Squared Extrapolation Methods (SQUAREM): A New Class of Simple and Efficient Numerical Schemes for Accelerating the Convergence of the EM Algorithm

We derive a new class of iterative schemes for accelerating the convergence of the EM algorithm, by exploiting the connection between fixed point iterations and extrapolation methods. First, we present a general formulation of one-step iterative schemes, which are obtained by cycling with the extrapolation methods. We, then square the one-step schemes to obtain the new class of methods, which we call SQUAREM. Squaring a one-step iterative scheme is simply applying it twice within each cycle of the extrapolation method. Here we focus on the first order or rank-one extrapolation methods for two reasons, (1) simplicity, and (2) computational efficiency. In particular, we study two first order extrapolation methods, the reduced rank extrapolation (RRE1) and minimal polynomial extrapolation (MPE1). The convergence of the new schemes, both one-step and squared, is non-monotonic with respect to the residual norm. The first order one-step and SQUAREM schemes are linearly convergent, like the EM algorithm but they have a faster rate of convergence. We demonstrate, through five different examples, the effectiveness of the first order SQUAREM schemes, SqRRE1 and SqMPE1, in accelerating the EM algorithm. The SQUAREM schemes are also shown to be vastly superior to their one-step counterparts, RRE1 and MPE1, in terms of computational efficiency. The proposed extrapolation schemes can fail due to the numerical problems of stagnation and near breakdown. We have developed a new hybrid iterative scheme that combines the RRE1 and MPE1 schemes in such a manner that it overcomes both stagnation and near breakdown. The squared first order hybrid scheme, SqHyb1, emerges as the iterative scheme of choice based on our numerical experiments. It combines the fast convergence of the SqMPE1, while avoiding near breakdowns, with the stability of SqRRE1, while avoiding stagnations. The SQUAREM methods can be incorporated very easily into an existing EM algorithm. They only require the basic EM step for their implementation and do not require any other auxiliary quantities such as the complete data log likelihood, and its gradient or hessian. They are an attractive option in problems with a very large number of parameters, and in problems where the statistical model is complex, the EM algorithm is slow and each EM step is computationally demanding.

Reconstruction of patient-specific 3D bone surface from 2D calibrated fluoroscopic images and point distribution model

Reconstruction of patient-specific 3D bone surface from 2D calibrated fluoroscopic images and a point distribution model is discussed. We present a 2D/3D reconstruction scheme combining statistical extrapolation and regularized shape deformation with an iterative image-to-model correspondence establishing algorithm, and show its application to reconstruct the surface of proximal femur. The image-to-model correspondence is established using a non-rigid 2D point matching process, which iteratively uses a symmetric injective nearest-neighbor mapping operator and 2D thin-plate splines based deformation to find a fraction of best matched 2D point pairs between features detected from the fluoroscopic images and those extracted from the 3D model. The obtained 2D point pairs are then used to set up a set of 3D point pairs such that we turn a 2D/3D reconstruction problem to a 3D/3D one. We designed and conducted experiments on 11 cadaveric femurs to validate the present reconstruction scheme. An average mean reconstruction error of 1.2 mm was found when two fluoroscopic images were used for each bone. It decreased to 1.0 mm when three fluoroscopic images were used.

Effective water treatment for rural communities in Suriname : a comparison of point-of-use ceramic filters and centralized treatment with sand filters

For countless communities around the world, acquiring access to safe drinking water is a daily challenge which many organizations endeavor to meet. The villages in the interior of Suriname have been the focus of many improved drinking water projects as most communities are without year-round access. Unfortunately, as many as 75% of the systems in Suriname fail within several years of implementation. These communities, scattered along the rivers and throughout the jungle, lack many of the resources required to sustain a centralized water treatment system. However, the centralized system in the village of Bendekonde on the Upper Suriname River has been operational for over 10 years and is often touted by other communities. The Bendekonde system is praised even though the technology does not differ significantly from other failed systems. Many of the water systems that fail in the interior fail due to a lack of resources available to the community to maintain the system. Typically, the more complex a system becomes, so does the demand for additional resources. Alternatives to centralized systems include technologies such as point-of-use water filters, which can greatly reduce the necessity for outside resources. In particular, ceramic point-of-use water filters offer a technology that can be reasonably managed in a low resource setting such as that in the interior of Suriname. This report investigates the appropriateness and effectiveness of ceramic filters constructed with local Suriname clay and compares the treatment effectiveness to that of the Bendekonde system. Results of this study showed that functional filters could be produced from Surinamese clay and that they were more effective, in a controlled laboratory setting, than the field performance of the Bendekonde system for removing total coliform. However, the Bendekonde system was more successful at removing E. coli. In a life-cycle assessment, ceramic water filters manufactured in Suriname and used in homes for a lifespan of 2 years were shown to have lower cumulative energy demand, as well as lower global warming potential than a centralized system similar to that used in Bendekonde.

