### Article

## Internal Wave Breathers in the Slightly Stratified Fluid

The theory of long nonlinear oscillating wave packets (breathers) in a stratified fluid with a small density difference in a

gravitational field is developed. The theory is based on the Gardner equation and its modifications, which are fully integrable with modern methods of the nonlinear wave theory. Examples of the breather generation are given and the conditions for their stability are discussed.

**I**n this paper for the explain of the mechanism of formation of smooth strips (slicks) on the sea surface under the action of internal waves are used the film of surface-active substances, attendees everywhere in the sea. Experimental data on the real characteristics of marine films of surface-active substances are used for the calculation of histograms of contrast in the spectrum of wind ripples in the centimeter range for various parameters of the internal wave and wind wave lengths within the "film" mechanism of the effects of internal waves on the spectrum of wind-generated waves. It is shown that the ripple in the wavelength range 2-3 cm contrast weakly depends on the parameters of the internal waves (although with increasing internal wave amplitude), and the average number of 6-7 dB. For greater lengths ripple contrast is strongly dependent on the ratio of the rate of flow of water particles in the internal waves to the phase velocity of the internal wave. This dispersion deviations from average contrast values around the average value, which indicates a strong variation of contrast in each case. Nevertheless, it can be concluded relatively low sensitivity of "film" mechanism of action internal waves on the sea surface to a particular type of surface-active substances.

**Purpose:** Numerical modeling of internal baroclinic disturbances of different shapes in a model lake with variable depth, analysis of velocity field of wave-induced current, especially in the near-bed layer.

**Approach:** The study is carried out with the use of numerical full nonlinear nonhydrostatic model for stratified fluid.

**Findings:** The full nonlinear numerical modeling of internal wave dynamics in a stratified lake is carried out. The calculated distributions of near-bed velocities are analyzed; the significance of 3D effects for the velocity fields is emphasized; the regions of maximal (where internal waves are the main driving factor for sediment resuspension and erosion processes on the bed) and minimal velocities are marked out.

**Originality:** The results are new and can have practical application for many applied problems, especially ecological and economical, concerned with the processes of propagation of natural and anthropogenic pollutions in natural basins and the investigation of water quality, as well as with influence upon engineering structures and sediment transport.

Properties of rogue waves in the basin of intermediate depth are discussed in comparison with known properties of rogue waves in deep waters. Based on observations of rogue waves in the ocean of intermediate depth we demonstrate that the modulational instability can still play a significant role in their formation for basins of 20m and larger depth. For basins of smaller depth, the influence of modulational instability is less probable. By using the rational solutions of the nonlinear Schrodinger equation (breathers), it is shown that the rogue wave packet becomes wider and contains more individual waves in intermediate rather than in deep waters, which is also confirmed by observations.

One of the key advances in genome assembly that has led to a significant improvement in contig lengths has been improved algorithms for utilization of paired reads (mate-pairs). While in most assemblers, mate-pair information is used in a post-processing step, the recently proposed Paired de Bruijn Graph (PDBG) approach incorporates the mate-pair information directly in the assembly graph structure. However, the PDBG approach faces difficulties when the variation in the insert sizes is high. To address this problem, we first transform mate-pairs into edge-pair histograms that allow one to better estimate the distance between edges in the assembly graph that represent regions linked by multiple mate-pairs. Further, we combine the ideas of mate-pair transformation and PDBGs to construct new data structures for genome assembly: pathsets and pathset graphs.

Papers about natural protection territories

Many environmental stimuli present a quasi-rhythmic structure at different timescales that the brain needs to decompose and integrate. Cortical oscillations have been proposed as instruments of sensory de-multiplexing, i.e., the parallel processing of different frequency streams in sensory signals. Yet their causal role in such a process has never been demonstrated. Here, we used a neural microcircuit model to address whether coupled theta–gamma oscillations, as observed in human auditory cortex, could underpin the multiscale sensory analysis of speech. We show that, in continuous speech, theta oscillations can flexibly track the syllabic rhythm and temporally organize the phoneme-level response of gamma neurons into a code that enables syllable identification. The tracking of slow speech fluctuations by theta oscillations, and its coupling to gamma-spiking activity both appeared as critical features for accurate speech encoding. These results demonstrate that cortical oscillations can be a key instrument of speech de-multiplexing, parsing, and encoding.

Neuronal nicotinic acetylcholine receptors (NNRs) of the α7 subtype have been shown to contribute to the release of dopamine in the nucleus accumbens. The site of action and the underlying mechanism, however, are unclear. Here we applied a circuit modeling approach, supported by electrochemical in vivo recordings, to clarify this issue. Modeling revealed two potential mechanisms for the drop in accumbal dopamine efflux evoked by the selective α7 partial agonist TC-7020. TC-7020 could desensitize α7 NNRs located predominantly on dopamine neurons or glutamatergic afferents to them or, alternatively, activate α7 NNRs located on the glutamatergic afferents to GABAergic interneurons in the ventral tegmental area. Only the model based on desensitization, however, was able to explain the neutralizing effect of coapplied PNU-120596, a positive allosteric modulator. According to our results, the most likely sites of action are the preterminal α7 NNRs controlling glutamate release from cortical afferents to the nucleus accumbens. These findings offer a rationale for the further investigation of α7 NNR agonists as therapy for diseases associated with enhanced mesolimbic dopaminergic tone, such as schizophrenia and addiction

Let k be a field of characteristic zero, let G be a connected reductive algebraic group over k and let g be its Lie algebra. Let k(G), respectively, k(g), be the field of k- rational functions on G, respectively, g. The conjugation action of G on itself induces the adjoint action of G on g. We investigate the question whether or not the field extensions k(G)/k(G)^G and k(g)/k(g)^G are purely transcendental. We show that the answer is the same for k(G)/k(G)^G and k(g)/k(g)^G, and reduce the problem to the case where G is simple. For simple groups we show that the answer is positive if G is split of type A_n or C_n, and negative for groups of other types, except possibly G_2. A key ingredient in the proof of the negative result is a recent formula for the unramified Brauer group of a homogeneous space with connected stabilizers. As a byproduct of our investigation we give an affirmative answer to a question of Grothendieck about the existence of a rational section of the categorical quotient morphism for the conjugating action of G on itself.

Let G be a connected semisimple algebraic group over an algebraically closed field k. In 1965 Steinberg proved that if G is simply connected, then in G there exists a closed irreducible cross-section of the set of closures of regular conjugacy classes. We prove that in arbitrary G such a cross-section exists if and only if the universal covering isogeny Ĝ → G is bijective; this answers Grothendieck's question cited in the epigraph. In particular, for char k = 0, the converse to Steinberg's theorem holds. The existence of a cross-section in G implies, at least for char k = 0, that the algebra k[G]G of class functions on G is generated by rk G elements. We describe, for arbitrary G, a minimal generating set of k[G]G and that of the representation ring of G and answer two Grothendieck's questions on constructing generating sets of k[G]G. We prove the existence of a rational (i.e., local) section of the quotient morphism for arbitrary G and the existence of a rational cross-section in G (for char k = 0, this has been proved earlier); this answers the other question cited in the epigraph. We also prove that the existence of a rational section is equivalent to the existence of a rational W-equivariant map T- - - >G/T where T is a maximal torus of G and W the Weyl group.