Rational Function Interpolation of Electromagnetic Transfer Functions of High-Speed Interconnect Systems from Discrete Time-Domain and Frequency-Domain Data

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.

Mixture of time-dependent growth models with an application to blue swimmer crab length-frequency data

Understanding how aquatic species grow is fundamental in fisheries because stock assessment often relies on growth dependent statistical models. Length-frequency-based methods become important when more applicable data for growth model estimation are either not available or very expensive. In this article, we develop a new framework for growth estimation from length-frequency data using a generalized von Bertalanffy growth model (VBGM) framework that allows for time-dependent covariates to be incorporated. A finite mixture of normal distributions is used to model the length-frequency cohorts of each month with the means constrained to follow a VBGM. The variances of the finite mixture components are constrained to be a function of mean length, reducing the number of parameters and allowing for an estimate of the variance at any length. To optimize the likelihood, we use a minorization–maximization (MM) algorithm with a Nelder–Mead sub-step. This work was motivated by the decline in catches of the blue swimmer crab (BSC) (Portunus armatus) off the east coast of Queensland, Australia. We test the method with a simulation study and then apply it to the BSC fishery data.

Decoherence models for discrete-time quantum walks and their application to neutral atom experiments

We discuss decoherence in discrete-time quantum walks in terms of a phenomenological model that distinguishes spin and spatial decoherence. We identify the dominating mechanisms that affect quantum-walk experiments realized with neutral atoms walking in an optical lattice. From the measured spatial distributions, we determine with good precision the amount of decoherence per step, which provides a quantitative indication of the quality of our quantum walks. In particular, we find that spin decoherence is the main mechanism responsible for the loss of coherence in our experiment. We also find that the sole observation of ballistic-instead of diffusive-expansion in position space is not a good indicator of the range of coherent delocalization. We provide further physical insight by distinguishing the effects of short- and long-time spin dephasing mechanisms. We introduce the concept of coherence length in the discrete-time quantum walk, which quantifies the range of spatial coherences. Unexpectedly, we find that quasi-stationary dephasing does not modify the local properties of the quantum walk, but instead affects spatial coherences. For a visual representation of decoherence phenomena in phase space, we have developed a formalism based on a discrete analogue of the Wigner function. We show that the effects of spin and spatial decoherence differ dramatically in momentum space.

An introduction to mathematical models of coagulation-fragmentation processes: a discrete deterministic mean-field approach

We summarise the properties and the fundamental mathematical results associated with basic models which describe coagulation and fragmentation processes in a deterministic manner and in which cluster size is a discrete quantity (an integer multiple of some basic unit size). In particular, we discuss Smoluchowski's equation for aggregation, the Becker-Döring model of simultaneous aggregation and fragmentation, and more general models involving coagulation and fragmentation.

Comparing simulation output accuracy of discrete event and agent based models: a quantitative approach

In our research we investigate the output accuracy of discrete event simulation models and agent based simulation models when studying human centric complex systems. In this paper we focus on human reactive behaviour as it is possible in both modelling approaches to implement human reactive behaviour in the model by using standard methods. As a case study we have chosen the retail sector, and here in particular the operations of the fitting room in the women wear department of a large UK department store. In our case study we looked at ways of determining the efficiency of implementing new management policies for the fitting room operation through modelling the reactive behaviour of staff and customers of the department. First, we have carried out a validation experiment in which we compared the results from our models to the performance of the real system. This experiment also allowed us to establish differences in output accuracy between the two modelling methods. In a second step a multi-scenario experiment was carried out to study the behaviour of the models when they are used for the purpose of operational improvement. Overall we have found that for our case study example both, discrete event simulation and agent based simulation have the same potential to support the investigation into the efficiency of implementing new management policies.

Some misspecfication problems in long-memory time series models

Doctor of Philosophy in Mathematics

Learning data-driven models of non-verbal behaviors for building rapport using an intelligent virtual agent

