is immune to the topology and labelling issues highlighted by other CAD based optimisation processes. It considers every continuous (“real value”) parameter type as an optimisation variable, and it can be adapted to work with any CAD modelling software, as long as it has an API which provides access to the values of the parameters which control the model shape and allows the model geometry to be exported. To calculate the movement of the boundary the methodology employs finite differences on the shape of the 3D CAD models before and after the parameter perturbation. The implementation procedure includes calculating the geometrical movement along a normal direction between two discrete representations of the original and perturbed geometry respectively. Parametric design velocities can then be directly linked with adjoint surface sensitivities to extract the gradients to use in a gradient-based optimization algorithm.
The optimisation of a flow optimisation problem is presented, in which the power dissipation of the flow in an automotive air duct is to be reduced by changing the parameters of the CAD geometry created in CATIA V5. The flow sensitivities are computed with the continuous adjoint method for a laminar and turbulent flow [4] and are combined with the parametric design velocities to compute the cost function gradients. A line-search algorithm is then used to update the design variables and proceed further with optimisation process.

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Thesis (Ph.D.)--University of Washington, 2016-08

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We present new methodologies to generate rational function approximations of broadband electromagnetic responses of linear and passive networks of high-speed interconnects, and to construct SPICE-compatible, equivalent circuit representations of the generated rational functions. These new methodologies are driven by the desire to improve the computational efficiency of the rational function fitting process, and to ensure enhanced accuracy of the generated rational function interpolation and its equivalent circuit representation. Toward this goal, we propose two new methodologies for rational function approximation of high-speed interconnect network responses. The first one relies on the use of both time-domain and frequency-domain data, obtained either through measurement or numerical simulation, to generate a rational function representation that extrapolates the input, early-time transient response data to late-time response while at the same time providing a means to both interpolate and extrapolate the used frequency-domain data. The aforementioned hybrid methodology can be considered as a generalization of the frequency-domain rational function fitting utilizing frequency-domain response data only, and the time-domain rational function fitting utilizing transient response data only. In this context, a guideline is proposed for estimating the order of the rational function approximation from transient data. The availability of such an estimate expedites the time-domain rational function fitting process. The second approach relies on the extraction of the delay associated with causal electromagnetic responses of interconnect systems to provide for a more stable rational function process utilizing a lower-order rational function interpolation. A distinctive feature of the proposed methodology is its utilization of scattering parameters. For both methodologies, the approach of fitting the electromagnetic network matrix one element at a time is applied. It is shown that, with regard to the computational cost of the rational function fitting process, such an element-by-element rational function fitting is more advantageous than full matrix fitting for systems with a large number of ports. Despite the disadvantage that different sets of poles are used in the rational function of different elements in the network matrix, such an approach provides for improved accuracy in the fitting of network matrices of systems characterized by both strongly coupled and weakly coupled ports. Finally, in order to provide a means for enforcing passivity in the adopted element-by-element rational function fitting approach, the methodology for passivity enforcement via quadratic programming is modified appropriately for this purpose and demonstrated in the context of element-by-element rational function fitting of the admittance matrix of an electromagnetic multiport.

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Queueing systems constitute a central tool in modeling and performance analysis. These types of systems are in our everyday life activities, and the theory of queueing systems was developed to provide models for forecasting behaviors of systems subject to random demand. The practical and useful applications of the discrete-time queues make the researchers to con- tinue making an e ort in analyzing this type of models. Thus the present contribution relates to a discrete-time Geo/G/1 queue in which some messages may need a second service time in addition to the rst essential service. In day-to-day life, there are numerous examples of queueing situations in general, for example, in manufacturing processes, telecommunication, home automation, etc, but in this paper a particular application is the use of video surveil- lance with intrusion recognition where all the arriving messages require the main service and only some may require the subsidiary service provided by the server with di erent types of strategies. We carry out a thorough study of the model, deriving analytical results for the stationary distribution. The generating functions of the number of messages in the queue and in the system are obtained. The generating functions of the busy period as well as the sojourn times of a message in the server, the queue and the system are also provided.

