887 resultados para Sparse potentials
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The indoline dyes D102, D131, D149, and D205 have been characterized when adsorved on fluorine-doped tin oxide (FTO) and TiO2 electrode surfaces. Adsorption from 50:50 acetonitrile - tert-butanol onto flourine-doped tin oxide (FTO) allows approximate Langmuirian binding constants of 6.5 x 10(4), 2.01 x 10(3), 2.0 x 10(4), and 1.5 x 10(4) mol-1 dm3, respectively, to be determined. Voltammetric data obtained in acetonitrile/0.1 M NBu4PF6 indicate reversible on-electron oxidation at Emid = 0.94, 0.91, 0.88, and 0.88 V vs Ag/AgCI(3 M KCI), respectively, with dye aggregation (at high coverage) causing additional peak features at more positive potentials. Slow chemical degradation processes and electron transfer catalysis for iodine oxidation were observed for all four oxidezed indolinium cations. When adsorbed onto TiO2 nanoparticle films (ca. 9nm particle diameter and ca.3/um thickness of FTO0, reversible voltammetric responses with Emid = 1.08, 1.156, 0.92 and 0.95 V vs Ag/AgCI(3 M KCI), respectively, suggest exceptionally fast hole hopping diffusion (with Dapp > 5 x 10(-9) m2 s-1) for adsorbed layers of four indoline dyes, presumably due to pie-pie stacking in surface aggregates. Slow dye degradation is shown to affect charge transport via electron hopping. Spectrelectrochemical data for the adsorbed indoline dyes on FTO-TiO2 revealed a red-shift of absorption peaks after oxidation and the presence of a strong charge transfer band in the near-IR region. The implications of the indoline dye reactivity and fast hole mobility for solar cell devices are discussed.
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The hysteresis modulation for power electronic converters is attractive in many different applications because of its unmatched dynamic response and wide command-tracking bandwidth. Its application and beneftis for two-level converters are well understood, but the extension of this strategy to multilevel converters is still under development. This paper summarizes and reviews the various hysteresis modulation approaches available in the literature for multilevel converters. The pros and cons of various techniques are described and compared for tracking the reference signal in order to attain an adequate switching optimization, excellent dynamic responses and high accuracy in steady-state operation. By using the recently developed multilevel hysteresis modulation approaches the advantages of using several accessible dc potentials in a multilevel inverter has been fully exploited. All of these hysteresis modulation approaches are testing for tracking a current reference when applied to a fivelevel inveter. The relevant simulation and experimental result are also presented. This study will provide a useful framweork and point of reference for the future development of hysteresis modulation for multilevel converters.
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Cell based therapies as they apply to tissue engineering and regenerative medicine, require cells capable of self renewal and differentiation, and a prerequisite is to be able to prepare an effective dose of ex vivo expanded cells for autologous transplants. The in vivo identification of a source of physiologically relevant cell types suitable for cell therapies therefore figures as an integral part of tissue engineering. Stem cells serve as a reserve for biological repair, having the potential to differentiate into a number of specialised cell types within the body; they therefore represent the most useful candidates for cell based therapies. The primary goal of stem cell research is to produce cells that are both patient specific, as well as having properties suitable for the specific conditions for which they are intended to remedy. From a purely scientific perspective, stem cells allow scientists to gain a deeper understanding of developmental biology and regenerative therapies. Stem cells have acquired a number of uses for applications in regenerative medicine, immunotherapy, gene therapy, but it is in the area of tissue engineering that they generate most excitement, primarily as a result of their capacity for self-renewal and pluripotency. A unique feature of stem cells is their ability to maintain an uncommitted quiescent state in vivo and then, once triggered by conditions such as disease, injury or natural wear or tear, serve as a reservoir and natural support system to replenish lost cells. Although these cells retain the plasticity to differentiate into various tissues, being able to control this differentiation process is still one of the biggest challenges facing stem cell research. In an effort to harness the potential of these cells a number of studies have been conducted using both embryonic/foetal and adult stem cells. The use of embryonic stem cells (ESC) have been hampered by strong ethical and political concerns, this despite their perceived versatility due to their pluripotency. Ethical issues aside, other concerns raised with ESCs relates to the possibility of tumorigenesis, immune rejection and complications with immunosuppressive therapies, all of which adds layers of complications to the application ESC in research and which has led to the search for alternative sources for stem cells. The adult tissues in higher organisms harbours cells, termed adult stem cells, and these cells are reminiscent of unprogrammed stem cells. A number of sources of adult stem cells have been described. Bone marrow is by far the most accessible