There is a growing societal need to address the increasing prevalence of behavioral health issues, such as obesity, alcohol or drug use, and general lack of treatment adherence for a variety of health problems. The statistics, worldwide and in the USA, are daunting. Excessive alcohol use is the third leading preventable cause of death in the United States (with 79,000 deaths annually), and is responsible for a wide range of health and social problems. On the positive side though, these behavioral health issues (and associated possible diseases) can often be prevented with relatively simple lifestyle changes, such as losing weight with a diet and/or physical exercise, or learning how to reduce alcohol consumption. Medicine has therefore started to move toward finding ways of preventively promoting wellness, rather than solely treating already established illness.^ Evidence-based patient-centered Brief Motivational Interviewing (BMI) interventions have been found particularly effective in helping people find intrinsic motivation to change problem behaviors after short counseling sessions, and to maintain healthy lifestyles over the long-term. Lack of locally available personnel well-trained in BMI, however, often limits access to successful interventions for people in need. To fill this accessibility gap, Computer-Based Interventions (CBIs) have started to emerge. Success of the CBIs, however, critically relies on insuring engagement and retention of CBI users so that they remain motivated to use these systems and come back to use them over the long term as necessary.^ Because of their text-only interfaces, current CBIs can therefore only express limited empathy and rapport, which are the most important factors of health interventions. Fortunately, in the last decade, computer science research has progressed in the design of simulated human characters with anthropomorphic communicative abilities. Virtual characters interact using humans’ innate communication modalities, such as facial expressions, body language, speech, and natural language understanding. By advancing research in Artificial Intelligence (AI), we can improve the ability of artificial agents to help us solve CBI problems.^ To facilitate successful communication and social interaction between artificial agents and human partners, it is essential that aspects of human social behavior, especially empathy and rapport, be considered when designing human-computer interfaces. Hence, the goal of the present dissertation is to provide a computational model of rapport to enhance an artificial agent’s social behavior, and to provide an experimental tool for the psychological theories shaping the model. Parts of this thesis were already published in [LYL+12, AYL12, AL13, ALYR13, LAYR13, YALR13, ALY14].^

Improving Resource Management in Virtualized Data Centers using Application Performance Models

The rapid growth of virtualized data centers and cloud hosting services is making the management of physical resources such as CPU, memory, and I/O bandwidth in data center servers increasingly important. Server management now involves dealing with multiple dissimilar applications with varying Service-Level-Agreements (SLAs) and multiple resource dimensions. The multiplicity and diversity of resources and applications are rendering administrative tasks more complex and challenging. This thesis aimed to develop a framework and techniques that would help substantially reduce data center management complexity. We specifically addressed two crucial data center operations. First, we precisely estimated capacity requirements of client virtual machines (VMs) while renting server space in cloud environment. Second, we proposed a systematic process to efficiently allocate physical resources to hosted VMs in a data center. To realize these dual objectives, accurately capturing the effects of resource allocations on application performance is vital. The benefits of accurate application performance modeling are multifold. Cloud users can size their VMs appropriately and pay only for the resources that they need; service providers can also offer a new charging model based on the VMs performance instead of their configured sizes. As a result, clients will pay exactly for the performance they are actually experiencing; on the other hand, administrators will be able to maximize their total revenue by utilizing application performance models and SLAs. This thesis made the following contributions. First, we identified resource control parameters crucial for distributing physical resources and characterizing contention for virtualized applications in a shared hosting environment. Second, we explored several modeling techniques and confirmed the suitability of two machine learning tools, Artificial Neural Network and Support Vector Machine, to accurately model the performance of virtualized applications. Moreover, we suggested and evaluated modeling optimizations necessary to improve prediction accuracy when using these modeling tools. Third, we presented an approach to optimal VM sizing by employing the performance models we created. Finally, we proposed a revenue-driven resource allocation algorithm which maximizes the SLA-generated revenue for a data center.

Application of Mixture Models to Survival Data

Survival models are being widely applied to the engineering field to model time-to-event data once censored data is here a common issue. Using parametric models or not, for the case of heterogeneous data, they may not always represent a good fit. The present study relays on critical pumps survival data where traditional parametric regression might be improved in order to obtain better approaches. Considering censored data and using an empiric method to split the data into two subgroups to give the possibility to fit separated models to our censored data, we’ve mixture two distinct distributions according a mixture-models approach. We have concluded that it is a good method to fit data that does not fit to a usual parametric distribution and achieve reliable parameters. A constant cumulative hazard rate policy was used as well to check optimum inspection times using the obtained model from the mixture-model, which could be a plus when comparing with the actual maintenance policies to check whether changes should be introduced or not.

Calibration of the maximum carboxylation velocity (Vcmax) using data mining techniques and ecophysiological data from the Brazilian Semiarid region, for use in Dynamic Global Vegetation Models.

The semiarid region of northeastern Brazil, the Caatinga, is extremely important due to its biodiversity and endemism. Measurements of plant physiology are crucial to the calibration of Dynamic Global Vegetation Models (DGVMs) that are currently used to simulate the responses of vegetation in face of global changes. In a field work realized in an area of preserved Caatinga forest located in Petrolina, Pernambuco, measurements of carbon assimilation (in response to light and CO2) were performed on 11 individuals of Poincianella microphylla, a native species that is abundant in this region. These data were used to calibrate the maximum carboxylation velocity (Vcmax) used in the INLAND model. The calibration techniques used were Multiple Linear Regression (MLR), and data mining techniques as the Classification And Regression Tree (CART) and K-MEANS. The results were compared to the UNCALIBRATED model. It was found that simulated Gross Primary Productivity (GPP) reached 72% of observed GPP when using the calibrated Vcmax values, whereas the UNCALIBRATED approach accounted for 42% of observed GPP. Thus, this work shows the benefits of calibrating DGVMs using field ecophysiological measurements, especially in areas where field data is scarce or non-existent, such as in the Caatinga

