Kolmogorov condition near hyperbolic singularities of integrable Hamiltonian systems

In this paper we show that, if an integrable Hamiltonian system admits a nondegenerate hyperbolic singularity then it will satisfy the Kolmogorov condegeneracy condition near that singularity (under a mild additional condition, which is trivial if the singularity contains a fixed point)Comment: revised version, 11p, accepted for publication in a sepecial volume in Regular and Chaotic Dynamics in honor of Richard Cushma

Birkhoff Coordinates for the Focusing NLS Equation

In this paper we construct Birkhoff coordinates for the focusing nonlinear Schrödinger equation near the zero solutio

The Maslov index and nondegenerate singularities of integrable systems

We consider integrable Hamiltonian systems in R^{2n} with integrals of motion F = (F_1,...,F_n) in involution. Nondegenerate singularities are critical points of F where rank dF = n-1 and which have definite linear stability. The set of nondegenerate singularities is a codimension-two symplectic submanifold invariant under the flow. We show that the Maslov index of a closed curve is a sum of contributions +/- 2 from the nondegenerate singularities it is encloses, the sign depending on the local orientation and stability at the singularities. For one-freedom systems this corresponds to the well-known formula for the Poincar\'e index of a closed curve as the oriented difference between the number of elliptic and hyperbolic fixed points enclosed. We also obtain a formula for the Liapunov exponent of invariant (n-1)-dimensional tori in the nondegenerate singular set. Examples include rotationally symmetric n-freedom Hamiltonians, while an application to the periodic Toda chain is described in a companion paper.Comment: 27 pages, 1 figure; published versio

Foliations of Isonergy Surfaces and Singularities of Curves

It is well known that changes in the Liouville foliations of the isoenergy surfaces of an integrable system imply that the bifurcation set has singularities at the corresponding energy level. We formulate certain genericity assumptions for two degrees of freedom integrable systems and we prove the opposite statement: the essential critical points of the bifurcation set appear only if the Liouville foliations of the isoenergy surfaces change at the corresponding energy levels. Along the proof, we give full classification of the structure of the isoenergy surfaces near the critical set under our genericity assumptions and we give their complete list using Fomenko graphs. This may be viewed as a step towards completing the Smale program for relating the energy surfaces foliation structure to singularities of the momentum mappings for non-degenerate integrable two degrees of freedom systems.Comment: 30 pages, 19 figure

Systems of Hess-Appel'rot Type and Zhukovskii Property

We start with a review of a class of systems with invariant relations, so called {\it systems of Hess--Appel'rot type} that generalizes the classical Hess--Appel'rot rigid body case. The systems of Hess-Appel'rot type carry an interesting combination of both integrable and non-integrable properties. Further, following integrable line, we study partial reductions and systems having what we call the {\it Zhukovskii property}: these are Hamiltonian systems with invariant relations, such that partially reduced systems are completely integrable. We prove that the Zhukovskii property is a quite general characteristic of systems of Hess-Appel'rote type. The partial reduction neglects the most interesting and challenging part of the dynamics of the systems of Hess-Appel'rot type - the non-integrable part, some analysis of which may be seen as a reconstruction problem. We show that an integrable system, the magnetic pendulum on the oriented Grassmannian $Gr^+(4,2)$ has natural interpretation within Zhukovskii property and it is equivalent to a partial reduction of certain system of Hess-Appel'rot type. We perform a classical and an algebro-geometric integration of the system, as an example of an isoholomorphic system. The paper presents a lot of examples of systems of Hess-Appel'rot type, giving an additional argument in favor of further study of this class of systems.Comment: 42 page

De novo mutations in EIF2B1 affecting eIF2 signaling cause neonatal/early onset diabetes and transient hepatic dysfunction

Permanent neonatal diabetes is caused by reduced β-cell number or impaired β-cell function. Understanding the genetic basis of this disorder highlights fundamental β-cell mechanisms. We performed trio genome sequencing for 44 permanent neonatal diabetes patients and their unaffected parents to identify causative de novo variants. Replication studies were performed in 188 patients diagnosed with diabetes before 2 years of age without a genetic diagnosis. EIF2B1 (encoding the eIF2B complex α subunit) was the only gene with novel de novo variants (all missense) in at least three patients. Replication studies identified 2 further patients with de novo EIF2B1 variants. In addition to diabetes, 4/5 patients had hepatitis-like episodes in childhood. The EIF2B1 de novo mutations were found to map to the same protein surface. We propose that these variants render the eIF2B complex insensitive to eIF2 phosphorylation which occurs under stress conditions and triggers expression of stress-response genes. Failure of eIF2B to sense eIF2 phosphorylation likely leads to unregulated unfolded protein response and cell death. Our results establish de novo EIF2B1 mutations as a novel cause of permanent diabetes and liver dysfunction. These findings confirm the importance of cell stress regulation for β-cells and highlight EIF2B1’s fundamental role within this pathway.Includes NIHR and Wellcome Trust. Wellcome Trust 200848/Z/16/

