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

GABAA receptors can initiate the formation of functional inhibitory GABAergic synapses.

The mechanisms that underlie the selection of an inhibitory GABAergic axon's postsynaptic targets and the formation of the first contacts are currently unknown. To determine whether expression of GABAA receptors (GABAA Rs) themselves - the essential functional postsynaptic components of GABAergic synapses - can be sufficient to initiate formation of synaptic contacts, a novel co-culture system was devised. In this system, the presynaptic GABAergic axons originated from embryonic rat basal ganglia medium spiny neurones, whereas their most prevalent postsynaptic targets, i.e. α1/β2/γ2-GABAA Rs, were expressed constitutively in a stably transfected human embryonic kidney 293 (HEK293) cell line. The first synapse-like contacts in these co-cultures were detected by colocalization of presynaptic and postsynaptic markers within 2 h. The number of contacts reached a plateau at 24 h. These contacts were stable, as assessed by live cell imaging; they were active, as determined by uptake of a fluorescently labelled synaptotagmin vesicle-luminal domain-specific antibody; and they supported spontaneous and action potential-driven postsynaptic GABAergic currents. Ultrastructural analysis confirmed the presence of characteristics typical of active synapses. Synapse formation was not observed with control or N-methyl-d-aspartate receptor-expressing HEK293 cells. A prominent increase in synapse formation and strength was observed when neuroligin-2 was co-expressed with GABAA Rs, suggesting a cooperative relationship between these proteins. Thus, in addition to fulfilling an essential functional role, postsynaptic GABAA Rs can promote the adhesion of inhibitory axons and the development of functional synapses

Efferent Control of the Electrical and Mechanical Properties of Hair Cells in the Bullfrog's Sacculus

Background: Hair cells in the auditory, vestibular, and lateral-line systems respond to mechanical stimulation and transmit information to afferent nerve fibers. The sensitivity of mechanoelectrical transduction is modulated by the efferent pathway, whose activity usually reduces the responsiveness of hair cells. The basis of this effect remains unknown. Methodology and Principal Findings: We employed immunocytological, electrophysiological, and micromechanical approaches to characterize the anatomy of efferent innervation and the effect of efferent activity on the electrical and mechanical properties of hair cells in the bullfrog’s sacculus. We found that efferent fibers form extensive synaptic terminals on all macular and extramacular hair cells. Macular hair cells expressing the Ca 2+-buffering protein calretinin contain half as many synaptic ribbons and are innervated by twice as many efferent terminals as calretinin-negative hair cells. Efferent activity elicits inhibitory postsynaptic potentials in hair cells and thus inhibits their electrical resonance. In hair cells that exhibit spiking activity, efferent stimulation suppresses the generation of action potentials. Finally, efferent activity triggers a displacement of the hair bundle’s resting position. Conclusions and Significance: The hair cells of the bullfrog’s sacculus receive a rich efferent innervation with the heaviest projection to calretinin-containing cells. Stimulation of efferent axons desensitizes the hair cells and suppresses their spiking activity. Although efferent activation influences mechanoelectrical transduction, the mechanical effects on hair bundles ar

Fast and Slow Effects of Medial Olivocochlear Efferent Activity in Humans

Background: The medial olivocochlear (MOC) pathway modulates basilar membrane motion and auditory nerve activity on both a fast (10–100 ms) and a slow (10–100 s) time scale in guinea pigs. The slow MOC modulation of cochlear activity is postulated to aide in protection against acoustic trauma. However in humans, the existence and functional roles of slow MOC effects remain unexplored. Methodology/Principal Findings: By employing contralateral noise at moderate to high levels (68 and 83 dB SPL) as an MOC reflex elicitor, and spontaneous otoacoustic emissions (SOAEs) as a non-invasive probe of the cochlea, we demonstrated MOC modulation of human cochlear output both on a fast and a slow time scale, analogous to the fast and slow MOC efferent effects observed on basilar membrane vibration and auditory nerve activity in guinea pigs. The magnitude of slow effects was minimal compared with that of fast effects. Consistent with basilar membrane and auditory nerve activity data, SOAE level was reduced by both fast and slow MOC effects, whereas SOAE frequency was elevated by fast and reduced by slow MOC effects. The magnitudes of fast and slow effects on SOAE level were positively correlated. Conclusions/Significance: Contralateral noise up to 83 dB SPL elicited minimal yet significant changes in both SOAE leve

Damages of the tibial post in constrained total knee prostheses in the early postoperative course – a scanning electron microscopic study of polyethylene inlays

