Dynamical diseases of brain systems: different routes to epileptic seizures

In this overview, we consider epilepsies as dynamical diseases of brain systems since they are manifestations of the property of neuronal networks to display multistable dynamics. To illustrate this concept we may assume that at least two states of the epileptic brain are possible: the interictal state characterized by a normal, apparently random, steady-state electroencephalography (EEG) ongoing activity, and the ictal state, that is characterized by paroxysmal occurrence of synchronous oscillations and is generally called, in neurology, a seizure. The transition between these two states can either occur: 1) as a continuous sequence of phases, like in some cases of mesial temporal lobe epilepsy (MTLE); or 2) as a sudden leap, like in most cases of absence seizures. In the mathematical terminology of nonlinear systems, we can say that in the first case the system's attractor gradually deforms from an interictal to an ictal attractor. The causes for such a deformation can be either endogenous or external. In this type of ictal transition, the seizure possibly may be anticipated in its early, preclinical phases. In the second case, where a sharp critical transition takes place, we can assume that the system has at least two simultaneous interictal and ictal attractors all the time. To which attractor the trajectories converge, depends on the initial conditions and the system's parameters. An essential question in this scenario is how the transition between the normal ongoing and the seizure activity takes place. Such a transition can occur either due to the influence of external or endogenous factors or due to a random perturbation and, thus, it will be unpredictable. These dynamical changes may not be detectable from the analysis of the ongoing EEG, but they may be observable only by measuring the system's response to externally administered stimuli. In the special cases of reflex epilepsy, the leap between the normal ongoing attractor and the ictal attractor is caused by a well-defined external perturbation. Examples from these different scenarios are presented and discussed.     

Determination of the shear impedance of viscoelastic liquids using cylindrical piezoceramic resonators

In this paper, a new method for determining the rheological parameters of viscoelastic liquids is presented. To this end, we used the perturbation method applied to shear vibrations of cylindrical piezoceramic resonators. The resonator was viscoelastically loaded on the outer cylindrical surface. Due to this loading, the resonant frequency and quality factor of the resonator changed. According to the perturbation method, the change in the complex resonant frequency /spl Delta/~/spl omega/ = /spl Delta/w/sup re/ + j/spl Delta//spl omega//sup im/ is directly proportional to the specific acoustic impedance for cylindrical waves Zc of a viscoelastic liquid surrounding the resonator, i.e., /spl Delta/~w /spl sim/ jZ/sub c/, where j = (-1)/sup 1/2/. Hence, the measurement of the real and imaginary parts of the complex resonant frequency determines the real part, R/sub c/, and imaginary part, X/sub c/, of the complex acoustic impedance for cylindrical waves Z/sub c/ of an investigated liquid. Further-more, the specific impedance Z/sub L/ for plane waves was related to the specific impedance Z/sub c/ for cylindrical waves. Using theoretical formulas established and the results of the experiments performed, the shear storage modulus /spl mu/ and the viscosity /spl eta/ for various liquids (e.g., epoxy resins) were determined. Moreover, the authors derived for cylindrical resonators a formula that relates the shift in resonant frequency to the viscosity of the liquid. This formula is analogous to the Kanazawa-Gordon formula that was derived for planar resonators and Newtonian liquids.     

Tiny Signals from the Human Brain: Acquisition and Processing of Biomagnetic Fields in Magnetoencephalography

Low-temperature superconductivity plays an important role in some specific biomedical applications, and, in particular, in non-invasive imaging methods of human brain activity. Superconducting magnets are indispensable for functional magnetic resonance imaging (fMRI) which allows functional imaging of the brain with high spatial but poor temporal resolution. Superconducting quantum interference devices (SQUIDs) are the most sensitive magnetic field detectors. Up to a few hundreds of SQUIDs are nowdays used in modern whole-head magnetoencephalography (MEG) systems. They allow tracking brain activation with a superior temporal resolution of milliseconds, which is a quintessential condition for the monitoring of brain dynamics and the understanding of information processing in the human brain. We introduce the prerequisites of MEG data acquisition and briefly review two established methods of biomagnetic signal processing: The concept of signal averaging, and the subsequent source identification as a solution of the biomagnetic inverse problem. Beside these standard techniques, we discuss advanced methods for signal processing in MEG, which take into account the frequency content of the recorded signal. We briefly refer to the prospects of Fourier analysis and wavelet transform in MEG data analysis, and suggest matching pursuit as a promising tool for signal decomposition and reconstruction with high resolution in time-frequency plane.     

Comments on ?On Hamiltonian Cycles as Optimal p-Cycles?

For original paper by D.A. Schupke see ibid., vol.9, no 4, p.360-2, April 2005. It is shown that in the above letter by Schupke corollaries related to a necessary condition on the network to ensure that a set of Hamiltonian p-cycles is able to reach the theoretical logical redundancy bound are wrongly calculated     

Pressure distribution in an assembly of wooden cylinders with various aspect ratios under uniaxial confined compression

Understanding how forces propagate in granular assemblages is important for equipment design and process control in many technologies. Yet, it remains poorly understood. In this study, a cuboidal assembly comprising cylinders of various lengths (aspect ratios AR ranging from 0.9 to 3.6) were subjected to uniaxial confined compression tests. Samples were vertically compressed until the top platen exerted a pressure of 50 kPa on the uppermost particles. This maximum pressure corresponds to the hydrostatic pressure of an approximately 15 m high column of chopped wood that may be encountered in real storage structures. The nonlinear loading curves were obtained depended on the aspect ratios of the cylinders. The modulus of elasticity, calculated from the linear elastic part of the stress–strain curve, monotonically decreased from 10.2 to 8.6 MPa as the aspect ratio increased from 1.2 to 3.6. The elastic modulus and volume fraction exhibited similar trends as functions of the aspect ratio. The horizontal-to-vertical pressure ratio was calculated as the horizontal pressure exerted on the wider walls to the vertical pressure exerted on the top lid during loading–unloading cycles. For ARs up to 3.6, the pressure ratio was approximately 0.31; for the longest cylinders (AR = 3.6), it decreased to approximately 0.27, probably because the assumption of the representative chamber volume was invalidated at this AR.     