source of two potent populations of adult stem cells, namely haematopoietic stem cells (HSCs) and bone marrow mesenchymal stem cells (BMSCs). Autologously harvested adult stem cells can, in contrast to embryonic stem cells, readily be used in autografts, since immune rejection is not an issue; and their use in scientific research has not attracted the ethical concerns which have been the case with embryonic stem cells. The major limitation to their use, however, is the fact that adult stem cells are exceedingly rare in most tissues. This fact makes identifying and isolating these cells problematic; bone marrow being perhaps the only notable exception. Unlike the case of HSCs, there are as yet no rigorous criteria for characterizing MSCs. Changing acuity about the pluripotency of MSCs in recent studies has expanded their potential application; however, the underlying molecular pathways which impart the features distinctive to MSCs remain elusive. Furthermore, the sparse in vivo distribution of these cells imposes a clear limitation to their study in vitro. Also, when MSCs are cultured in vitro, there is a loss of the in vivo microenvironment, resulting in a progressive decline in proliferation potential and multipotentiality. This is further exacerbated with increased passage numbers in culture, characterized by the onset of senescence related changes. As a consequence, it is necessary to establish protocols for generating large numbers of MSCs but without affecting their differentiation potential. MSCs are capable of differentiating into mesenchymal tissue lineages, including bone, cartilage, fat, tendon, muscle, and marrow stroma. Recent findings indicate that adult bone marrow may also contain cells that can differentiate into the mature, nonhematopoietic cells of a number of tissues, including cells of the liver, kidney, lung, skin, gastrointestinal tract, and myocytes of heart and skeletal muscle. MSCs can readily be expanded in vitro and can be genetically modified by viral vectors and be induced to differentiate into specific cell lineages by changing the microenvironment–properties which makes these cells ideal vehicles for cellular gene therapy. MSCs can also exert profound immunosuppressive effects via modulation of both cellular and innate immune pathways, and this property allows them to overcome the issue of immune rejection. Despite the many attractive features associated with MSCs, there are still many hurdles to overcome before these cells are readily available for use in clinical applications. The main concern relates to in vivo characterization and identification of MSCs. The lack of a universal biomarker, sparse in vivo distribution, and a steady age related decline in their numbers, makes it an obvious need to decipher the reprogramming pathways and critical molecular players which govern the characteristics unique to MSCs. This book presents a comprehensive insight into the biology of adult stem cells and their utility in current regeneration therapies. The adult stem cell populations reviewed in this book include bone marrow derived MSCs, adipose derived stem cells (ASCs), umbilical cord blood stem cells, and placental stem cells. The features such as MSC circulation and trafficking, neuroprotective properties, and the nurturing roles and differentiation potential of multiple lineages have been discussed in details. In terms of therapeutic applications, the strengths of MSCs have been presented and their roles in disease treatments such as osteoarthritis, Huntington’s disease, periodontal regeneration, and pancreatic islet transplantation have been discussed. An analysis comparing osteoblast differentiation of umbilical cord blood stem cells and MSCs has been reviewed, as has a comparison of human placental stem cells and ASCs, in terms of isolation, identification and therapeutic applications of ASC in bone, cartilage regeneration, as well as myocardial regeneration. It is my sincere hope that this book will update the reader as to the research progress of MSC biology and potential use of these cells in clinical applications. It will be the best reward to all contributors of this book, if their efforts herein may in some way help the readers in any part of their study, research, and career development.
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Recommender systems are one of the recent inventions to deal with ever growing information overload. Collaborative filtering seems to be the most popular technique in recommender systems. With sufficient background information of item ratings, its performance is promising enough. But research shows that it performs very poor in a cold start situation where previous rating data is sparse. As an alternative, trust can be used for neighbor formation to generate automated recommendation. User assigned explicit trust rating such as how much they trust each other is used for this purpose. However, reliable explicit trust data is not always available. In this paper we propose a new method of developing trust networks based on user’s interest similarity in the absence of explicit trust data. To identify the interest similarity, we have used user’s personalized tagging information. This trust network can be used to find the neighbors to make automated recommendations. Our experiment result shows that the proposed trust based method outperforms the traditional collaborative filtering approach which uses users rating data. Its performance improves even further when we utilize trust propagation techniques to broaden the range of neighborhood.