Reliability, Validity and Psychometric Properties of the Greek Translation of the Center for Epidemiological Studies-Depression (CES-D) Scale

INTRODUCTION: The aim of the current study was to assess the reliability, validity and psychometric properties of the Greek translation of the Center for Epidemiological Studies- Depression Scale (CES-D). METHODS: 40 depressed patients 29.65 ± 9.38 years old, and 120 normal controls 27.23 ± 10.62 years old entered the study. In 20 of them (12 patients and 8 controls) the instrument was re-applied 1-2 days later. Translation and Back Translation was made. Clinical Diagnosis was reached by consensus of two examiners with the use of the SCAN v.2.0 and the IPDE. Statistical Analysis included ANOVA, the Pearson Product Moment Correlation Coefficient, Principal Components Analysis and Discriminant Function Analysis and the calculation of Cronbach's alpha (α) RESULTS: Both Sensitivity and specificity exceed 90.00 at 23/24, Chronbach's alpha for the total scale was equal to 0.95. Factor analysis revealed three factors (positive affect, irritability and interpersonal relationships, depressed affect and somatic complains). The test-retest reliability was satisfactory (Pearson's R between 0.45 and 0.95 for individual items and 0.71 for total score). CONCLUSION: The Greek translation of the CES-D scale is both reliable and valid and is suitable for clinical and research use with satisfactory properties. Its properties are similar to those reported in the international literature. However one should always have in mind the limitations inherent in the use of self-report scales

A preliminary investigation into the prevalence and prediction of problematic cell phone use

Abstract Background and aims Likening mobile phone use dependency to the classification of excessive behaviors may be necessarily equivalent in seriousness to previously established addictions such as problematic computing or excessive gambling. The aim of the study explores into the behavior of excessive use of mobile phones as a pathological behavior. Methods Two studies investigated criteria for problematic mobile phone usage by examining student (Study 1, N = 301) and nonstudent (Study 2, N = 362) responses to a set of adapted mobile phone addiction inventories. Study 1 investigated cell phone addiction inventories as constructs designed to measure problematic cell phone use. Additionally, Study 2 sought to predict age, depression, extraversion, emotional stability, impulse control, and self-esteem as independent variables that augment respondents' perceptions of problematic use. Results The results from Study 1 and Study 2 indicate that 10 to 25% of the participants tested exhibited problematic cell phone usage. Additionally, age, depression, extraversion, and low impulse control are the most suitable predictors for problematic use. Conclusions The results of the two studies indicate that problematic mobile phone use does occur and ought to be taken seriously by the psychological community. Presently, there is limited data providing conclusive evidence for a comprehensible categorization of cell phone addiction, as well as a unified explanatory model specific to problematic mobile phone use. Studies such as this one may contribute substantial findings, adding scientific significance, and offering a valuable submission for the ongoing progress of creating intervention frameworks relative to “virtual addictions”

Genetički polimorfizmi u dijabetesu: Utjecaj na terapiju oralnim antidijabeticima

