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

Measurement of charm production at central rapidity in proton-proton collisions at s=2.76\sqrt{s} = 2.76 TeV

The $p_{\rm T}$-differential production cross sections of the prompt (B feed-down subtracted) charmed mesons D$^0$, D$^+$, and D$^{*+}$ in the rapidity range $|y|<0.5$, and for transverse momentum $1< p_{\rm T} <12$ GeV/$c$, were measured in proton-proton collisions at $\sqrt{s} = 2.76$ TeV with the ALICE detector at the Large Hadron Collider. The analysis exploited the hadronic decays D$^0 \rightarrow$K$\pi$, D$^+ \rightarrow$K$\pi\pi$, D$^{*+} \rightarrow$D$^0\pi$, and their charge conjugates, and was performed on a $L_{\rm int} = 1.1$ nb$^{-1}$ event sample collected in 2011 with a minimum-bias trigger. The total charm production cross section at $\sqrt{s} = 2.76$ TeV and at 7 TeV was evaluated by extrapolating to the full phase space the $p_{\rm T}$-differential production cross sections at $\sqrt{s} = 2.76$ TeV and our previous measurements at $\sqrt{s} = 7$ TeV. The results were compared to existing measurements and to perturbative-QCD calculations. The fraction of cdbar D mesons produced in a vector state was also determined.Comment: 20 pages, 5 captioned figures, 4 tables, authors from page 15, published version, figures at http://aliceinfo.cern.ch/ArtSubmission/node/307

Particle-yield modification in jet-like azimuthal di-hadron correlations in Pb-Pb collisions at sNN\sqrt{s_{\rm NN}} = 2.76 TeV

The yield of charged particles associated with high-$p_{\rm T}$ trigger particles ($8 < p_{\rm T} < 15$ GeV/$c$) is measured with the ALICE detector in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV relative to proton-proton collisions at the same energy. The conditional per-trigger yields are extracted from the narrow jet-like correlation peaks in azimuthal di-hadron correlations. In the 5% most central collisions, we observe that the yield of associated charged particles with transverse momenta $p_{\rm T}> 3$ GeV/$c$ on the away-side drops to about 60% of that observed in pp collisions, while on the near-side a moderate enhancement of 20-30% is found.Comment: 15 pages, 2 captioned figures, 1 table, authors from page 10, published version, figures at http://aliceinfo.cern.ch/ArtSubmission/node/350

Rare coding variants in genes encoding GABA(A) receptors in genetic generalised epilepsies : an exome-based case-control study

Background Genetic generalised epilepsy is the most common type of inherited epilepsy. Despite a high concordance rate of 80% in monozygotic twins, the genetic background is still poorly understood. We aimed to investigate the burden of rare genetic variants in genetic generalised epilepsy. Methods For this exome-based case-control study, we used three different genetic generalised epilepsy case cohorts and three independent control cohorts, all of European descent. Cases included in the study were clinically evaluated for genetic generalised epilepsy. Whole-exome sequencing was done for the discovery case cohort, a validation case cohort, and two independent control cohorts. The replication case cohort underwent targeted next-generation sequencing of the 19 known genes encoding subunits of GABA(A) receptors and was compared to the respective GABA(A) receptor variants of a third independent control cohort. Functional investigations were done with automated two-microelectrode voltage clamping in Xenopus laevis oocytes. Findings Statistical comparison of 152 familial index cases with genetic generalised epilepsy in the discovery cohort to 549 ethnically matched controls suggested an enrichment of rare missense (Nonsyn) variants in the ensemble of 19 genes encoding GABA(A) receptors in cases (odds ratio [OR] 2.40 [95% CI 1.41-4.10]; p(Nonsyn)=0.0014, adjusted p(Nonsyn)=0.019). Enrichment for these genes was validated in a whole-exome sequencing cohort of 357 sporadic and familial genetic generalised epilepsy cases and 1485 independent controls (OR 1.46 [95% CI 1.05-2.03]; p(Nonsyn)=0.0081, adjusted p(Nonsyn)=0.016). Comparison of genes encoding GABA(A) receptors in the independent replication cohort of 583 familial and sporadic genetic generalised epilepsy index cases, based on candidate-gene panel sequencing, with a third independent control cohort of 635 controls confirmed the overall enrichment of rare missense variants for 15 GABA(A) receptor genes in cases compared with controls (OR 1.46 [95% CI 1.02-2.08]; p(Nonsyn)=0.013, adjusted p(Nonsyn)=0.027). Functional studies for two selected genes (GABRB2 and GABRA5) showed significant loss-of-function effects with reduced current amplitudes in four of seven tested variants compared with wild-type receptors. Interpretation Functionally relevant variants in genes encoding GABA(A) receptor subunits constitute a significant risk factor for genetic generalised epilepsy. Examination of the role of specific gene groups and pathways can disentangle the complex genetic architecture of genetic generalised epilepsy. Copyright (C) 2018 The Author(s). Published by Elsevier Ltd.Peer reviewe

