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Multidimensional projection with radial basis function and control points selection

Amorim, Elisa Portes dos Santos; Brazil, Emilio Vital; Nonato, Luis Gustavo; Samavati, Faramarz; Sousa, Mario Costa
Fonte: Keio Universiy, Faculty of Science and Technology; ACM SIGGRAPH; Eurographics; Yokohama Publicador: Keio Universiy, Faculty of Science and Technology; ACM SIGGRAPH; Eurographics; Yokohama
Tipo: Conferência ou Objeto de Conferência
ENG
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36.05%
Multidimensional projection techniques provide an appealing approach for multivariate data analysis, for their ability to translate high-dimensional data into a low-dimensional representation that preserves neighborhood information. In recent years, pushed by the ever increasing data complexity in many areas, numerous advances in such techniques have been observed, primarily in terms of computational efficiency and support for interactive applications. Both these achievements were made possible due to the introduction of the concept of control points, which are used in many different multidimensional projection techniques. However, little attention has been drawn towards the process of control points selection. In this work we propose a novel multidimensional projection technique based on radial basis functions (RBF). Our method uses RBF to create a function that maps the data into a low-dimensional space by interpolating the previously calculated position of control points. We also present a built-in method for the control points selection based on “forward-selection” and “Orthogonal Least Squares” techniques. We demonstrate that the proposed selection process allows our technique to work with only a few control points while retaining the projection quality and avoiding redundant control points; Foundation CMG Industrial Research Chair program in Scalable; Alberta Innovates Academy (AITF); NSERC

Multinodal Load Forecasting in Power Electric Systems using a Neural Network with Radial Basis Function

Altran, Alessandra Bonato; Minussi, Carlos Roberto; Martins Lopes, Mara Lucia; Chavarette, Fábio Roberto; Peruzzi, Nelson Jose; Zhou, M
Fonte: Trans Tech Publications Ltd Publicador: Trans Tech Publications Ltd
Tipo: Conferência ou Objeto de Conferência Formato: 39-44
ENG
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In this paper we present the results of the use of a methodology for multinodal load forecasting through an artificial neural network-type Multilayer Perceptron, making use of radial basis functions as activation function and the Backpropagation algorithm, as an algorithm to train the network. This methodology allows you to make the prediction at various points in power system, considering different types of consumers (residential, commercial, industrial) of the electric grid, is applied to the problem short-term electric load forecasting (24 hours ahead). We use a database (Centralised Dataset - CDS) provided by the Electricity Commission de New Zealand to this work.

Codificação de certos codigos de Goppa geometricos utilizando a teoria de Bases de Grobner e codigos sobre a curva Norma-Traço; Encoding geometric Goppa codes via Grobner basis and codes on Norm-Trace curves

Guilherme Chaud Tizziotti
Fonte: Biblioteca Digital da Unicamp Publicador: Biblioteca Digital da Unicamp
Tipo: Tese de Doutorado Formato: application/pdf
Publicado em 03/06/2008 PT
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Estendemos resultados de Heegard, Little e Saints relacionados a bases de Gröbner para códigos Hermitianos pontuais. Trabalhamos com códigos Hermitianos bipontuais e n-pontuais, e com códigos sobre a curva Norma-Traço. Além disso, determinamos o semigrupo de Weierstrass de um certo par de pontos racionais sobre a curva Norma-Traço e com esse semigrupo conseguimos melhorar a cota da distância mínima de códigos construídos sobre tais curvas.; We extend results of Heegard, Little and Saints concerning the Gröbner basis algorithm for one-point Hermitian codes. We work with two-point and n-point Hermitian codes and codes arising from the Norm-Trace curve. We also determine the Weierstrass semigroup at a certain pair of rational points in such curves and uses these computations to improve the lower bound on the minimum distance of two-point algebraic geometry codes arising from them.

Reduced-Basis Approximation of the Viscosity-Parametrized Incompressible Navier-Stokes Equation: Rigorous A Posteriori Error Bounds

Veroy, K.; Patera, Anthony T.
Fonte: MIT - Massachusetts Institute of Technology Publicador: MIT - Massachusetts Institute of Technology
Tipo: Artigo de Revista Científica Formato: 536131 bytes; application/pdf
EN_US
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We present a technique for the rapid and reliable prediction of linear-functional outputs of elliptic partial differential equations with affine (or approximately affine) parameter dependence. The essential components are (i) rapidly uniformly convergent global reduced-basis approximations — Galerkin projection onto a space WN spanned by solutions of the governing partial differential equation at N selected points in parameter space; (ii) a posteriori error estimation — relaxations of the residual equation that provide inexpensive yet sharp and rigorous bounds for the error in the outputs of interest; and (iii) offline/online computational procedures — stratagems which decouple the generation and projection stages of the approximation process. The operation count for the online stage — in which, given a new parameter value, we calculate the output of interest and associated error bound — depends only on N (typically very small) and the parametric complexity of the problem. In this paper we extend our methodology to the viscosity-parametrized incompressible Navier-Stokes equations. There are two critical new ingredients: first, the now-classical Brezzi-Rappaz-Raviart framework for (here, a posteriori) error analysis of approximations of nonlinear elliptic partial differential equations; and second...