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The Electrocardiogram (ECG) is an important bio-signal representing the sum total of millions of cardiac cell depolarization potentials. It contains important insight into the state of health and nature of the disease afflicting the heart. Heart rate variability (HRV) refers to the regulation of the sinoatrial node, the natural pacemaker of the heart by the sympathetic and parasympathetic branches of the autonomic nervous system. The HRV signal can be used as a base signal to observe the heart's functioning. These signals are non-linear and non-stationary in nature. So, higher order spectral (HOS) analysis, which is more suitable for non-linear systems and is robust to noise, was used. An automated intelligent system for the identification of cardiac health is very useful in healthcare technology. In this work, we have extracted seven features from the heart rate signals using HOS and fed them to a support vector machine (SVM) for classification. Our performance evaluation protocol uses 330 subjects consisting of five different kinds of cardiac disease conditions. We demonstrate a sensitivity of 90% for the classifier with a specificity of 87.93%. Our system is ready to run on larger data sets.
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In this work a novel hybrid approach is presented that uses a combination of both time domain and frequency domain solution strategies to predict the power distribution within a lossy medium loaded within a waveguide. The problem of determining the electromagnetic fields evolving within the waveguide and the lossy medium is decoupled into two components, one for computing the fields in the waveguide including a coarse representation of the medium (the exterior problem) and one for a detailed resolution of the lossy medium (the interior problem). A previously documented cell-centred Maxwell’s equations numerical solver can be used to resolve the exterior problem accurately in the time domain. Thereafter the discrete Fourier transform can be applied to the computed field data around the interface of the medium to estimate the frequency domain boundary condition in-formation that is needed for closure of the interior problem. Since only the electric fields are required to compute the power distribution generated within the lossy medium, the interior problem can be resolved efficiently using the Helmholtz equation. A consistent cell-centred finite-volume method is then used to discretise this equation on a fine mesh and the underlying large, sparse, complex matrix system is solved for the required electric field using the iterative Krylov subspace based GMRES iterative solver. It will be shown that the hybrid solution methodology works well when a single frequency is considered in the evaluation of the Helmholtz equation in a single mode waveguide. A restriction of the scheme is that the material needs to be sufficiently lossy, so that any penetrating waves in the material are absorbed.
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The Dark Ages are generally held to be a time of technological and intellectual stagnation in western development. But that is not necessarily the case. Indeed, from a certain perspective, nothing could be further from the truth. In this paper we draw historical comparisons, focusing especially on the thirteenth and fourteenth centuries, between the technological and intellectual ruptures in Europe during the Dark Ages, and those of our current period. Our analysis is framed in part by Harold Innis’s2 notion of "knowledge monopolies". We give an overview of how these were affected by new media, new power struggles, and new intellectual debates that emerged in thirteenth and fourteenth century Europe. The historical salience of our focus may seem elusive. Our world has changed so much, and history seems to be an increasingly far-from-favoured method for understanding our own period and its future potentials. Yet our seemingly distant historical focus provides some surprising insights into the social dynamics that are at work today: the fracturing of established knowledge and power bases; the democratisation of certain "sacred" forms of communication and knowledge, and, conversely, the "sacrosanct" appropriation of certain vernacular forms; challenges and innovations in social and scientific method and thought; the emergence of social world-shattering media practices; struggles over control of vast networks of media and knowledge monopolies; and the enclosure of public discursive and social spaces for singular, manipulative purposes. The period between the eleventh and fourteenth centuries in Europe prefigured what we now call the Enlightenment, perhaps moreso than any other period before or after; it shaped what the Enlightenment was to become. We claim no knowledge of the future here. But in the "post-everything" society, where history is as much up for sale as it is for argument, we argue that our historical perspective provides a useful analogy for grasping the wider trends in the political economy of media, and for recognising clear and actual threats to the future of the public sphere in supposedly democratic societies.
