Simulation studies of correlation functions and relaxation in polymeric systems

We investigate the statics and dynamics of a glassy,non-entangled, short bead-spring polymer melt with moleculardynamics simulations. Temperature ranges from slightlyabove the mode-coupling critical temperature to the liquidregime where features of a glassy liquid are absent. Ouraim is to work out the polymer specific effects on therelaxation and particle correlation. We find the intra-chain static structure unaffected bytemperature, it depends only on the distance of monomersalong the backbone. In contrast, the distinct inter-chainstructure shows pronounced site-dependence effects at thelength-scales of the chain and the nearest neighbordistance. There, we also find the strongest temperaturedependence which drives the glass transition. Both the siteaveraged coupling of the monomer and center of mass (CM) andthe CM-CM coupling are weak and presumably not responsiblefor a peak in the coherent relaxation time at the chain'slength scale. Chains rather emerge as soft, easilyinterpenetrating objects. Three particle correlations arewell reproduced by the convolution approximation with theexception of model dependent deviations. In the spatially heterogeneous dynamics of our system weidentify highly mobile monomers which tend to follow eachother in one-dimensional paths forming ``strings''. Thesestrings have an exponential length distribution and aregenerally short compared to the chain length. Thus, arelaxation mechanism in which neighboring mobile monomersmove along the backbone of the chain seems unlikely.However, the correlation of bonded neighbors is enhanced. When liquids are confined between two surfaces in relativesliding motion kinetic friction is observed. We study ageneric model setup by molecular dynamics simulations for awide range of sliding speeds, temperatures, loads, andlubricant coverings for simple and molecular fluids. Instabilities in the particle trajectories are identified asthe origin of kinetic friction. They lead to high particlevelocities of fluid atoms which are gradually dissipatedresulting in a friction force. In commensurate systemsfluid atoms follow continuous trajectories for sub-monolayercoverings and consequently, friction vanishes at low slidingspeeds. For incommensurate systems the velocity probabilitydistribution exhibits approximately exponential tails. Weconnect this velocity distribution to the kinetic frictionforce which reaches a constant value at low sliding speeds. This approach agrees well with the friction obtaineddirectly from simulations and explains Amontons' law on themicroscopic level. Molecular bonds in commensurate systemslead to incommensurate behavior, but do not change thequalitative behavior of incommensurate systems. However,crossed chains form stable load bearing asperities whichstrongly increase friction.

Longitudinal evolution of cognitive functions in patients with multiple system atrophy: a prospective study

Introduction and Background: Multiple system atrophy (MSA) is a sporadic, adult-onset, progressive neurodegenerative disease characterized clinically by parkinsonism, cerebellar ataxia, and autonomic failure. We investigated cognitive functions longitudinally in a group of probable MSA patients, matching data with sleep parameters. Patients and Methods: 10 patients (7m/3f) underwent a detailed interview, a general and neurological examination, laboratory exams, MRI scans, a cardiovascular reflexes study, a battery of neuropsychological tests, and video-polysomnographic recording (VPSG). Patients were revaluated (T1) a mean of 16±5 (range: 12-28) months after the initial evaluation (T0). At T1, the neuropsychological assessment and VPSG were repeated. Results: The mean patient age was 57.8±6.4 years (range: 47-64) with a mean age at disease onset of 53.2±7.1 years (range: 43-61) and symptoms duration at T0 of 60±48 months (range: 12-144). At T0, 7 patients showed no cognitive deficits while 3 patients showed isolated cognitive deficits. At T1, 1 patient worsened developing multiple cognitive deficits from a normal condition. At T0 and T1, sleep efficiency was reduced, REM latency increased, NREM sleep stages 1-2 slightly increased. Comparisons between T1 and T0 showed a significant worsening in two tests of attention and no significant differences of VPSG parameters. No correlation was found between neuropsychological results and VPSG findings or RBD duration. Discussion and Conclusions: The majority of our patients do not show any cognitive deficits at T0 and T1, while isolated cognitive deficits are present in the remaining patients. Attention is the cognitive function which significantly worsened. Our data confirm the previous findings concerning the prevalence, type and the evolution of cognitive deficits in MSA. Regarding the developing of a condition of dementia, our data did not show a clear-cut diagnosis of dementia. We confirm a mild alteration of sleep structure. RBD duration does not correlate with neuropsychological findings.

Applications of elliptic functions to solve differential equations

In questa tesi si mostrano alcune applicazioni degli integrali ellittici nella meccanica Hamiltoniana, allo scopo di risolvere i sistemi integrabili. Vengono descritte le funzioni ellittiche, in particolare la funzione ellittica di Weierstrass, ed elenchiamo i tipi di integrali ellittici costruendoli dalle funzioni di Weierstrass. Dopo aver considerato le basi della meccanica Hamiltoniana ed il teorema di Arnold Liouville, studiamo un esempio preso dal libro di Moser-Integrable Hamiltonian Systems and Spectral Theory, dove si prendono in considerazione i sistemi integrabili lungo la geodetica di un'ellissoide, e il sistema di Von Neumann. In particolare vediamo che nel caso n=2 abbiamo un integrale ellittico.

Lateralization of cognitive functions after stroke in childhood

A child's brain shows a remarkable ability to recover from adverse events such as stroke. Language functions recover particularly well, while visuo-spatial skills are more affected by brain damage, regardless of its localization. This study investigated the lateralization of language and visual search after childhood stroke.

Zeros of Weakly Holomorphic Modular Forms of Levels 2 and 3

Let M-k(#)(N) be the space of weakly holomorphic modular forms for Gamma(0)(N) that are holomorphic at all cusps except possibly at infinity. We study a canonical basis for M-k(#)(2) and M-k(#)(3) and prove that almost all modular forms in this basis have the property that the majority of their zeros in a fundamental domain lie on a lower boundary arc of the fundamental domain.

Cognitive and behavioral aspects of executive functions in children born very preterm

This study investigated whether children aged between 8 and 12 years born very preterm (VPT) and/or at very low birth weight (VLBW) performed lower than same-aged term-born controls in cognitive and behavioral aspects of three executive functions: inhibition, working memory, and shifting. Special attention was given to sex differences. Fifty-two VPT/VLBW children (26 girls, 50%) born in the cohort of 1998-2003 and 36 same-aged term-born children (18 girls, 50%) were recruited. As cognitive measures, children completed tasks of inhibition (Color-Word Interference Test, D-KEFS; Delis, Kaplan, & Kramer, 2001 ), working memory (digit span backwards, HAWIK-IV; Petermann & Petermann, 2008 ), and shifting (Trail Making Test, number-letter-switching, D-KEFS; Delis et al., 2001 ). As behavioral measures, mothers completed the Behavior Rating Inventory of Executive Function (BRIEF; Gioia, Isquith, Guy, & Kenworthy, 2000 ). Scales of interest were inhibit, working memory, and shift. Analyses of the cognitive aspects of executive functions revealed that VPT/VLBW children performed significantly lower than controls in the shifting task but not in the working memory and inhibition tasks. Analyses of behavioral aspects of executive functions revealed that VPT/VLBW children displayed more problems than the controls in working memory in everyday life but not in inhibition and shifting. No sex differences could be detected either in cognitive or behavioral aspects of executive functions. To conclude, cognitive and behavioral measures of executive functions were not congruent in VPT/VLBW children. In clinical practice, the combination of cognitive and behavioral instruments is required to disclose children's executive difficulties.