Reduced-Basis Methods for Inverse Problems in Partial Differential Equations

Nguyen, C.N.; Liu, Guirong; Patera, Anthony T.
Fonte: MIT - Massachusetts Institute of Technology Publicador: MIT - Massachusetts Institute of Technology
Tipo: Artigo de Revista Científica Formato: 15952 bytes; application/pdf
EN_US
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We present a technique for the rapid, reliable, and accurate evaluation of functional outputs of parametrized elliptic partial differential equations. The essential ingredients are (i) rapidly globally convergent reduced-basis approximations – Galerkin projection onto a space WN spanned by the solutions of the governing partial differential equations at N selected points in parameter space; (ii) a posteriori error estimation - relaxations of the error-residual equation that provide sharp and inexpensive bounds for the error in the output of interest; and (iii) off-line/online computational procedures – methods that decouple the generation and projection stages of the approximation process. The operation count for the online stage – in which, given a new parameter, we calculate the output of interest and associated error bounds – depends only on N (typically very small) and the parametric dependencies of the problem. In this study, we first develop rigorous a posteriori error estimators for (affine in the parameter) noncoercive problems such as the Helmholtz (reduced-wave) equation. The critical ingredients are the residual, an appropriate bound conditioner, and a piecewise-constant lower bound for the inf-sup stability factor. In addition...

Unconventional Monetary Policy Normalization in High-Income Countries : Implications for Emerging Market Capital Flows and Crisis Risks

Burns, Andrew; Kida, Mizuho; Lim, Jamus Jerome; Mohapatra, Sanket; Stocker, Marc
Fonte: World Bank, Washington, DC Publicador: World Bank, Washington, DC
EN_US
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As the recovery in high-income countries firms amid a gradual withdrawal of extraordinary monetary stimulus, developing countries can expect stronger demand for their exports as global trade regains momentum, but also rising interest rates and potentially weaker capital inflows. This paper assesses the implications of a normalization of policy and activity in high-income countries for financial flows and crisis risks in developing countries. In the most likely scenario, a relatively orderly process of normalization would imply a slowdown in capital inflows amounting to 0.6 percent of developing-country GDP between 2013 and 2016, driven in particular by weaker portfolio investments. However, the risk of more abrupt adjustments remains significant, especially if increased market volatility accompanies the unwinding of unprecedented central bank interventions. According to simulations, abrupt changes in market expectations, resulting in global bond yields increasing by 100 to 200 basis points within a couple of quarters...

Financial Inclusion and Consumer Protection in Peru

Superintendence of Banks, Insurance and AFPs of Peru; Consultative Group to Assist the Poor
Fonte: World Bank, Washington, DC Publicador: World Bank, Washington, DC
Tipo: Relatório
EN_US
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As part of its Global Policy Initiative, Consultative Group to Assist the Poor (CGAP) partnered with the Superintendence of Banks, Insurance and AFPs of Peru in late 2008, with the purpose of enhancing the understanding of the issues and trends in consumer relations when financial services are delivered through branchless banking, particularly through agents, which are used in ever increasing scale in Peru. The product was this joint report. Three other countries with relevant experience in branchless banking (Kenya, Brazil and India) participated in a similar exercise at approximately the same time. As in the case of Peru, the exercise gave an opportunity for regulators of each jurisdiction to look at their regulatory and institutional framework for protecting branchless banking users, evaluate their regulatory and supervisory actions, and identify areas for improvements. A forthcoming CGAP focus note complements the effort, by making an overall evaluation of the lessons learned in these countries and drawing on the knowledge from other pioneer countries such as South Africa...

