Functional approach for pairing in finite systems: How to define restoration of broken symmetries in Energy Density Functional theory ?

The Multi-Reference Energy Density Functional (MR-EDF) approach (also called configuration mixing or Generator Coordinate Method), that is commonly used to treat pairing in finite nuclei and project onto particle number, is re-analyzed. It is shown that, under certain conditions, the MR-EDF energy can be interpreted as a functional of the one-body density matrix of the projected state with good particle number. Based on this observation, we propose a new approach, called Symmetry-Conserving EDF (SC-EDF), where the breaking and restoration of symmetry are accounted for simultaneously. We show, that such an approach is free from pathologies recently observed in MR-EDF and can be used with a large flexibility on the density dependence of the functional.Comment: proceeding of the conference "Many body correlations from dilute to dense Nuclear systems", Paris, February 201

High Dimensional Classification with combined Adaptive Sparse PLS and Logistic Regression

Motivation: The high dimensionality of genomic data calls for the development of specific classification methodologies, especially to prevent over-optimistic predictions. This challenge can be tackled by compression and variable selection, which combined constitute a powerful framework for classification, as well as data visualization and interpretation. However, current proposed combinations lead to instable and non convergent methods due to inappropriate computational frameworks. We hereby propose a stable and convergent approach for classification in high dimensional based on sparse Partial Least Squares (sparse PLS). Results: We start by proposing a new solution for the sparse PLS problem that is based on proximal operators for the case of univariate responses. Then we develop an adaptive version of the sparse PLS for classification, which combines iterative optimization of logistic regression and sparse PLS to ensure convergence and stability. Our results are confirmed on synthetic and experimental data. In particular we show how crucial convergence and stability can be when cross-validation is involved for calibration purposes. Using gene expression data we explore the prediction of breast cancer relapse. We also propose a multicategorial version of our method on the prediction of cell-types based on single-cell expression data. Availability: Our approach is implemented in the plsgenomics R-package.Comment: 9 pages, 3 figures, 4 tables + Supplementary Materials 8 pages, 3 figures, 10 table

Magnetic hyperthermia in single-domain monodisperse FeCo nanoparticles: Evidences for Stoner-Wohlfarth behaviour and large losses

We report on hyperthermia measurements on a colloidal solution of 15 nm monodisperse FeCo nanoparticles (NPs). Losses as a function of the magnetic field display a sharp increase followed by a plateau, which is what is expected for losses of ferromagnetic single-domain NPs. The frequency dependence of the coercive field is deduced from hyperthermia measurement and is in quantitative agreement with a simple model of non-interacting NPs. The measured losses (1.5 mJ/g) compare to the highest of the literature, though the saturation magnetization of the NPs is well below the bulk one.Comment: 14 pages, 3 figure

Observations of Above-Surface Littoral Foraging in Two Sea Ducks, Barrow's Goldeneye, Bucephala islandica, and Surf Scoter, Melanitta perspicillata, in Coastal Southwestern British Columbia

Barrow's Goldeneyes (Bucephala islandica) and Surf Scoters (Melanitta perspicillata) were observed on four separate occasions, by three different observers, foraging on Bay Mussels (Mytilus trossulus) above the water surface. This unique foraging behaviour could be attributed to diurnal spring tides and reduced lower intertidal mussel abundance

Transfemoral treatment for iliac occlusive disease with endoluminal stent-grafts

Objectives:Percutaneous treatment of iliac artery occlusive disease has replaced open vascular reconstruction for several indications. A balloon angioplasty with or without stent is not an option in the presence of infrainguinal extension of the disease. The authors describe a technique that allows the construction of an aorto- or iliofemoral graft through a single groin incision, using a 4 mm PTFE graft, anchoring it proximally with a Palmaz stent and dilating both to the desired diameter.Design:Retrospective non-randomised study.Materials and Methods:Nineteen procedures were performed in 16 patients mainly because of ischaemic rest pain, often with trophic skin changes or minor gangrene. Three patients had a bilateral procedure. Twelve patients had one or more associated procedures: 10 distal bypasses, one thrombectomy, one reimplantation of a distal bypass on the iliofemoral graft, one contralateral profundaplasty and two stents of the contralateral common iliac artery.Results:Two patients died, one of small bowel ischaemia and the other of a myocardial infarction. During the mean follow-up of 8.8 months, two graft thromboses occurred. In another patient bilateral stenting of a residual stenosis was necessary.Conclusions:Our experience shows that the reported technique is feasible. Whether the procedure is truly “less invasive” and the long-term results acceptable remains to be shown

