Tight Risk Bounds for Multi-Class Margin Classifiers

We consider a problem of risk estimation for large-margin multi-class classifiers. We propose a novel risk bound for the multi-class classification problem. The bound involves the marginal distribution of the classifier and the Rademacher complexity of the hypothesis class. We prove that our bound is tight in the number of classes. Finally, we compare our bound with the related ones and provide a simplified version of the bound for the multi-class classification with kernel based hypotheses.Comment: 11 page

Structure of (22\u3cem\u3eS\u3c/em\u3e)-3\u3cem\u3eβ\u3c/em\u3e-Acetoxy-20-(3-isopropylisoxazolin-5-yl)-4,4,14 \u3cem\u3eα\u3c/em\u3e-trimethylpregn-8(9)-ene

C32H51NO3, Mr = 497·7, orthorhombic, P212121, a = 7·577 (2), b = 10·510 (2), c = 35·399 (7) Å, V = 2819 (1) Å3, Z = 4, Dx = 1·173 g cm-3, λ (Mo Kα) = 0·71073 Å, μ = 0·69 cm-1, F(000) = 1096, T = 153 K, R = 0·0497 for 2235 observed reflections. The compound investigated is found to be a (22S)-epimer

Атмосферні процеси і географічні фактори формування клімату України

У статті розглядаються питання кліматотворення досліджуваних територій і зокрема України. Клімат формується під дією космічно-земних процесів на фоні взаємодії геосфер Землі. Розрізняють кліматотвірні процеси зовнішнього (астрономічного) і внутрішнього (атмосферного) походження, а також географічні фактори кліматотворення, як фон, на якому функціонують кліматотвірні процеси. In the article the questions are considered the formation climate of the research territory including Ukrain. The climate is formation under the influence cosmos-earth processes against background interaction of the geosphere of the Earth. The formation climate processes are discern of the external (astronomic) and internal (atmospheric) origin and the geographic factors of the formation climet as the background against the formation climet processes are function

Features of chemical-mineralogical composition and processing properties for medium-ferrous bauxites

The features of chemical-mineralogical composition and processing properties of bauxites from Iksinsk and Severoonezhsk deposits are investigated in the paper. It is found that the studied bauxites are coarsely dispersed and low-dispersive, high-alumina clay raw materials with a high content of colouring oxides. According to their mineralogical composition, Iksinsk and Severoonezhsk bauxites are boehmitehydrargillite-kaolinite clay bauxites. Moreover, Iksinsk bauxite samples are characterized by the total absence of quartz impurities. The samples of plastic molding based on Iksinsk bauxites are fully sintered at 1500 °С with the formation of strong structures with a compressive strength of 70- 120 MPa (depending on the variety of bauxites). The samples based on Severoonezhsk bauxites are fully sintered at 1450 °С, and they are characterized by a compressive strength to 70 MPa in the sintered state