Lebanon Economic Monitor, Spring 2013

World Bank
Fonte: Washington, DC Publicador: Washington, DC
Tipo: Relatório
EN_US
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The Lebanon Economic Monitor provides an update on key economic developments and policies over the past six months. It also presents findings from recent World Bank work on Lebanon. The political standoff combined with an escalating Syrian conflict hampered growth in 2012, and is projected to continue doing so through the first half of 2013. Economic growth in 2012 is estimated to have decelerated to 1.4 percent due to a weak second half of 2012 following a downturn in the security situation. The major fiscal expansion that took place in 2012 is creating fiscal challenges for 2013, particularly in the context of a promised increase in public salaries. The fiscal expansion, measured by the change in the central government s primary fiscal balance, reached a staggering 4.6 percentage points of GDP in 2012. The overall fiscal deficit reached 9.4 percent of GDP in 2012. Inflationary pressures rose despite tepid economic activity. Headline inflation accelerated notably in the second half of 2012. Core inflation has also been on an upward trend...

Behavior of the Fiber and the Base Points of Parametrizations Under Projections

Pérez Díaz, Sonia; Sendra Pons, Juan Rafael
Fonte: Springer Publicador: Springer
Tipo: info:eu-repo/semantics/article; info:eu-repo/semantics/submittedVersion Formato: application/pdf
ENG
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This is the author’s version of a work that was accepted for publication in Mathematics in Computer Science. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Mathematics in Computer Science Volume 7, Issue 2 (2013), Page 167-184 DOI 10.1007/s11786-013-0139-8; Given a rational parametrization P( t ), t = (t1, . . . , tr ), of an r-dimensional unirational variety, we analyze the behavior of the variety of the base points of P( t ) in connection to its generic fibre, when successively eliminating the parameters ti . For this purpose. we introduce a sequence of generalized resultants whose primitive and content parts contain the different components of the projected variety of the base points and the fibre. In addition, when the dimension of the base points is strictly smaller than 1 (as in the well known cases of curves and surfaces), we show that the last element in the sequence of resultants is the univariate polynomial in the corresponding Gröbner basis of the ideal associated to the fibre; assuming that the ideal is in t1-general position and radical.; This work has been partially supported by the Spanish Ministerio de Ciencia e Innovación under the project MTM2008-04699-C03-01 and by the Ministerio de Economía y Competitividad under the project MTM2011-25816-C02-01; both authors are members of the of the Research Group ASYNACS (Ref. CCEE2011/R34).

Global Economic Prospects 2009 : Commodities at the Crossroads

World Bank
Fonte: World Bank Publicador: World Bank
Tipo: Publications & Research :: Publication; Publications & Research :: Publication
ENGLISH
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The release of this year's global economic prospects finds the world economy at a crossroads. Markets all over the world are engulfed in a global economic crisis, with stock markets sharply down and volatile, almost all currencies having depreciated substantially against the dollar, and risk premiums on a wide range of debt having increased by 600 or more basis points. Commodity markets too have turned a corner. Following several years of increase, prices have plummeted, and although well above their 1990s levels, they have given up most of the increases of the past 24 months. Chapter one of this report examines the medium-term implications of this crisis for developing-country growth, inflation, and world trade. Chapter two looks at longer-term supply and demand prospects in commodity markets. It takes into account the long-term growth prospects of developing countries and their rising share in world GDP (gross domestic product), the declining quality of new pools of resources, and the influence of technology on both demand and supply. Finally...

Croatia Public Finance Review : Restructuring Spending for Stability and Growth

World Bank
Fonte: Banco Mundial Publicador: Banco Mundial
Tipo: Economic & Sector Work; Economic & Sector Work :: Other Financial Sector Study
ENGLISH; EN_US
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The Croatia poverty rate, as measured by the international line of moderate poverty at dollar 5 in public-private partnership (PPP) terms, is estimated at 2.8 percent for 2012. The share of the population at risk of poverty, based on a higher national and relative poverty line, also declined substantially prior to the 2008 global financial crisis, although has subsequently increased markedly. The global financial crisis, with the loss of credit, has exposed Croatia's macroeconomic vulnerabilities. This report shows that without addressing macroeconomic weaknesses, through sustained fiscal adjustment and institutional reforms, Croatia will not be able to reignite higher growth and benefit fully from European Union (EU) membership, and the quest for future prosperity may prove elusive. Similarly, without accelerating structural reforms, especially in the area of labor market, investment climate, and public sector efficiency, Croatia will face further stifled competitiveness and any prospects for recovery of growth and jobs. Focusing on the fiscal and public sector related deficiencies...

Russian Economic Report, April 2015; The Dawn of a New Economic Era?

