24 research outputs found
Topological monodromy as an obstruction to Hamiltonization of nonholonomic systems: pro or contra?
The phenomenon of a topological monodromy in integrable Hamiltonian and
nonholonomic systems is discussed. An efficient method for computing and
visualizing the monodromy is developed. The comparative analysis of the
topological monodromy is given for the rolling ellipsoid of revolution problem
in two cases, namely, on a smooth and on a rough plane. The first of these
systems is Hamiltonian, the second is nonholonomic. We show that, from the
viewpoint of monodromy, there is no difference between the two systems, and
thus disprove the conjecture by Cushman and Duistermaat stating that the
topological monodromy gives a topological obstruction for Hamiltonization of
the rolling ellipsoid of revolution on a rough plane.Comment: 31 pages, 11 figure
Effects of memristor-based coupling in the ensemble of FitzHugh-Nagumo elements
In this paper, we study the impact of electrical and memristor-based
couplings on some neuron-like spiking regimes, previously observed in the
ensemble of two identical FitzHugh-Nagumo elements with chemical excitatory
coupling. We demonstrate how increasing strength of these couplings affects on
such stable periodic regimes as spiking in-phase, anti-phase and sequential
activity. We show that the presence of electrical and memristor-based coupling
does not essentially affect regimes of in-phase activity. Such regimes do not
changes remaining stable ones. However, it is not the case for regimes of
anti-phase and sequential activity. All such regimes can transform into
periodic or chaotic ones which are very similar to the regimes of in-phase
activity. Concerning the regimes of sequential activity, this transformation
depends continuously on the coupling parameters, whereas some anti-phase
regimes can disappear via a saddle-node bifurcation and nearby orbits tend to
regimes of in-phase activity. Also, we show that new interesting neuron-like
phenomena can appear from the regimes of sequential activity when increasing
the strength of electrical and/or memristor-based coupling. The corresponding
regimes can be associated with the appearance of spiral attractors containing a
saddle-focus equilibrium with homoclinic orbit and, thus, they correspond to
chaotic motions near the invariant manifold of synchronization, which contains
all in-phase limit cycles. Such new regimes can lead to the emergence of
extreme events in the system of coupled neurons. In particular, the interspike
intervals can become arbitrarily large when orbit pass very close to the
saddle-focus. Finally, we show that the further increase in the strength of
electrical coupling and/or memristor-based coupling leads to decreasing
interspike intervals and, thus, it helps to avoid such extreme behavior
Integrability in SFT and new representation of KP tau-function
We are investigating the properties of vacuum and boundary states in the CFT
of free bosons under the conformal transformation. We show that transformed
vacuum (boundary state) is given in terms of tau-functions of dispersionless KP
(Toda) hierarchies. Applications of this approach to string field theory is
considered. We recognize in Neumann coefficients the matrix of second
derivatives of tau-function of dispersionless KP and identify surface states
with the conformally transformed vacuum of free field theory.Comment: 25 pp, LaTeX, reference added in the Section 3.