Description of Pairing correlation in Many-Body finite systems with density functional theory

Different steps leading to the new functional for pairing based on natural orbitals and occupancies proposed in ref. [D. Lacroix and G. Hupin, arXiv:1003.2860] are carefully analyzed. Properties of quasi-particle states projected onto good particle number are first reviewed. These properties are used (i) to prove the existence of such a functional (ii) to provide an explicit functional through a 1/N expansion starting from the BCS approach (iii) to give a compact form of the functional summing up all orders in the expansion. The functional is benchmarked in the case of the picked fence pairing Hamiltonian where even and odd systems, using blocking technique are studied, at various particle number and coupling strength, with uniform and random single-particle level spacing. In all cases, a very good agreement is found with a deviation inferior to 1% compared to the exact energy.Comment: 14 pages, 9 figure

Out of equilibrium transport through an Anderson impurity: Probing scaling laws within the equation of motion approach

We study non-equilibrium electron transport through a quantum impurity coupled to metallic leads using the equation of motion technique at finite temperature T. Assuming that the interactions are taking place solely in the impurity and focusing in the infinite Hubbard limit, we compute the out of equilibrium density of states and the differential conductance G_2(T,V) to test several scaling laws. We find that G_2(T,V)/G_2(T,0) is a universal function of both eV/T_K and T/T_K, being T_K the Kondo temperature. The effect of an in plane magnetic field on the splitting of the zero bias anomaly in the differential conductance is also analyzed. For a Zeeman splitting \Delta, the computed differential conductance peak splitting depends only on \Delta/T_K, and for large fields approaches the value of 2\Delta . Besides the traditional two leads setup, we also consider other configurations that mimics recent experiments, namely, an impurity embedded in a mesoscopic wire and the presence of a third weakly coupled lead. In these cases, a double peak structure of the Kondo resonance is clearly obtained in the differential conductance while the amplitude of the highest peak is shown to decrease as \ln(eV/T_K). Several features of these results are in qualitative agreement with recent experimental observations reported on quantum dots.Comment: 9 pages, 7 figure

Fermi Surface of The One-dimensional Kondo Lattice Model

We show a strong indication of the existence of a large Fermi surface in the one-dimensional Kondo lattice model. The characteristic wave vector of the model is found to be $k_F=(1+\rho )\pi /2$, $\rho$ being the density of the conduction electrons. This result is at first obtained for a variant of the model that includes an antiferromagnetic Heisenberg interaction $J_H$ between the local moments. It is then directly observed in the conventional Kondo lattice $(J_H=0)$, in the narrow range of Kondo couplings where the long distance properties of the model are numerically accessible.Comment: 11 pages, 6 figure

Internal structure of nanoparticles of Al generated by laser ablation in liquid ethanol

Al NPs are synthesized by laser ablation of a bulk Al target immersed into liquid ethanol saturated with hydrogen at atmospheric pressure. The nanoparticles possess a well-distinguished core-shell structure. High Resolution Transmission Electron Microscopy shows several layers inside the Al nanoparticle: oxide layer, amorphous Al, single crystal Al, and a cavity in the center. Formation of the cavity is attributed to the sharp increase of hydrogen dissolution in Al upon its melting and its eventual release after the solidification

Particle-Number Restoration within the Energy Density Functional Formalism

We give a detailed analysis of the origin of spurious divergences and finite steps that have been recently identified in particle-number restoration calculations within the nuclear energy density functional framework. We isolate two distinct levels of spurious contributions to the energy. The first one is encoded in the definition of the basic energy density functional itself whereas the second one relates to the canonical procedure followed to extend the use of the energy density functional to multi-reference calculations. The first level of spuriosity relates to the long-known self-interaction problem and to the newly discussed self-pairing interaction process which might appear when describing paired systems with energy functional methods using auxiliary reference states of Bogoliubov or BCS type. A minimal correction to the second level of spuriosity to the multi-reference nuclear energy density functional proposed in [D. Lacroix, T. Duguet, M. Bender, arXiv:0809.2041] is shown to remove completely the anomalies encountered in particle-number restored calculations. In particular, it restores sum-rules over (positive) particle numbers that are to be fulfilled by the particle-number-restored formalism. The correction is found to be on the order of several hundreds of keVs up to about 1 MeV in realistic calculations, which is small compared to the total binding energy, but often accounts for a substantial percentage of the energy gain from particle-number restoration and is on the same energy scale as the excitations one addresses with multi-reference energy density functional methods.Comment: 37 pages, 14 figures, accepted for publication in PR