156 research outputs found
Introduction to Khovanov Homologies. I. Unreduced Jones superpolynomial
An elementary introduction to Khovanov construction of superpolynomials.
Despite its technical complexity, this method remains the only source of a
definition of superpolynomials from the first principles and therefore is
important for development and testing of alternative approaches. In this first
part of the review series we concentrate on the most transparent and
unambiguous part of the story: the unreduced Jones superpolynomials in the
fundamental representation and consider the 2-strand braids as the main
example. Already for the 5_1 knot the unreduced superpolynomial contains more
items than the ordinary Jones.Comment: 33 page
Quantitative Assessment of Early Diabetic Retinopathy Using Fractal Analysis
OBJECTIVE—Fractal analysis can quantify the geometric complexity of the retinal vascular branching pattern and may therefore offer a new method to quantify early diabetic microvascular damage. In this study, we examined the relationship between retinal fractal dimension and retinopathy in young individuals with type 1 diabetes
Critical phenomena in complex networks
The combination of the compactness of networks, featuring small diameters,
and their complex architectures results in a variety of critical effects
dramatically different from those in cooperative systems on lattices. In the
last few years, researchers have made important steps toward understanding the
qualitatively new critical phenomena in complex networks. We review the
results, concepts, and methods of this rapidly developing field. Here we mostly
consider two closely related classes of these critical phenomena, namely
structural phase transitions in the network architectures and transitions in
cooperative models on networks as substrates. We also discuss systems where a
network and interacting agents on it influence each other. We overview a wide
range of critical phenomena in equilibrium and growing networks including the
birth of the giant connected component, percolation, k-core percolation,
phenomena near epidemic thresholds, condensation transitions, critical
phenomena in spin models placed on networks, synchronization, and
self-organized criticality effects in interacting systems on networks. We also
discuss strong finite size effects in these systems and highlight open problems
and perspectives.Comment: Review article, 79 pages, 43 figures, 1 table, 508 references,
extende
Challenges of beta-deformation
A brief review of problems, arising in the study of the beta-deformation,
also known as "refinement", which appears as a central difficult element in a
number of related modern subjects: beta \neq 1 is responsible for deviation
from free fermions in 2d conformal theories, from symmetric omega-backgrounds
with epsilon_2 = - epsilon_1 in instanton sums in 4d SYM theories, from
eigenvalue matrix models to beta-ensembles, from HOMFLY to super-polynomials in
Chern-Simons theory, from quantum groups to elliptic and hyperbolic algebras
etc. The main attention is paid to the context of AGT relation and its possible
generalizations.Comment: 20 page
Muscle architecture and passive lengthening properties of the gastrocnemius medialis and Achilles tendon in children who idiopathically toe-walk
Children who idiopathically toe-walk (ITW) habitually operate at greater plantarflexion angles and thus, at shorter muscle-tendon unit (MTU) lengths than typically developing (TD) children. Therefore, it is often assumed that habitual use of the gastrocnemius muscle in this way will cause remodelling of the muscle-tendon architecture compared to TD children. However, the gastrocnemius muscle architecture of children who ITW has never been measured. It is essential that we gain a better understanding of these muscle-tendon properties, to ensure that appropriate clinical interventions can be provided for these children. Five children who ITW (age 8 ± 2 years) and 14 TD children (age 10 ± 2 years) participated in this study. Ultrasound was combined with isokinetic dynamometry and surface electromyography, to measure muscle architecture at common positions and passive lengthening properties of the gastrocnemius muscle and tendon across full range of motion. Regardless of which common condition groups were compared under, both the absolute and normalised to MTU muscle belly and fascicle lengths were always longer, and the Achilles tendon length was always shorter in children who ITW than TD children (p 0.05); however, passive joint stiffness was greater in children who ITW at maximum dorsiflexion (p = 0.001) and at a joint moment common to all participants (p = 0.029). Consequently, the findings of this pilot study indicate a remodelling of the relative MTU that does not support the concept that children who ITW commonly experience muscle shortening. Therefore, greater consideration of the muscle and tendon properties are required when prescribing clinical interventions that aim to lengthen the MTU, and treatments may be better targeted at the Achilles tendon in children who ITW
Long-term outcomes of the global tuberculosis and COVID-19 co-infection cohort
Background: Longitudinal cohort data of patients with tuberculosis (TB) and coronavirus disease 2019 (COVID-19) are lacking. In our global study, we describe long-term outcomes of patients affected by TB and COVID-19. Methods: We collected data from 174 centres in 31 countries on all patients affected by COVID-19 and TB between 1 March 2020 and 30 September 2022. Patients were followed-up until cure, death or end of cohort time. All patients had TB and COVID-19; for analysis purposes, deaths were attributed to TB, COVID-19 or both. Survival analysis was performed using Cox proportional risk-regression models, and the log-rank test was used to compare survival and mortality attributed to TB, COVID-19 or both. Results: Overall, 788 patients with COVID-19 and TB (active or sequelae) were recruited from 31 countries, and 10.8% (n=85) died during the observation period. Survival was significantly lower among patients whose death was attributed to TB and COVID-19 versus those dying because of either TB or COVID-19 alone (p<0.001). Significant adjusted risk factors for TB mortality were higher age (hazard ratio (HR) 1.05, 95% CI 1.03-1.07), HIV infection (HR 2.29, 95% CI 1.02-5.16) and invasive ventilation (HR 4.28, 95% CI 2.34-7.83). For COVID-19 mortality, the adjusted risks were higher age (HR 1.03, 95% CI 1.02-1.04), male sex (HR 2.21, 95% CI 1.24-3.91), oxygen requirement (HR 7.93, 95% CI 3.44-18.26) and invasive ventilation (HR 2.19, 95% CI 1.36-3.53). Conclusions: In our global cohort, death was the outcome in >10% of patients with TB and COVID-19. A range of demographic and clinical predictors are associated with adverse outcomes
Changes in seasonal streamflow extremes experienced in rivers of Northwestern South America (Colombia)
A measure of the variability in seasonal extreme streamflow was estimated for the Colombian Caribbean coast, using monthly time series of freshwater discharge from ten watersheds. The aim was to detect modifications in the streamflow monthly distribution, seasonal trends, variance and extreme monthly values. A 20-year length time moving window, with 1-year successive shiftments, was applied to the monthly series to analyze the seasonal variability of streamflow. The seasonal-windowed data were statistically fitted through the Gamma distribution function. Scale and shape parameters were computed using the Maximum Likelihood Estimation (MLE) and the bootstrap method for 1000 resample. A trend analysis was performed for each windowed-serie, allowing to detect the window of maximum absolute values for trends. Significant temporal shifts in seasonal streamflow distribution and quantiles (QT), were obtained for different frequencies.
Wet and dry extremes periods increased significantly in the last decades. Such increase did not occur simultaneously through the region. Some locations exhibited continuous increases only at minimum QT
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