Bounding the ground-state energy of a many-body system with the differential method

This paper promotes the differential method as a new fruitful strategy for estimating a ground-state energy of a many-body system. The case of an arbitrary number of attractive Coulombian particles is specifically studied and we make some favorable comparison of the differential method to the existing approaches that rely on variational principles. A bird's-eye view of the treatment of more general interactions is also given.Comment: version 1->2 (main revisions): subsection 2.2, equation (18), footnote 6 have been adde

Odyssey 2 : A mission toward Neptune and Triton to test General Relativity

Odyssey 2 will be proposed in December 2010 for the next call of M3 missions for Cosmic Vision 2015-2025. This mission, under a Phase 0 study performed by CNES, will aim at Neptune and Triton. Two sets of objectives will be pursued. The first one is to perform a set of gravitation experiments at the Solar System scale. Experimental tests of gravitation have always shown good agreement with General Relativity. There are however drivers to continue testing General Relativity, and to do so at the largest possible scales. From a theoretical point of view, Einstein's theory of gravitation shows inconsistencies with a quantum description of Nature and unified theories predict deviations from General Relativity. From an observational point of view, as long as dark matter and dark energy are not observed through other means than their gravitational effects, they can be considered as a manifestation of a modification of General Relativity at cosmic scales. The scientific objectives are to: (i) test the gravitation law at the Solar System scale; (ii) measure the Eddington parameter; and (iii) investigate the navigation anomalies during fly-bys. To fulfil these objectives, the following components are to be on board the spacecraft: (i) the Gravity Advanced Package (GAP), which is an electrostatic accelerometer to which a rotating stage is added; (ii) radio-science; (iii) laser ranging, to improve significantly the measure of the Eddington parameter. The second set of objectives is to enhance our knowledge of Neptune and Triton. Several instruments dedicated to planetology are foreseen: camera, spectrometer, dust and particle detectors, and magnetometer. Depending on the ones kept, the mission could provide information on the gravity field, the atmosphere and the magnetosphere of the two bodies as well as on the surface geology of Triton and on the nature of the planetary rings around Neptune.Comment: 61st International Astronautical Congress (Prague, Czech Republic - September 2010), 7 page

New Lower Bound on Fermion Binding Energies

We derive a new lower bound for the ground state energy $E^{\rm F}(N,S)$ of N fermions with total spin S in terms of binding energies $E^{\rm F}(N-1,S \pm 1/2)$ of (N-1) fermions. Numerical examples are provided for some simple short-range or confining potentials.Comment: 4 pages, 1 eps figur

Testing Hall-Post Inequalities With Exactly Solvable N-Body Problems

The Hall--Post inequalities provide lower bounds on $N$-body energies in terms of $N'$-body energies with $N'<N$. They are rewritten and generalized to be tested with exactly-solvable models of Calogero-Sutherland type in one and higher dimensions. The bound for $N$ spinless fermions in one dimension is better saturated at large coupling than for noninteracting fermions in an oscillatorComment: 7 pages, Latex2e, 2 .eps figure

Improved lower bounds for the ground-state energy of many-body systems

New lower bounds for the binding energy of a quantum-mechanical system of interacting particles are presented. The new bounds are expressed in terms of two-particle quantities and improve the conventional bounds of the Hall-Post type. They are constructed by considering not only the energy in the two-particle system, but also the structure of the pair wave function. We apply the formal results to various numerical examples, and show that in some cases dramatic improvement over the existing bounds is reached.Comment: 29 pages, 5 figures, to be published in Phys. Rev.

Multilineage Differentiation for Formation of Innervated Skeletal Muscle Fibers from Healthy and Diseased Human Pluripotent Stem Cells.