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A new method for estimating the time to colonization of Methicillin-resistant Staphylococcus Aureus (MRSA) patients is developed in this paper. The time to colonization of MRSA is modelled using a Bayesian smoothing approach for the hazard function. There are two prior models discussed in this paper: the first difference prior and the second difference prior. The second difference prior model gives smoother estimates of the hazard functions and, when applied to data from an intensive care unit (ICU), clearly shows increasing hazard up to day 13, then a decreasing hazard. The results clearly demonstrate that the hazard is not constant and provide a useful quantification of the effect of length of stay on the risk of MRSA colonization which provides useful insight.

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Neurodegenerative disorders are heterogenous in nature and include a range of ataxias with oculomotor apraxia, which are characterised by a wide variety of neurological and ophthalmological features. This family includes recessive and dominant disorders. A subfamily of autosomal recessive cerebellar ataxias are characterised by defects in the cellular response to DNA damage. These include the well characterised disorders Ataxia-Telangiectasia (A-T) and Ataxia-Telangiectasia Like Disorder (A-TLD) as well as the recently identified diseases Spinocerebellar ataxia with axonal neuropathy Type 1 (SCAN1), Ataxia with Oculomotor Apraxia Type 2 (AOA2), as well as the subject of this thesis, Ataxia with Oculomotor Apraxia Type 1 (AOA1). AOA1 is caused by mutations in the APTX gene, which is located at chromosomal locus 9p13. This gene codes for the 342 amino acid protein Aprataxin. Mutations in APTX cause destabilization of Aprataxin, thus AOA1 is a result of Aprataxin deficiency. Aprataxin has three functional domains, an N-terminal Forkhead Associated (FHA) phosphoprotein interaction domain, a central Histidine Triad (HIT) nucleotide hydrolase domain and a C-terminal C2H2 zinc finger. Aprataxins FHA domain has homology to FHA domain of the DNA repair protein 5’ polynucleotide kinase 3’ phosphatase (PNKP). PNKP interacts with a range of DNA repair proteins via its FHA domain and plays a critical role in processing damaged DNA termini. The presence of this domain with a nucleotide hydrolase domain and a DNA binding motif implicated that Aprataxin may be involved in DNA repair and that AOA1 may be caused by a DNA repair deficit. This was substantiated by the interaction of Aprataxin with proteins involved in the repair of both single and double strand DNA breaks (XRay Cross-Complementing 1, XRCC4 and Poly-ADP Ribose Polymerase-1) and the hypersensitivity of AOA1 patient cell lines to single and double strand break inducing agents. At the commencement of this study little was known about the in vitro and in vivo properties of Aprataxin. Initially this study focused on generation of recombinant Aprataxin proteins to facilitate examination of the in vitro properties of Aprataxin. Using recombinant Aprataxin proteins I found that Aprataxin binds to double stranded DNA. Consistent with a role for Aprataxin as a DNA repair enzyme, this binding is not sequence specific. I also report that the HIT domain of Aprataxin hydrolyses adenosine derivatives and interestingly found that this activity is competitively inhibited by DNA. This provided initial evidence that DNA binds to the HIT domain of Aprataxin. The interaction of DNA with the nucleotide hydrolase domain of Aprataxin provided initial evidence that Aprataxin may be a DNA-processing factor. Following these studies, Aprataxin was found to hydrolyse 5’adenylated DNA, which can be generated by unscheduled ligation at DNA breaks with non-standard termini. I found that cell extracts from AOA1 patients