Multiple Testing and Variable Selection along Least Angle Regression's path

In this article, we investigate multiple testing and variable selection using Least Angle Regression (LARS) algorithm in high dimensions under the Gaussian noise assumption. LARS is known to produce a piecewise affine solutions path with change points referred to as knots of the LARS path. The cornerstone of the present work is the expression in closed form of the exact joint law of K-uplets of knots conditional on the variables selected by LARS, namely the so-called post-selection joint law of the LARS knots. Numerical experiments demonstrate the perfect fit of our finding. Our main contributions are three fold. First, we build testing procedures on variables entering the model along the LARS path in the general design case when the noise level can be unknown. This testing procedures are referred to as the Generalized t-Spacing tests (GtSt) and we prove that they have exact non-asymptotic level (i.e., Type I error is exactly controlled). In that way, we extend a work from (Taylor et al., 2014) where the Spacing test works for consecutive knots and known variance. Second, we introduce a new exact multiple false negatives test after model selection in the general design case when the noise level can be unknown. We prove that this testing procedure has exact non-asymptotic level for general design and unknown noise level. Last, we give an exact control of the false discovery rate (FDR) under orthogonal design assumption. Monte-Carlo simulations and a real data experiment are provided to illustrate our results in this case. Of independent interest, we introduce an equivalent formulation of LARS algorithm based on a recursive function.Comment: 62 pages; new: FDR control and power comparison between Knockoff, FCD, Slope and our proposed method; new: the introduction has been revised and now present a synthetic presentation of the main results. We believe that this introduction brings new insists compared to previous version

A Rice method proof of the Null-Space Property over the Grassmannian

The Null-Space Property (NSP) is a necessary and sufficient condition for the recovery of the largest coefficients of solutions to an under-determined system of linear equations. Interestingly, this property governs also the success and the failure of recent developments in high-dimensional statistics, signal processing, error-correcting codes and the theory of polytopes. Although this property is the keystone of $\ell\_{1}$-minimization techniques, it is an open problem to derive a closed form for the phase transition on NSP. In this article, we provide the first proof of NSP using random processes theory and the Rice method. As a matter of fact, our analysis gives non-asymptotic bounds for NSP with respect to unitarily invariant distributions. Furthermore, we derive a simple sufficient condition for NSP.Comment: 18 Pages, some Figure

Perceptions of Fishermen Households on the Long-Term Impact of Coastal Resources Management in Panguil Bay

Coastal resources management (CRM) has flourished as a management approach for attaining a more sustainable form of economic development in the coastal areas of the Philippines. Its proliferation, coupled with the reasonably long time it has been in implementation, now calls for an evaluation of its long-term impact as a management and development approach. In this study, the long-term impact of CRM is evaluated not from the perspectives of technical people but based on the perception of its intended primary beneficiaries--the fishermen households. It does so not by looking into a specific CRM program or project but by observing the succession of CRM activities conducted in a single coastal area--Panguil Bay, Mindanao--over many years. The objectives were to ascertain if CRM works, identify its major constraints if it does not, and recommend future courses of actions to address the constraints.coastal resources management, long-term impact indicators, ladder diagram, Panguil Bay

Perceptions of Fishermen Households on the Long-Term Impact of Coastal Resources Management in Panguil Bay

Coastal resources management (CRM) has flourished as a management approach for attaining a more sustainable form of economic development in the coastal areas of the Philippines. Its proliferation, coupled with the reasonably long time it has been in implementation, now calls for an evaluation of its long-term impact as a management and development approach. In this study, the long-term impact of CRM is evaluated not from the perspectives of technical people but based on the perception of its intended primary beneficiaries--the fishermen households. It does so not by looking into a specific CRM program or project but by observing the succession of CRM activities conducted in a single coastal area--Panguil Bay, Mindanao--over many years. The objectives were to ascertain if CRM works, identify its major constraints if it does not, and recommend future courses of actions to address the constraints.coastal resources management, long-term impact indicators, ladder diagram, Panguil Bay

Strong-coupling analysis of scanning tunneling spectra in Bi2_2Sr2_2Ca2_2Cu3_3O10+δ_{10+\delta}

We study a series of spectra measured in the superconducting state of optimally-doped Bi-2223 by scanning tunneling spectroscopy. Each spectrum, as well as the average of spectra presenting the same gap, is fitted using a strong-coupling model taking into account the band structure, the BCS gap, and the interaction of electrons with the spin resonance. After describing our measurements and the main characteristics of the strong-coupling model, we report the whole set of parameters determined from the fits, and we discuss trends as a function of the gap magnitude. We also simulate angle-resolved photoemission spectra, and compare with recent experimental results.Comment: Published versio

A Novel Hybrid CNN-AIS Visual Pattern Recognition Engine

Machine learning methods are used today for most recognition problems. Convolutional Neural Networks (CNN) have time and again proved successful for many image processing tasks primarily for their architecture. In this paper we propose to apply CNN to small data sets like for example, personal albums or other similar environs where the size of training dataset is a limitation, within the framework of a proposed hybrid CNN-AIS model. We use Artificial Immune System Principles to enhance small size of training data set. A layer of Clonal Selection is added to the local filtering and max pooling of CNN Architecture. The proposed Architecture is evaluated using the standard MNIST dataset by limiting the data size and also with a small personal data sample belonging to two different classes. Experimental results show that the proposed hybrid CNN-AIS based recognition engine works well when the size of training data is limited in siz

Effects due to a scalar coupling on the particle-antiparticle production in the Duffin-Kemmer-Petiau theory

The Duffin-Kemmer-Petiau formalism with vector and scalar potentials is used to point out a few misconceptions diffused in the literature. It is explicitly shown that the scalar coupling makes the DKP formalism not equivalent to the Klein-Gordon formalism or to the Proca formalism, and that the spin-1 sector of the DKP theory looks formally like the spin-0 sector. With proper boundary conditions, scattering of massive bosons in an arbitrary mixed vector-scalar square step potential is explored in a simple way and effects due to the scalar coupling on the particle-antiparticle production and localization of bosons are analyzed in some detail

Juicio, que de la dedicatoria de la traduccion de la carta de guia de casados hizo la curiosidad de un ocioso, mal hallado con las inconsideradas noticias, que contiene, y le ofrece a Vicente de Senosiain, mercader de libros en Madrid

Copia digital. Valladolid : Junta de Castilla y León. Consejería de Cultura y Turismo, 2009-2010Encabezamiento tomado del CCPBSign. : [ ]1, A-C4Port. con orla tip.Sign. guillotinad

Relativistic confinement of neutral fermions with a trigonometric tangent potential

The problem of neutral fermions subject to a pseudoscalar potential is investigated. Apart from the solutions for $E=\pm mc^{2}$, the problem is mapped into the Sturm-Liouville equation. The case of a singular trigonometric tangent potential ($\sim \mathrm{tan} \gamma x$) is exactly solved and the complete set of solutions is discussed in some detail. It is revealed that this intrinsically relativistic and true confining potential is able to localize fermions into a region of space arbitrarily small without the menace of particle-antiparticle production.Comment: 12 page