World Bank Group
Fonte: Washington, DC Publicador: Washington, DC
Tipo: Report; Economic & Sector Work; Economic & Sector Work :: Economic Updates and Modeling
ENGLISH; EN_US
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Russia's economy experienced two shocks in 2014. On top of the structural crisis that began in 2012, Russia had to deal with cyclical and idiosyncratic challenges to the economy. One of the new shocks illustrates Russia s integration into the world economy through its natural resource exports, and thus its dependence on the global commodity cycle: oil prices more than halved between July and December 2014, giving Russia a terms-of-trade shock. The ruble lost 46 percent of its value against the US dollar, which worsened already eroded business and consumer confidence. The monetary tightening in response made credit expensive, further dampening domestic demand. The other, more idiosyncratic, shock was related to the geopolitical tensions that began in March 2014 and led to economic sanctions. The tensions not only heightened perceptions that Russian investments had become riskier, they also dramatically increased the costs of external borrowing for Russian banks and firms. Spreads on Russian credit default swaps peaked in December at 578 basis points...

Long-Term Fiscal Risks and Sustainability in an Oil-Rich Country : The Case of Russia

Bogetic, Zeljko; Smits, Karlis; Budina, Nina; van Wijnbergen, Sweder
Fonte: Banco Mundial Publicador: Banco Mundial
Tipo: Publications & Research :: Policy Research Working Paper
ENGLISH
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Russia entered the global crisis with strong fiscal position, low public debt, and large fiscal and monetary reserves, which helped it cushion the crisis shocks. But the rise in the non-oil fiscal deficit in 2007-08 and, more importantly, the massive impact of the global crisis in late 2008 and 2009 have dramatically altered Russia's medium-term and long-term economic and fiscal outlook. While Russia is emerging from this crisis on a much stronger footing than during the 1998-09 crisis thanks to its strong-pre crisis fundamentals, large fiscal reserves and solid management of the crisis, it will nevertheless need to implement sustained fiscal adjustment in the coming years. Both revenue and expenditure measures will be needed. This will require 2-3 percentage points of GDP in fiscal adjustment for about five years in addition to keeping total expenditure levels at a relatively low 31.5 percent of GDP, consistent with long-term social expenditure needs and requirements of long-term fiscal sustainability. Following a period of adjustment...

Global Economic Prospects 2010 : Crisis, Finance, and Growth

World Bank
Fonte: World Bank Publicador: World Bank
Tipo: Publications & Research :: Publication; Publications & Research :: Publication
ENGLISH
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35.83%
The world economy is emerging from the throes of a historically deep and synchronized recession provoked by the bursting of a global financial bubble. The consequences of the initial bubble and the crisis have been felt in virtually every economy, whether or not it participated directly in the risky behaviors that precipitated the boom-and-bust cycle. And while growth rates have picked up, the depth of the recession means that it will take years before unemployment and spare capacity are reabsorbed. This year's global economic prospects examines the consequences of the crisis for both the short and medium term growth prospects of developing countries. It concludes that the crisis and the regulatory reaction to the financial excesses of the preceding several years may have lasting impacts on financial markets, raising borrowing costs and lowering levels of credit and international capital flows. As a result, the rate of growth of potential output in developing countries may be reduced by between 0.2 and 0.7 percentage points annually over the next five to seven years as economies adjust to tighter financial conditions. Overall...

The Caribbean Catastrophe Risk Insurance Initiative : A Review of CCRIF's Operation After Its Second Season

World Bank
Fonte: Washington, DC Publicador: Washington, DC
Tipo: Publications & Research :: Working Paper; Publications & Research
ENGLISH; EN_US
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This report provides an external assessment of the operations of the Caribbean Catastrophe Risk Insurance Facility (CCRIF) during its second policy year from June 1, 2008 to May 31, 2009. Developed at members and associate members of the Caribbean Community (CARICOM's) request following the devastation wrought on Grenada and the Cayman Islands by Hurricane Ivan in 2004, CCRIF was established in May 2007. The World Bank and a number of donors contributed to CCRIF's start-up capital and also underwrote a portion of some members' initial participation fees and premium payments during CCRIF's first three policy years. A multi-donor trust fund continues to reimburse CCRIF for certain eligible expenditures, thus facilitating continued growth of CCRIF's reserves and risk-bearing capacity. The report aims to contribute to on-going discussions within the broader disaster risk management community about the possibilities for scaling up the role of CCRIF in the Caribbean and replicating or adapting CCRIF's innovative model of ex ante disaster risk financing in other disaster-prone regions of the world. Rolling out the second-generation loss model...

