Spectral flow and level spacing of edge states for quantum Hall hamiltonians

We consider a non relativistic particle on the surface of a semi-infinite cylinder of circumference $L$ submitted to a perpendicular magnetic field of strength $B$ and to the potential of impurities of maximal amplitude $w$. This model is of importance in the context of the integer quantum Hall effect. In the regime of strong magnetic field or weak disorder $B>>w$ it is known that there are chiral edge states, which are localised within a few magnetic lengths close to, and extended along the boundary of the cylinder, and whose energy levels lie in the gaps of the bulk system. These energy levels have a spectral flow, uniform in $L$, as a function of a magnetic flux which threads the cylinder along its axis. Through a detailed study of this spectral flow we prove that the spacing between two consecutive levels of edge states is bounded below by $2\pi\alpha L^{-1}$ with $\alpha>0$, independent of $L$, and of the configuration of impurities. This implies that the level repulsion of the chiral edge states is much stronger than that of extended states in the usual Anderson model and their statistics cannot obey one of the Gaussian ensembles. Our analysis uses the notion of relative index between two projections and indicates that the level repulsion is connected to topological aspects of quantum Hall systems.Comment: 22 pages, no figure

Multivariate risks and depth-trimmed regions

We describe a general framework for measuring risks, where the risk measure takes values in an abstract cone. It is shown that this approach naturally includes the classical risk measures and set-valued risk measures and yields a natural definition of vector-valued risk measures. Several main constructions of risk measures are described in this abstract axiomatic framework. It is shown that the concept of depth-trimmed (or central) regions from the multivariate statistics is closely related to the definition of risk measures. In particular, the halfspace trimming corresponds to the Value-at-Risk, while the zonoid trimming yields the expected shortfall. In the abstract framework, it is shown how to establish a both-ways correspondence between risk measures and depth-trimmed regions. It is also demonstrated how the lattice structure of the space of risk values influences this relationship.Comment: 26 pages. Substantially revised version with a number of new results adde

Depression of the ULF geomagnetic pulsation related to ionospheric irregularities

We consider a depression in intensity of ULF magnetic pulsations, which is observed on the ground surface due to appearance of the irregularities in the ionosphere. It is supposed that oblique Alfven waves in the ULF frequency range are downgoing from the magnetosphere and the horizontal irregularities of ionospheric conductivity are created by upgoing atmospheric gravity waves from seismic source. Unlike the companion paper by Molchanov et al. (2003), we used a simple model of the ionospheric layer but took into consideration the lateral inhomogeneity of the perturbation region in the ionosphere. It is shown that ULF intensity could be essentially decreased for frequencies f = 0.001-0.1 Hz at nighttime but the change is negligible at daytime in coincidence with observational results

Morphogenetic basis of the unified state register of soil resources of Russia

Nomenclature and taxonomic diversity of soils and their horizon-profile diagnostics/descriptions define morphogenetic soil indicators used in the Unified State Register of Soil Resources of Russia (with Russian abbreviation of EGRPR). Most of these soil indicators are of non-metric origin, i.e., established conventionally by agreement. Subject area of soil science includes a hierarchy of 5 types of soil objects (pit, profile, horizon, morphological element and sample), 380 indicators, 607 methods and 3019 values of the indicators

Potential of Theranostics in Visualisation of the Tumour Microenvironment and Elimination of Its Immunosuppressive Components

Theranostics is a promising branch of nuclear medicine that uses radiopharmaceuticals for diagnosis and treatment of cancer, and immunotheranostics is a special area in it. The aim of the study was to summarise the potential of theranostics for visualisation of the tumour microenvironment and elimination of its immunosuppressive components. The article presents up-to-date information on the composition and interaction of various cell subpopulations in the tumour microenvironment, as well as on the role of cancer stem cells in its formation. It describes defects of signalling pathways and potential targets for theranostics of cancer stem cells. Also, the article provides a description of the mechanism of interaction between the tumour and the immune system in the process of carcinogenesis. The review offers a detailed analysis of approaches to assessing the type of tumour microenvironment in order to individualise treatment and develop a rational design of clinical studies of theranostic couples. The authors present their own data on the distribution of subpopulations of lymphocytes and myeloid-derived suppressor cells in patients with metastatic tumours. The authors have considered the nuances of creating and using various molecules for targeted delivery in the development of diagnostic and therapeutic radiopharmaceuticals. The most promising diagnostic and therapeutic isotopes are described from the point of view of assessing the microenvironment and the possibility of influencing it. The article highlights modern and promising methods of pre-targeting to reduce the toxicity and increase the effectiveness of theranostics. Furthermore, having compared the advantages and disadvantages of theranostics with those of other systemic treatment options for metastatic tumours, the authors outline possible ways to overcome the shortcomings of theranostics

About possibility to locate an EQ epicenter using parameters of ELF/ULF preseismic emission

A relation between parameters of preseismic ULF/ELF emissions and EQ is studied. The magnetic data measured at Karymshino station (Kamchatka, Russia) along with data on local seismic activity during eight years of observations (2001–2008) are taken for the analysis. Source azimuth is detected in different techniques, based on the analysis of the total field and its polarized pulsed component. The latter technique shows a better accuracy in the source azimuth detection. The errors of the method are associated with existence of non-seismic sources and with use of one-point observation. The second error can be eliminated by development of multi-point observations

Use of iodine and selenium enriched fodder rations for production of fortified young lamb

The article is devoted to preventive measures to eliminate the problem of dysmicroelementosis in order to increase the productivity of young sheep. The article presents the results of studies of the influence of feeding rations on the growth and development of young sheep of the Edilbaev breed, on the level of their meat productivity and the qualitative characteristics of biologically fortified lamb. Feed additives based on Yoddar-Zn and DAFS-25 were added to the main ration of lambs at the age of four months, once a day, being added into a fodder mixture with concentrates. For the experiment the herd of lambs was divided to four groups of 25 heads each.The changes in live weight at the age of four, five, six and seven months were analyzed, and it was found that at the age of seven months, the absolute average weight gain in the experimental groups varied from 3.45 kg to 4.49 kg, in the control group it was 3.1 kg, while the largest live weight gain was recorded in group III which received both feed additives based on Yoddar-Zn and DAFS-25.There were no significant differences in the parameters of body measurements, with the exception of group III, where the chest circumference increased by 7.2%, and the height of a lamb at the withers increased in average by 8.1%. It was found that group III had the highest meat density coefficient, equal to 3.9, and the cross-sectional area of m. Longissimus dorsi was equal to 13.61 cm2. It was noted that the amount of free amino acids of the lamb group III is 18.8% higher than the meat of the control group. The lamb obtained from the animals of the experimental groups showed a higher protein content and less fat. The ratio of water to protein in all samples was slightly higher than 3.7, which corresponds to the Federa number for meat raw materials. Enriching the rations of the Edilbaevskoy sheep with feed additives Yoddar-Zn and DAFS-25 promotes the stimulation of growth and development of animals, increases the productivity and nutritional value of lamb

Poisson Statistics for the Largest Eigenvalues in Random Matrix Ensemble

The paper studies the spectral properties of large Wigner, band and sample covariance random matrices with heavy tails of the marginal distributions of matrix entries.Comment: This is an extended version of my talk at the QMath 9 conference at Giens, France on September 13-17, 200