scholarly journals Linear flows and Morse graphs: Topological consequences in low dimensions

2013 ◽  
Vol 439 (8) ◽  
pp. 2177-2194
Author(s):  
Víctor Ayala ◽  
Ivan Jirón
Keyword(s):  
2019 ◽  
Vol 4 (6) ◽  
Author(s):  
Y.-N. Young ◽  
Yoichiro Mori ◽  
Michael J. Miksis
Keyword(s):  

2007 ◽  
Vol 27 (5) ◽  
pp. 1509-1524 ◽  
Author(s):  
FRITZ COLONIUS ◽  
ROBERTA FABBRI ◽  
RUSSELL JOHNSON

AbstractAverages of functionals along trajectories are studied by evaluating the averages along chains. This yields results for the possible limits and, in particular, for ergodic limits. Applications to Lyapunov exponents and to concepts of rotation numbers of linear Hamiltonian flows and of general linear flows are given.


Fractals ◽  
2015 ◽  
Vol 23 (04) ◽  
pp. 1550042 ◽  
Author(s):  
CÉCILE MONTHUS

For Gaussian Spin-Glasses in low dimensions, we introduce a simple Strong Disorder renormalization at zero temperature in order to construct ground states for Periodic and Anti-Periodic boundary conditions. The numerical study in dimensions [Formula: see text] (up to sizes [Formula: see text]) and [Formula: see text] (up to sizes [Formula: see text]) yields that Domain Walls are fractal of dimensions [Formula: see text] and [Formula: see text], respectively.


1995 ◽  
Vol 87 (1-4) ◽  
pp. 99-104 ◽  
Author(s):  
Francisco Guil ◽  
Manuel Mañas
Keyword(s):  

2019 ◽  
pp. 223-249
Author(s):  
Shavkat Ayupov ◽  
Bakhrom Omirov ◽  
Isamiddin Rakhimov

2020 ◽  
Vol 5 (10) ◽  
pp. 1642-1657
Author(s):  
Cian Cummins ◽  
Guillaume Pino ◽  
Daniele Mantione ◽  
Guillaume Fleury

Recently engineered high χ-low N block copolymers for nanolithography are evaluated. Synthetic routes together with thin film processing strategies are highlighted that could enable the relentless scaling for logic technologies at sub-10 nanometres.


2017 ◽  
Vol 49 (4) ◽  
pp. 1067-1090 ◽  
Author(s):  
Nicolás García Trillos ◽  
Dejan Slepčev ◽  
James von Brecht

Abstract We investigate the estimation of the perimeter of a set by a graph cut of a random geometric graph. For Ω ⊆ D = (0, 1)d with d ≥ 2, we are given n random independent and identically distributed points on D whose membership in Ω is known. We consider the sample as a random geometric graph with connection distance ε > 0. We estimate the perimeter of Ω (relative to D) by the, appropriately rescaled, graph cut between the vertices in Ω and the vertices in D ∖ Ω. We obtain bias and variance estimates on the error, which are optimal in scaling with respect to n and ε. We consider two scaling regimes: the dense (when the average degree of the vertices goes to ∞) and the sparse one (when the degree goes to 0). In the dense regime, there is a crossover in the nature of the approximation at dimension d = 5: we show that in low dimensions d = 2, 3, 4 one can obtain confidence intervals for the approximation error, while in higher dimensions one can obtain only error estimates for testing the hypothesis that the perimeter is less than a given number.


2021 ◽  
Vol 2 (Supplement_1) ◽  
pp. A5-A5
Author(s):  
E Chachos ◽  
L Shen ◽  
S Maskevich ◽  
Y Yap ◽  
J Stone ◽  
...  

Abstract Introduction Sleep and affect are closely related. Late adolescence and emerging adulthood are associated with unique sleep patterns and risk for mood disturbances. This daily study examined whether dysfunctional beliefs and attitudes about sleep (DBAS), a modifiable cognitive vulnerability factor, moderated daily sleep-affect associations. Methods 421 community adolescents (n=205, 54.1% females, M±SDage=16.9±0.87) and emerging adults (n=216, 73.1% females, M±SDage=21.31±1.73) self-reported sleep and affect (adapted 12-item PANAS) and wore an actigraphy device for 7–28 days, providing >5000 daily observations. Linear mixed models tested whether DBAS moderated daily associations between self-reported and actigraphic sleep duration (total sleep time), sleep efficiency, and next-day affect on between and within-person levels. Both valence (positive/negative) and arousal (high/low) dimensions of affect were examined. Covariates included age, gender, ethnicity, day of week, and previous-day affect. Results DBAS significantly moderated associations between average sleep and next-day positive, but not negative, affect. Individuals with higher DBAS had significantly lower high arousal positive affect as average sleep duration (actigraphic: p=.002; self-reported: p=.014) and efficiency (actigraphic: p=.014) decreased. Similar moderation was found for average self-reported sleep duration and low arousal positive affect (p=.032). No significant results emerged on the within-person level. Previous-day affect significantly predicted next-day affect across models and outcomes (all p<.001). Discussion Adolescents and emerging adults with more negative views about sleep may experience dampened positive affect in shorter, or poorer, sleep periods. DBAS may constitute a modifiable factor increasing affective vulnerability on a global but not day-to-day level, and a therapeutic target for sleep-related affect disturbances in youths.


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