Bayesian change-point analysis in linear regression model with scale mixtures of normal distributions

In this thesis, we consider Bayesian inference on the detection of variance change-point models with scale mixtures of normal (for short SMN) distributions. This class of distributions is symmetric and thick-tailed and includes as special cases: Gaussian, Student-t, contaminated normal, and slash distributions. The proposed models provide greater flexibility to analyze a lot of practical data, which often show heavy-tail and may not satisfy the normal assumption. As to the Bayesian analysis, we specify some prior distributions for the unknown parameters in the variance change-point models with the SMN distributions. Due to the complexity of the joint posterior distribution, we propose an efficient Gibbs-type with Metropolis- Hastings sampling algorithm for posterior Bayesian inference. Thereafter, following the idea of [1], we consider the problems of the single and multiple change-point detections. The performance of the proposed procedures is illustrated and analyzed by simulation studies. A real application to the closing price data of U.S. stock market has been analyzed for illustrative purposes.

Variations of the FEAST Eigenvalue Algorithm

FEAST is a recently developed eigenvalue algorithm which computes selected interior eigenvalues of real symmetric matrices. It uses contour integral resolvent based projections. A weakness is that the existing algorithm relies on accurate reasoned estimates of the number of eigenvalues within the contour. Examining the singular values of the projections on moderately-sized, randomly-generated test problems motivates orthogonalization-based improvements to the algorithm. The singular value distributions provide experimentally robust estimates of the number of eigenvalues within the contour. The algorithm is modified to handle both Hermitian and general complex matrices. The original algorithm (based on circular contours and Gauss-Legendre quadrature) is extended to contours and quadrature schemes that are recursively subdividable. A general complex recursive algorithm is implemented on rectangular and diamond contours. The accuracy of different quadrature schemes for various contours is investigated.

Walking near a conformal fixed point

We investigate the 2-d O(3) model with a q-term as a toy model for slowly walking 4-d non-Abelian gauge theories. Using the very efficient meron-cluster algorithm, an accurate investigation of the scale dependence of the renormalized coupling is carried out for different values of the vacuum angle q. Approaching q = p, the infrared dynamics of the 2-d O(3) model is determined by a non-trivial conformal fixed point. We provide evidence for a slowly walking behavior near the fixed point and we perform a finite-size scaling analysis of the mass gap.

Metal Artifact Reduction in Pelvic Computed Tomography With Hip Prostheses: Comparison of Virtual Monoenergetic Extrapolations From Dual-Energy Computed Tomography and an Iterative Metal Artifact Reduction Algorithm in a Phantom Study.

OBJECTIVE The aim of this study was to directly compare metal artifact reduction (MAR) of virtual monoenergetic extrapolations (VMEs) from dual-energy computed tomography (CT) with iterative MAR (iMAR) from single energy in pelvic CT with hip prostheses. MATERIALS AND METHODS A human pelvis phantom with unilateral or bilateral metal inserts of different material (steel and titanium) was scanned with third-generation dual-source CT using single (120 kVp) and dual-energy (100/150 kVp) at similar radiation dose (CT dose index, 7.15 mGy). Three image series for each phantom configuration were reconstructed: uncorrected, VME, and iMAR. Two independent, blinded radiologists assessed image quality quantitatively (noise and attenuation) and subjectively (5-point Likert scale). Intraclass correlation coefficients (ICCs) and Cohen κ were calculated to evaluate interreader agreements. Repeated measures analysis of variance and Friedman test were used to compare quantitative and qualitative image quality. Post hoc testing was performed using a corrected (Bonferroni) P < 0.017. RESULTS Agreements between readers were high for noise (all, ICC ≥ 0.975) and attenuation (all, ICC ≥ 0.986); agreements for qualitative assessment were good to perfect (all, κ ≥ 0.678). Compared with uncorrected images, VME showed significant noise reduction in the phantom with titanium only (P < 0.017), and iMAR showed significantly lower noise in all regions and phantom configurations (all, P < 0.017). In all phantom configurations, deviations of attenuation were smallest in images reconstructed with iMAR. For VME, there was a tendency toward higher subjective image quality in phantoms with titanium compared with uncorrected images, however, without reaching statistical significance (P > 0.017). Subjective image quality was rated significantly higher for images reconstructed with iMAR than for uncorrected images in all phantom configurations (all, P < 0.017). CONCLUSIONS Iterative MAR showed better MAR capabilities than VME in settings with bilateral hip prosthesis or unilateral steel prosthesis. In settings with unilateral hip prosthesis made of titanium, VME and iMAR performed similarly well.

