Risk Bounds for Mixture Density Estimation

In this paper we focus on the problem of estimating a bounded density using a finite combination of densities from a given class. We consider the Maximum Likelihood Procedure (MLE) and the greedy procedure described by Li and Barron. Approximation and estimation bounds are given for the above methods. We extend and improve upon the estimation results of Li and Barron, and in particular prove an $O(\\frac{1}{\\sqrt{n}})$ bound on the estimation error which does not depend on the number of densities in the estimated combination.

High Density Single Crystalline GaN Nanodot Arrays Fabricated Using Template-Assisted Selective Growth

High density, uniform GaN nanodot arrays with controllable size have been synthesized by using template-assisted selective growth. The GaN nanodots with average diameter 40nm, 80nm and 120nm were selectively grown by metalorganic chemical vapor deposition (MOCVD) on a nano-patterned SiO2/GaN template. The nanoporous SiO2 on GaN surface was created by inductively coupled plasma etching (ICP) using anodic aluminum oxide (AAO) template as a mask. This selective regrowth results in highly crystalline GaN nanodots confirmed by high resolution transmission electron microscopy. The narrow size distribution and uniform spatial position of the nanoscale dots offer potential advantages over self-assembled dots grown by the Stranski–Krastanow mode.

Hilbert space on probability density functions with Aitchison geometry

Compositional data analysis motivated the introduction of a complete Euclidean structure in the simplex of D parts. This was based on the early work of J. Aitchison (1986) and completed recently when Aitchinson distance in the simplex was associated with an inner product and orthonormal bases were identified (Aitchison and others, 2002; Egozcue and others, 2003). A partition of the support of a random variable generates a composition by assigning the probability of each interval to a part of the composition. One can imagine that the partition can be refined and the probability density would represent a kind of continuous composition of probabilities in a simplex of infinitely many parts. This intuitive idea would lead to a Hilbert-space of probability densities by generalizing the Aitchison geometry for compositions in the simplex into the set probability densities

A comparison of the alr and ilr transformations for kernel density estimation of compositional data

In a seminal paper, Aitchison and Lauder (1985) introduced classical kernel density estimation techniques in the context of compositional data analysis. Indeed, they gave two options for the choice of the kernel to be used in the kernel estimator. One of these kernels is based on the use the alr transformation on the simplex SD jointly with the normal distribution on RD-1. However, these authors themselves recognized that this method has some deficiencies. A method for overcoming these dificulties based on recent developments for compositional data analysis and multivariate kernel estimation theory, combining the ilr transformation with the use of the normal density with a full bandwidth matrix, was recently proposed in Martín-Fernández, Chacón and Mateu- Figueras (2006). Here we present an extensive simulation study that compares both methods in practice, thus exploring the finite-sample behaviour of both estimators

Comparing methods for dimensionality reduction when data are density functions

Functional Data Analysis (FDA) deals with samples where a whole function is observed for each individual. A particular case of FDA is when the observed functions are density functions, that are also an example of infinite dimensional compositional data. In this work we compare several methods for dimensionality reduction for this particular type of data: functional principal components analysis (PCA) with or without a previous data transformation and multidimensional scaling (MDS) for diferent inter-densities distances, one of them taking into account the compositional nature of density functions. The difeerent methods are applied to both artificial and real data (households income distributions)

Modeling and Classifying Breast Tissue Density in Mammograms

We present a new approach to model and classify breast parenchymal tissue. Given a mammogram, first, we will discover the distribution of the different tissue densities in an unsupervised manner, and second, we will use this tissue distribution to perform the classification. We achieve this using a classifier based on local descriptors and probabilistic Latent Semantic Analysis (pLSA), a generative model from the statistical text literature. We studied the influence of different descriptors like texture and SIFT features at the classification stage showing that textons outperform SIFT in all cases. Moreover we demonstrate that pLSA automatically extracts meaningful latent aspects generating a compact tissue representation based on their densities, useful for discriminating on mammogram classification. We show the results of tissue classification over the MIAS and DDSM datasets. We compare our method with approaches that classified these same datasets showing a better performance of our proposal