<p>Abstract</p> <p>Background</p> <p>Investigation of the risk of fracture of the polyethylene (PE) inlay in constrained total knee prostheses.</p> <p>Methods</p> <p>Three unused and seven polyethylene inlays that had been implanted in a patient's knee for an average of 25.4 months (min 1.1 months, max 50.2 months) were investigated using scanning electron microscopy (SEM). All inlays were of the same type and size (Genesis II constrained, Smith & Nephew). The PE surface at the transition from the plateau to the post was analyzed.</p> <p>Results</p> <p>The unused inlays had fissure-free surfaces. All inlays that had been implanted in a patient's knee already had distinct fissures at the front and backside of the post.</p> <p>Conclusion</p> <p>The fissures of the transition from the plateau to the post indicated a loading-induced irreversible mechanical deformation and possibly cause the fracture of the inlay.</p

Tidal Volume Single Breath Washout of Two Tracer Gases - A Practical and Promising Lung Function Test

Small airway disease frequently occurs in chronic lung diseases and may cause ventilation inhomogeneity (VI), which can be assessed by washout tests of inert tracer gas. Using two tracer gases with unequal molar mass (MM) and diffusivity increases specificity for VI in different lung zones. Currently washout tests are underutilised due to the time and effort required for measurements. The aim of this study was to develop and validate a simple technique for a new tidal single breath washout test (SBW) of sulfur hexafluoride (SF(6)) and helium (He) using an ultrasonic flowmeter (USFM)

IP-10 detection in urine is associated with lung diseases

<p>Abstract</p> <p>Background</p> <p>blood cytokines and chemokines have been proposed as biomarkers for tuberculosis (TB). Recently, some immune mediators found in the urine of patients with renal dysfunctions have also been suggested as potential biomarkers. Finding biomarkers for TB in urine would present several advantages over blood in terms of collection and safety. The objective of this study was to investigate the presence of cytokines and chemokines in the urine of patients with pulmonary TB at the time of diagnosis. In a subgroup, the evaluation was also performed during TB treatment and at therapy completion. Patients with lung diseases other than TB, and healthy subjects were also enrolled.</p> <p>Methods</p> <p>urine samples from 138 individuals, after exclusion of renal dysfunctions, were collected during an 18 month-period. Among them, 58 received a diagnosis of pulmonary TB, 28 resulted having lung diseases other than TB, and 34 were healthy subjects. Moreover, 18 TB patients, 9 of whom were tested 2 months after AFB smear sputum reversion and 9 of whom were cured of TB were also included. Cytokines and chemokines in urine were evaluated using a Cytometric-Bead-Array-Flex-Set. IP-10 detection in 49 subjects was also carried out in parallel by using an Enzyme Linked ImmunoSorbent Assay (ELISA).</p> <p>Results</p> <p>IFN-γ, TNF-α, IL-2, IL-8, MIP-1α, MIP-1β and RANTES were poorly detected in all urine samples. Conversely, IP-10 was consistently detected in urine and its level was significantly increased in patients with lung disease compared to healthy subjects (p < 0.001). Increased IP-10 levels were found in both pulmonary TB and lung diseases other than TB. Moreover lower IP-10 levels were found in cured-TB patients compared to the levels at the time of diagnosis, and this difference was close to significance (p = 0.06). Interestingly, we demonstrated a significant correlation between the data obtained by flow cytometry and ELISA (r²0.82, p < 0.0001).</p> <p>Conclusions</p> <p>IP-10, in contrast to IFN-γ, TNF-α, IL-2, IL-8, MIP-1α, MIP-1β and RANTES, is detectable in the urine of patients with pulmonary diseases in the absence of renal dysfunctions. Moreover, the IP-10 level in cured-TB patients is comparable to that found in healthy subjects. More studies are needed to further investigate the clinical utility of these findings.</p

Beyond in-phase and anti-phase coordination in a model of joint action

In 1985, Haken, Kelso and Bunz proposed a system of coupled nonlinear oscillators as a model of rhythmic movement patterns in human bimanual coordination. Since then, the Haken–Kelso–Bunz (HKB) model has become a modelling paradigm applied extensively in all areas of movement science, including interpersonal motor coordination. However, all previous studies have followed a line of analysis based on slowly varying amplitudes and rotating wave approximations. These approximations lead to a reduced system, consisting of a single differential equation representing the evolution of the relative phase of the two coupled oscillators: the HKB model of the relative phase. Here we take a different approach and systematically investigate the behaviour of the HKB model in the full four-dimensional state space and for general coupling strengths. We perform detailed numerical bifurcation analyses and reveal that the HKB model supports previously unreported dynamical regimes as well as bistability between a variety of coordination patterns. Furthermore, we identify the stability boundaries of distinct coordination regimes in the model and discuss the applicability of our findings to interpersonal coordination and other joint action tasks