SPHERICAL TWISTS, SO(n) AND THE LIFTING OF THEIR TWIST PATHS TO Spin(n) IN LOW DIMENSIONS

2011 ◽  
Vol 63 (3) ◽  
pp. 723-751 ◽  
Author(s):  
A. Taheri
Keyword(s):  
Low Dimensions ◽  
Spherical Twists

scholarly journals FRACTAL DIMENSION OF SPIN-GLASSES INTERFACES IN DIMENSION d = 2 AND d = 3 VIA STRONG DISORDER RENORMALIZATION AT ZERO TEMPERATURE

Fractals ◽  
2015 ◽  
Vol 23 (04) ◽  
pp. 1550042 ◽  
Author(s):  
CÉCILE MONTHUS
Keyword(s):  
Fractal Dimension ◽  
Boundary Conditions ◽  
Spin Glasses ◽  
Periodic Boundary ◽  
Domain Walls ◽  
Numerical Study ◽  
Periodic Boundary Conditions ◽  
Zero Temperature ◽  
Low Dimensions ◽  
Strong Disorder

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.

Classification of Filiform Leibniz Algebras in Low Dimensions

2019 ◽  
pp. 223-249
Author(s):  
Shavkat Ayupov ◽  
Bakhrom Omirov ◽  
Isamiddin Rakhimov
Keyword(s):  
Low Dimensions ◽  
Leibniz Algebras

scholarly journals Engineering block copolymer materials for patterning ultra-low dimensions

2020 ◽  
Vol 5 (10) ◽  
pp. 1642-1657
Author(s):  
Cian Cummins ◽  
Guillaume Pino ◽  
Daniele Mantione ◽  
Guillaume Fleury
Keyword(s):  
Thin Film ◽  
Block Copolymer ◽  
Block Copolymers ◽  
Low Dimensions ◽  
Processing Strategies ◽  
Synthetic Routes ◽  
Film Processing ◽  
Thin Film Processing

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.

scholarly journals Estimating perimeter using graph cuts

2017 ◽  
Vol 49 (4) ◽  
pp. 1067-1090 ◽  
Author(s):  
Nicolás García Trillos ◽  
Dejan Slepčev ◽  
James von Brecht
Keyword(s):  
Confidence Intervals ◽  
Error Estimates ◽  
Approximation Error ◽  
Higher Dimensions ◽  
Geometric Graph ◽  
Graph Cut ◽  
Average Degree ◽  
Random Geometric Graph ◽  
Low Dimensions ◽  
Variance Estimates

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.

scholarly journals O010 The role of dysfunctional beliefs and attitudes about sleep in the association between daily sleep and affect in adolescents and emerging adults

2021 ◽  
Vol 2 (Supplement_1) ◽  
pp. A5-A5
Author(s):  
E Chachos ◽  
L Shen ◽  
S Maskevich ◽  
Y Yap ◽  
J Stone ◽  
...  
Keyword(s):  
Positive Affect ◽  
Emerging Adults ◽  
Sleep Duration ◽  
Cognitive Vulnerability ◽  
Sleep Time ◽  
Dysfunctional Beliefs ◽  
Low Dimensions ◽  
Modifiable Factor ◽  
Beliefs And Attitudes

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.

scholarly journals Visual e-commerce values filtering framework with spatial database metric

2020 ◽  
Vol 17 (3) ◽  
pp. 983-1006
Author(s):  
M. Kopecky ◽  
P. Vojtas
Keyword(s):  
User Behavior ◽  
Spatial Database ◽  
Synthetic Data ◽  
Combinatorial Search ◽  
Fuzzy Information ◽  
Additional Method ◽  
Analytic Hierarchy ◽  
Low Dimensions ◽  
Customer Preference ◽  
Linear Relaxations

Our customer preference model is based on aggregation of partly linear relaxations of value filters often used in e-commerce applications. Relaxation is motivated by the Analytic Hierarchy Processing method and combining fuzzy information in web accessible databases. In low dimensions our method is well suited also for data visualization. The process of translating models (user behavior) to programs (learned recommendation) is formalized by Challenge-Response Framework ChRF. ChRF resembles remote process call and reduction in combinatorial search problems. In our case, the model is automatically translated to a program using spatial database features. This enables us to define new metrics with visual motivation. We extend the conference paper with inductive ChRF, new representation of user and an additional method and metric. We provide experiments with synthetic data (items) and users.

scholarly journals Ternary and n-ary f-distributive structures

2018 ◽  
Vol 16 (1) ◽  
pp. 32-45 ◽  
Author(s):  
Indu R. U. Churchill ◽  
M. Elhamdadi ◽  
M. Green ◽  
A. Makhlouf
Keyword(s):  
Cohomology Theory ◽  
Extension Theory ◽  
Low Dimensions

AbstractWe introduce and study ternary f-distributive structures, Ternary f-quandles and more generally their higher n-ary analogues. A classification of ternary f-quandles is provided in low dimensions. Moreover, we study extension theory and introduce a cohomology theory for ternary, and more generally n-ary, f-quandles. Furthermore, we give some computational examples.

Unfolding Models for Asymmetric Dissimilarity Data With External Information Based on Path Structures

2018 ◽  
Vol 6 (3) ◽  
pp. 53-66
Author(s):  
Kensuke Tanioka ◽  
Hiroshi Yadohisa
Keyword(s):  
Principal Component ◽  
External Information ◽  
Visualization Method ◽  
Low Dimensions ◽  
Dissimilarity Data ◽  
Asymmetric Relation ◽  
Loading Matrix ◽  
Unfolding Models ◽  
Asymmetric Multidimensional Scaling ◽  
Path Structure

This article contains asymmetric dissimilarity data which is observed in various situations. In asymmetric dissimilarity data, dissimilarity from subject i to j and from subject j to i are not the same necessarily. Asymmetric multidimensional scaling (AMDS) is a visualization method for describing the asymmetric relations between subjects, given asymmetric dissimilarity data for subjects. It is sure that AMDS is a useful tool for interpreting the asymmetric relation, however, existing AMDS cannot be considered for the external information, even if the external information of the same subjects for the asymmetric dissimilarity data is given. If the estimated coordinates can be interpreted from the loading matrix for the external information like principal component analysis (PCA), the AMDS become more useful. This is because we can interpret the relation between the estimated asymmetries and the factors of the external information on the low dimensions. In this article, we proposed new AMDS with external information. In addition to that, the proposed method can consider the path structure for variables like SEM.

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