Assemblathon 2: evaluating de novo methods of genome assembly in three vertebrate species
Background: The process of generating raw genome sequence data continues to become cheaper, faster, and more accurate. However, assembly of such data into high-quality, finished genome sequences remains challenging. Many genome assembly tools are available, but they differ greatly in terms of their performance (speed, scalability, hardware requirements, acceptance of newer read technologies) and in their final output (composition of assembled sequence). More importantly, it remains largely unclear how to best assess the quality of assembled genome sequences. The Assemblathon competitions are intended to assess current state-of-the-art methods in genome assembly. Results: In Assemblathon 2, we provided a variety of sequence data to be assembled for three vertebrate species (a bird, a fish, and snake). This resulted in a total of 43 submitted assemblies from 21 participating teams. We evaluated these assemblies using a combination of optical map data, Fosmid sequences, and several statistical methods. From over 100 different metrics, we chose ten key measures by which to assess the overall quality of the assemblies. Conclusions: Many current genome assemblers produced useful assemblies, containing a significant representation of their genes and overall genome structure. However, the high degree of variability between the entries suggests that there is still much room for improvement in the field of genome assembly and that approaches which work well in assembling the genome of one species may not necessarily work well for another
On the origin of chaotic attractors with two zero Lyapunov exponents in a system of five biharmonically coupled phase oscillators
We study chaotic dynamics in a system of four differential equations
describing the dynamics of five identical globally coupled phase oscillators
with biharmonic coupling. We show that this system exhibits strange spiral
attractors (Shilnikov attractors) with two zero (indistinguishable from zero in
numerics) Lyapunov exponents in a wide region of the parameter space. We
explain this phenomenon by means of bifurcation analysis of the
three-dimensional Poincar\'e map for the system under consideration. We show
that the chaotic dynamics develop here near a codimension three bifurcation,
when a periodic orbit (fixed point in the Poincar\'e map) has the triplet of multipliers. As it is known, the asymptotic flow normal form for this
bifurcation coincides with the three-dimensional
Arneodo-Coullet-Spiegel-Tresser (ACST) system in which spiral attractors exist.
Based on this, we conclude that the additional near-zero Lyapunov exponent for
orbits in the observed attractors appear due to the fact that the corresponding
three-dimensional Poincar\'e map is close to the time-shift map of the
three-dimensional ACST-system.Comment: 18 pages, 7 figure
On 1:3 Resonance Under Reversible Perturbations of Conservative Cubic Hénon Maps
We consider reversible nonconservative perturbations of the conservative cubic Hénon maps and study their influence on the 1:3 resonance, i. e., bifurcations of fixed points with eigenvalues . It follows from [1] that this resonance is degenerate for when the corresponding fixed point is elliptic. We show that bifurcations of this point under reversible perturbations give rise to four 3-periodic orbits, two of them are symmetric and conservative (saddles in the case of map and elliptic orbits in the case of map ), the other two orbits are nonsymmetric and they compose symmetric couples of dissipative orbits (attracting and repelling orbits in the case of map and saddles with the Jacobians less than 1 and greater than 1 in the case of map ). We show that these local symmetry-breaking bifurcations can lead to mixed dynamics due to accompanying global reversible bifurcations of symmetric nontransversal homo- and heteroclinic cycles. We also generalize the results of [1] to the case of the p:q resonances with odd q and show that all of them are also degenerate for the maps with .
EIDSS Application for CCHF Foci Activity Epi-Analysis and Prediction in Kazakhstan
Electronic Integrated Disease Surveillance System (EIDSS) was used to applied epi-analysis and prediction capabilities for situation in CCHF foci in Kazakhstan. Three indicators were used: population density in the CCHF-disadvantaged area; tick infection rate; human incidence rate. Maps generated in EIDSS allowed visualizing information and conducting a milti-factor epi-analysis. The CCHF outbreaks risk areas were identified. EIDSS software is easy to use, available for practical epidemiologists and can be used for analysis and prediction of vector-borne virus infections foci. EIDSS can serve as a basic working tool for field epidemiologists and the basis for managerial decision-making by the concerned ministries
New clathrate-like compound Eu7Cu44Sb23-δ: synthesis, crystal and electronic structure, and the effect of As-for-Sb substitution on the magnetic properties
A new intermetallic compound, ternary antimonide Eu7Cu44Sb23-delta [Fm-3m, a = 17.4346(1)angstrom, delta = 0.5(1)] is reported. The compound forms a continuous substitutional solid solution with its Eu7Cu44As23 archetype. The gradual substitution of Sb for As evokes partial disorder in the copper-pnictogen framework that becomes more pronounced with an increase of the Sb content and changes magnetic properties. Whereas Eu7Cu44As23 is metallic ferromagnet below 17 K, Eu7Cu44Sb23-delta shows paramagnetic behavior down to 1.8 K according to the magnetic measurements, while retaining metallic properties according to the DFT calculations. The origin of the disorder, the structure-property relationships, as well as prospects of further substitution in the anionic sub lattice are discussed