Resumo:
The Dark Ages are generally held to be a time of technological and intellectual stagnation in western development. But that is not necessarily the case. Indeed, from a certain perspective, nothing could be further from the truth. In this paper we draw historical comparisons, focusing especially on the thirteenth and fourteenth centuries, between the technological and intellectual ruptures in Europe during the Dark Ages, and those of our current period. Our analysis is framed in part by Harold Innis’s2 notion of "knowledge monopolies". We give an overview of how these were affected by new media, new power struggles, and new intellectual debates that emerged in thirteenth and fourteenth century Europe. The historical salience of our focus may seem elusive. Our world has changed so much, and history seems to be an increasingly far-from-favoured method for understanding our own period and its future potentials. Yet our seemingly distant historical focus provides some surprising insights into the social dynamics that are at work today: the fracturing of established knowledge and power bases; the democratisation of certain "sacred" forms of communication and knowledge, and, conversely, the "sacrosanct" appropriation of certain vernacular forms; challenges and innovations in social and scientific method and thought; the emergence of social world-shattering media practices; struggles over control of vast networks of media and knowledge monopolies; and the enclosure of public discursive and social spaces for singular, manipulative purposes. The period between the eleventh and fourteenth centuries in Europe prefigured what we now call the Enlightenment, perhaps moreso than any other period before or after; it shaped what the Enlightenment was to become. We claim no knowledge of the future here. But in the "post-everything" society, where history is as much up for sale as it is for argument, we argue that our historical perspective provides a useful analogy for grasping the wider trends in the political economy of media, and for recognising clear and actual threats to the future of the public sphere in supposedly democratic societies.
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Cell based therapies require cells capable of self renewal and differentiation, and a prerequisite is the ability to prepare an effective dose of ex vivo expanded cells for autologous transplants. The in vivo identification of a source of physiologically relevant cell types suitable for cell therapies is therefore an integral part of tissue engineering. Bone marrow is the most easily accessible source of mesenchymal stem cells (MSCs), and harbours two distinct populations of adult stem cells; namely hematopoietic stem cells (HSCs) and bone mesenchymal stem cells (BMSCs). Unlike HSCs, there are yet no rigorous criteria for characterizing BMSCs. Changing understanding about the pluripotency of BMSCs in recent studies has expanded their potential application; however, the underlying molecular pathways which impart the features distinctive to BMSCs remain elusive. Furthermore, the sparse in vivo distribution of these cells imposes a clear limitation to their in vitro study. Also, when BMSCs are cultured in vitro there is a loss of the in vivo microenvironment which results in a progressive decline in proliferation potential and multipotentiality. This is further exacerbated with increased passage number, characterized by the onset of senescence related changes. Accordingly, establishing protocols for generating large numbers of BMSCs without affecting their differentiation potential is necessary. The principal aims of this thesis were to identify potential molecular factors for characterizing BMSCs from osteoarthritic patients, and also to attempt to establish culture protocols favourable for generating large number of BMSCs, while at the same time retaining their proliferation and differentiation potential. Previously published studies concerning clonal cells have demonstrated that BMSCs are heterogeneous populations of cells at various stages of growth. Some cells are higher in the hierarchy and represent the progenitors, while other cells occupy a lower position in the hierarchy and are therefore more committed to a particular lineage. This feature of BMSCs was made evident by the work of Mareddy et al., which involved generating clonal populations of BMSCs from bone marrow of osteoarthritic patients, by a single cell clonal culture method. Proliferation potential and differentiation capabilities were used to group cells into fast growing and slow growing clones. The study presented here is a continuation of the work of Mareddy et al. and employed immunological and array based techniques to identify the primary molecular factors involved in regulating phenotypic characteristics exhibited by contrasting clonal populations. The subtractive immunization (SI) was used to generate novel antibodies against favourably expressed proteins in the fast growing clonal cell population. The difference between the clonal populations at the transcriptional level was determined using a Stem Cell RT2 Profiler TM PCR Array which focuses on stem cell pathway gene expression. Monoclonal antibodies (mAb) generated by SI were able to effectively highlight differentially expressed antigenic determinants, as was evident by Western blot analysis and confocal microscopy. Co-immunoprecipitation, followed by mass spectroscopy analysis, identified a favourably expressed protein as the cytoskeletal protein vimentin. The stem cell gene array highlighted genes that were highly upregulated in the fast growing clonal cell population. Based on their functions these genes were grouped into growth factors, cell fate