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

Effect of the first wave of COVID-19 on Poison Control Centre activities in 21 European countries : an EAPCCT initiative

Peer reviewe

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