do not have DNA-adenylate hydrolase activity indicating that Aprataxin is the only DNA-adenylate hydrolase in mammalian cells. I further characterised this activity by examining the contribution of the zinc finger and FHA domains to DNA-adenylate hydrolysis by the HIT domain. I found that deletion of the zinc finger ablated the activity of the HIT domain against adenylated DNA, indicating that the zinc finger may be required for the formation of a stable enzyme-substrate complex. Deletion of the FHA domain stimulated DNA-adenylate hydrolysis, which indicated that the activity of the HIT domain may be regulated by the FHA domain. Given that the FHA domain is involved in protein-protein interactions I propose that the activity of Aprataxins HIT domain may be regulated by proteins which interact with its FHA domain. We examined this possibility by measuring the DNA-adenylate hydrolase activity of extracts from cells deficient for the Aprataxin-interacting DNA repair proteins XRCC1 and PARP-1. XRCC1 deficiency did not affect Aprataxin activity but I found that Aprataxin is destabilized in the absence of PARP-1, resulting in a deficiency of DNA-adenylate hydrolase activity in PARP-1 knockout cells. This implies a critical role for PARP-1 in the stabilization of Aprataxin. Conversely I found that PARP-1 is destabilized in the absence of Aprataxin. PARP-1 is a central player in a number of DNA repair mechanisms and this implies that not only do AOA1 cells lack Aprataxin, they may also have defects in PARP-1 dependant cellular functions. Based on this I identified a defect in a PARP-1 dependant DNA repair mechanism in AOA1 cells. Additionally, I identified elevated levels of oxidized DNA in AOA1 cells, which is indicative of a defect in Base Excision Repair (BER). I attribute this to the reduced level of the BER protein Apurinic Endonuclease 1 (APE1) I identified in Aprataxin deficient cells. This study has identified and characterised multiple DNA repair defects in AOA1 cells, indicating that Aprataxin deficiency has far-reaching cellular consequences. Consistent with the literature, I show that Aprataxin is a nuclear protein with nucleoplasmic and nucleolar distribution. Previous studies have shown that Aprataxin interacts with the nucleolar rRNA processing factor nucleolin and that AOA1 cells appear to have a mild defect in rRNA synthesis. Given the nucleolar localization of Aprataxin I examined the protein-protein interactions of Aprataxin and found that Aprataxin interacts with a number of rRNA transcription and processing factors. Based on this and the nucleolar localization of Aprataxin I proposed that Aprataxin may have an alternative role in the nucleolus. I therefore examined the transcriptional activity of Aprataxin deficient cells using nucleotide analogue incorporation. I found that AOA1 cells do not display a defect in basal levels of RNA synthesis, however they display defective transcriptional responses to DNA damage. In summary, this thesis demonstrates that Aprataxin is a DNA repair enzyme responsible for the repair of adenylated DNA termini and that it is required for stabilization of at least two other DNA repair proteins. Thus not only do AOA1 cells have no Aprataxin protein or activity, they have additional deficiencies in PolyADP Ribose Polymerase-1 and Apurinic Endonuclease 1 dependant DNA repair mechanisms. I additionally demonstrate DNA-damage inducible transcriptional defects in AOA1 cells, indicating that Aprataxin deficiency confers a broad range of cellular defects and highlighting the complexity of the cellular response to DNA damage and the multiple defects which result from Aprataxin deficiency. My detailed characterization of the cellular consequences of Aprataxin deficiency provides an important contribution to our understanding of interlinking DNA repair processes.

