Elliptic CR-manifolds and shear invariant ODE with additional symmetries

We classify the ODEs that correspond to elliptic CR-manifolds with maximal isotropy. It follows that the dimension of the isotropy group of an elliptic CR-manifold can be only 10 (for the quadric), 4 (for the listed examples) or less. This is in contrast with the situation of hyperbolic CR-manifolds, where the dimension can be 10 (for the quadric), 6 or 5 (for semi-quadrics) or less than 4. We also prove that, for all elliptic CR-manifolds with non-linearizable istropy group, except for two special manifolds, the points with non-linearizable isotropy form exactly some complex curve on the manifold

Role of interference and entanglement in quantum neural processing

The role of interference and entanglement in quantum neural processing is discussed. It is argued that on contrast to the quantum computing the problem of the use of exponential resources as the payment for the absense of entanglement does not exist for quantum neural processing. This is because of corresponding systems, as any modern classical artificial neural systems, do not realize functions precisely, but approximate them by training on small sets of examples. It can permit to implement quantum neural systems optically, because in this case there is no need in exponential resources of optical devices (beam-splitters etc.). On the other hand, the role of entanglement in quantum neural processing is still very important, because it actually associates qubit states: this is necessary feature of quantum neural memory models.Comment: 15 pages, PD

Invariants of elliptic and hyperbolic CR-structures of codimension 2

We reduce CR-structures on smooth elliptic and hyperbolic manifolds of CR-codimension 2 to parallelisms thus solving the problem of global equivalence for such manifolds. The parallelism that we construct is defined on a sequence of two principal bundles over the manifold, takes values in the Lie algebra of infinitesimal automorphisms of the quadric corresponding to the Levi form of the manifold, and behaves ``almost'' like a Cartan connection. The construction is explicit and allows us to study the properties of the parallelism as well as those of its curvature form. It also leads to a natural class of ``semi-flat'' manifolds for which the two bundles reduce to a single one and the parallelism turns into a true Cartan connection. In addition, for real-analytic manifolds we describe certain local normal forms that do not require passing to bundles, but in many ways agree with the structure of the parallelism.Comment: 42 pages, see also http://wwwmaths.anu.edu.au/research.reports/97mrr.htm

Neural Replicator Analysis for virus genomes binomial systematics in metagenomics

We have presented some arguments to substantiate the usefulness of neural replicator analysis (NRA) for constructing variants of the natural binomial classification of virus genomes based only on knowledge of their complete genomic sequences, without involving other data on the phenotype, functions, encoded proteins, etc., and also without the need of genomic sequences alignment. Perhaps this will make sense when processing metagenomic data. This makes it possible to construct the binomial classification accepted for the viruses themselves. We restrict ourselves to three families of viruses having dsDNA circular genomes (Papillomaviridae, Polyomaviridae and Caulimoviridae) and partly to the family Geminiviridae having ssDNA genomes though the approach presented can be also applied to genomes of other dsDNA, ssDNA and ssRNA viruses, including linear ones (some results for Mitoviridae are also presented). It is argued that binomial classification of virus genomes which is difficult to apply in all cases can nevertheless be informative tool of revealing virus properties, areal of hosts, forms of diseases and can also show the connections of the viruses belonging to different families and even to different kingdoms.Comment: 48 pages, 27 figure

Can the natural system of viruses reconcile the current taxonomy with an alternative classification useful to clinicians?

In 2022, a group of basic and clinical virologists, bioinformaticians, and evolutionary and structural biologists met in Oxford, UK, to develop a consensus on methodologies used to classify viruses. They concluded that virus taxonomy, which is hierarchical and based on evolution, is only one of many possible ways to classify viruses. This taxonomy, while satisfying the four principles they set out, faces difficulties in coordinating with other classification systems useful to clinicians, infectious disease specialists, agronomists, etc. One example discussed is the grouping of different viral strains that cause different diseases into the species Enterovirus C. Here we show that the use of a previously proposed variant of a natural virus classification system based on the use of Neural Replicator Analysis can resolve this contradiction by establishing the fine structure of the Enterovirus C species, in which strains that cause different diseases are placed in several different cells of the binomial table of viruses. A key element in enabling this is the sophisticated preprocessing of the original viral genomes using neural replicators.Comment: 11 pages, 4 figures. arXiv admin note: substantial text overlap with arXiv:2212.0547

Dry Magnetic Separation of Iron Ore of the Bakchar Deposit

Currently, the development of iron ore of the Bakchar deposit (Tomsk region) is considered promising because of the extremely large reserves of iron ore. Ores of this deposit are related to the high-grade type and expected to have a magnetic concentration for iron extraction. The main task of magnetic separation is to increase the total iron content in concentrates to a value which allows its further metallurgical processing. Ferruginous ore particles have a rounded shape that facilitates a separation process. The paper considers the influence of technological parameters on the magnetic concentrate yield and recovery rate of iron-containing fractions