A Novel Breast Tissue Density Classification Methodology

It has been shown that the accuracy of mammographic abnormality detection methods is strongly dependent on the breast tissue characteristics, where a dense breast drastically reduces detection sensitivity. In addition, breast tissue density is widely accepted to be an important risk indicator for the development of breast cancer. Here, we describe the development of an automatic breast tissue classification methodology, which can be summarized in a number of distinct steps: 1) the segmentation of the breast area into fatty versus dense mammographic tissue; 2) the extraction of morphological and texture features from the segmented breast areas; and 3) the use of a Bayesian combination of a number of classifiers. The evaluation, based on a large number of cases from two different mammographic data sets, shows a strong correlation ( and 0.67 for the two data sets) between automatic and expert-based Breast Imaging Reporting and Data System mammographic density assessment

Automatic classification of breast density

A recent trend in digital mammography is computer-aided diagnosis systems, which are computerised tools designed to assist radiologists. Most of these systems are used for the automatic detection of abnormalities. However, recent studies have shown that their sensitivity is significantly decreased as the density of the breast increases. This dependence is method specific. In this paper we propose a new approach to the classification of mammographic images according to their breast parenchymal density. Our classification uses information extracted from segmentation results and is based on the underlying breast tissue texture. Classification performance was based on a large set of digitised mammograms. Evaluation involves different classifiers and uses a leave-one-out methodology. Results demonstrate the feasibility of estimating breast density using image processing and analysis techniques