Inversiones en servicios : Nuevas territorialidades en la expansión de call centers en el interior de la Argentina, 2002-2010

En la Argentina, el año 2002 marca el inicio de una serie de transformaciones productivas con fuerte impacto sobre las dinámicas territoriales, a partir de la llegada de inversiones extranjeras directas. Una importante porción de dichas inversiones se orienta a desarrollar actividades de baja jerarquización, en donde la competitividad se obtiene vía la reducción de los costos laborales y el otorgamiento de ventajas impositivas y subsidios hacia las empresas. La significativa expansión de la actividad de los call centers tercerizadores -que, en los últimos años, se localizan masiva y vertiginosamente en las principales ciudades del interior de nuestro país- es la evidencia empírica de este fenómeno. Analizar sus características, junto con una detallada descripción de las interacciones de los organismos estatales y los sectores políticos, sociales y económicos involucrados en la instalación de los call centers, no solo permite observar las transformaciones territoriales -en tanto se insertan nuevas actividades productivas y de empleo- sino que visibiliza mecanismos de cooperación y/o conflicto mediante los cuales los actores nacionales y foráneos posibilitan y modelan la inserción de lo global en lo local, materializando así novedosas lógicas de organización territorial, que representamos bajo el concepto "nuevas territorialidades". A lo largo de todo el trabajo, intentamos que nuestra mirada de estos procesos pueda dar cuenta de las (a)simetrías de poder entre los agentes económicos y actores estatales y extraestatales, en el marco de espacios locales periféricos en una época de globalización

Una justicia corporativa : Saberes, prácticas y estrategias judiciales hacia el interior del Tribunal del Consulado de Buenos Aires (1794-1821)

El presente artículo tiene como objetivo analizar algunos de los saberes, las prácticas y las estrategias judiciales que distintos comerciantes pusieron en juego dentro del fuero consular. Estos provenían en buena medida de la propia actividad comercial, por lo que los consideramos como una extensión de su función económica como comerciantes. Tomaremos aquí las trayectorias de dos comerciantes porteños de reconocimiento en la plaza porteña, que ocuparon, en distintos momentos, cargos de importancia dentro del Consulado porteño. Asimismo, mostraremos quiénes son sus oponentes en los pleitos citados y detallaremos las características que asumen los conflictos en cada caso

Inversiones en servicios : Nuevas territorialidades en la expansión de call centers en el interior de la Argentina, 2002-2010

En la Argentina, el año 2002 marca el inicio de una serie de transformaciones productivas con fuerte impacto sobre las dinámicas territoriales, a partir de la llegada de inversiones extranjeras directas. Una importante porción de dichas inversiones se orienta a desarrollar actividades de baja jerarquización, en donde la competitividad se obtiene vía la reducción de los costos laborales y el otorgamiento de ventajas impositivas y subsidios hacia las empresas. La significativa expansión de la actividad de los call centers tercerizadores -que, en los últimos años, se localizan masiva y vertiginosamente en las principales ciudades del interior de nuestro país- es la evidencia empírica de este fenómeno. Analizar sus características, junto con una detallada descripción de las interacciones de los organismos estatales y los sectores políticos, sociales y económicos involucrados en la instalación de los call centers, no solo permite observar las transformaciones territoriales -en tanto se insertan nuevas actividades productivas y de empleo- sino que visibiliza mecanismos de cooperación y/o conflicto mediante los cuales los actores nacionales y foráneos posibilitan y modelan la inserción de lo global en lo local, materializando así novedosas lógicas de organización territorial, que representamos bajo el concepto "nuevas territorialidades". A lo largo de todo el trabajo, intentamos que nuestra mirada de estos procesos pueda dar cuenta de las (a)simetrías de poder entre los agentes económicos y actores estatales y extraestatales, en el marco de espacios locales periféricos en una época de globalización

Una justicia corporativa : Saberes, prácticas y estrategias judiciales hacia el interior del Tribunal del Consulado de Buenos Aires (1794-1821)

El presente artículo tiene como objetivo analizar algunos de los saberes, las prácticas y las estrategias judiciales que distintos comerciantes pusieron en juego dentro del fuero consular. Estos provenían en buena medida de la propia actividad comercial, por lo que los consideramos como una extensión de su función económica como comerciantes. Tomaremos aquí las trayectorias de dos comerciantes porteños de reconocimiento en la plaza porteña, que ocuparon, en distintos momentos, cargos de importancia dentro del Consulado porteño. Asimismo, mostraremos quiénes son sus oponentes en los pleitos citados y detallaremos las características que asumen los conflictos en cada caso

