Exponential times in the one-dimensional Gross--Petaevskii equation with multiple well potential

We consider the Gross-Petaevskii equation in 1 space dimension with a $n$-well trapping potential. We prove, in the semiclassical limit, that the finite dimensional eigenspace associated to the lowest n eigenvalues of the linear operator is slightly deformed by the nonlinear term into an almost invariant manifold M. Precisely, one has that solutions starting on M, or close to it, will remain close to M for times exponentially long with the inverse of the size of the nonlinearity. As heuristically expected the effective equation on M is a perturbation of a discrete nonlinear Schroedinger equation. We deduce that when the size of the nonlinearity is large enough then tunneling among the wells essentially disappears: that is for almost all solutions starting close to M their restriction to each of the wells has norm approximatively constant over the considered time scale. In the particular case of a double well potential we give a more precise result showing persistence or destruction of the beating motions over exponentially long times. The proof is based on canonical perturbation theory; surprisingly enough, due to the Gauge invariance of the system, no non-resonance condition is required

Stability of spectral eigenspaces in nonlinear Schrodinger equations

We consider the time-dependent non linear Schrodinger equations with a double well potential in dimensions d =1 and d=2. We prove, in the semiclassical limit, that the finite dimensional eigenspace associated to the lowest two eigenvalues of the linear operator is almost invariant for any time

Mitochondrial diabetes in children: seek and you will find it

Maternally Inherited Diabetes and Deafness (MIDD) is a rare form of diabetes due to defects in mitochondrial DNA (mtDNA). 3243 A.G is the mutation most frequently associated with this condition, but other mtDNA variants have been linked with a diabetic phenotype suggestive of MIDD. From 1989 to 2009, we clinically diagnosed mitochondrial diabetes in 11 diabetic children. Diagnosis was based on the presence of one or more of the following criteria: 1) maculopathy; 2) hearing impairment; 3) maternal heritability of diabetes/impaired fasting glucose and/or hearing impairment and/or maculopathy in three consecutive generations (or in two generations if 2 or 3 members of a family were affected). We sequenced the mtDNA in the 11 probands, in their mothers and in 80 controls. We identified 33 diabetes-suspected mutations, 1/33 was 3243A.G. Most patients (91%) and their mothers had mutations in complex I and/or IV of the respiratory chain. We measured the activity of these two enzymes and found that they were less active in mutated patients and their mothers than in the healthy control pool. The prevalence of hearing loss (36% vs 75–98%) and macular dystrophy (54% vs 86%) was lower in our mitochondrial diabetic adolescents than reported in adults. Moreover, we found a hitherto unknown association between mitochondrial diabetes and celiac disease. In conclusion, mitochondrial diabetes should be considered a complex syndrome with several phenotypic variants. Moreover, deafness is not an essential component of the disease in children. The whole mtDNA should be screened because the 3243A.G variant is not as frequent in children as in adults. In fact, 91% of our patients were mutated in the complex I and/or IV genes. The enzymatic assay may be a useful tool with which to confirm the pathogenic significance of detected variants

Nonequilibrium superconducting thin films with sub-gap and pair-breaking photon illumination

We calculate nonequilibrium quasiparticle and phonon distributions for a number of widely-used low transition temperature thin-film superconductors under constant, uniform illumination by sub-gap probe and pair-breaking signal photons simultaneously. From these distributions we calculate material-characteristic parameters that allow rapid evaluation of an effective quasiparticle temperature using a simple analytical expression, for all materials studied (Mo, Al, Ta, Nb, and NbN) for all photon energies. We also explore the temperature and energy-dependence of the low-energy quasiparticle generation efficiency $\eta$ by pair-breaking signal photons finding $\eta \approx 0.6$ in the limit of thick films at low bath temperatures that is material-independent. Taking the energy distribution of excess quasiparticles into account, we find $\eta \to 1$ as the bath temperature approaches the transition temperature in agreement with the assumption of the two-temperature model of the nonequilibrium response that is appropriate in that regime. The behaviour of $\eta$ with signal frequency scaled by the superconducting energy gap is also shown to be material-independent, and is in qualitative agreement with recent experimental results. An enhancement of $\eta$ in the presence of sub-gap (probe) photons is shown to be most significant at signal frequencies near the superconducting gap frequency and arises due to multiple photon absorption events that increase the average energy of excess quasiparticles above that in the absence of the probe.This is the author accepted manuscript. The final version is available via IOP Science at http://iopscience.iop.org/0953-2048/28/5/054002/

Identification of candidate children for maturity-onset diabetes of the young type 2 (MODY2) gene testing: a seven-item clinical flowchart (7-iF)

