Deformations of the Tracy-Widom distribution

In random matrix theory, the Tracy-Widom (TW) distribution describes the behavior of the largest eigenvalue. We consider here two models in which TW undergoes transformations. In the first one disorder is introduced in the Gaussian ensembles by superimposing an external source of randomness. A competition between TW and a normal (Gaussian) distribution results, depending on the spreading of the disorder. The second model consists of removing at random a fraction of (correlated) eigenvalues of a random matrix. The usual formalism of Fredholm determinants extends naturally. A continuous transition from TW to the Weilbull distribution, characteristic of extreme values of an uncorrelated sequence, is obtained.

Geographic variation in the chicken turtle, Deirochelys reticularia Latreille / Albert Schwartz.

v.34:no.41(1956)

Décollement de rétine rhegmatogène et hypertonie: penser au syndrome de Schwartz-Matsuo [Rhegmatogenous retinal detachment and hypertension: Schwartz-Matsuo syndrome]

PURPOSE: To assess the usefulness of electron microscopy of the aqueous cells when confronted with the clinical association of rhegmatogenous retinal detachment after trauma, high intraocular pressure (IOP) and aqueous cells. METHOD: We report a clinical history of a 50-years-old man who had ocular trauma with perforation in 1944, intraocular lens for traumatic cataract in 1988, Yag capsulotomy in 1993 and retinal detachment with oral dialysis, high IOP and aqueous cells in anterior chamber in 1995. During the surgical therapy we performed an anterior chamber puncture to analyse the aqueous cells. An electron microscopic study was performed on 0.2 ml of aqueous humor mixed in the same volume of 2.5% glutaraldehyde and fixed with 1% osmium acid. RESULTS: Electron microscopic ultrastructural study of the aqueous cells showed numerous photoreceptor outer segments, some of them appearing degenerated. CONCLUSION: The combination of rhegmatogenous retinal detachment with tears near the ora serrata, high IOP and aqueous cells in the anterior chamber should lead the physician to do an anterior chamber puncture and analyse the aqueous cells structure. The combination of those three clinical signs associated with the photoreceptor outer segments in the anterior chamber allowed to diagnose the Schwartz-Matsuo syndrome.

Comparison of the glomerular filtration rate in children by the new revised Schwartz formula and a new generalized formula.

The most widely used formula for estimating glomerular filtration rate (eGFR) in children is the Schwartz formula. It was revised in 2009 using iohexol clearances with measured GFR (mGFR) ranging between 15 and 75 ml/min × 1.73 m(2). Here we assessed the accuracy of the Schwartz formula using the inulin clearance (iGFR) method to evaluate its accuracy for children with less renal impairment comparing 551 iGFRs of 392 children with their Schwartz eGFRs. Serum creatinine was measured using the compensated Jaffe method. In order to find the best relationship between iGFR and eGFR, a linear quadratic regression model was fitted and a more accurate formula was derived. This quadratic formula was: 0.68 × (Height (cm)/serum creatinine (mg/dl))-0.0008 × (height (cm)/serum creatinine (mg/dl))(2)+0.48 × age (years)-(21.53 in males or 25.68 in females). This formula was validated using a split-half cross-validation technique and also externally validated with a new cohort of 127 children. Results show that the Schwartz formula is accurate until a height (Ht)/serum creatinine value of 251, corresponding to an iGFR of 103 ml/min × 1.73 m(2), but significantly unreliable for higher values. For an accuracy of 20 percent, the quadratic formula was significantly better than the Schwartz formula for all patients and for patients with a Ht/serum creatinine of 251 or greater. Thus, the new quadratic formula could replace the revised Schwartz formula, which is accurate for children with moderate renal failure but not for those with less renal impairment or hyperfiltration.