Effect of Efavirenz on High-Density Lipoprotein Antioxidant Properties in HIV-Infected Patients

WHAT IS ALREADY KNOWN ABOUT THIS SUBJECT: * In previous work, we showed a long-term and concentration-dependent beneficial effect of the non-nucleoside reverse transcriptase inhibitor efavirenz (EFV) on high-density lipoproteins (HDL) in human immunodeficiency virus (HIV)-infected patients. * Furthermore, it has been suggested that instead of the current practice of only measuring HDL-chelesterol values, the evaluation of HDL function, namely its antioxidant properties, might be an improved tool for identifying subjects at increased risk for cardiovascular events. * Paraoxonase-1 (PON-1) is an enzyme associated with HDL that is responsible for HDL antioxidant function. WHAT THIS STUDY ADDS: * In the present work, we studied the effect of EFV on the activity of PON-1 and showed, for the first time, that EFV-based antiretroviral therapy is associated with a better antioxidant function, i.e. with a higher PON-1 activity. AIMS: A long-term and concentration-dependent beneficial effect of efavirenz (EFV) on cholesterol associated with high-density lipoprotein (HDL-c) in human immunodeficiency virus (HIV)-infected patients has been documented. Furthermore, it has been suggested that, instead of the current practice of only measuring HDL-c values, the evaluation of HDL quality might be an improved tool for identifying subjects at increased risk of cardiovascular events. Paraoxonase-1 (PON-1) is an enzyme associated with HDL that is involved in the onset of cardiovascular disease and responsible for HDL antioxidant function. The aim of the present study was to investigate the effect of EFV on the circulating activity of PON-1 in HIV-infected patients. METHODS: The patients included were adults with a documented HIV-1 infection, nontreated or treated with antiretroviral regimens including EFV 600 mg once daily as first therapeutic regimen for at least 3 months. The influence of treatment with EFV, HDL-c and CD4 cell count on PON-1 activity was analysed. RESULTS: HIV-infected White patients treated with EFV had higher PON-1 activity [77.35 U l(-1) (65.66, 89.04)] (P < 0.05) and higher PON-1 activity : HDL-c ratio [1.88 (1.49, 2.28)] (P < 0.01) than untreated patients. PON-1 activity was higher in Black patients (P < 0.001) and in patients with a CD4 cell count >500 cells ml(-1) (P= 0.0120). CONCLUSIONS: EFV-based antiretroviral regimens are associated with HDL particles with a better antioxidant function, i.e. with a higher PON-1 activity. The PON-1 activity of Black patients is higher than that found in Whites regardless of treatment. Ethnicity should be taken into consideration when studying drug effects on PON-1 activity.

Humoral response towards high density lipoprotein : a new mechanism for atherogenesis

