Necessary and sufficient conditions of solution uniqueness in ℓ1\ell_1 minimization

This paper shows that the solutions to various convex $\ell_1$ minimization problems are \emph{unique} if and only if a common set of conditions are satisfied. This result applies broadly to the basis pursuit model, basis pursuit denoising model, Lasso model, as well as other $\ell_1$ models that either minimize $f(Ax-b)$ or impose the constraint $f(Ax-b)\leq\sigma$, where $f$ is a strictly convex function. For these models, this paper proves that, given a solution $x^*$ and defining I=\supp(x^*) and s=\sign(x^*_I), $x^*$ is the unique solution if and only if $A_I$ has full column rank and there exists $y$ such that $A_I^Ty=s$ and $|a_i^Ty|_\infty<1$ for $i\not\in I$. This condition is previously known to be sufficient for the basis pursuit model to have a unique solution supported on $I$. Indeed, it is also necessary, and applies to a variety of other $\ell_1$ models. The paper also discusses ways to recognize unique solutions and verify the uniqueness conditions numerically.Comment: 6 pages; revised version; submitte

Three-dimensional jamming and flows of soft glassy materials

Various disordered dense systems such as foams, gels, emulsions and colloidal suspensions, exhibit a jamming transition from a liquid state (they flow) to a solid state below a yield stress. Their structure, thoroughly studied with powerful means of 3D characterization, exhibits some analogy with that of glasses which led to call them soft glassy materials. However, despite its importance for geophysical and industrial applications, their rheological behavior, and its microscopic origin, is still poorly known, in particular because of its nonlinear nature. Here we show from two original experiments that a simple 3D continuum description of the behaviour of soft glassy materials can be built. We first show that when a flow is imposed in some direction there is no yield resistance to a secondary flow: these systems are always unjammed simultaneously in all directions of space. The 3D jamming criterion appears to be the plasticity criterion encountered in most solids. We also find that they behave as simple liquids in the direction orthogonal to that of the main flow; their viscosity is inversely proportional to the main flow shear rate, as a signature of shear-induced structural relaxation, in close similarity with the structural relaxations driven by temperature and density in other glassy systems.Comment: http://www.nature.com/nmat/journal/v9/n2/abs/nmat2615.htm

Supersymmetric QCD: Exact Results and Strong Coupling

We revisit two longstanding puzzles in supersymmetric gauge theories. The first concerns the question of the holomorphy of the coupling, and related to this the possible definition of an exact (NSVZ) beta function. The second concerns instantons in pure gluodynamics, which appear to give sensible, exact results for certain correlation functions, which nonetheless differ from those obtained using systematic weak coupling expansions. For the first question, we extend an earlier proposal of Arkani-Hamed and Murayama, showing that if their regulated action is written suitably, the holomorphy of the couplings is manifest, and it is easy to determine the renormalization scheme for which the NSVZ formula holds. This scheme, however, is seen to be one of an infinite class of schemes, each leading to an exact beta function; the NSVZ scheme, while simple, is not selected by any compelling physical consideration. For the second question, we explain why the instanton computation in the pure supersymmetric gauge theory is not reliable, even at short distances. The semiclassical expansion about the instanton is purely formal; if infrared divergences appear, they spoil arguments based on holomorphy. We demonstrate that infrared divergences do not occur in the perturbation expansion about the instanton, but explain that there is no reason to think this captures all contributions from the sector with unit topological charge. That one expects additional contributions is illustrated by dilute gas corrections. These are infrared divergent, and so difficult to define, but if non-zero give order one, holomorphic, corrections to the leading result. Exploiting an earlier analysis of Davies et al, we demonstrate that in the theory compactified on a circle of radius beta, due to infrared effects, finite contributions indeed arise which are not visible in the formal limit that beta goes to infinity.Comment: 28 pages, two references added, one typo correcte

Developmental Acquisition of a Rapid Calcium-Regulated Vesicle Supply Allows Sustained High Rates of Exocytosis in Auditory Hair Cells