ATP and Presentation Service for Mizar Formalizations

This paper describes the Automated Reasoning for Mizar ( $\textsf{Miz}\mathbb{AR}$ ) service, which integrates several automated reasoning, artificial intelligence, and presentation tools with Mizar and its authoring environment. The service provides ATP assistance to Mizar authors in finding and explaining proofs, and offers generation of Mizar problems as challenges to ATP systems. The service is based on a sound translation from the Mizar language to that of first-order ATP systems, and relies on the recent progress in application of ATP systems in large theories containing tens of thousands of available facts. We present the main features of $\textsf{Miz}\mathbb{AR}$ services, followed by an account of initial experiments in finding proofs with the ATP assistance. Our initial experience indicates that the tool offers substantial help in exploring the Mizar library and in preparing new Mizar articles.     

Example for equivalence of dual and information-based optimal control

An information-based control (IBC) has been formulated for a class of dual control problems with quadratic cost and unknown, constant parameters. Simple dual control problem has been solved by dynamic programming. Then, the solution was compared with the solution obtained by IBC. It has been shown that an appropriate choice of the intensity of learning allows to recover the optimal dual control for at least one nontrivial class of dual control problems.     

The motion planning problem and exponential stabilisation of a heavy chain. Part I†

A model of a heavy chain system with a punctual load (tip mass) in the form of a system of partial differential equations is interpreted as an abstract semigroup system on a Hilbert state space. Our aim is to solve the output motion planning problem of the same nature as in the case of an unloaded heavy chain (Grabowski, P. (2003 Grabowski, P. 2003. Abstract Semigroup Model of Heavy Chain System with Application to a Motion Planning Problem. Proceedings of 9th IEEE International Conference: Methods and Models in Automation and Robotics. 25–28 August2003, Mi?dzyzdroje, Poland. pp.77–86. (IS1-2-3.PDF) [Google Scholar]), ‘Abstract Semigroup Model of Heavy Chain System with Application to a Motion Planning Problem’, in Proceedings of 9th IEEE International Conference: Methods and Models in Automation and Robotics, 25–28 August, Mi?dzyzdroje, Poland, pp. 77–86 (IS1-2-3.PDF)). In order to solve this problem we first analyse its well-posedness and some basic properties. Next, we solve the output motion planning problem using a substitute of the inverse of the input–output operator represented in terms of the Laplace transforms. A problem of exponential stabilisation is also formulated and solved using a stabiliser of the colocated type. The exponential stabilisation is proved using the method of Lyapunov functionals combined with some frequency-domain tools. The method of Lyapunov functionals can be replaced by the spectral or exact controllability approach as shown in the second part (Grabowski, P. (2008 Grabowski, P. 2008. ‘The Motion Planning Problem and Exponential Stabilisation of a Heavy Chain. Part II’. Opuscula Mathematica, 28: 481–505. (2008) (Special issue dedicated to the memory of Professor Andrzej Lasota) [Google Scholar]), ‘The Motion Planning Problem and Exponential Stabilisation of a Heavy Chain. Part II’, Opuscula Mathematica, 28 (2008 Grabowski, P. 2008. ‘The Motion Planning Problem and Exponential Stabilisation of a Heavy Chain. Part II’. Opuscula Mathematica, 28: 481–505. (2008) (Special issue dedicated to the memory of Professor Andrzej Lasota) [Google Scholar]) (Special issue dedicated to the memory of Professor Andrzej Lasota), 481–505) of the present article. A laboratory setup which allows verification of the results in practice is described in detail. Its dynamical model is used as an example to illustrate the theoretical results.     

Analytical stable CGPC design for minimum-phase systems

The continuous-time generalized predictive control (CGPC) using a long horizon cost function has superior robustness as compared to several other control strategies suitable for adaptive control. The main purpose of this paper is to put forward an analytical, explicit stable CGPC control design method for minimum-phase SISO systems that is based on a set of closed-loop characteristics with definite time-domain specifications. Explicit formulae for closed-loop characteristic polynomials are given and then the prototype design characteristic polynomials are catalogued that can serve as a basis for fully analytical design procedure assuring both the nominal stability and nominal performance specifications. A numerical example is given in order to illustrate the approach.     

CHANGES OF RHEOLOGICAL PROPERTIES OF APPLE TISSUE UNDERGOING CONVECTIVE DRYING

ABSTRACT

The aim of this work was to investigate rheological properties of apple cubes undergoing convective drying. Compression-relaxation test was used to follow changes of properties under investigation.

Raw apple appeared to be very heterogeneous material from the rheological point of view. The relationship between stress and strain was concave downwards and the concavity increased until water content of 2·5 g/g d.m. was reached. Then the relationship begun to straighten and for dry material developed stress was linearly dependent on strain. The resistance of deformation decreased with decreasing water content. Analysis of relaxation showed that the rate of relaxation increased with decreasing water content and the unrelaxed stress was smaller the lower was the water content.

Apple cubes undergoing drying are pictured as material composed of three compartments with different rheological properties. The outer layer is dry, inelastic and difficult to deform. Underneath is moist material with no turgor and relatively easy to compress, and the core with properties of raw apples. During drying the second layer grows in expense of the core and porous structure with many voids filled with air is formed. Share of each compartment in the volume of apple cube undergoing drying affects average rheological properties of the material.