Due to new genetic insights, etiologic classification of diabetes is under constant scrutiny. Hundreds, or even thousands, of genes are linked with type 2 diabetes. Three common variants (Lys23 of KCNJ11, Pro12 of PPARG, and the T allele at rs7903146 of TCF7L2) have been shown to be predisposed to type 2 diabetes mellitus across many large studies. Individually, each of these polymorphisms is only moderately predisposed to type 2 diabetes. On the other hand, monogenic forms of diabetes such as MODY and neonatal diabetes are characterized by unique clinical features and the possibility of applying a tailored treatment. Genetic polymorphisms in drug-metabolizing enzymes, transporters, receptors, and other drug targets have been linked to interindividual differences in the efficacy and toxicity of a number of medications. Mutations in genes important in drug absorption, distribution, metabolism and excretion (ADME) play a critical role in pharmacogenetics of diabetes. There are currently five major classes of oral pharmacological agents available to treat type 2 diabetes: sulfonylureas, meglitinides, metformin (a biguanide), thiazolidinediones, and α-glucosidase inhibitors. Other classes are also mentioned in literature. In this work, different types of genetic mutations (mutations of the gene for glucokinase, HNF 1, HNF1ß and Kir6.2 and SUR1 subunit of KATP channel, PPAR-γ, OCT1 and OCT2, cytochromes, direct drug-receptor (KCNJ11), as well as the factors that influence the development of the disease (TCF7L2) and variants of genes that lead to hepatosteatosis caused by thiazolidinediones) and their influence on the response to therapy with oral antidiabetics will be reviewed.Dijabetes tipa 2 dosegao je proporcije epidemije u SAD (> 18 milijuna) i cijelom svijetu (170 milijuna oboljelih osoba) te ima tendenciju daljnjeg dramatičnog rasta. Stoga se u posljednje vrijeme ulažu napori da se otkriju i razviju novi farmakološki agensi za liječenje ove bolesti. Klasifikacija šećerne bolesti proširena je uspjesima istraživača na području genetike. Da bismo razumjeli farmakogenetiku antidijabetika neophodno je razumjeti genetiku samog dijabetesa. Kao što će biti prikazano u ovom radu veliki broj gena koji su povezani s razvojem dijabetesa takođe utječu i na odgovor na terapiju antidijabeticima. S druge strane, mutacije gena koji utječu na ADME (apsorpcija, distribucija, metabolizam i ekskrecija) lijeka imaju značajan utjecaj na farmakogenetiku oralnih antidijabetika. Utvrđeno je da je dijabetes genetički heterogena bolest. Uobičajeni oblici dijabetesa su gotovo uvijek poligenski i za razvoj same bolesti vrlo su značajne snažne interakcije među različitim genima kao i između gena i okoliša. Zbog toga mutacije ili polimorfizmi koji u manjoj mjeri utječu na funkciju gena mogu postati klinički značajni samo u slučaju kada se kombiniraju s drugim faktorima odnosno genima. Smatra se da u razvoju dijabetesa mogu sudjelovati stotine pa čak i tisuće gena. Do 2006. identificirano je nekoliko uobičajenih alela koji povećavaju rizik za razvoj dijabetesa, od kojih su najznačajniji PPARG (Pro12), KCNJ11 (Lys23) i TCF7L2 (T na rs7903146). Do danas je najveći uspjeh postignut u identifikaciji gena odgovornih za razmjerno rijetke oblike ove bolesti poput ”Maturity-onset diabetes of the young” (MODY) i neonatalnog dijabetesa. Monogenske oblike dijabetesa odlikuju jedinstvene kliničke karakteristike i mogućnost primjene individualnog tretmana. Genetički polimorfizmi enzima koji utječu na metabolizam lijekova, transportera, receptora i drugih ciljeva djelovanja lijekova povezani su s interindividualnim razlikama u efikasnosti i toksičnosti mnogih lijekova. Vrlo je važno da se na temelju farmakogenetičkih istraživanja mogu predvidjeti neki neželjeni efekti lijekova. Trenutačno postoji pet glavnih klasa oralnih antidijabetika: sulfoniluree, meglitinidi, metformin (bigvanid), tiazolidindioni i inhibitori α-glukozidaze. U literaturi se također spominju inhibitori dipeptidil peptidaze IV (DPP-IV), selektivni antagonisti kanabinoidnog receptora 1 (CB-1), glukagonu slični peptid 1 mimetici i amilin mimetici. Razumijevanje mehanizama koji rezultiraju disfunkcijom β stanica na fiziološkom i molekularnom nivou neophodno je za napredak u razumijevanju tretmana dijabetesa. U ovom radu dat je pregled različitih genetičkih mutacija (mutacije gena za glukokinazu, HNF 1, HNF1ß, Kir6.2 i SUR 1 podjedinicu KATP kanala ß stanica, PPAR-γ, OCT1 i OCT2, citohrome, KCNJ11, faktore koji utječu na razvoj bolesti (TCF7L2) i varijante gena koji dovode do hepatosteatoze uzrokovane tiazolidindionima) te njihov utjecaj na odgovor na terapiju oralnim antidijabeticima