Convex recovery of a structured signal from independent random linear measurements

This chapter develops a theoretical analysis of the convex programming method for recovering a structured signal from independent random linear measurements. This technique delivers bounds for the sampling complexity that are similar with recent results for standard Gaussian measurements, but the argument applies to a much wider class of measurement ensembles. To demonstrate the power of this approach, the paper presents a short analysis of phase retrieval by trace-norm minimization. The key technical tool is a framework, due to Mendelson and coauthors, for bounding a nonnegative empirical process.Comment: 18 pages, 1 figure. To appear in "Sampling Theory, a Renaissance." v2: minor corrections. v3: updated citations and increased emphasis on Mendelson's contribution

A statistical interpretation of the correlation between intermediate mass fragment multiplicity and transverse energy

Multifragment emission following Xe+Au collisions at 30, 40, 50 and 60 AMeV has been studied with multidetector systems covering nearly 4-pi in solid angle. The correlations of both the intermediate mass fragment and light charged particle multiplicities with the transverse energy are explored. A comparison is made with results from a similar system, Xe+Bi at 28 AMeV. The experimental trends are compared to statistical model predictions.Comment: 7 pages, submitted to Phys. Rev.

Isotopic composition of fragments in multifragmentation of very large nuclear systems: effects of the chemical equilibrium

Studies on the isospin of fragments resulting from the disassembly of highly excited large thermal-like nuclear emitting sources, formed in the ^{197}Au + ^{197}Au reaction at 35 MeV/nucleon beam energy, are presented. Two different decay systems (the quasiprojectile formed in midperipheral reactions and the unique source coming from the incomplete fusion of projectile and target in the most central collisions) were considered; these emitting sources have the same initial N/Z ratio and excitation energy (E^* ~= 5--6 MeV/nucleon), but different size. Their charge yields and isotopic content of the fragments show different distributions. It is observed that the neutron content of intermediate mass fragments increases with the size of the source. These evidences are consistent with chemical equilibrium reached in the systems. This fact is confirmed by the analysis with the statistical multifragmentation model.Comment: 9 pages, 4 ps figure

Relation Between Chiral Susceptibility and Solutions of Gap Equation in Nambu--Jona-Lasinio Model

We study the solutions of the gap equation, the thermodynamic potential and the chiral susceptibility in and beyond the chiral limit at finite chemical potential in the Nambu--Jona-Lasinio (NJL) model. We give an explicit relation between the chiral susceptibility and the thermodynamic potential in the NJL model. We find that the chiral susceptibility is a quantity being able to represent the furcation of the solutions of the gap equation and the concavo-convexity of the thermodynamic potential in NJL model. It indicates that the chiral susceptibility can identify the stable state and the possibility of the chiral phase transition in NJL model.Comment: 21 pages, 6 figures, misprints are correcte

Low Complexity Regularization of Linear Inverse Problems

Inverse problems and regularization theory is a central theme in contemporary signal processing, where the goal is to reconstruct an unknown signal from partial indirect, and possibly noisy, measurements of it. A now standard method for recovering the unknown signal is to solve a convex optimization problem that enforces some prior knowledge about its structure. This has proved efficient in many problems routinely encountered in imaging sciences, statistics and machine learning. This chapter delivers a review of recent advances in the field where the regularization prior promotes solutions conforming to some notion of simplicity/low-complexity. These priors encompass as popular examples sparsity and group sparsity (to capture the compressibility of natural signals and images), total variation and analysis sparsity (to promote piecewise regularity), and low-rank (as natural extension of sparsity to matrix-valued data). Our aim is to provide a unified treatment of all these regularizations under a single umbrella, namely the theory of partial smoothness. This framework is very general and accommodates all low-complexity regularizers just mentioned, as well as many others. Partial smoothness turns out to be the canonical way to encode low-dimensional models that can be linear spaces or more general smooth manifolds. This review is intended to serve as a one stop shop toward the understanding of the theoretical properties of the so-regularized solutions. It covers a large spectrum including: (i) recovery guarantees and stability to noise, both in terms of $\ell^2$-stability and model (manifold) identification; (ii) sensitivity analysis to perturbations of the parameters involved (in particular the observations), with applications to unbiased risk estimation ; (iii) convergence properties of the forward-backward proximal splitting scheme, that is particularly well suited to solve the corresponding large-scale regularized optimization problem

Stream and slope weathering effects on organic-rich mudstone geochemistry and implications for hydrocarbon source rock assessment: a Bowland Shale case study

