Integrative Approach - New Level Knowledge of Functions: Opportunities and Prospects

In this article, the example of the mechanisms of heart rhythmogenesis in the intact organism is used to demonstrate the new capabilities provided by an integrative approach. It is shown that the rhythm is formed in the brain, transmitted to the heart in the form of signals along the vagus nerves and reproduces the heart. Evidence: the heart rhythm reproduces the natural efferent signals in the vagus nerves in the cardio-respiratory synchronism and in the intact organism sino-atrial node performs the functions of the latent pacemaker. Integration of the two hierarchical levels of rhythmogenesis (brain and intracardiac) provides the reliability and functional perfection of cardiac rhythm generation in the body. It is expedient to extend the presented methodology for scientific analysis to other organism systems

Quantum Geometry of 3-Dimensional Lattices and Tetrahedron Equation

We study geometric consistency relations between angles of 3-dimensional (3D) circular quadrilateral lattices -- lattices whose faces are planar quadrilaterals inscribable into a circle. We show that these relations generate canonical transformations of a remarkable "ultra-local" Poisson bracket algebra defined on discrete 2D surfaces consisting of circular quadrilaterals. Quantization of this structure allowed us to obtain new solutions of the tetrahedron equation (the 3D analog of the Yang-Baxter equation) as well as reproduce all those that were previously known. These solutions generate an infinite number of non-trivial solutions of the Yang-Baxter equation and also define integrable 3D models of statistical mechanics and quantum field theory. The latter can be thought of as describing quantum fluctuations of lattice geometry.Comment: Plenary talk at the XVI International Congress on Mathematical Physics, 3-8 August 2009, Prague, Czech Republi

An integrable 3D lattice model with positive Boltzmann weights

In this paper we construct a three-dimensional (3D) solvable lattice model with non-negative Boltzmann weights. The spin variables in the model are assigned to edges of the 3D cubic lattice and run over an infinite number of discrete states. The Boltzmann weights satisfy the tetrahedron equation, which is a 3D generalisation of the Yang-Baxter equation. The weights depend on a free parameter 0<q<1 and three continuous field variables. The layer-to-layer transfer matrices of the model form a two-parameter commutative family. This is the first example of a solvable 3D lattice model with non-negative Boltzmann weights.Comment: HyperTex is disabled due to conflicts with some macro

Exact solution of the Faddeev-Volkov model

The Faddeev-Volkov model is an Ising-type lattice model with positive Boltzmann weights where the spin variables take continuous values on the real line. It serves as a lattice analog of the sinh-Gordon and Liouville models and intimately connected with the modular double of the quantum group U_q(sl_2). The free energy of the model is exactly calculated in the thermodynamic limit. In the quasi-classical limit c->infinity the model describes quantum fluctuations of discrete conformal transformations connected with the Thurston's discrete analogue of the Riemann mappings theorem. In the strongly-coupled limit c->1 the model turns into a discrete version of the D=2 Zamolodchikov's ``fishing-net'' model.Comment: 4 page

Diagnostics of plasma in the ionospheric D-region: detection and study of different ionospheric disturbance types

Here we discuss our recent investigations of the ionospheric plasma by using very low and low frequency (VLF/LF) radio waves. We give a review of how to detect different low ionospheric reactions (sudden ionospheric disturbances) to various terrestrial and extra-terrestrial events, show their classification according to intensity and time duration, and present some methods for their detections in time and frequency domains. Investigations of detection in time domain are carried out for intensive long-lasting perturbations induced by solar X-ray flares and for short-lasting perturbations caused by gamma ray bursts. We also analyze time variations of signals used in the low ionospheric monitoring after earthquake events. In addition, we describe a procedure for the detection of acoustic and gravity waves from the VLF/LF signal analysis in frequency domain. The research of the low ionospheric plasma is based on data collected by the VLF/LF receivers located in Belgrade, Serbia

Fractional Brownian fields, duality, and martingales

In this paper the whole family of fractional Brownian motions is constructed as a single Gaussian field indexed by time and the Hurst index simultaneously. The field has a simple covariance structure and it is related to two generalizations of fractional Brownian motion known as multifractional Brownian motions. A mistake common to the existing literature regarding multifractional Brownian motions is pointed out and corrected. The Gaussian field, due to inherited ``duality'', reveals a new way of constructing martingales associated with the odd and even part of a fractional Brownian motion and therefore of the fractional Brownian motion. The existence of those martingales and their stochastic representations is the first step to the study of natural wavelet expansions associated to those processes in the spirit of our earlier work on a construction of natural wavelets associated to Gaussian-Markov processes.Comment: Published at http://dx.doi.org/10.1214/074921706000000770 in the IMS Lecture Notes Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org