MODY2 is the most prevalent monogenic form of diabetes in Italy with an estimated prevalence of about 0.5–1.5%. MODY2 is potentially indistinguishable from other forms of diabetes, however, its identification impacts on patients’ quality of life and healthcare resources. Unfortunately, DNA direct sequencing as diagnostic test is not readily accessible and expensive. In addition current guidelines, aiming to establish when the test should be performed, proved a poor detection rate. Aim of this study is to propose a reliable and easy-to-use tool to identify candidate patients for MODY2 genetic testing. We designed and validated a diagnostic flowchart in the attempt to improve the detection rate and to increase the number of properly requested tests. The flowchart, called 7-iF, consists of 7 binary ‘‘yes or no’’ questions and its unequivocal output is an indication for whether testing or not. We tested the 7-iF to estimate its clinical utility in comparison to the clinical suspicion alone. The 7-iF, in a prospective 2-year study (921 diabetic children) showed a precision of about the 76%. Using retrospective data, the 7-iF showed a precision in identifying MODY2 patients of about 80% compared to the 40% of the clinical suspicion. On the other hand, despite a relatively high number of missing MODY2 patients, the 7-iF would not suggest the test for 90% of the non-MODY2 patients, demonstrating that a wide application of this method might 1) help less experienced clinicians in suspecting MODY2 patients and 2) reducing the number of unnecessary tests. With the 7-iF, a clinician can feel confident of identifying a potential case of MODY2 and suggest the molecular test without fear of wasting time and money. A Qaly-type analysis estimated an increase in the patients’ quality of life and savings for the health care system of about 9 million euros per year

Diabete Tipo 1, Tipo 2 e Tipo X

Il muro concettuale secondo il quale il diabete in età pediatrica ha preferibilmente una patogenesi autoimmune sta ormai definitivamente crollando. Il diabete in età infantile e adolescenziale è molto più eterogeneo dal punto di vista eziopatogenetico di quanto si pensasse. In presenza di una qualsiasi iperglicemia è ormai diventato importantissimo chiedersi la patogenesi di questo sintomo utilizzando tutti gli strumenti che abbiamo oggi a disposizione

Younger age at onset and sex predict celiac disease in children and adolescents with type 1 diabetes: an Italian multicenter study

OBJECTIVE— To estimate the prevalence of biopsy-confirmed celiac disease in Italian children and adolescents with type 1 diabetes and to assess whether age at onset of type 1 diabetes is independently associated with diagnosis of celiac disease. RESEARCH DESIGNANDMETHODS— The study group was a clinic-based cohort of children and adolescents with type 1 diabetes cared for in 25 Italian centers for childhood diabetes. Yearly screening for celiac disease was performed using IgA/IgG anti-gliadin and IgA anti-endomysium antibodies. RESULTS— Of the 4,322 children and adolescents (age 11.8 4.2 years) identified with type 1 diabetes, biopsy-confirmed celiac disease was diagnosed in 292 (prevalence 6.8%, 95% confidence interval [CI] 6.0 –7.6), with a higher risk seen in girls than in boys (odds ratio [OR] 1.93, 1.51–2.47). In 89% of these, diabetes was diagnosed before celiac disease. In logistic regression analyses, being younger at onset of diabetes, being female, and having a diagnosis of a thyroid disorder were independently associated with the risk of having diabetes and celiac disease. In comparison with subjects who were older than 9 years at onset of diabetes, subjects who were younger than 4 years at onset had an OR of 3.27 (2.20–4.85). CONCLUSIONS— We have provided evidence that 1) the prevalence of biopsy-confirmed celiac disease in children and adolescents with type 1 diabetes is high (6.8%); 2) the risk of having both diseases is threefold higher in children diagnosed with type 1 diabetes at age 4 years than in those age 9 years; and 3) girls have a higher risk of having both diseases than boys

Glucokinase (GCK) Mutations and Their Characterization in MODY2 Children of Southern Italy

Type 2 Maturity Onset Diabetes of the Young (MODY2) is a monogenic autosomal disease characterized by a primary defect in insulin secretion and hyperglycemia. It results from GCK gene mutations that impair enzyme activity. Between 2006 and 2010, we investigated GCK mutations in 66 diabetic children from southern Italy with suspected MODY2. Denaturing High Performance Liquid Chromatography (DHPLC) and sequence analysis revealed 19 GCK mutations in 28 children, six of which were novel: p.Glu40Asp, p.Val154Leu, p.Arg447Glyfs, p.Lys458_Cys461del, p.Glu395_Arg397del and c.580-2A>T. We evaluated the effect of these 19 mutations using bioinformatic tools such as Polymorphism Phenotyping (Polyphen), Sorting Intolerant From Tolerant (SIFT) and in silico modelling. We also conducted a functional study to evaluate the pathogenic significance of seven mutations that are among the most severe mutations found in our population, and have never been characterized: p.Glu70Asp, p.His137Asp, p.Phe150Tyr, p.Val154Leu, p.Gly162Asp, p.Arg303Trp and p.Arg392Ser. These seven mutations, by altering one or more kinetic parameters, reduced enzyme catalytic activity by >40%. All mutations except p.Glu70Asp displayed thermal-instability, indeed >50% of enzyme activity was lost at 50°C/30 min. Thus, these seven mutations play a pathogenic role in MODY2 insurgence. In conclusion, this report revealed six novel GCK mutations and sheds some light on the structure-function relationship of human GCK mutations and MODY2