RESUMO:Aterosclerose é uma das principais causas de morbilidade e mortalidade no mundo ocidental. É responsável, direta ou indiretamente, pela maior percentagem de gastos com a saúde na maioria dos países europeus. A “teoria lipídica” da aterosclerose, que se baseia na dislipidemia como causa primária para a doença vascular tem algumas implicações práticas importantes: permite a definição de linhas de orientação e protocolos simples e ainda estabelece alvos terapêuticos que podem ser atingidos na maior parte dos casos com a atual intervenção farmacológica. A associação da aterosclerose com o sistema imunológico (a “teoria imunológica”), forneceu por sua vez novas formas de explorar os mecanismos envolvidos e abriu novas perspetivas para um conhecimento mais completo da doença. No entanto, levanta dificuldades evidentes no que diz respeito às possibilidades terapêuticas. De todos os intervenientes no processo aterosclerótico (bioquímicos, imunológicos e anatómicos), as lipoproteínas de elevada densidade (HDL) são atualmente reconhecidas como um dos fatores mais importantes na aterogénese. Isto é baseado no reconhecimento das múltiplas propriedades anti-aterogénicas das HDL como por exemplo: a anti-oxidante, a anti-inflamatória e a antitrombótica, bem como o seu importante papel na melhoraria da função endotelial. Atualmente, é consensual que as funções anti-aterogénicas das HDL vão além do seu papel no transporte reverso do colesterol (RCT) e a importância das HDL no processo aterosclerótico baseia-se não apenas no seu papel protetor impedindo a formação da placa de ateroma, mas também na estabilização destas, prevenindo a sua ruptura e, consequentemente o evento trombótico. Como fundamentais no processo aterosclerótico estão reconhecidos dois principais conjuntos de eventos: um caracterizado por alterações no metabolismo das lipoproteínas que resultam em lipoproteínas pró-inflamatórias e pró-oxidantes que interagem com os componentes celulares da parede arterial e que conduzem à formação da placa de ateroma; o outro evento é a resposta imunológica desencadeada contra um novo conjunto de antigénios que por sua vez leva à produção de citoquinas pró-inflamatórias. Dada a complexidade da HDL e das suas múltiplas funções estas lipoproteínas tornaram-se um potencial alvo para a resposta auto-imune, e cujas consequências podem explicar algumas das associações identificados em estudos clínicos e epidemiológicos. Contudo esta interação entre o sistema imunológico e HDL nunca foi exaustivamente estudada. Portanto, pomos a hipótese de que em condições oxidativas e pró-inflamatórias, um aumento do antigénio (HDL) conduz a um consequente acréscimo na produção de anticorpos anti-HDL (aHDL) responsáveis pela alteração quantitativa e / ou qualitativa das HDL. O conceito de que estes anticorpos podem contribuir tanto para a evolução a longo prazo do processo aterosclerótico, como para o desencadeamento de eventos clínicos pode também explicar a heterogeneidade encontrada em cada doente e nos grandes estudos clínicos, no que diz respeito aos fatores de risco e outcomes clínicos. Para além disso, a confirmação desta hipótese pode permitir explicar porque é que as intervenções terapêuticas atualmente em desenvolvimento para aumentar os níveis de HDL, não conseguem mostrar a tão esperada redução do risco vascular. O objetivo geral desta tese foi identificar e caracterizar a resposta humoral contra os componentes da HDL, e avaliar possíveis mecanismos que possam contribuir para a modificação das propriedades anti-aterogénicas das HDL. Para alcançar este objetivo investigou-se: 1) A presença de anticorpos aHDL em doentes com lúpus eritematoso sistémico (SLE) e em doentes com manifestações clínicas de aterosclerose, como os doentes com doença arterial coronária (CAD), acidente vascular cerebral isquémico (IS) e diabetes tipo 2; 2) Os principais alvos antigénicos dentro do complexo das HDL e a associação entre os títulos de anticorpos aHDL e diferentes características clínicas destas doenças; 3) As modificações das funções normais associadas às HDL, em particular da função anti-oxidante e anti-inflamatória; 4) A atividade biológica dos anticorpos aHDL isolados do soro de doentes através de um conjunto de experiências in vitro de inibição da atividade da paraoxonase 1 (PON1) e da expressão de moléculas de adesão em culturas de células endoteliais. Para tal foi necessário estabelecer um método de isolamento dos anticorpos. Os anticorpos aHDL isolados do soro de doentes foram utilizados de forma a identificar as potenciais alterações dos sistemas celulares utilizados; 5) O efeito de fármacos usados no tratamento das dislipidemias, em particular o ácido nicotínico e as estatinas, na variação dos títulos de anticorpos aHDL através de ensaios clínicos randomizados, controlados com placebo e em dupla