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## High-frequency forced oscillations in neuronlike elements

We analyzed a generic relaxation oscillator under moderately strong forcing at a frequency much greater that the natural intrinsic frequency of the oscillator. Additionally, the forcing is of the same sign and, thus, has a nonzero average, matching neuroscience applications. We found that, first, the transition to high-frequency synchronous oscillations occurs mostly through periodic solutions with virtually no chaotic regimes present. Second, the amplitude of the high-frequency oscillations is large, suggesting an important role for these oscillations in applications. Third, the 1:1 synchronized solution may lose stability, and, contrary to other cases, this occurs at smaller, but not at higher frequency differences between intrinsic and forcing oscillations. We analytically built a map that gives an explanation of these properties. Thus, we found a way to substantially “overclock” the oscillator with only a moderately strong external force. Interestingly, in application to neuroscience, both excitatory and inhibitory inputs can force the high-frequency oscillations.

In this paper, we propose an adaptive model of data storage in a heterogeneous distributed cloud environment. Our system utilizes the methods of secret sharing schemes and error correction codes based on Redundant Residue Number System (RRNS). We consider data uploading, storing and downloading. To minimize data access, we use data transfer mechanism between cloud providers. We provide theoretical analysis and experimental evaluation of our scheme with six real data storage providers. We show how dynamic adaptive strategies not only increase security, reliability, and reduction of data redundancy but allow processing encrypted data. We also discuss potentials of this approach, and address methods for mitigating the risks of confidentiality, integrity, and availability associated with the loss of information, denial of access for a long time, and information leakage.

We study the stability conditions of the multiserver queueing system in which each customer requires a random number of servers simultaneously. The input flow is supposed to be a regenerative one and service times of a given customer are independent at the occupied servers. The service time has an exponential, phase-type or hyper-exponential distribution. We define an auxiliary service process that is the number of completed services by all m servers under the assumption that there are always customers in the system. Then we construct the sequence of common regeneration points for the regenerative input flow and the auxiliary service process. It allows us to deduce the stability criterion of the model under consideration. It turns out that the stability condition does not depend on the structure of the input flow, only the rate of this process plays a role. Nevertheless the distribution of the service time is a very important factor. We give examples which show that the stability condition can not be expressed in terms of the mean of the service time.

The concept of regression is considered with an emphasis on the differences between the positions of Freud and Jung regarding its significance. The paper discusses the results of experimental analyses of individual experience dynamics (from gene expression changes and impulse neuronal activity in animals to prosocial behaviour in healthy humans at different ages, and humans in chronic pain) in those situations where regression occurs: stress, disease, learning, highly emotional states and alcohol intoxication. Common mechanisms of regression in all these situations are proposed. The mechanisms of regression can be described as reversible dedifferentiation, which is understood as a relative increase of the representation of low-differentiated (older) systems in the actualized experience. In all of the cases of dedifferentiation mentioned above, the complexity of the systemic organization of behaviour significantly decreases.

Movement control of artificial limbs has made big advances in recent years. New sensor and control technology enhanced the functionality and usefulness of artificial limbs to the point that complex movements, such as grasping, can be performed to a limited extent. To date, the most successful results were achieved by applying recurrent neural networks (RNNs), However, in the domain of artificial hands, experiments so far were limited to non-mobile wrists, which significantly reduces the functionality of such prostheses. In this paper, for the first time, we present empirical results on gesture recognition with both mobile and non-mobile wrists. Furthermore, we demonstrate that recurrent neural networks with simple recurrent units (SRU) outperform regular RNNs in both cases in terms of gesture recognition accuracy, on data acquired by an arm band sensing electromagnetic signals from arm muscles (via surface electromyography or sEMG). Finally, we show that adding domain adaptation techniques to continuous gesture recognition with RNN improves the transfer ability between subjects, where a limb controller trained on data from one person is used for another person.

This paper is focused on stability conditions of a multi-server queueing system with regenerative input flow where a random number of servers is simultaneously required for each customer and each server's completion time is constant. It turns out that the stability condition depends on the rate of the input flow and not on its structure.

We consider certain spaces of functions on the circle, which naturally appear in harmonic analysis, and superposition operators on these spaces. We study the following question: which functions have the property that each their superposition with a homeomorphism of the circle belongs to a given space? We also study the multidimensional case.

We consider the spaces of functions on the m-dimensional torus, whose Fourier transform is p -summable. We obtain estimates for the norms of the exponential functions deformed by a C1 -smooth phase. The results generalize to the multidimensional case the one-dimensional results obtained by the author earlier in “Quantitative estimates in the Beurling—Helson theorem”, Sbornik: Mathematics, 201:12 (2010), 1811 – 1836.

We consider the spaces of function on the circle whose Fourier transform is p-summable. We obtain estimates for the norms of exponential functions deformed by a C1 -smooth phase.

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.