determination and maintenance of embryonic and neural stem cell renewal. Furthermore, on a closer analysis it was established that the cytoskeletal protein vimentin and nine out of ten genes identified by gene array were associated with chondrogenesis or cartilage repair, consistent with the potential role played by BMSCs in defect repair and maintaining tissue homeostasis, by modulating the gene expression pattern to compensate for degenerated cartilage in osteoarthritic tissues. The gene array also presented transcripts for embryonic lineage markers such as FOXA2 and Sox2, both of which were significantly over expressed in fast growing clonal populations. A recent groundbreaking study by Yamanaka et al imparted embryonic stem cell (ESCs) -like characteristic to somatic cells in a process termed nuclear reprogramming, by the ectopic expression of the genes Sox2, cMyc and Oct4. The expression of embryonic lineage markers in adult stem cells may be a mechanism by which the favourable behaviour of fast growing clonal cells is determined and suggests a possible active phenomenon of spontaneous reprogramming in fast growing clonal cells. The expression pattern of these critical molecular markers could be indicative of the competence of BMSCs. For this reason, the expression pattern of Sox2, Oct4 and cMyc, at various passages in heterogeneous BMSCs population and tissue derived cells (osteoblasts and chondrocytes), was investigated by a real-time PCR and immunoflourescence staining. A strong nuclear staining was observed for Sox2, Oct4 and cMyc, which gradually weakened accompanied with cytoplasmic translocation after several passage. The mRNA and protein expression of Sox2, Oct4 and cMyc peaked at the third passage for osteoblasts, chondrocytes and third passage for BMSCs, and declined with each subsequent passage, indicating towards a possible mechanism of spontaneous reprogramming. This study proposes that the progressive decline in proliferation potential and multipotentiality associated with increased passaging of BMSCs in vitro might be a consequence of loss of these propluripotency factors. We therefore hypothesise that the expression of these master genes is not an intrinsic cell function, but rather an outcome of interaction of the cells with their microenvironment; this was evident by the fact that when removed from their in vivo microenvironment, BMSCs undergo a rapid loss of stemness after only a few passages. One of the most interesting aspects of this study was the integration of factors in the culture conditions, which to some extent, mimicked the in vivo microenvironmental niche of the BMSCs. A number of studies have successfully established that the cellular niche is not an inert tissue component but is of prime importance. The total sum of stimuli from the microenvironment underpins the complex interplay of regulatory mechanisms which control multiple functions in stem cells most importantly stem cell renewal. Therefore, well characterised factors which affect BMSCs characteristics, such as fibronectin (FN) coating, and morphogens such as FGF2 and BMP4, were incorporated into the cell culture conditions. The experimental set up was designed to provide insight into the expression pattern of the stem cell related transcription factors Sox2, cMyc and Oct4, in BMSCs with respect to passaging and changes in culture conditions. Induction of these pluripotency markers in somatic cells by retroviral transfection has been shown to confer pluripotency and an ESCs like state. Our study demonstrated that all treatments could transiently induce the expression of Sox2, cMyc and Oct4, and favourably affect the proliferation potential of BMSCs. The combined effect of these treatments was able to induce and retain the endogenous nuclear expression of stem cell transcription factors in BMSCs over an extended number of in vitro passages. Our results therefore suggest that the transient induction and manipulation of endogenous expression of transcription factors critical for stemness can be achieved by modulating the culture conditions; the benefit of which is to circumvent the need for genetic manipulations. In summary, this study has explored the role of BMSCs in the diseased state of osteoarthritis, by employing transcriptional profiling along with SI. In particular this study pioneered the use of primary cells for generating novel antibodies by SI. We established that somatic cells and BMSCs have a basal level of expression of pluripotency markers. Furthermore, our study indicates that intrinsic signalling mechanisms of BMSCs are intimately linked with extrinsic cues from the microenvironment and that these signals appear to be critical for retaining the expression of genes to maintain cell stemness in long term in vitro culture. This project provides a basis for developing an “artificial niche” required for reversion of commitment and maintenance of BMSC in their uncommitted homeostatic state.
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One of the nice properties of kernel classifiers such as SVMs is that they often produce sparse solutions. However, the decision functions of these classifiers cannot always be used to estimate the conditional probability of the class label. We investigate the relationship between these two properties and show that these are intimately related: sparseness does not occur when the conditional probabilities can be unambiguously estimated. We consider a family of convex loss functions and derive sharp asymptotic results for the fraction of data that becomes support vectors. This enables us to characterize the exact trade-off between sparseness and the ability to estimate conditional probabilities for these loss functions.
