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

Predictors of delayed culture conversion among Ugandan patients.

BACKGROUND: Estimates of month-2 culture conversion, a proxy indicator of tuberculosis (TB) treatment efficacy in phase-2 trials can vary by culture-type and geographically with lower rates reported among African sites. The sub-study aimed at comparing TB detection rates of different culture media, within and across rifampicin-based regimens (R10, 15 and 20 mg/Kg) over a 6-month treatment follow-up period, and to establish predictors of month-2 culture non-conversion among HIV-negative TB patients enrolled at RIFATOX trial site in Uganda. METHODS: Unlike in other Rifatox Trial sites, it is only in Uganda were Lowenstein-Jensen (LJ) and Mycobacteria growth indicator tube (MGIT) were used throughout 6-months for treatment monitoring. Conversion rates were compared at month-2, 4 and 6 across cultures and treatment-type. Binomial regression analysis performed for predictors of month-2 non-conversion. RESULTS: Of the 100 enrolled patients, 45% had converted based on combined LJ and MGIT by month-2, with no significant differences across treatment arms, p = 0.721. LJ exhibited higher conversion rates than MGIT at month-2 (58.4% vs 56.0%, p = 0.0707) and month-4 (98.9% vs 88.4%, p = 0.0391) respectively, more so within the high-dose rifampicin arms. All patients had converted by month-6. Time-to-TB detection (TTD) on MGIT and social service jobs independently predict month-2 non-conversion. CONCLUSION: The month-2 culture conversion used in phase 2 clinical trials as surrogate marker of treatment efficacy is influenced by the culture method used for monitoring mycobacterial response to TB treatment. Therefore, multi-centric TB therapeutic trials using early efficacy endpoint should use the same culture method across sites. The Time-to-detection of MTB on MGIT prior to treatment and working in Social service jobs bear an increased risk of culture non-conversion at month-2. TRIAL REGISTRATION: ISRCTN ISRCTN55670677 . Registered 09th November 2010. Retrospectively registered

"I'm not being rude, I'd want somebody normal" Adolescents' perception of their peers with Tourette's syndrome; an exploratory study

Background: Tourette’s syndrome (TS) is a highly stigmatised condition, and typically developing adolescents’ motives and reason for excluding individuals with TS have not been examined. Aims: The aim of the study was to understand how TS is conceptualised by adolescents and explore how individuals with TS are perceived by their typically developing peers. Method: Free text writing and focus groups were used to elicit the views of twenty-two year ten students from a secondary school in South East England. Grounded theory was used to develop an analytical framework. Result: Participants’ understanding about the condition was construed from misconceptions, unfamiliarity and unanswered questions. Adolescents who conceived TS as a disorder beyond the individual’s control perceived their peers as being deprived of agency and strength and as straying from the boundaries of normalcy. People with TS were viewed as individuals deserving pity, and in need of support. Although participants maintained they had feelings of social politeness towards those with TS, they would avoid initiating meaningful social relationships with them due to fear of “social contamination”. Intergroup anxiety would also inhibit a close degree of social contact. Participants that viewed those with TS as responsible for their condition expressed a plenary desire for social distance. However, these behavioural intentions were not limited to adolescents that elicited inferences of responsibility to people with TS, indicating that attributional models of stigmatisation may be of secondary importance in the case of TS. Implications for interventions to improve school belonging among youths with TS are discussed

Baseline Predictors of Sputum Culture Conversion in Pulmonary Tuberculosis: Importance of Cavities, Smoking, Time to Detection and W-Beijing Genotype

Background: Time to detection (TTD) on automated liquid mycobacterial cultures is an emerging biomarker of tuberculosis outcomes. The M. tuberculosis W-Beijing genotype is spreading globally, indicating a selective advantage. There is a paucity of data on the association between baseline TTD and W-Beijing genotype and tuberculosis outcomes. Aim: To assess baseline predictors of failure of sputum culture conversion, within the first 2 months of antitubercular therapy, in participants with pulmonary tuberculosis. Design: Between May 2005 and August 2008 we conducted a prospective cohort study of time to sputum culture conversion in ambulatory participants with first episodes of smear and culture positive pulmonary tuberculosis attending two primary care clinics in Cape Town, South Africa. Rifampicin resistance (diagnosed on phenotypic susceptibility testing) was an exclusion criterion. Sputum was collected weekly for 8 weeks for mycobacterial culture on liquid media (BACTEC MGIT 960). Due to missing data, multiple imputation was performed. Time to sputum culture conversion was analysed using a Cox-proportional hazards model. Bayesian model averaging determined the posterior effect probability for each variable. Results: 113 participants were enrolled (30.1% female, 10.5% HIV-infected, 44.2% W-Beijing genotype, and 89% cavities). On Kaplan Meier analysis 50.4% of participants underwent sputum culture conversion by 8 weeks. The following baseline factors were associated with slower sputum culture conversion: TTD (adjusted hazard ratio (aHR) = 1.11, 95% CI 1.02; 1.2), lung cavities (aHR = 0.13, 95% CI 0.02; 0.95), ever smoking (aHR = 0.32, 95% CI 0.1; 1.02) and the W-Beijing genotype (aHR = 0.51, 95% CI 0.25; 1.07). On Bayesian model averaging, posterior probability effects were strong for TTD, lung cavitation and smoking and moderate for W-Beijing genotype. Conclusion: We found that baseline TTD, smoking, cavities and W-Beijing genotype were associated with delayed 2 month sputum culture. Larger studies are needed to confirm the relationship between the W-Beijing genotype and sputum culture conversion.Publisher's versio