ocultação. Os métodos utilizados neste trabalho incluíram: técnicas imunológicas (como por exemplo, enzyme-linked immunoabsorbent assay - ELISA, ensaio imunoturbidimetrico e cromatografia de imuno-afinidade) técnicas bioquímicas (tais como a quantificação de atividade enzimática por espectrofotometria e por luminescência), experiências com cultura de células e citometria de fluxo. Os nossos resultados mostram que: 1) A presença de anticorpos aHDL, e mais especificamente anticorpos contra alguns do seus principais componentes como a apolipoproteína A-I (ApoA-I, principal apolipoproteína presente nas HDL) e a PON1 (o enzima que mais contribui para a propriedade anti-oxidante das HDL), quer em doentes com doenças auto-imunes, como o SLE, quer em doentes com manifestações clínicas de aterosclerose, como CAD, IS e diabetes tipo 2. Os doentes apresentaram títulos de anticorpos IgG aHDL, aApoA-I e aPON1 significativamente mais elevados do que controlos saudáveis com a mesma idade e sexo. 2) A correlação positiva estatisticamente significativa entre os títulos de aHDL e aApoA-I e aPON1 sugere que estes sejam dois dos principais alvos antigénicos dentro do complexo das HDL. Os anticorpos encontrados nestes doentes estão associados com a diminuição da atividade da PON1 e a uma redução da capacidade anti-oxidante total (TAC) do soro, um aumento dos biomarcadores de disfunção endotelial (como por exemplo dos metabolitos do óxido nítrico - NO2- e NO3-, as moléculas de adesão vascular e intracelular - VCAM-1 e ICAM-1 e os níveis de 3-nitrotirosina). Nos doentes com SLE os títulos destes estão associados a um aumento do dano cardiovascular e à atividade global da doença avaliados pelas escalas SLICC/ACR DI e BILAG score, respetivamente. Enquanto que nos doentes com diabetes tipo 2 estes anticorpos estão associados com um aumento dos níveis de glicemia em jejum (FGP) e hemoglobina glicada (HbA1c). 3) Após se ter estabelecido um método de isolamento dos anticorpos que permite isolar quantidades significativas de anticorpos do soro de doentes sem perder a sua especificidade, foi identificada a capacidade dos anticorpos isolados do soro de doentes inibirem de uma forma dependente da concentração a atividade da PON1 até um máximo de 70% no caso dos doentes com SLE e ente 7-52% no caso dos anticorpos isolados de doentes com CAD e IS. 4) O efeito anti-inflamatório das HDL na inibição da produção de VCAM-1 induzida por citoquinas (como o TNF-) foi revertido em mais de 80% pelos anticorpos aHDL isolados do soro de doentes. 5) A angiogenesis induzida por HDL através do aumento do fator de crescimento do endotélio vascular (VEGF) foi anulada em 65% pelos anticorpos aHDL isolados do soro de doentes. 6) Os atuais agentes farmacológicos disponíveis para aumentar as concentrações de HDL-C estão associados a um aumento dos títulos de anticorpos.-------- ABSTRACTAtherosclerosis is the major cause of morbidity and mortality in the western world. It is also responsible, directly or indirectly, for the highest percentage of health costs in most European countries. Despite the use of new technologies for the diagnosis of vascular disease and regardless of the major advances in treatment, the atherosclerosis-related clinical burden is still raising. The “lipid theory” of atherogenesis, which identifies dyslipidemia as the primary cause of this vascular disease has some important practical implications: it allows the definition of simple guidelines and establishes therapeutic targets which can be generally met with current pharmacologic intervention. The association between atherosclerosis an the immune system (the immune concept) has in turn provided new ways of exploring the mechanisms involved in this condition and has opened new perspectives in the understanding of the disease. However, it raises obvious difficulties when it comes to treatment options. Of all the players (biochemical, immunological and anatomical) involved in this matter, high-density lipoproteins (HDL) are currently recognised as one of the most important factors in atherogenesis. This is based on the recognition of HDL's multiple anti-atherogenic properties: anti-oxidant, anti-inflammatory and antithrombotic, as well as its capacity to improve endothelial function. Nowadays, it is widely recognized that the anti-atherogenic functions of HDL go beyond reverse cholesterol transport (RCT), and the importance of HDL is based not just on its ability to reduce atheroma formation but also on its ability to stabilise plaques, therefore preventing their rupture and ultimately thrombosis. Two main set of events have been recognised as fundamental in atherogenesis: one, characterized by lipoprotein metabolism alterations, resulting in pro-inflammatory and pro-oxidative lipoproteins, which interact with the normal cellular elements of the arterial wall leading