This study contributes to the exploration and quantification of the weathering of organic-rich mudstones under temperate climatic conditions. Bowland Shales, exposed by a stream and slope, were sampled in order to develop a model for the effects of weathering on the mudstone geochemistry, including major and trace element geochemistry, Rock-Eval pyrolysis and δ13Corg. Four weathering grades (I – IV) are defined using a visual classification scheme; visually fresh and unaltered (I), chemically altered (II, III) and ‘paper shale’ that typifies weathered mudstone on slopes (IV). Bedload abrasion in the stream exposes of visually fresh and geochemically unaltered mudstone. Natural fractures are conduits for oxidising meteoric waters that promote leaching at the millimetre scale and/or precipitation of iron oxide coatings along fracture surfaces. On the slope, bedding-parallel fractures formed (and may continue to form) in response to chemical and/or physical weathering processes. These fractures develop along planes of weakness, typically along laminae comprising detrital grains, and exhibit millimetre- and centimetre-scale leached layers and iron oxide coatings. Fracture surfaces are progressively exposed to physical weathering processes towards the outcrop surface, and results in disintegration of the altered material along fracture surfaces. Grade IV, ‘paper shale’ mudstone is chemically unaltered but represents a biased record driven by initial heterogeneity in the sedimentary fabric. Chemically weathered outcrop samples exhibit lower concentrations of both ‘free’ (S1) (up to 0.6 mgHC/g rock) and ‘bound’ (S2) (up to 3.2 mgHC/g rock) hydrocarbon, reduced total organic carbon content (up to 0.34 wt%), reduced hydrogen index (up to 58 mgHC/gTOC), increased oxygen index (up to 19 mgCO + CO2/gTOC) and increased Tmax (up to 11 °C) compared with unaltered samples. If analysis of chemically weathered samples is unavoidable, back-extrapolation of Rock-Eval parameters can assist in the estimation of pre-weathering organic compositions. Combining Cs/Cu with oxygen index is a proxy for identifying the weathering progression from fresh material (I) to ‘paper shale’ (IV). This study demonstrates that outcrop samples in temperate climates can provide information for assessing hydrocarbon potential of organic-rich mudstones

Search for direct production of charginos and neutralinos in events with three leptons and missing transverse momentum in √s = 7 TeV pp collisions with the ATLAS detector

A search for the direct production of charginos and neutralinos in final states with three electrons or muons and missing transverse momentum is presented. The analysis is based on 4.7 fb−1 of proton–proton collision data delivered by the Large Hadron Collider and recorded with the ATLAS detector. Observations are consistent with Standard Model expectations in three signal regions that are either depleted or enriched in Z-boson decays. Upper limits at 95% confidence level are set in R-parity conserving phenomenological minimal supersymmetric models and in simplified models, significantly extending previous results

Jet size dependence of single jet suppression in lead-lead collisions at sqrt(s(NN)) = 2.76 TeV with the ATLAS detector at the LHC

Measurements of inclusive jet suppression in heavy ion collisions at the LHC provide direct sensitivity to the physics of jet quenching. In a sample of lead-lead collisions at sqrt(s) = 2.76 TeV corresponding to an integrated luminosity of approximately 7 inverse microbarns, ATLAS has measured jets with a calorimeter over the pseudorapidity interval |eta| < 2.1 and over the transverse momentum range 38 < pT < 210 GeV. Jets were reconstructed using the anti-kt algorithm with values for the distance parameter that determines the nominal jet radius of R = 0.2, 0.3, 0.4 and 0.5. The centrality dependence of the jet yield is characterized by the jet "central-to-peripheral ratio," Rcp. Jet production is found to be suppressed by approximately a factor of two in the 10% most central collisions relative to peripheral collisions. Rcp varies smoothly with centrality as characterized by the number of participating nucleons. The observed suppression is only weakly dependent on jet radius and transverse momentum. These results provide the first direct measurement of inclusive jet suppression in heavy ion collisions and complement previous measurements of dijet transverse energy imbalance at the LHC.Comment: 15 pages plus author list (30 pages total), 8 figures, 2 tables, submitted to Physics Letters B. All figures including auxiliary figures are available at http://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/PAPERS/HION-2011-02

Search for the standard model Higgs boson decaying into two photons in pp collisions at sqrt(s)=7 TeV

A search for a Higgs boson decaying into two photons is described. The analysis is performed using a dataset recorded by the CMS experiment at the LHC from pp collisions at a centre-of-mass energy of 7 TeV, which corresponds to an integrated luminosity of 4.8 inverse femtobarns. Limits are set on the cross section of the standard model Higgs boson decaying to two photons. The expected exclusion limit at 95% confidence level is between 1.4 and 2.4 times the standard model cross section in the mass range between 110 and 150 GeV. The analysis of the data excludes, at 95% confidence level, the standard model Higgs boson decaying into two photons in the mass range 128 to 132 GeV. The largest excess of events above the expected standard model background is observed for a Higgs boson mass hypothesis of 124 GeV with a local significance of 3.1 sigma. The global significance of observing an excess with a local significance greater than 3.1 sigma anywhere in the search range 110-150 GeV is estimated to be 1.8 sigma. More data are required to ascertain the origin of this excess.Comment: Submitted to Physics Letters

Search for new physics in events with opposite-sign leptons, jets, and missing transverse energy in pp collisions at sqrt(s) = 7 TeV

A search is presented for physics beyond the standard model (BSM) in final states with a pair of opposite-sign isolated leptons accompanied by jets and missing transverse energy. The search uses LHC data recorded at a center-of-mass energy sqrt(s) = 7 TeV with the CMS detector, corresponding to an integrated luminosity of approximately 5 inverse femtobarns. Two complementary search strategies are employed. The first probes models with a specific dilepton production mechanism that leads to a characteristic kinematic edge in the dilepton mass distribution. The second strategy probes models of dilepton production with heavy, colored objects that decay to final states including invisible particles, leading to very large hadronic activity and missing transverse energy. No evidence for an event yield in excess of the standard model expectations is found. Upper limits on the BSM contributions to the signal regions are deduced from the results, which are used to exclude a region of the parameter space of the constrained minimal supersymmetric extension of the standard model. Additional information related to detector efficiencies and response is provided to allow testing specific models of BSM physics not considered in this paper.Comment: Replaced with published version. Added journal reference and DO