Inversiones en servicios : Nuevas territorialidades en la expansión de call centers en el interior de la Argentina, 2002-2010

En la Argentina, el año 2002 marca el inicio de una serie de transformaciones productivas con fuerte impacto sobre las dinámicas territoriales, a partir de la llegada de inversiones extranjeras directas. Una importante porción de dichas inversiones se orienta a desarrollar actividades de baja jerarquización, en donde la competitividad se obtiene vía la reducción de los costos laborales y el otorgamiento de ventajas impositivas y subsidios hacia las empresas. La significativa expansión de la actividad de los call centers tercerizadores -que, en los últimos años, se localizan masiva y vertiginosamente en las principales ciudades del interior de nuestro país- es la evidencia empírica de este fenómeno. Analizar sus características, junto con una detallada descripción de las interacciones de los organismos estatales y los sectores políticos, sociales y económicos involucrados en la instalación de los call centers, no solo permite observar las transformaciones territoriales -en tanto se insertan nuevas actividades productivas y de empleo- sino que visibiliza mecanismos de cooperación y/o conflicto mediante los cuales los actores nacionales y foráneos posibilitan y modelan la inserción de lo global en lo local, materializando así novedosas lógicas de organización territorial, que representamos bajo el concepto "nuevas territorialidades". A lo largo de todo el trabajo, intentamos que nuestra mirada de estos procesos pueda dar cuenta de las (a)simetrías de poder entre los agentes económicos y actores estatales y extraestatales, en el marco de espacios locales periféricos en una época de globalización

Una justicia corporativa : Saberes, prácticas y estrategias judiciales hacia el interior del Tribunal del Consulado de Buenos Aires (1794-1821)

El presente artículo tiene como objetivo analizar algunos de los saberes, las prácticas y las estrategias judiciales que distintos comerciantes pusieron en juego dentro del fuero consular. Estos provenían en buena medida de la propia actividad comercial, por lo que los consideramos como una extensión de su función económica como comerciantes. Tomaremos aquí las trayectorias de dos comerciantes porteños de reconocimiento en la plaza porteña, que ocuparon, en distintos momentos, cargos de importancia dentro del Consulado porteño. Asimismo, mostraremos quiénes son sus oponentes en los pleitos citados y detallaremos las características que asumen los conflictos en cada caso

An approach to operational modal analysis using the expectation maximization algorithm

This paper presents the Expectation Maximization algorithm (EM) applied to operational modal analysis of structures. The EM algorithm is a general-purpose method for maximum likelihood estimation (MLE) that in this work is used to estimate state space models. As it is well known, the MLE enjoys some optimal properties from a statistical point of view, which make it very attractive in practice. However, the EM algorithm has two main drawbacks: its slow convergence and the dependence of the solution on the initial values used. This paper proposes two different strategies to choose initial values for the EM algorithm when used for operational modal analysis: to begin with the parameters estimated by Stochastic Subspace Identification method (SSI) and to start using random points. The effectiveness of the proposed identification method has been evaluated through numerical simulation and measured vibration data in the context of a benchmark problem. Modal parameters (natural frequencies, damping ratios and mode shapes) of the benchmark structure have been estimated using SSI and the EM algorithm. On the whole, the results show that the application of the EM algorithm starting from the solution given by SSI is very useful to identify the vibration modes of a structure, discarding the spurious modes that appear in high order models and discovering other hidden modes. Similar results are obtained using random starting values, although this strategy allows us to analyze the solution of several starting points what overcome the dependence on the initial values used.

Variable threshold algorithm for division of labor analyzed as a dynamical system

Division of labor is a widely studied aspect of colony behavior of social insects. Division of labor models indicate how individuals distribute themselves in order to perform different tasks simultaneously. However, models that study division of labor from a dynamical system point of view cannot be found in the literature. In this paper, we define a division of labor model as a discrete-time dynamical system, in order to study the equilibrium points and their properties related to convergence and stability. By making use of this analytical model, an adaptive algorithm based on division of labor can be designed to satisfy dynamic criteria. In this way, we have designed and tested an algorithm that varies the response thresholds in order to modify the dynamic behavior of the system. This behavior modification allows the system to adapt to specific environmental and collective situations, making the algorithm a good candidate for distributed control applications. The variable threshold algorithm is based on specialization mechanisms. It is able to achieve an asymptotically stable behavior of the system in different environments and independently of the number of individuals. The algorithm has been successfully tested under several initial conditions and number of individuals.