to atheroma formation; the other, the immune cellular response towards new sets of antigens which lead to the production of pro-inflammatory cytokines. Given to HDL complexity and multiple functions this lipoprotein has became a potential target for an auto-immune response, the consequences of which may explain some of the association identified in epidemiological and clinical studies, though the interaction between the immune system and HDL has never been thoroughly addressed. Therefore, we hypothesized that under oxidative and pro-inflammatory conditions, the increase in the antigen (HDL) would lead to a consequent increase in the production of anti-HDL (aHDL) antibodies be responsible for quantitative and/or qualitative changes of HDL. The concept that these antibodies may contribute either to the long-term evolution of atherosclerosis or to the triggering of clinical events may also explain the heterogeneity found in individual patients and in large cohorts regarding risk factors and clinical outcomes. Moreover this may be a major breakthrough in understanding why therapeutic interventions that increase HDL levels, failed to show the anticipated reduction in vascular risk. The overall aims of this thesis were to identified and characterize the humoral response towards HDL components and to evaluate the possible mechanisms that may contribute to the modifications of the anti-atherogenic properties of HDL. To achieve this objective we investigated: 1) the presence of aHDL antibodies in patients with systemic lupus erythematosus (SLE) and in patients with atherosclerosis-related clinical events, such as coronary artery disease (CAD), ischemic stroke (IS) and type 2 diabetes; 2) the association between the titres of aHDL antibodies and different clinical features of these diseases; 3) the modifications of the anti-atherogenic properties of HDL; 4) the biologic effect of aHDL antibodies isolated from serum of patients on the anti-oxidant and anti-inflammatory properties of HDL; 5) the effect of different pharmacologic treatments for dyslipidemia on the prevalence and activity of aHDL antibodies. The methodologies used in this work included immunologic-related techniques (e.g. enzyme-linked immunoabsorbent assay – ELISA, immunoturbidimetric immunoassay and immunoaffinity chromatography), biochemical techniques (enzymatic assays with quantification by spectrophotometry and luminescence methods), cell culture experiments and flow cytometry. Our results indicate that: 1) The titres of IgG aHDL, anti-apolipoprotein A-I (aApoA-I) and anti-paraoxonase 1 (aPON1) antibodies were higher in patients with SLE, CAD, IS and type 2 diabetes when compared with age and sex matched healthy controls. 2) The antibodies found in these patients were associated with decreased PON1 activity, (the enzyme responsible for most of the anti-oxidant effect of HDL), reduced total anti-oxidant capacity (TAC) of serum and increased biomarkers of endothelial dysfunction (nitric oxide metabolites, adhesion molecules, nitrotyrosine). In patients with SLE the antibody titres were associated with an increase in disease-related cardiovascular damage and activity whereas in patients with type 2 diabetes they were directly related with the fasting glucose plasma (FGP) levels and the glycosylated haemoglobin (HbA1c). 3) The antibodies isolated from serum of our patients, directly inhibited HDL-associated PON1 activity in a dose dependent way ranging from 7 to 52%. 4) The anti-inflammatory effect of HDL, measured by the percentage of inhibition of the cytokine-induced production of vascular adhesion molecules (VCAM-1), was reduced in more than 80% by aHDL antibodies isolated from our patients. 5) The HDL-induced angiogenesis by increasing vascular endothelial growth factor (VEGF) levels was abrogated in 65% by the antibodies isolated from serum of patients. 6) The current available pharmacologic agents for increasing HDL-C concentrations were associated with an increase in the titres of IgG aApoA-I antibodies. This increase was higher in the extended release niacin when compared to statins probably due to their dampening effect on oxidative stress. In conclusion, aHDL antibodies are present in different pathologic conditions. aHDL antibodies represent a family of self-reacting immunoglobulins, of which ApoA-I and PON1 might be the most relevant targets. These antibodies are biologically active, interfering with the HDL anti-oxidant and anti-inflammatory properties and, consequently, with the atherosclerotic process. The pathogenic potential of these antibodies may lead to the identification of a new biomarker for vascular disease, whilst presenting itself as a novel target for a different treatment approach which may redefine the treatment strategies and clinical trials design for HDL interventions in the future.