Reduced-Basis Output Bound Methods for Parametrized Partial Differential Equations

Prud'homme, C.; Rovas, D.V.; Veroy, K.; Machiels, L.; Maday, Y.; Patera, Anthony T.; Turinici, G.
Fonte: MIT - Massachusetts Institute of Technology Publicador: MIT - Massachusetts Institute of Technology
Tipo: Artigo de Revista Científica Formato: 554202 bytes; application/pdf
EN_US
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We present a technique for the rapid and reliable prediction of linear-functional outputs of elliptic (and parabolic) partial differential equations with affine parameter dependence. The essential components are (i) (provably) rapidly convergent global reduced-basis approximations -- Galerkin projection onto a space WN spanned by solutions of the governing partial differential equation at N selected points in parameter space; (ii) a posteriori error estimation -- relaxations of the error-residual equation that provide inexpensive yet sharp and rigorous bounds for the error in the outputs of interest; and (iii) off-line/on-line computational procedures -- methods which decouple the generation and projection stages of the approximation process. The operation count for the on-line stage -- in which, given a new parameter value, we calculate the output of interest and associated error bound -- depends only on N (typically very small) and the parametric complexity of the problem; the method is thus ideally suited for the repeated and rapid evaluations required in the context of parameter estimation, design, optimization, and real-time control.; Singapore-MIT Alliance (SMA)

Studies on Barlow points, Gauss points and Superconvergent points in 1D with Lagrangian and Hermitian finite element basis

Pinto Júnior,David Soares
Fonte: Sociedade Brasileira de Matemática Aplicada e Computacional Publicador: Sociedade Brasileira de Matemática Aplicada e Computacional
Tipo: Artigo de Revista Científica Formato: text/html
Publicado em 01/01/2008 EN
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In this work, we consider the superconvergence property of the finite element derivative for Lagrange's and Hermite's Family elements in the one dimensional interpolation problem. We also compare the Barlow points, Gauss points and Superconvergence points in the sense of Taylor's Series, confirming that they are not the same as believed before. We prove a not evident and new superconvergence property of Hermite's basis as well which shows that the centroid is not only a superconvergent for u'h but an O(h5) accuracy point.

An optimal experimental design perspective on redial basis function regression

Fokoue, Ernest; Goel, Prem
Fonte: Rochester Instituto de Tecnologia Publicador: Rochester Instituto de Tecnologia
Tipo: Tese de Doutorado
EN_US
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This paper provides a new look at radial basis function regression that reveals striking similarities with the traditional optimal experimental design framework. We show theoreti- cally and computationally that the so-called relevant vectors derived through the relevance vector machine (RVM) and corresponding to the centers of the radial basis function net- work, are very similar and often identical to the support points obtained through various optimal experimental design criteria like D-optimality. This allows us to provide a sta- tistical meaning to the relevant centers in the context of radial basis function regression, but also opens the door to a variety of ways of approach optimal experimental design in multivariate settings.

Stable radial basis function selection via mixture modelling of the sample path

Fokoue, Ernest
Fonte: Rochester Instituto de Tecnologia Publicador: Rochester Instituto de Tecnologia
Tipo: Relatório
EN_US
Relevância na Pesquisa
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We consider a fully Bayesian treatment of radial basis function regression, and propose a solution to the the instability of basis selection. Indeed, when bases are selected solely according to the magnitude of their posterior inclusion probabilities, it is often the case that many bases in the same neighborhood end up getting selected leading to redundancy and ultimately inaccuracy of the representation. In this paper, we propose a straightforward solution to the problem based on post-processing the sample path yielded by the model space search technique. Specifically, we perform an a posteriori model-based clustering of the sample path via a mixture of Gaussians, and then select the points closer to the means of the Gaussians. Our solution is found to be more stable and yields a better performance on simulated and real tasks.

Polynomials and their Potential Theory for Gaussian Radial Basis Function Interpolation

Driscoll, Tobin A.; Platte, Rodrigo B.
Fonte: Department of Mathematical Sciences Publicador: Department of Mathematical Sciences
Tipo: Relatório Formato: 667615 bytes; application/pdf
EN_US
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We explore a connection between Gaussian radial basis functions and polynomials. Using standard tools of potential theory, we find that these radial functions are susceptible to the Runge phenomenon, not only in the limit of increasingly flat functions, but also in the finite shape parameter case. We show that there exist interpolation node distributions that prevent such phenomena and allow stable approximations. Using polynomials also provides an explicit interpolation formula that avoids the difficulties of inverting interpolation matrices, without imposing restrictions on the shape parameter or number of points.; Supported by NSF DMS-0104229