Long-range Angular Correlations On The Near And Away Side In P-pb Collisions At √snn=5.02 Tev

7191/Mar294

ϒ production in p–Pb collisions at √sNN=8.16 TeV

ϒ production in p–Pb interactions is studied at the centre-of-mass energy per nucleon–nucleon collision √sNN = 8.16 TeV with the ALICE detector at the CERN LHC. The measurement is performed reconstructing bottomonium resonances via their dimuon decay channel, in the centre-of-mass rapidity intervals 2.03 < ycms < 3.53 and −4.46 < ycms < −2.96, down to zero transverse momentum. In this work, results on the ϒ(1S) production cross section as a function of rapidity and transverse momentum are presented. The corresponding nuclear modification factor shows a suppression of the ϒ(1S) yields with respect to pp collisions, both at forward and backward rapidity. This suppression is stronger in the low transverse momentum region and shows no significant dependence on the centrality of the interactions. Furthermore, the ϒ(2S) nuclear modification factor is evaluated, suggesting a suppression similar to that of the ϒ(1S). A first measurement of the ϒ(3S) has also been performed. Finally, results are compared with previous ALICE measurements in p–Pb collisions at √sNN = 5.02 TeV and with theoretical calculations.publishedVersio

Centrality Dependence Of The Pseudorapidity Density Distribution For Charged Particles In Pb-pb Collisions At √snn=2.76tev

7264/Mai61062

Neutron emission from electromagnetic dissociation of Pb nuclei at √ s NN = 2.76 TeV measured with the ALICE ZDC

The ALICE Zero Degree Calorimeter system (ZDC) is composed of two identical sets of calorimeters, placed at opposite sides with respect to the interaction point, 114 meters away from it, complemented by two small forward electromagnetic calorimeters (ZEM). Each set of detectors consists of a neutron (ZN) and a proton (ZP) ZDC. They are placed at zero degrees with respect to the LHC axis and allow to detect particles emitted close to beam direction, in particular neutrons and protons emerging from hadronic heavy-ion collisions (spectator nucleons) and those emitted from electromagnetic processes. For neutrons emitted by these two processes, the ZN calorimeters have nearly 100% acceptance. During the √ sNN = 2.76 TeV Pb-Pb data-taking, the ALICE Collaboration studied forward neutron emission with a dedicated trigger, requiring a minimum energy deposition in at least one of the two ZN. By exploiting also the information of the two ZEM calorimeters it has been possible to separate the contributions of electromagnetic and hadronic processes and to study single neutron vs. multiple neutron emission. The measured cross sections of single and mutual electromagnetic dissociation of Pb nuclei at √ s NN = 2.76 TeV, with neutron emission, are σ single EMD = 187:4 ± 0.2 (stat.)-11.2 +13.2 (syst.) b and σmutual EMD = 5.7 ± 0.1 (stat.) ±0.4 (syst.) b, respectively [1]. This is the first measurement of electromagnetic dissociation of 208Pb nuclei at the LHC energies, allowing a test of electromagnetic dissociation theory in a new energy regime. The experimental results are compared to the predictions from a relativistic electromagnetic dissociation model'701st International Conference on New Frontiers in Physics, ICFP 20122012-06-10Kolymbari, Crete; Greecesem informaçã

Multiplicity dependence of inclusive J/psi production at midrapidity in pp collisions at root s=13 TeV

Measurements of the inclusive J/psi yield as a function of charged-particle pseudorapidity density dN(ch)/d eta in pp collisions at root s = 13 TeV with ALICE at the LHC are reported. The J/psi meson yield is measured at midrapidity (vertical bar y vertical bar <0.9) in the dielectron channel, for events selected based on the charged-particle multiplicity at midrapidity (vertical bar eta vertical bar <1) and at forward rapidity (-3.7 <eta <-1.7 and 2.8 <eta <5.1); both observables are normalized to their corresponding averages in minimum bias events. The increase of the normalized J/psi yield with normalized dN(ch)/d eta is significantly stronger than linear and dependent on the transverse momentum. The data are compared to theoretical predictions, which describe the observed trends well, albeit not always quantitatively. (C) 2020 European Organization for Nuclear Research. Published by Elsevier B.V.Peer reviewe