Auditory hair cells (HCs) have the remarkable property to indefinitely sustain high rates of synaptic vesicle release during ongoing sound stimulation. The mechanisms of vesicle supply that allow such indefatigable exocytosis at the ribbon active zone remain largely unknown. To address this issue, we characterized the kinetics of vesicle recruitment and release in developing chick auditory HCs. Experiments were done using the intact chick basilar papilla from E10 (embryonic day 10) to P2 (two days post-hatch) by monitoring changes in membrane capacitance and Ca2+ currents during various voltage stimulations. Compared to immature pre-hearing HCs (E10-E12), mature post-hearing HCs (E18-P2) can steadily mobilize a larger readily releasable pool (RRP) of vesicles with faster kinetics and higher Ca2+ efficiency. As assessed by varying the inter-pulse interval of a 100 ms paired-pulse depolarization protocol, the kinetics of RRP replenishment were found much faster in mature HCs. Unlike mature HCs, exocytosis in immature HCs showed large depression during repetitive stimulations. Remarkably, when the intracellular concentration of EGTA was raised from 0.5 to 2 mM, the paired-pulse depression level remained unchanged in immature HCs but was drastically increased in mature HCs, indicating that the Ca2+ sensitivity of the vesicle replenishment process increases during maturation. Concomitantly, the immunoreactivity of the calcium sensor otoferlin and the number of ribbons at the HC plasma membrane largely increased, reaching a maximum level at E18-P2. Our results suggest that the efficient Ca2+-dependent vesicle release and supply in mature HCs essentially rely on the concomitant engagement of synaptic ribbons and otoferlin at the plasma membrane

Quantitative imaging of concentrated suspensions under flow

We review recent advances in imaging the flow of concentrated suspensions, focussing on the use of confocal microscopy to obtain time-resolved information on the single-particle level in these systems. After motivating the need for quantitative (confocal) imaging in suspension rheology, we briefly describe the particles, sample environments, microscopy tools and analysis algorithms needed to perform this kind of experiments. The second part of the review focusses on microscopic aspects of the flow of concentrated model hard-sphere-like suspensions, and the relation to non-linear rheological phenomena such as yielding, shear localization, wall slip and shear-induced ordering. Both Brownian and non-Brownian systems will be described. We show how quantitative imaging can improve our understanding of the connection between microscopic dynamics and bulk flow.Comment: Review on imaging hard-sphere suspensions, incl summary of methodology. Submitted for special volume 'High Solid Dispersions' ed. M. Cloitre, Vol. xx of 'Advances and Polymer Science' (Springer, Berlin, 2009); 22 pages, 16 fig

Empathy, engagement, entrainment: the interaction dynamics of aesthetic experience

A recent version of the view that aesthetic experience is based in empathy as inner imitation explains aesthetic experience as the automatic simulation of actions, emotions, and bodily sensations depicted in an artwork by motor neurons in the brain. Criticizing the simulation theory for committing to an erroneous concept of empathy and failing to distinguish regular from aesthetic experiences of art, I advance an alternative, dynamic approach and claim that aesthetic experience is enacted and skillful, based in the recognition of others’ experiences as distinct from one’s own. In combining insights from mainly psychology, phenomenology, and cognitive science, the dynamic approach aims to explain the emergence of aesthetic experience in terms of the reciprocal interaction between viewer and artwork. I argue that aesthetic experience emerges by participatory sense-making and revolves around movement as a means for creating meaning. While entrainment merely plays a preparatory part in this, aesthetic engagement constitutes the phenomenological side of coupling to an artwork and provides the context for exploration, and eventually for moving, seeing, and feeling with art. I submit that aesthetic experience emerges from bodily and emotional engagement with works of art via the complementary processes of the perception–action and motion–emotion loops. The former involves the embodied visual exploration of an artwork in physical space, and progressively structures and organizes visual experience by way of perceptual feedback from body movements made in response to the artwork. The latter concerns the movement qualities and shapes of implicit and explicit bodily responses to an artwork that cue emotion and thereby modulate over-all affect and attitude. The two processes cause the viewer to bodily and emotionally move with and be moved by individual works of art, and consequently to recognize another psychological orientation than her own, which explains how art can cause feelings of insight or awe and disclose aspects of life that are unfamiliar or novel to the viewer

Epigenetic marks in the mature pollen of Quercus suber L. (Fagaceae)

We have analysed the distribution of epigenetic marks for histone modifications at lysine residues H3 and H4, and DNA methylation, in the nuclei of mature pollen cells of the Angiosperm tree Quercus suber; a monoecious wind pollinated species with a protandrous system, and a long post-pollination period. The ultrasonic treatment developed for the isolation of pollen nuclei proved to be a fast and reliable method, preventing the interference of cell wall autofluorescence in the in situ immunolabelling assays. In contrast with previous studies on herbaceous species with short progamic phases, our results are consistent with a high level of silent (5-mC and H3K9me2) epigenetic marks on chromatin of the generative nucleus, and the prevalence of active marks (H3K9me3 and H4Kac) in the vegetative nucleus. The findings are discussed in terms of the pollination/fertilization timing strategy adopted by this plant specie

Neurochemical Changes in the Mouse Hippocampus Underlying the Antidepressant Effect of Genetic Deletion of P2X7 Receptors.

