ન્યાયમજરીમાં રજૂ થયેલ પ્રત્યક્ષ પ્રમાણનું તુલનાત્મક અને સમીક્ષાત્મક અધ્યયન

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Zariski Closures and Subgroup Separability

The main result of this article is a refinement of the well-known subgroup separability results of Hall and Scott for free and surface groups. We show that for any finitely generated subgroup, there is a finite dimensional representation of the free or surface group that separates the subgroup in the induced Zariski topology. As a corollary, we establish a polynomial upper bound on the size of the quotients used to separate a finitely generated subgroup in a free or surface group.Comment: Final version. To appear in Selecta Mat

A Deep Learning Approach to Structured Signal Recovery

In this paper, we develop a new framework for sensing and recovering structured signals. In contrast to compressive sensing (CS) systems that employ linear measurements, sparse representations, and computationally complex convex/greedy algorithms, we introduce a deep learning framework that supports both linear and mildly nonlinear measurements, that learns a structured representation from training data, and that efficiently computes a signal estimate. In particular, we apply a stacked denoising autoencoder (SDA), as an unsupervised feature learner. SDA enables us to capture statistical dependencies between the different elements of certain signals and improve signal recovery performance as compared to the CS approach

Topical clobetasol for the treatment of toxic epidermal necrolysis: study protocol for a randomized controlled trial.

BackgroundToxic epidermal necrolysis (TEN) is a rare systemic allergic drug eruption with high patient mortality. Currently, no established treatments have been shown to be effective for TEN beyond supportive care. Prior studies of systemic corticosteroids have yielded conflicting data, with some showing a possible benefit and others reporting in increased mortality. However, topical steroids have shown promise for treatment of ocular sequelae of TEN, such as scarring and vision loss. We have designed a randomized controlled trial to evaluate topical clobetasol for treatment of the epidermal manifestations of TEN. In addition, we propose genetic studies to characterize the TEN transcriptome and alterations in cutaneous gene expression that might occur following topical steroid treatment.Methods/designThis split-body randomized, double-blind, placebo-controlled Phase IIa proof-of-concept trial will evaluate the safety and efficacy of once-daily topical clobetasol applied to the skin of patients with TEN. This multicenter trial will recruit a total of 15 patients between the ages of 12 and 85 from the University of California Davis Medical Center and Shriners Hospital for Children inpatient burn units. Designated treatment areas on opposite sides of the body will be treated with blinded clobetasol 0.05% ointment or control petrolatum ointment daily for 14 days. On day 3 of therapy, a biopsy will be taken from the treated area for genetic studies. The primary study aims will be to establish the safety of topical clobetasol treatment and determine the time to cessation of skin detachment for the control and clobetasol-treated areas. Secondary endpoints will evaluate efficacy using parameters such as time to 90% re-epithelialization and percentage of affected skin at 0, 3, 6, 9, 12 and 15 days. Genomic DNA and RNA will be obtained from biopsy samples, to characterize the TEN transcriptome and identify changes in gene expression after topical steroid treatment.DiscussionTopical steroids have shown promise for treating ocular complications of TEN, but to date have not been evaluated for cutaneous manifestations of the disease. This trial will investigate clinical and molecular outcomes of topical clobetasol application and hopefully provide insight into the disease pathophysiology.Trial registrationClinicalTrials.gov NCT02319616. https://clinicaltrials.gov/ct2/show/NCT02351037