Litterfall production in intact and selectively logged forests in southern of Amazonia as a function of basal area of vegetation and plant density

Nutrient recycling in the forest is linked to the production and decomposition of litter, which are essential processes for forest maintenance, especially in regions of nutritionally poor soils. Human interventions in forest such as selecttive logging may have strong impacts on these processes. The objectives of this study were to estimate litterfall production and evaluate the influence of environmental factors (basal area of vegetation, plant density, canopy cover, and soil physicochemical properties) and anthropogenic factors (post-management age and exploited basal area) on this production, in areas of intact and exploited forest in southern Amazonia, located in the northern parts of Mato Grosso state. This study was conducted at five locations and the average annual production of litterfall was 10.6 Mg ha-1 year-1, higher than the values for the Amazon rainforest. There were differences in litterfall productions between study locations. Effects of historical logging intensity on litterfall production were not significant. Effects of basal area of vegetation and tree density on litterfall production were observed, highlighting the importance of local vegetation characteristics in litterfall production. This study demonstrated areas of transition between the Amazonia-Cerrado tend to have a higher litterfall production than Cerrado and Amazonia regions, and this information is important for a better understanding of the dynamics of nutrient and carbon cycling in these transition regions.

Goblet cell density association with tear function and ocular surface physiology

Purpose: To determine the relationship of goblet cell density (GCD) with tear function and ocular surface physiology. Methods: This was a cross-sectional study conducted in 35 asymptomatic subjects with mean age 23.8±3.6 years. Tear film assessment, conjunctiva and cornea examination were done in each subject. Conjunctival impression cytology was performed by applying Nitrocellulose Millipore MFTM-Membrane filter over the superior bulbar conjunctiva. The filter paper was than fixed with 96% ethanol and stained with Periodic Acid Schiff, Hematoxylin and Eosin. GCD was determined by optical microscopy. Relation between GCD and Schirmer score, tear break-up time (TBUT), bulbar redness, limbal redness and corneal staining was determined. Results: The mean GCD was 151±122 cells/mm2. GCD was found higher in eyes with higher Schirmer score but it was not significant (p = 0.75). There was a significant relationship ofGCDwith TBUT (p = 0.042). GCD was not correlated with bulbar redness (p = 0.126), and limbal redness (p = 0.054) as well as corneal staining (p = 0.079). No relationship of GCD with age and gender of the subjects (p > 0.05) was observed. Conclusion: GCD was found correlated with TBUT but no significant correlation was found with the aqueous portion of the tear, limbal as well as bulbar redness and corneal staining.

Sleep function: current questions and new approaches.

The mammalian brain oscillates through three distinct global activity states: wakefulness, non-rapid eye movement (NREM) sleep and REM sleep. The regulation and function of these 'vigilance' or 'behavioural' states can be investigated over a broad range of temporal and spatial scales and at different levels of functional organization, i.e. from gene expression to memory, in single neurons, cortical columns or the whole brain and organism. We summarize some basic questions that have arisen from recent approaches in the quest for the functions of sleep. Whereas traditionally sleep was viewed to be regulated through top-down control mechanisms, recent approaches have emphasized that sleep is emerging locally and regulated in a use-dependent (homeostatic) manner. Traditional markers of sleep homeostasis, such as the electroencephalogram slow-wave activity, have been linked to changes in connectivity and plasticity in local neuronal networks. Thus waking experience-induced local network changes may be sensed by the sleep homeostatic process and used to mediate sleep-dependent events, benefiting network stabilization and memory consolidation. Although many questions remain unanswered, the available data suggest that sleep function will best be understood by an analysis which integrates sleep's many functional levels with its local homeostatic regulation.