Hyperpolarization-Activated Current (Ih) in Ganglion-Cell Photoreceptors

Intrinsically photosensitive retinal ganglion cells (ipRGCs) express the photopigment melanopsin and serve as the primary retinal drivers of non-image-forming visual functions such as circadian photoentrainment, the pupillary light reflex, and suppression of melatonin production in the pineal. Past electrophysiological studies of these cells have focused on their intrinsic photosensitivity and synaptic inputs. Much less is known about their voltage-gated channels and how these might shape their output to non-image-forming visual centers. Here, we show that rat ipRGCs retrolabeled from the suprachiasmatic nucleus (SCN) express a hyperpolarization-activated inwardly-rectifying current (Ih). This current is blocked by the known Ih blockers ZD7288 and extracellular cesium. As in other systems, including other retinal ganglion cells, Ih in ipRGCs is characterized by slow kinetics and a slightly greater permeability for K+ than for Na+. Unlike in other systems, however, Ih in ipRGCs apparently does not actively contribute to resting membrane potential. We also explore non-specific effects of the common Ih blocker ZD7288 on rebound depolarization and evoked spiking and discuss possible functional roles of Ih in non-image-forming vision. This study is the first to characterize Ih in a well-defined population of retinal ganglion cells, namely SCN-projecting ipRGCs

Intraperitoneal drain placement and outcomes after elective colorectal surgery: international matched, prospective, cohort study

Despite current guidelines, intraperitoneal drain placement after elective colorectal surgery remains widespread. Drains were not associated with earlier detection of intraperitoneal collections, but were associated with prolonged hospital stay and increased risk of surgical-site infections.Background Many surgeons routinely place intraperitoneal drains after elective colorectal surgery. However, enhanced recovery after surgery guidelines recommend against their routine use owing to a lack of clear clinical benefit. This study aimed to describe international variation in intraperitoneal drain placement and the safety of this practice. Methods COMPASS (COMPlicAted intra-abdominal collectionS after colorectal Surgery) was a prospective, international, cohort study which enrolled consecutive adults undergoing elective colorectal surgery (February to March 2020). The primary outcome was the rate of intraperitoneal drain placement. Secondary outcomes included: rate and time to diagnosis of postoperative intraperitoneal collections; rate of surgical site infections (SSIs); time to discharge; and 30-day major postoperative complications (Clavien-Dindo grade at least III). After propensity score matching, multivariable logistic regression and Cox proportional hazards regression were used to estimate the independent association of the secondary outcomes with drain placement. Results Overall, 1805 patients from 22 countries were included (798 women, 44.2 per cent; median age 67.0 years). The drain insertion rate was 51.9 per cent (937 patients). After matching, drains were not associated with reduced rates (odds ratio (OR) 1.33, 95 per cent c.i. 0.79 to 2.23; P = 0.287) or earlier detection (hazard ratio (HR) 0.87, 0.33 to 2.31; P = 0.780) of collections. Although not associated with worse major postoperative complications (OR 1.09, 0.68 to 1.75; P = 0.709), drains were associated with delayed hospital discharge (HR 0.58, 0.52 to 0.66; P &lt; 0.001) and an increased risk of SSIs (OR 2.47, 1.50 to 4.05; P &lt; 0.001). Conclusion Intraperitoneal drain placement after elective colorectal surgery is not associated with earlier detection of postoperative collections, but prolongs hospital stay and increases SSI risk

Outcomes from elective colorectal cancer surgery during the SARS-CoV-2 pandemic

This study aimed to describe the change in surgical practice and the impact of SARS-CoV-2 on mortality after surgical resection of colorectal cancer during the initial phases of the SARS-CoV-2 pandemic