A unified evaluation of iterative projection algorithms for phase retrieval

Iterative projection algorithms are successfully being used as a substitute of lenses to recombine, numerically rather than optically, light scattered by illuminated objects. Images obtained computationally allow aberration-free diffraction-limited imaging and the possibility of using radiation for which no lenses exist. The challenge of this imaging technique is transfered from the lenses to the algorithms. We evaluate these new computational ``instruments'' developed for the phase retrieval problem, and discuss acceleration strategies.Comment: 12 pages, 9 figures, revte

Global Newtonian limit for the Relativistic Boltzmann Equation near Vacuum

We study the Cauchy Problem for the relativistic Boltzmann equation with near Vacuum initial data. Unique global in time "mild" solutions are obtained uniformly in the speed of light parameter $c \ge 1$. We furthermore prove that solutions to the relativistic Boltzmann equation converge to solutions of the Newtonian Boltzmann equation in the limit as $c\to\infty$ on arbitrary time intervals $[0,T]$, with convergence rate $1/c^{2-\epsilon}$ for any $\epsilon \in(0,2)$. This may be the first proof of unique global in time validity of the Newtonian limit for a Kinetic equation.Comment: 35 page

Neonatal Diabetes Mellitus.

Neonatal Diabetes (ND) mellitus is a rare genetic disease (1 in 90,000 live births). It is defined by the presence of severe hyperglycaemia associated with insufficient or no circulating insulin, occurring mainly before 6 months of age and rarely between 6 months and 1 year. Such hyperglycaemia requires either transient treatment with insulin in about half of cases, or permanent insulin treatment. The disease is explained by two major groups of mechanism: malformation of the pancreas with altered insulin-secreting cells development/survival or abnormal function of the existing pancreatic β cell. The most frequent genetic causes of neonatal diabetes mellitus with abnormal β cell function are abnormalities of the 6q24 locus and mutations of the ABCC8 or KCNJ11 genes coding for the potassium channel in the pancreatic β cell. Other genes are associated with pancreas malformation or insufficient β cells development or destruction of β cells. Clinically, compared to patients with an ABCC8 or KCNJ11 mutation, patients with a 6q24 abnormality have lower birth weight and height, are younger at diagnosis and remission, and have a higher malformation frequency. Patients with an ABCC8 or KCNJ11 mutation have neurological and neuropsychological disorders in all those tested carefully. Up to 86% of patients who go into remission have recurrent diabetes when they reach puberty, with no difference due to the genetic origin. All these results reinforce the importance of prolonged follow-up by a multidisciplinary pediatric team, and later doctors specializing in adult medicine. 90% of the patients with an ABCC8 or KCNJ11 mutation as well as those with 6q24 anomalies are amenable to a successful switch from insulin injection to oral sulfonylureas

The effects of superconductor-stabilizer interfacial resistance on quench of a pancake coil made out of coated conductor

We present the results of numerical analysis of normal zone propagation in a stack of $YBa_2Cu_3O_{7-x}$ coated conductors which imitates a pancake coil. Our main purpose is to determine whether the quench protection quality of such coils can be substantially improved by increased contact resistance between the superconducting film and the stabilizer. We show that with increased contact resistance the speed of normal zone propagation increases, the detection of a normal zone inside the coil becomes possible earlier, when the peak temperature inside the normal zone is lower, and stability margins shrink. Thus, increasing contact resistance may become a viable option for improving the prospects of coated conductors for high $T_c$ magnets applications.Comment: 9 pages, 4 figure

Hybrid Newton-type method for a class of semismooth equations

In this paper, we present a hybrid method for the solution of a class of composite semismooth equations encountered frequently in applications. The method is obtained by combining a generalized finite-difference Newton method to an inexpensive direct search method. We prove that, under standard assumptions, the method is globally convergent with a local rate of convergence which is superlinear or quadratic. We report also several numerical results obtained applying the method to suitable reformulations of well-known nonlinear complementarity problem