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Online learning algorithms have recently risen to prominence due to their strong theoretical guarantees and an increasing number of practical applications for large-scale data analysis problems. In this paper, we analyze a class of online learning algorithms based on fixed potentials and nonlinearized losses, which yields algorithms with implicit update rules. We show how to efficiently compute these updates, and we prove regret bounds for the algorithms. We apply our formulation to several special cases where our approach has benefits over existing online learning methods. In particular, we provide improved algorithms and bounds for the online metric learning problem, and show improved robustness for online linear prediction problems. Results over a variety of data sets demonstrate the advantages of our framework.
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Computational models for cardiomyocyte action potentials (AP) often make use of a large parameter set. This parameter set can contain some elements that are fitted to experimental data independently of any other element, some elements that are derived concurrently with other elements to match experimental data, and some elements that are derived purely from phenomenological fitting to produce the desired AP output. Furthermore, models can make use of several different data sets, not always derived for the same conditions or even the same species. It is consequently uncertain whether the parameter set for a given model is physiologically accurate. Furthermore, it is only recently that the possibility of degeneracy in parameter values in producing a given simulation output has started to be addressed. In this study, we examine the effects of varying two parameters (the L-type calcium current (I(CaL)) and the delayed rectifier potassium current (I(Ks))) in a computational model of a rabbit ventricular cardiomyocyte AP on both the membrane potential (V(m)) and calcium (Ca(2+)) transient. It will subsequently be determined if there is degeneracy in this model to these parameter values, which will have important implications on the stability of these models to cell-to-cell parameter variation, and also whether the current methodology for generating parameter values is flawed. The accuracy of AP duration (APD) as an indicator of AP shape will also be assessed.
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CCTV and surveillance networks are increasingly being used for operational as well as security tasks. One emerging area of technology that lends itself to operational analytics is soft biometrics. Soft biometrics can be used to describe a person and detect them throughout a sparse multi-camera network. This enables them to be used to perform tasks such as determining the time taken to get from point to point, and the paths taken through an environment by detecting and matching people across disjoint views. However, in a busy environment where there are 100's if not 1000's of people such as an airport, attempting to monitor everyone is highly unrealistic. In this paper we propose an average soft biometric, that can be used to identity people who look distinct, and are thus suitable for monitoring through a large, sparse camera network. We demonstrate how an average soft biometric can be used to identify unique people to calculate operational measures such as the time taken to travel from point to point.
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This paper proposes the use of eigenvoice modeling techniques with the Cross Likelihood Ratio (CLR) as a criterion for speaker clustering within a speaker diarization system. The CLR has previously been shown to be a robust decision criterion for speaker clustering using Gaussian Mixture Models. Recently, eigenvoice modeling techniques have become increasingly popular, due to its ability to adequately represent a speaker based on sparse training data, as well as an improved capture of differences in speaker characteristics. This paper hence proposes that it would be beneficial to capitalize on the advantages of eigenvoice modeling in a CLR framework. Results obtained on the 2002 Rich Transcription (RT-02) Evaluation dataset show an improved clustering performance, resulting in a 35.1% relative improvement in the overall Diarization Error Rate (DER) compared to the baseline system.
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Experimental action potential (AP) recordings in isolated ventricular myoctes display significant temporal beat-to-beat variability in morphology and duration. Furthermore, significant cell-to-cell differences in AP also exist even for isolated cells originating from the same region of the same heart. However, current mathematical models of ventricular AP fail to replicate the temporal and cell-to-cell variability in AP observed experimentally. In this study, we propose a novel mathematical framework for the development of phenomenological AP models capable of capturing cell-to-cell and temporal variabilty in cardiac APs. A novel stochastic phenomenological model of the AP is developed, based on the deterministic Bueno-Orovio/Fentonmodel. Experimental recordings of AP are fit to the model to produce AP models of individual cells from the apex and the base of the guinea-pig ventricles. Our results show that the phenomenological model is able to capture the considerable differences in AP recorded from isolated cells originating from the location. We demonstrate the closeness of fit to the available experimental data which may be achieved using a phenomenological model, and also demonstrate the ability of the stochastic form of the model to capture the observed beat-to-beat variablity in action potential duration.