Effect of atazanavir versus other protease inhibitor-containing antiretroviral therapy on endothelial function in HIV-infected persons: randomised controlled trial.

OBJECTIVE: Impaired endothelial function was demonstrated in HIV-infected persons on protease inhibitor (PI)-containing antiretroviral therapy, probably due to altered lipid metabolism. Atazanavir is a PI causing less atherogenic lipoprotein changes. This study determined whether endothelial function improves after switching from other PI to atazanavir. DESIGN: Randomised, observer-blind, treatment-controlled trial. SETTING: Three university-based outpatient clinics. PATIENTS: 39 HIV-infected persons with suppressed viral replication on PI-containing regimens and fasting low-density lipoprotein (LDL)-cholesterol greater than 3 mmol/l. INTERVENTION: Patients were randomly assigned to continue the current PI or change to unboosted atazanavir. MAIN OUTCOME MEASURES: Endpoints at week 24 were endothelial function assessed by flow-mediated dilation (FMD) of the brachial artery, lipid profiles and serum inflammation and oxidative stress parameters. RESULTS: Baseline characteristics and mean FMD values of the two treatment groups were comparable (3.9% (SD 1.8) on atazanavir versus 4.0% (SD 1.5) in controls). After 24 weeks' treatment, FMD decreased to 3.3% (SD 1.4) and 3.4% (SD 1.7), respectively (all p = ns). Total cholesterol improved in both groups (p<0.0001 and p = 0.01, respectively) but changes were more pronounced on atazanavir (p = 0.05, changes between groups). High-density lipoprotein and triglyceride levels improved on atazanavir (p = 0.03 and p = 0.003, respectively) but not in controls. Serum inflammatory and oxidative stress parameters did not change; oxidised LDL improved significantly in the atazanavir group. CONCLUSIONS: The switch from another PI to atazanavir in treatment-experienced patients did not result in improvement of endothelial function despite significantly improved serum lipids. Atherogenic lipid profiles and direct effects of antiretroviral drugs on the endothelium may affect vascular function. Trial registration number: NCT00447070.

Estimated frequency of B-chromosomes and population density of Astyanax scabripinnis paranae in a small stream

A study was made of the frequency of B-chromosomes and the population density of Astyanax scabripinnis paranae (Pisces, Characidae, Tetragonopterinae) from three stretches of the Cascatinha stream (Botucatu, SP). In the first stretch the population was estimated to be about 212 individuals and among 35 karyotyped specimens, 23 carried one macro B-chromosome; in the second stretch the population was estimated to be about 650 individuals and among 20 specimens karyotyped, two possessed one macro B-chromosome; in the third stretch the population was estimated to be about 107 individuals and among 10 specimens karyotyped, one carried one macro B-chromosome. A significant difference was observed in the frequency of macro B-chromosomes in females (57%) and males (8.7%) (P = 0.0001). These data suggest that the B-chromosome frequency and the populational density are not directly related. The hypothesis of the existence of some adaptive effect conferred by the B-chromosomes to the specimens from the first stretch of the Cascatinha stream is presented and discussed

Evaluation of the Efficiency of Line-Start Permanent-Magnet Machines as a Function of the Operating Temperature