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Recently, the numerical modelling and simulation for anomalous subdiffusion equation (ASDE), which is a type of fractional partial differential equation( FPDE) and has been found with widely applications in modern engineering and sciences, are attracting more and more attentions. The current dominant numerical method for modelling ASDE is Finite Difference Method (FDM), which is based on a pre-defined grid leading to inherited issues or shortcomings. This paper aims to develop an implicit meshless approach based on the radial basis functions (RBF) for numerical simulation of the non-linear ASDE. The discrete system of equations is obtained by using the meshless shape functions and the strong-forms. The stability and convergence of this meshless approach are then discussed and theoretically proven. Several numerical examples with different problem domains are used to validate and investigate accuracy and efficiency of the newly developed meshless formulation. The results obtained by the meshless formulations are also compared with those obtained by FDM in terms of their accuracy and efficiency. It is concluded that the present meshless formulation is very effective for the modeling and simulation of the ASDE. Therefore, the meshless technique should have good potential in development of a robust simulation tool for problems in engineering and science which are governed by the various types of fractional differential equations.

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Optimal design for generalized linear models has primarily focused on univariate data. Often experiments are performed that have multiple dependent responses described by regression type models, and it is of interest and of value to design the experiment for all these responses. This requires a multivariate distribution underlying a pre-chosen model for the data. Here, we consider the design of experiments for bivariate binary data which are dependent. We explore Copula functions which provide a rich and flexible class of structures to derive joint distributions for bivariate binary data. We present methods for deriving optimal experimental designs for dependent bivariate binary data using Copulas, and demonstrate that, by including the dependence between responses in the design process, more efficient parameter estimates are obtained than by the usual practice of simply designing for a single variable only. Further, we investigate the robustness of designs with respect to initial parameter estimates and Copula function, and also show the performance of compound criteria within this bivariate binary setting.

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This paper establishes practical stability results for an important range of approximate discrete-time filtering problems involving mismatch between the true system and the approximating filter model. Using local consistency assumption, the practical stability established is in the sense of an asymptotic bound on the amount of bias introduced by the model approximation. Significantly, these practical stability results do not require the approximating model to be of the same model type as the true system. Our analysis applies to a wide range of estimation problems and justifies the common practice of approximating intractable infinite dimensional nonlinear filters by simpler computationally tractable filters.

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This paper establishes a practical stability result for discrete-time output feedback control involving mismatch between the exact system to be stabilised and the approximating system used to design the controller. The practical stability is in the sense of an asymptotic bound on the amount of error bias introduced by the model approximation, and is established using local consistency properties of the systems. Importantly, the practical stability established here does not require the approximating system to be of the same model type as the exact system. Examples are presented to illustrate the nature of our practical stability result.

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Biochemical reactions underlying genetic regulation are often modelled as a continuous-time, discrete-state, Markov process, and the evolution of the associated probability density is described by the so-called chemical master equation (CME). However the CME is typically difficult to solve, since the state-space involved can be very large or even countably infinite. Recently a finite state projection method (FSP) that truncates the state-space was suggested and shown to be effective in an example of a model of the Pap-pili epigenetic switch. However in this example, both the model and the final time at which the solution was computed, were relatively small. Presented here is a Krylov FSP algorithm based on a combination of state-space truncation and inexact matrix-vector product routines. This allows larger-scale models to be studied and solutions for larger final times to be computed in a realistic execution time. Additionally the new method computes the solution at intermediate times at virtually no extra cost, since it is derived from Krylov-type methods for computing matrix exponentials. For the purpose of comparison the new algorithm is applied to the model of the Pap-pili epigenetic switch, where the original FSP was first demonstrated. Also the method is applied to a more sophisticated model of regulated transcription. Numerical results indicate that the new approach is significantly faster and extendable to larger biological models.

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Biologists are increasingly conscious of the critical role that noise plays in cellular functions such as genetic regulation, often in connection with fluctuations in small numbers of key regulatory molecules. This has inspired the development of models that capture this fundamentally discrete and stochastic nature of cellular biology - most notably the Gillespie stochastic simulation algorithm (SSA). The SSA simulates a temporally homogeneous, discrete-state, continuous-time Markov process, and of course the corresponding probabilities and numbers of each molecular species must all remain positive. While accurately serving this purpose, the SSA can be computationally inefficient due to very small time stepping so faster approximations such as the Poisson and Binomial τ-leap methods have been suggested. This work places these leap methods in the context of numerical methods for the solution of stochastic differential equations (SDEs) driven by Poisson noise. This allows analogues of Euler-Maruyuma, Milstein and even higher order methods to be developed through the Itô-Taylor expansions as well as similar derivative-free Runge-Kutta approaches. Numerical results demonstrate that these novel methods compare favourably with existing techniques for simulating biochemical reactions by more accurately capturing crucial properties such as the mean and variance than existing methods.

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In 1980 Alltop produced a family of cubic phase sequences that nearly meet the Welch bound for maximum non-peak correlation magnitude. This family of sequences were shown by Wooters and Fields to be useful for quantum state tomography. Alltop’s construction used a function that is not planar, but whose difference function is planar. In this paper we show that Alltop type functions cannot exist in fields of characteristic 3 and that for a known class of planar functions, x^3 is the only Alltop type function.