Counting and computing regions of DD-decomposition: algebro-geometric approach

New methods for $D$-decomposition analysis are presented. They are based on topology of real algebraic varieties and computational real algebraic geometry. The estimate of number of root invariant regions for polynomial parametric families of polynomial and matrices is given. For the case of two parametric family more sharp estimate is proven. Theoretic results are supported by various numerical simulations that show higher precision of presented methods with respect to traditional ones. The presented methods are inherently global and could be applied for studying $D$-decomposition for the space of parameters as a whole instead of some prescribed regions. For symbolic computations the Maple v.14 software and its package RegularChains are used.Comment: 16 pages, 8 figure

Paleolithic Man of Denisova Cave and Zoogeography of Pleistocene Mammals of Northwestern Altai

Mammal population of the northwestern Altai included residents, autochthonous species, cosmopolitans, and migrants. The last clearly indicate biogeographical relationships of the biota of the Altai Mountains in the Pleistocene. Most of them penetrated into the Altai from the south. The majority of ungulates and rodents migrated from Central Asia. Yak, red dog, and snow leopard came from the Himalayas, Pamir, and Tien Shan. The natural environment of the Altai Mountains in the Pleistocene enabled migrations of these mammals from the south to north. The same opportunity was true of the ancient man. It is possible to assume that humans migrated from southeastern Asia and Indochina along the eastern foothills of the Himalayas and Nan Shan Mountains to the northwest, to the Zaisan Depression and Altai. This resulted in inevitable exchange of gene material of Paleolithic human populations of southeastern Asia and the Altai