Induced pluripotent stem cells (iPSCs) obtained by reprogramming primary somatic cells have revolutionized the fields of cell biology and disease modeling. However, the number protocols for generating mature muscle fibers with sarcolemmal organization using iPSCs remain limited, and partly mimic the complexity of mature skeletal muscle. Methods: We used a novel combination of small molecules added in a precise sequence for the simultaneous codifferentiation of human iPSCs into skeletal muscle cells and motor neurons. Results: We show that the presence of both cell types reduces the production time for millimeter-long multinucleated muscle fibers with sarcolemmal organization. Muscle fiber contractions are visible in 19-21 days, and can be maintained over long period thanks to the production of innervated multinucleated mature skeletal muscle fibers with autonomous cell regeneration of PAX7-positive cells and extracellular matrix synthesis. The sequential addition of specific molecules recapitulates key steps of human peripheral neurogenesis and myogenesis. Furthermore, this organoid-like culture can be used for functional evaluation and drug screening. Conclusion: Our protocol, which is applicable to hiPSCs from healthy individuals, was validated in Duchenne Muscular Dystrophy, Myotonic Dystrophy, Facio-Scapulo-Humeral Dystrophy and type 2A Limb-Girdle Muscular Dystrophy, opening new paths for the exploration of muscle differentiation, disease modeling and drug discovery

Genetic and Functional Assessment of the Role of the rs13431652-A and rs573225-A Alleles in the G6PC2 Promoter That Are Strongly Associated With Elevated Fasting Glucose Levels

OBJECTIVE Genome-wide association studies have identified a single nucleotide polymorphism (SNP), rs560887, located in a G6PC2 intron that is highly correlated with variations in fasting plasma glucose (FPG). G6PC2 encodes an islet-specific glucose-6-phosphatase catalytic subunit. This study examines the contribution of two G6PC2 promoter SNPs, rs13431652 and rs573225, to the association signal. RESEARCH DESIGN AND METHODS We genotyped 9,532 normal FPG participants (FPG <6.1 mmol/l) for three G6PC2 SNPs, rs13431652 (distal promoter), rs573225 (proximal promoter), rs560887 (3rd intron). We used regression analyses adjusted for age, sex, and BMI to assess the association with FPG and haplotype analyses to assess comparative SNP contributions. Fusion gene and gel retardation analyses characterized the effect of rs13431652 and rs573225 on G6PC2 promoter activity and transcription factor binding. RESULTS Genetic analyses provide evidence for a strong contribution of the promoter SNPs to FPG variability at the G6PC2 locus (rs13431652: β = 0.075, P = 3.6 × 10−35; rs573225 β = 0.073 P = 3.6 × 10−34), in addition to rs560887 (β = 0.071, P = 1.2 × 10−31). The rs13431652-A and rs573225-A alleles promote increased NF-Y and Foxa2 binding, respectively. The rs13431652-A allele is associated with increased FPG and elevated promoter activity, consistent with the function of G6PC2 in pancreatic islets. In contrast, the rs573225-A allele is associated with elevated FPG but reduced promoter activity. CONCLUSIONS Genetic and in situ functional data support a potential role for rs13431652, but not rs573225, as a causative SNP linking G6PC2 to variations in FPG, though a causative role for rs573225 in vivo cannot be ruled out

Functionals of the Brownian motion, localization and metric graphs

We review several results related to the problem of a quantum particle in a random environment. In an introductory part, we recall how several functionals of the Brownian motion arise in the study of electronic transport in weakly disordered metals (weak localization). Two aspects of the physics of the one-dimensional strong localization are reviewed : some properties of the scattering by a random potential (time delay distribution) and a study of the spectrum of a random potential on a bounded domain (the extreme value statistics of the eigenvalues). Then we mention several results concerning the diffusion on graphs, and more generally the spectral properties of the Schr\"odinger operator on graphs. The interest of spectral determinants as generating functions characterizing the diffusion on graphs is illustrated. Finally, we consider a two-dimensional model of a charged particle coupled to the random magnetic field due to magnetic vortices. We recall the connection between spectral properties of this model and winding functionals of the planar Brownian motion.Comment: Review article. 50 pages, 21 eps figures. Version 2: section 5.5 and conclusion added. Several references adde