A short proof of the Kac-Ward formula

We present a short proof of the Kac-Ward formula for the partition function of the Ising model on planar graphs.Comment: 8 pages, 2 figure

Functional Potential of the Novosibirsk Urban Region in Russian Federation

The research presented in this article focuses on the urban region of Novosibirsk, which is one of the most industrialized part of Siberia and the Asian part of Russian Federation. The research was based on two methods of determining the functions of cities in the national settlement system: a research programme concerning the genesis of functional development and a research programme of specialized functions, the purpose of which is to determine the economic base of territorial units. To show relationships between the core of the region and its peripheral area there was provided a case study analyzing the territorial units forming the southern settlement belt along the Novosibirsk-Cherepanovo regional railway line over a distance of approx. 100 km. The presented results have shown the general tendencies in the transformations of the Novosibirsk urban region both in long-term perspective and in contemporary circumstances

Random walk loop soups and conformal loop ensembles

The random walk loop soup is a Poissonian ensemble of lattice loops; it has been extensively studied because of its connections to the discrete Gaussian free field, but was originally introduced by Lawler and Trujillo Ferreras as a discrete version of the Brownian loop soup of Lawler and Werner, a conformally invariant Poissonian ensemble of planar loops with deep connections to conformal loop ensembles (CLEs) and the Schramm-Loewner evolution (SLE). Lawler and Trujillo Ferreras showed that, roughly speaking, in the continuum scaling limit, ``large'' lattice loops from the random walk loop soup converge to ``large'' loops from the Brownian loop soup. Their results, however, do not extend to clusters of loops, which are interesting because the connection between Brownian loop soup and CLE goes via cluster boundaries. In this paper, we study the scaling limit of clusters of ``large'' lattice loops, showing that they converge to Brownian loop soup clusters. In particular, our results imply that the collection of outer boundaries of outermost clusters composed of ``large'' lattice loops converges to CLE.Comment: 30 pages, 7 figures, to appear in Probab. Theory Related Field

Cadmium-induced changes in hatchability and in the activity of aminotransaminases and selected lysosomal hydrolases in the blood plasma of Muscovy ducklings (Cairina moschata)

The aim of this study was to determine the effect of cadmium on Muscovy ducklings (Cairina moschata) based on hatching results and the activity of enzymes in the blood plasma. On day 6 of incubation, hatching eggs were injected into the egg albumen with 50 μl of saline solution containing Cd ions (CdCl2) at concentrations of 0 (control group), 1.3, 4.0, 7.5, 15.0 and 30 μg/egg, using 50 eggs per group. A gradual decrease in hatchability, from 52% in the control to 4% in the highest Cd dose group, was observed, with the LD50 calculated as 8 μg/egg. However, the impact of cadmium on the incidence of malformations of duck embryos has not been proven. Compared to the control group, N-acetyl-β-Dglucosaminidase activity increased by 30–50% (P ≤ 0.05) in the blood serum of ducklings in the groups receiving more than 7.5 μg Cd/egg, whereas an elevated activity of arylsulphatase (by 45%) was observed for a lower dose only (4 μg Cd/egg). A gradual increase in the activity of alanine and aspartate aminotransferases was observed (P ≤ 0.05), starting from the lowest exposure of 1.3 μg Cd/egg, by 155% and 53%, respectively. In conclusion, the results prove the dosedependent toxic impact of cadmium on embryogenesis and on the studied blood plasma enzyme activities of ducklings