Comprehensive characterization of SDH-deficient GIST using NGS data and iPSC models

Gastrointestinal stromal tumors (GIST) are the most common di tumors of the gastrointestinal tract, arising from the interstitial cells of Cajal (ICCs) or their precursors. The vast majority of GISTs (75–85% of GIST) harbor KIT or PDGFRA mutations. A small percentage of GIST (about 10‐15%) do not harbor any of these driver mutations and have historically been called wild-type (WT). Among them, from 20% to 40% show loss of function of the succinate dehydrogenase complex (SDH), also defined as SDH‐deficient GIST. SDH-deficient GISTs display distinctive clinical and pathological features, and can be sporadic or associated with Carney triad or Carney-Stratakis syndrome. These tumors arise most frequently in the stomach with predilection to distal stomach and antrum, have a multi-nodular growth, display a histological epithelioid phenotype, and present frequent lympho-vascular invasion. Occurrence of lymph node metastases and indolent course are representative features of SDH-deficient GISTs. This subset of GIST is known for the immunohistochemical loss of succinate dehydrogenase subunit B (SDHB), which signals the loss of function of the entire SDH-complex. The overall aim of my PhD project consists of the comprehensive characterization of SDH deficient GIST. Throughout the project, clinical, molecular and cellular characterizations were performed using next-generation sequencing technologies (NGS), that has the potential to allow the identification of molecular patterns useful for the diagnosis and development of novel treatments. Moreover, while there are many different cell lines and preclinical models of KIT/PDGFRA mutant GIST, no reliable cell model of SDH-deficient GIST has currently been developed, which could be used for studies on tumor evolution and in vitro assessments of drug response. Therefore, another aim of this project was to develop a pre-clinical model of SDH deficient GIST using the novel technology of induced pluripotent stem cells (iPSC).

Assessing the fit of unidimensional IRT models for binary data under model misspecification

Model misspecification affects the classical test statistics used to assess the fit of the Item Response Theory (IRT) models. Robust tests have been derived under model misspecification, as the Generalized Lagrange Multiplier and Hausman tests, but their use has not been largely explored in the IRT framework. In the first part of the thesis, we introduce the Generalized Lagrange Multiplier test to detect differential item response functioning in IRT models for binary data under model misspecification. By means of a simulation study and a real data analysis, we compare its performance with the classical Lagrange Multiplier test, computed using the Hessian and the cross-product matrix, and the Generalized Jackknife Score test. The power of these tests is computed empirically and asymptotically. The misspecifications considered are local dependence among items and non-normal distribution of the latent variable. The results highlight that, under mild model misspecification, all tests have good performance while, under strong model misspecification, the performance of the tests deteriorates. None of the tests considered show an overall superior performance than the others. In the second part of the thesis, we extend the Generalized Hausman test to detect non-normality of the latent variable distribution. To build the test, we consider a seminonparametric-IRT model, that assumes a more flexible latent variable distribution. By means of a simulation study and two real applications, we compare the performance of the Generalized Hausman test with the M2 limited information goodness-of-fit test and the Likelihood-Ratio test. Additionally, the information criteria are computed. The Generalized Hausman test has a better performance than the Likelihood-Ratio test in terms of Type I error rates and the M2 test in terms of power. The performance of the Generalized Hausman test and the information criteria deteriorates when the sample size is small and with a few items.

Data driven regularization models of non-linear ill-posed inverse problems in imaging

Imaging technologies are widely used in application fields such as natural sciences, engineering, medicine, and life sciences. A broad class of imaging problems reduces to solve ill-posed inverse problems (IPs). Traditional strategies to solve these ill-posed IPs rely on variational regularization methods, which are based on minimization of suitable energies, and make use of knowledge about the image formation model (forward operator) and prior knowledge on the solution, but lack in incorporating knowledge directly from data. On the other hand, the more recent learned approaches can easily learn the intricate statistics of images depending on a large set of data, but do not have a systematic method for incorporating prior knowledge about the image formation model. The main purpose of this thesis is to discuss data-driven image reconstruction methods which combine the benefits of these two different reconstruction strategies for the solution of highly nonlinear ill-posed inverse problems. Mathematical formulation and numerical approaches for image IPs, including linear as well as strongly nonlinear problems are described. More specifically we address the Electrical impedance Tomography (EIT) reconstruction problem by unrolling the regularized Gauss-Newton method and integrating the regularization learned by a data-adaptive neural network. Furthermore we investigate the solution of non-linear ill-posed IPs introducing a deep-PnP framework that integrates the graph convolutional denoiser into the proximal Gauss-Newton method with a practical application to the EIT, a recently introduced promising imaging technique. Efficient algorithms are then applied to the solution of the limited electrods problem in EIT, combining compressive sensing techniques and deep learning strategies. Finally, a transformer-based neural network architecture is adapted to restore the noisy solution of the Computed Tomography problem recovered using the filtered back-projection method.