Recent investigations have revealed that the genetic deletion of P2X7 receptors (P2rx7) results in an antidepressant phenotype in mice. However, the link between the deficiency of P2rx7 and changes in behavior has not yet been explored. In the present study, we studied the effect of genetic deletion of P2rx7 on neurochemical changes in the hippocampus that might underlie the antidepressant phenotype. P2X7 receptor deficient mice (P2rx7-/-) displayed decreased immobility in the tail suspension test (TST) and an attenuated anhedonia response in the sucrose preference test (SPT) following bacterial endotoxin (LPS) challenge. The attenuated anhedonia was reproduced through systemic treatments with P2rx7 antagonists. The activation of P2rx7 resulted in the concentration-dependent release of [3H]glutamate in P2rx7+/+ but not P2rx7-/- mice, and the NR2B subunit mRNA and protein was upregulated in the hippocampus of P2rx7-/- mice. The brain-derived neurotrophic factor (BDNF) expression was higher in saline but not LPS-treated P2rx7-/- mice; the P2rx7 antagonist Brilliant blue G elevated and the P2rx7 agonist benzoylbenzoyl ATP (BzATP) reduced BDNF level. This effect was dependent on the activation of NMDA and non-NMDA receptors but not on Group I metabotropic glutamate receptors (mGluR1,5). An increased 5-bromo-2-deoxyuridine (BrdU) incorporation was also observed in the dentate gyrus derived from P2rx7-/- mice. Basal level of 5-HT was increased, whereas the 5HIAA/5-HT ratio was lower in the hippocampus of P2rx7-/- mice, which accompanied the increased uptake of [3H]5-HT and an elevated number of [3H]citalopram binding sites. The LPS-induced elevation of 5-HT level was absent in P2rx7-/- mice. In conclusion there are several potential mechanisms for the antidepressant phenotype of P2rx7-/- mice, such as the absence of P2rx7-mediated glutamate release, elevated basal BDNF production, enhanced neurogenesis and increased 5-HT bioavailability in the hippocampus

Toxoplasma gondii IgG Serointensity Is Positively Associated With Frailty

Background: Persistent inflammation related to aging (inflammaging) is exacerbated by chronic infections and contributes to frailty in older adults. We hypothesized associations between Toxoplasma gondii (T. gondii), a common parasite causing an oligosymptomatic unremitting infection, and frailty, and secondarily between T. gondii and previously reported markers of immune activation in frailty.Methods: We analyzed available demographic, social, and clinical data in Spanish and Portuguese older adults [N = 601; age: mean (SD) 77.3 (8.0); 61% women]. Plasma T. gondii immunoglobulin G (IgG) serointensity was measured with an enzyme-linked immunosorbent assay. The Fried criteria were used to define frailty status. Validated translations of Mini-Mental State Examination, Geriatric Depression Scale, and the Charlson Comorbidity Index were used to evaluate confounders. Previously analyzed biomarkers that were significantly associated with frailty in both prior reports and the current study, and also related to T. gondii serointensity, were further accounted for in multivariable logistic models with frailty as outcome.Results: In T. gondii-seropositives, there was a significant positive association between T. gondii IgG serointensity and frailty, accounting for age (p = .0002), and resisting adjustment for multiple successive confounders. Among biomarkers linked with frailty, kynurenine/tryptophan and soluble tumor necrosis factor receptor II were positively associated with T. gondii serointensity in seropositives (p < .05). Associations with other biomarkers were not significant.Conclusions: This first reported association between T. gondii and frailty is limited by a cross-sectional design and warrants replication. While certain biomarkers of inflammaging were associated with both T. gondii IgG serointensity and frailty, they did not fully mediate the T. gondii-frailty association.This work was supported in part by the Spanish Ministry of Science and Innovation: MCIN/AEI/10.13039/501100011033(grant PID2020-113788RB-I00); Xunta de Galicia (grant ED431B 2022/16); Ministry of Education, Culture and Sport (grant BEAGAL18/00142 to V.V.); and Ministry of Economy and Competitiveness, cofinanced by the European Social Fund (grant RYC-2015-18394 to L.L.-L.). Additionally supported, in part, by the University of Maryland School of Medicine Center for Research on Aging in Baltimore, Maryland; a Clinical Science Research & Development Service Merit Award, Office of Research and Development, U.S. Department of Veterans Affairs, Washington, District of Columbia (grant 1 I01 CX001310-01 to T.T.P.); a R01 grant from the National Institute on Aging, National Institutes of Health, Bethesda, Maryland (grant NIA R01 AG018859 to E.J.K.); and by the Military and Veteran Microbiome: Consortium for Research and Education in Aurora, Colorado (L.A.B., A.J.H., C.A.L., T.T.P.). The opinions expressed in the article belong to the authors and cannot be construed as official positions or opinions of the funders, including the U.S. Veterans Affairs Administration and the National Institutes of Health. Data collected and used for the analyses reported in this article are not available because the initial consent did not include this sharing and because other primary analyses have not been completed. Funding for open access charge: Universidade da Coruna/CISUG