A "Trojan horse" strategy to reverse drug-resistance in brain tumors

Los gliomas malignos representan una de las formas más agresivas de los tumores del sistema nervioso central (SNC). De acuerdo con la clasificación de los tumores cerebrales de la Organización Mundial de la Salud (OMS), los astrocitomas han sido categorizados en cuatro grados, determinados por la patología subyacente. Es así como los gliomas malignos (o de alto grado) incluyen el glioma anaplásico (grado III) así como el glioblastoma multiforme (GBM, grado IV),estos últimos los más agresivos con el peor pronóstico (1). El manejo terapéutico de los tumores del SNC se basa en la cirugía, la radioterapia y la quimioterapia, dependiendo de las características del tumor, el estadio clínico y la edad (2),(3), sin embargo ninguno de los tratamientos estándar es completamente seguro y compatible con una calidad de vida aceptable (3), (4). En general, la quimioterapia es la primera opción en los tumores diseminados, como el glioblastoma invasivo y el meduloblastoma de alto riesgo o con metástasis múltiple, pero el pronóstico en estos pacientes es muy pobre (2),(3). Solamente nuevas terapias dirigidas (2) como las terapias anti-angiogénicas (4); o terapias génicas muestran un beneficio real en grupos limitados de pacientes con defectos moleculares específicos conocidos (4). De este modo, se hace necesario el desarrollo de nuevas terapias farmacológicas para atacar los tumores cerebrales. Frente a las terapias los gliomas malignos son con frecuencia quimioresistentes, y esta resistencia parece depender de al menos dos mecanismos: en primer lugar, la pobre penetración de muchas drogas anticáncer a través de la barrera hematoencefálica (BBB: Blood Brain Barrier), la barrera del fluido sangre-cerebroespinal (BCSFB: Blood-cerebrospinal fluid barrier) y la barrera sangre-tumor (BTB: blood-tumor barrier). Dicha resistencia se debe a la interacción de la droga con varios transportadores o bombas de eflujo de droga ABC (ABC: ATP-binding cassette) que se sobre expresan en las células endoteliales o epiteliales de estas barreras. En segundo lugar, estos transportadores de eflujo de drogas ABC propios de las células tumorales confieren un fenotipo conocido como resistencia a multidrogas (MDR: multidrug resistance), el cual es característico de varios tumores sólidos. Este fenotipo también está presente en los tumores del SNC y su papel en gliomas es objeto de investigación (5). Por consiguiente el suministro de medicamentos a través de la BBB es uno de los problemas vitales en los tratamientos de terapia dirigida. Estudios recientes han demostrado que algunas moléculas pequeñas utilizadas en estas terapias son sustratos de la glicoproteína P (Pgp: P-gycoprotein), así como también de otras bombas de eflujo como las proteínas relacionadas con la resistencia a multidrogas (MRPs: multidrug resistance-related proteins (MRPs) o la proteína relacionada con cáncer de seno (BCRP: breast-cancer resistance related protein)) que no permiten que las drogas de este tipo alcancen el tumor (1). Un sustrato de Pgp y BCRP es la DOXOrubicina (DOXO), un fármaco utilizado en la terapia anti cáncer, el cual es muy eficaz para atacar las células del tumor cerebral in vitro, pero con un uso clínico limitado por la poca entrega a través de la barrera hematoencefálica (BBB) y por la resistencia propia de los tumores. Por otra parte las células de BBB y las células del tumor cerebral tienen también proteínas superficiales, como el receptor de la lipoproteína de baja densidad (LDLR), que podría utilizarse como blanco terapéutico en BBB y tumores cerebrales. Es asi como la importancia de este estudio se basa en la generación de estrategias terapéuticas que promuevan el paso de las drogas a través de la barrera hematoencefalica y tumoral, y a su vez, se reconozcan mecanismos celulares que induzcan el incremento en la expresión de los transportadores ABC, de manera que puedan ser utilizados como blancos terapéuticos.Este estudio demostró que el uso de una nueva estrategia basada en el “Caballo de Troya”, donde se combina la droga DOXOrubicina, la cual es introducida dentro de un liposoma, salvaguarda la droga de manera que se evita su reconocimiento por parte de los transportadores ABC tanto de la BBB como de las células del tumor. La construcción del liposoma permitió utilizar el receptor LDLR de las células asegurando la entrada a través de la BBB y hacia las células tumorales a través de un proceso de endocitosis. Este mecanismo fue asociado al uso de estatinas o drogas anticolesterol las cuales favorecieron la expresión de LDLR y disminuyeron la actividad de los transportadores ABC por nitración de los mismos, incrementando la eficiencia de nuestro Caballo de Troya. Por consiguiente demostramos que el uso de una nueva estrategia o formulación denominada ApolipoDOXO más el uso de estatinas favorece la administración de fármacos a través de la BBB, venciendo la resistencia del tumor y reduciendo los efectos colaterales dosis dependiente de la DOXOrubicina. Además esta estrategia del "Caballo de Troya", es un nuevo enfoque terapéutico que puede ser considerado como una nueva estrategia para aumentar la eficacia de diferentes fármacos en varios tumores cerebrales y garantiza una alta eficiencia incluso en un medio hipóxico,característico de las células cancerosas, donde la expresión del transportador Pgp se vió aumentada. Teniendo en cuenta la relación entre algunas vías de señalización reconocidas como moduladores de la actividad de Pgp, este estudio presenta no solo la estrategia del Caballo de Troya, sino también otra propuesta terapéutica relacionada con el uso de Temozolomide más DOXOrubicina. Esta estrategia demostró que el temozolomide logra penetrar la BBB por que interviene en la via de señalización de la Wnt/GSK3/β-catenina, la cual modula la expresión del transportador Pgp. Se demostró que el TMZ disminuye la proteína y el mRNA de Wnt3 permitiendo plantear la hipótesis de que la droga al disminuir la transcripción del gen Wnt3 en células de BBB, incrementa la activación de la vía fosforilando la β-catenina y conduciendo a disminuir la β-catenina nuclear y por tanto su unión al promotor del gen mdr1. Con base en los resultados este estudio permitió el reconocimiento de tres mecanismos básicos relacionados con la expresión de los transportadores ABC y asociados a las estrategias empleadas: el primero fue el uso de las estatinas, el cual condujo a la nitración de los transportadores disminuyendo su actividad por la via del factor de transcripción NFκB; el segundo a partir del uso del temozolomide, el cual metila el gen de Wnt3 reduciendo la actividad de la via de señalización de la la β-catenina, disminuyendo la expresión del transportador Pgp. El tercero consistió en la determinación de la relación entre el eje RhoA/RhoA quinasa como un modulador de la via (no canónica) GSK3/β-catenina. Se demostró que la proteína quinasa RhoA promovió la activación de la proteína PTB1, la cual al fosforilar a GSK3 indujo la fosforilación de la β-catenina, lo cual dio lugar a su destrucción por el proteosoma, evitando su unión al promotor del gen mdr1 y por tanto reduciendo su expresión. En conclusión las estrategias propuestas en este trabajo incrementaron la citotoxicidad de las células tumorales al aumentar la permeabilidad no solo de la barrera hematoencefálica, sino también de la propia barrera tumoral. Igualmente, la estrategia del “Caballo de Troya” podría ser útil para la terapia de otras enfermedades asociadas al sistema nervioso central. Por otra parte estos estudios indican que el reconocimiento de mecanismos asociados a la expresión de los transportadores ABC podría constituir una herramienta clave en el desarrollo de nuevas terapias anticáncer.