The standard squirrel-cage induction machine has nearly reached its maximum efficiency. In order to further increase the energy efficiency of electrical machines, the use of permanent magnets in combination with the robust design and the line start capability of the induction machine is extensively investigated. Many experimental designs have been suggested in literature, but recently, these line-start permanent-magnet machines (LSPMMs) have become off-the-shelf products available in a power range up to 7.5 kW. The permanent magnet flux density is a function of the operating temperature. Consequently, the temperature will affect almost every electrical quantity of the machine, including current, torque, and efficiency. In this paper, the efficiency of an off-the-shelf 4-kW three-phase LSPMM is evaluated as a function of the temperature by both finite-element modeling and by practical measurements. In order to obtain stator, rotor, and permanent magnet temperatures, lumped thermal modeling is used.

ARMA modeling of time series based on rational approximation of spectral density function

This study is concerned with Autoregressive Moving Average (ARMA) models of time series. ARMA models form a subclass of the class of general linear models which represents stationary time series, a phenomenon encountered most often in practice by engineers, scientists and economists. It is always desirable to employ models which use parameters parsimoniously. Parsimony will be achieved by ARMA models because it has only finite number of parameters. Even though the discussion is primarily concerned with stationary time series, later we will take up the case of homogeneous non stationary time series which can be transformed to stationary time series. Time series models, obtained with the help of the present and past data is used for forecasting future values. Physical science as well as social science take benefits of forecasting models. The role of forecasting cuts across all fields of management-—finance, marketing, production, business economics, as also in signal process, communication engineering, chemical processes, electronics etc. This high applicability of time series is the motivation to this study.

Message Integrity in the World Wide Web: Use of Nested Hash Function and a Fast Stream Cipher

The focus of this work is to provide authentication and confidentiality of messages in a swift and cost effective manner to suit the fast growing Internet applications. A nested hash function with lower computational and storage demands is designed with a view to providing authentication as also to encrypt the message as well as the hash code using a fast stream cipher MAJE4 with a variable key size of 128-bit or 256-bit for achieving confidentiality. Both nested Hash function and MAJE4 stream cipher algorithm use primitive computational operators commonly found in microprocessors; this makes the method simple and fast to implement both in hardware and software. Since the memory requirement is less, it can be used for handheld devices for security purposes.

Using zero-norm constraint for sparse probability density function estimation

A new sparse kernel probability density function (pdf) estimator based on zero-norm constraint is constructed using the classical Parzen window (PW) estimate as the target function. The so-called zero-norm of the parameters is used in order to achieve enhanced model sparsity, and it is suggested to minimize an approximate function of the zero-norm. It is shown that under certain condition, the kernel weights of the proposed pdf estimator based on the zero-norm approximation can be updated using the multiplicative nonnegative quadratic programming algorithm. Numerical examples are employed to demonstrate the efficacy of the proposed approach.

Sparse probability density function estimation using the minimum integrated square error

We develop a new sparse kernel density estimator using a forward constrained regression framework, within which the nonnegative and summing-to-unity constraints of the mixing weights can easily be satisfied. Our main contribution is to derive a recursive algorithm to select significant kernels one at time based on the minimum integrated square error (MISE) criterion for both the selection of kernels and the estimation of mixing weights. The proposed approach is simple to implement and the associated computational cost is very low. Specifically, the complexity of our algorithm is in the order of the number of training data N, which is much lower than the order of N2 offered by the best existing sparse kernel density estimators. Numerical examples are employed to demonstrate that the proposed approach is effective in constructing sparse kernel density estimators with comparable accuracy to those of the classical Parzen window estimate and other existing sparse kernel density estimators.

A fast algorithm for sparse probability density function construction

A new sparse kernel density estimator is introduced. Our main contribution is to develop a recursive algorithm for the selection of significant kernels one at time using the minimum integrated square error (MISE) criterion for both kernel selection. The proposed approach is simple to implement and the associated computational cost is very low. Numerical examples are employed to demonstrate that the proposed approach is effective in constructing sparse kernel density estimators with competitive accuracy to existing kernel density estimators.