Using the techniques of approximation and factorization of convolution operators we study the problem of irregular sampling of band-limited functions on a locally compact Abelian group $G$. The results of this paper relate to earlier work by Feichtinger and Gröchenig in a similar way as Kluvánek’s work published in 1969 relates to the classical Shannon Sampling Theorem. Generally speaking we claim that reconstruction is possible as long as there is sufficient high sampling density. Moreover, the iterative reconstruction algorithms apply simultaneously to families of Banach spaces.
The effect of antigenic bacterial lysate IRS-19 on the recovery of blood cells was studied in mice injured by a single dose of 7 Gy irradiation. The preirradiation administration of IRS-19 accelerated the recovery of leukocytes, reticulocytes and platelets in peripheral blood. The recovery of leukocytes 9-14 days after irradiation in protected animals was accompanied by a higher level of band forms of granulocytes as well as activated lymphoid and monocytoid cells., N.O. Macková, P. Fedoročko., and Obsahuje bibliografii
We study finite perimeter sets in step 2 Carnot groups. In this way we extend the classical De Giorgi’s theory, developed in Euclidean spaces by De Giorgi, as well as its generalization, considered by the authors, in Heisenberg groups. A structure theorem for sets of finite perimeter and consequently a divergence theorem are obtained. Full proofs of these results, comments and an exhaustive bibliography can be found in our preprint (2001).
Recurrent neural networks, in contrast to the classical feedforward neural networks, handle better the inputs that have space-time structure, e.g. symbolic time series. Since the classic gradient methods for recurrent neural network training on longer input sequences converge very poorly and slowly, alternative approaches are needed. We describe the training method with the Extended Kalman Filter and with its modifications Unscented Kalman Filter, nprKF and with their joint versions. The Joint Unscented Kalman Filter was not used for this purpose before. We compare the performance of these filters and of the classic Truncated Backpropagation Through Time (BPTT(h)) in two experiments for next-symbol prediction - word sequence generated by Reber automaton and the sequence generated by quantising the activations of a laser in a chaotic regime. All the new filters achieved significantly better results.