The mapping of the local contributions of Fermi and Coulomb correlation into intracule and extracule density distributions

The contributions of the correlated and uncorrelated components of the electron-pair density to atomic and molecular intracule I(r) and extracule E(R) densities and its Laplacian functions ∇2I(r) and ∇2E(R) are analyzed at the Hartree-Fock (HF) and configuration interaction (CI) levels of theory. The topologies of the uncorrelated components of these functions can be rationalized in terms of the corresponding one-electron densities. In contrast, by analyzing the correlated components of I(r) and E(R), namely, IC(r) and EC(R), the effect of electron Fermi and Coulomb correlation can be assessed at the HF and CI levels of theory. Moreover, the contribution of Coulomb correlation can be isolated by means of difference maps between IC(r) and EC(R) distributions calculated at the two levels of theory. As application examples, the He, Ne, and Ar atomic series, the C2-2, N2, O2+2 molecular series, and the C2H4 molecule have been investigated. For these atoms and molecules, it is found that Fermi correlation accounts for the main characteristics of IC(r) and EC(R), with Coulomb correlation increasing slightly the locality of these functions at the CI level of theory. Furthermore, IC(r), EC(R), and the associated Laplacian functions, reveal the short-ranged nature and high isotropy of Fermi and Coulomb correlation in atoms and molecules

The relevance of the Laplacian of intracule and extracule density distributions for analyzing electron-electron interactions in molecules

A topological analysis of intracule and extracule densities and their Laplacians computed within the Hartree-Fock approximation is presented. The analysis of the density distributions reveals that among all possible electron-electron interactions in atoms and between atoms in molecules only very few are located rigorously as local maxima. In contrast, they are clearly identified as local minima in the topology of Laplacian maps. The conceptually different interpretation of intracule and extracule maps is also discussed in detail. An application example to the C2H2, C2H4, and C2H6 series of molecules is presented

Nuclear magnetic resonance chemical shifts with the statistical average of orbital-dependent model potentials in Kohn-Sham density functional theory

The performance of the SAOP potential for the calculation of NMR chemical shifts was evaluated. SAOP results show considerable improvement with respect to previous potentials, like VWN or BP86, at least for the carbon, nitrogen, oxygen, and fluorine chemical shifts. Furthermore, a few NMR calculations carried out on third period atoms (S, P, and Cl) improved when using the SAOP potential

Effect of basis set superposition error on the electron density of molecular complexes

The effect of basis set superposition error (BSSE) on molecular complexes is analyzed. The BSSE causes artificial delocalizations which modify the first order electron density. The mechanism of this effect is assessed for the hydrogen fluoride dimer with several basis sets. The BSSE-corrected first-order electron density is obtained using the chemical Hamiltonian approach versions of the Roothaan and Kohn-Sham equations. The corrected densities are compared to uncorrected densities based on the charge density critical points. Contour difference maps between BSSE-corrected and uncorrected densities on the molecular plane are also plotted to gain insight into the effects of BSSE correction on the electron density

A quantum molecular similarity analysis of changes in molecular electron density caused by basis set flotation and electric field application

Quantum molecular similarity (QMS) techniques are used to assess the response of the electron density of various small molecules to application of a static, uniform electric field. Likewise, QMS is used to analyze the changes in electron density generated by the process of floating a basis set. The results obtained show an interrelation between the floating process, the optimum geometry, and the presence of an external field. Cases involving the Le Chatelier principle are discussed, and an insight on the changes of bond critical point properties, self-similarity values and density differences is performed

A comparative analysis by means of quantum molecular similarity measures of density distributions derived from conventional ab initio and density functional methods

A procedure based on quantum molecular similarity measures (QMSM) has been used to compare electron densities obtained from conventional ab initio and density functional methodologies at their respective optimized geometries. This method has been applied to a series of small molecules which have experimentally known properties and molecular bonds of diverse degrees of ionicity and covalency. Results show that in most cases the electron densities obtained from density functional methodologies are of a similar quality than post-Hartree-Fock generalized densities. For molecules where Hartree-Fock methodology yields erroneous results, the density functional methodology is shown to yield usually more accurate densities than those provided by the second order Møller-Plesset perturbation theory