Preasymptotic Convergence of Randomized Kaczmarz Method

Kaczmarz method is one popular iterative method for solving inverse problems, especially in computed tomography. Recently, it was established that a randomized version of the method enjoys an exponential convergence for well-posed problems, and the convergence rate is determined by a variant of the condition number. In this work, we analyze the preasymptotic convergence behavior of the randomized Kaczmarz method, and show that the low-frequency error (with respect to the right singular vectors) decays faster during first iterations than the high-frequency error. Under the assumption that the inverse solution is smooth (e.g., sourcewise representation), the result explains the fast empirical convergence behavior, thereby shedding new insights into the excellent performance of the randomized Kaczmarz method in practice. Further, we propose a simple strategy to stabilize the asymptotic convergence of the iteration by means of variance reduction. We provide extensive numerical experiments to confirm the analysis and to elucidate the behavior of the algorithms.Comment: 20 page

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Type-i Optical Emissions In Gesi Quantum Dots

The authors studied the optical emission of GeSi quantum dots under externally applied biaxial stress using samples grown with different temperatures varying from 430 to 700 °C. The optical emission energy of samples grown at low temperatures is rather insensitive to the applied external stress, consistent with the type-II band alignment. However, for samples grown at high temperatures we observed a large blueshift, which suggests type-I alignment. The result implies that recombination strength can be controlled by the growth temperature, which can be useful for optical device applications. © 2007 American Institute of Physics.915Brunner, K., (2002) Rep. Prog. Phys., 65, p. 27Medeiros-Ribeiro, G., Bratkovski, A.M., Kamins, T.I., Ohlbert, D.A.A., Williams, R.S., (1998) Science, 279, p. 353Wan, J., Jin, G.L., Jiang, Z.M., Luo, Y.H., Liu, J.L., Wang, K.L., (2001) Appl. Phys. Lett., 78, p. 1763El Kurdi, M., Sauvage, S., Fishman, G., Boucaud, P., (2006) Phys. Rev. B, 73, p. 195327Yakimov, A.I., Dvurechenskii, A.V., Nikiforov, A.I., Bloshkin, A.A., Nenashev, A.V., Volodin, V.A., (2006) Phys. Rev. B, 73, p. 115333Dashiell, M.W., Denker, U., Müller, C., Costantini, G., Manzano, C., Kern, K., Schmidt, O.G., (2002) Appl. Phys. Lett., 80, p. 1279Larsson, M., Elfving, A., Holtz, P.O., Hansson, G.V., Ni, W.-X., (2003) Appl. Phys. Lett., 82, p. 4785Thewalt, M.L.W., Harrison, D.A., Reinhart, C.F., Wolk, J.A., Lafontaine, H., (1997) Phys. Rev. Lett., 79, p. 269Larsson, M., Elfving, A., Ni, W.-X., Hansson, G.V., Holtz, P.O., (2006) Phys. Rev. B, 73, p. 195319Schmidt, O.G., Eberl, K., (2000) Phys. Rev. B, 62, p. 16715Tudury, H.A.P., Nakaema, M.K.K., Iikawa, F., Brum, J.A., Ribeiro, E., Carvalho Jr., W., Bernussi, A.A., Gobbi, A.L., (2001) Phys. Rev. B, 64, p. 153301Gomes, P.F., Godoy, M.P.F., Nakaema, M.K.K., Iikawa, F., Lamas, T.E., Quivy, A.A., Brum, J.A., (2004) Phys. Status Solidi C, 3, p. 547De Godoy, M.P.F., Nakaema, M.K.K., Iikawa, F., Carvalho Jr. Wilson, Evaldo, R., Gobbi, A.L., (2004) Rev. Sci. Instrum., 75, p. 194

Plasma Brain-Derived Neurotrophic Factor Levels Predict the Clinical Outcome of Depression Treatment in a Naturalistic Study

Remission is the primary goal of treatment for major depressive disorder (MDD). However, some patients do not respond to treatment. The main purpose of this study was to determine whether brain-derived neurotrophic factor (BDNF) levels are correlated with treatment outcomes. In a naturalistic study, we assessed whether plasma BDNF levels were correlated with clinical outcomes by measuring plasma BDNF in patients with depressive syndrome (MADRS score ≥18), and subsequently comparing levels between the subgroup of patients who underwent remission (MADRS score ≤8) and the subgroup who were refractory to treatment (non-responders). Patients with depressive syndrome who underwent remission had significantly higher plasma BDNF levels (p<0.001), regardless of age or sex. We also found a significant negative correlation between MADRS scores and plasma BDNF levels within this group (ρ = –0.287, p = 0.003). In contrast, non-responders had significantly lower plasma BDNF levels (p = 0.029). Interestingly, plasma BDNF levels in the non-responder group were significantly higher than those in the remission group in the initial stage of depressive syndrome (p = 0.002). Our results show that plasma BDNF levels are associated with clinical outcomes during the treatment of depression. We suggest that plasma BDNF could potentially serve as a prognostic biomarker for depression, predicting clinical outcome

A Nested Case-Control Study of Intrauterine Exposure to Persistent Organochlorine Pollutants in Relation to Risk of Type 1 Diabetes

BACKGROUND: The incidence of type 1 diabetes in Europe is increasing at a rate of about 3% per year and there is also an increasing incidence throughout the world. Type 1 diabetes is a complex disease caused by multiple genetic and environmental factors. Persistent organochlorine pollutants (POPs) have been suggested as a triggering factor for developing childhood type 1 diabetes. The aim of this case-control study was to assess possible impacts of in utero exposure to POPs on type 1 diabetes. METHODOLOGY/ PRINCIPAL FINDINGS: The study was performed as a case-control study within a biobank in Malmö, a city located in the Southern part of Sweden. The study included 150 cases (children who had their diagnosis mostly before 18 years of age) and 150 controls, matched for gender and day of birth. 2,2',4,4',5,5'-hexachlorobiphenyl (PCB-153) and the major DDT metabolite 1,1-dichloro-2,2-bis (p-chlorophenyl)-ethylene (p,p'-DDE) were used as a biomarkers for POP exposure. When comparing the quartile with the highest maternal serum concentrations of PCB-153 with the other quartiles, an odds ratio (OR) of 0.73 (95% confidence interval [CI] 0.42, 1.27) was obtained. Similar results was obtained for p,p'-DDE (OR 0.56, 95% CI 0.29, 1.08). CONCLUSIONS: The hypothesis that in utero exposure to POPs will trigger the risk for developing type 1 diabetes was not supported by the results. The risk estimates did, although not statistically significant, go in the opposite direction. However, it is not reasonable to believe that exposure to POPs should protect against type 1 diabetes

The Schwarzian derivative and the Wiman-Valiron property

Consider a transcendental meromorphic function in the plane with finitely many critical values, such that the multiple points have bounded multiplicities and the inverse function has finitely many transcendental singularities. Using the Wiman-Valiron method it is shown that if the Schwarzian derivative is transcendental then the function has infinitely many multiple points, the inverse function does not have a direct transcendental singularity over infinity, and infinity is not a Borel exceptional value. The first of these conclusions was proved by Nevanlinna and Elfving via a fundamentally different method