Dynamic complexity of chaotic transitions in high-dimensional classical dynamics:Leu-Enkephalin folding

Leu-Enkephalin in explicit water is simulated using classical molecular dynamics. A ß-turn transition is investigated by calculating the topological complexity (in the "computational mechanics" framework [J. P. Crutchfield and K. Young, Phys. Rev. Lett., 63, 105 (1989)]) of the dynamics of both the peptide and the neighbouring water molecules. The complexity of the atomic trajectories of the (relatively short) simulations used in this study reflect the degree of phase space mixing in the system. It is demonstrated that the dynamic complexity of the hydrogen atoms of the peptide and almost all of the hydrogens of the neighbouring waters exhibit a minimum precisely at the moment of the ß-turn transition. This indicates the appearance of simplified periodic patterns in the atomic motion, which could correspond to high-dimensional tori in the phase space. It is hypothesized that this behaviour is the manifestation of the effect described in the approach to molecular transitions by Komatsuzaki and Berry [T. Komatsuzaki and R.S. Berry, Adv. Chem. Phys., 123, 79 (2002)], where a "quasi-regular" dynamics at the transition is suggested. Therefore, for the first time, the less chaotic character of the folding transition in a realistic molecular system is demonstrated. © Springer-Verlag Berlin Heidelberg 2006.

Classical and technological convergence:beyond the Solow-Swann model

Recent investigations into cross-country convergence follow Mankiw, Romer, and Weil (1992) in using a log-linear approximation to the Swan-Solow growth model to specify regressions. These studies tend to assume a common and exogenous technology. In contrast, the technology catch-up literature endogenises the growth of technology. The use of capital stock data renders the approximations and over-identification of the Mankiw model unnecessary and enables us, using dynamic panel estimation, to estimate the separate contributions of diminishing returns and technology transfer to the rate of conditional convergence. We find that both effects are important.

Complexity of classical dynamics of molecular systems. I. Methodology

Methods for the calculation of complexity have been investigated as a possible alternative for the analysis of the dynamics of molecular systems. “Computational mechanics” is the approach chosen to describe emergent behavior in molecular systems that evolve in time. A novel algorithm has been developed for symbolization of a continuous physical trajectory of a dynamic system. A method for calculating statistical complexity has been implemented and tested on representative systems. It is shown that the computational mechanics approach is suitable for analyzing the dynamic complexity of molecular systems and offers new insight into the process.

Complexity of classical dynamics of molecular systems. II. Finite statistical complexity of a water-Na+ system

The computational mechanics approach has been applied to the orientational behavior of water molecules in a molecular dynamics simulated water–Na + system. The distinctively different statistical complexity of water molecules in the bulk and in the first solvation shell of the ion is demonstrated. It is shown that the molecules undergo more complex orientational motion when surrounded by other water molecules compared to those constrained by the electric field of the ion. However the spatial coordinates of the oxygen atom shows the opposite complexity behavior in that complexity is higher for the solvation shell molecules. New information about the dynamics of water molecules in the solvation shell is provided that is additional to that given by traditional methods of analysis.

Processing of Knowledge about Optimization of Classical Optimizing Transformations

The article describes the structure of an ontology model for Optimization of a sequential program. The components of an intellectual modeling system for program optimization are described. The functions of the intellectual modeling system are defined.

A Note on a Classical Generating Function for the Jacobi Polynomials

Mathematics Subject Classification: 33C45.

Risk Measures for Classical and Perturbed Risk Processes - a Survey

2000 Mathematics Subject Classification: 60B10, 60G17, 60G51, 62P05.

Partial Ovoids and Partial Spreads of Classical Finite Polar Spaces

2000 Mathematics Subject Classification: 05B25, 51E20.

Calculus of Variations with Classical and Fractional Derivatives

MSC 2010: 49K05, 26A33

On Some Generalizations of Classical Integral Transforms

MSC 2010: 44A15, 44A20, 33C60

Weitzenböck Derivations and Classical Invariant Theory: I. Poincaré Series

2000 Mathematics Subject Classification: 13N15, 13A50, 16W25.

Weitzenböck Derivations and Classical Invariant Theory II: The Symbolic Method

2000 Mathematics Subject Classification: 13N15, 13A50, 13F20.

Nemlineáris dinamika klasszikus növekedési modellekben (Nonlinear dynamics in classical economic growth models)

Ebben a tanulmányban a klasszikus Harrod növekedési modellt nemlineáris kiterjesztéssel, keynesi és schumpeteri tradíciók bevezetésével reprezentatív ügynök modellbe alakítjuk. A híres Lucas kritika igazolásaként megmutatjuk, hogy az intrinsic gazdasági növekedési ütemek trajektóriái vagy egy turbulens káoszba szóródnak szét, vagy egy nagyméretű rendhez vezetnek, ami elsődlegesen a megfelelő fogyasztási függvény típusától függ, s bizonyos paraméterek piaci értékei, pedig csak másodlagos szerepet játszanak. A másik meglepő eredmény empirikus, ami szerint külkereskedelmi többlet, a hazai valuta bizonyos devizapiaci értékei mellett, különös attraktorokat generálhat. _____ In this paper the classical Harrodian growth model is transformed into a representative agent model by its nonlinear extensions and the Keynesian and Schumpeterian traditions. For the proof of the celebrated Lucas critique it is shown that the trajectories of intrinsic economic growth rates either are scattered into a turbulent chaos or lead to a large scale order. It depends on the type of the appropriate consumption function, and the market values of some parameters are playing only secondary role.Another surprising result is empirical: the international trade su±cit may generate strange attractors under some exchange rate values.

Musculoskeletal effects and injury risk in collegiate Indian classical and ballet dancers

Dancers of all forms often engage in aesthetic yet challenging movements. Their training, choreography, and performances require strength, stamina, flexibility, grace, passion, and emotion. Ballet and Bharatanatyam (an Indian classical dance form) dancers utilize two movements in each of their dance forms that are similar—a half-sitting pose and a full-sitting pose, both requiring external rotation of the legs and bending at the knee joints. The purpose of this study was to examine and compare the biomechanics of joint reaction forces and knee angles in both styles of dance for these particular poses. The study included nine female ballet dancers and seven female Bharatanatyam dancers. Hamstring and gastrocnemius flexibility were measured for each dancer. Knee angles, vertical peak forces, and moments were determined for dancers at the lowest point of their bending positions. Mann-Whitney U tests found significant differences in hamstring flexibility, right gastrocnemius flexibility, and knee angles for the full-sitting poses between ballet and Bharatanatyam dancers. No significant difference was found in the vertical peak forces as a ratio to total body weight and moments between the two styles of dance. Further research can be done to more directly assess a difference in injury risk between the ballet and Bharatanatyam dancers.

Jan Steen and The doctor’s visit: Classical Tradition in Golden Age Dutch painting (1st Part)

First one of a two-part analysis on the influence of the Classical Tradition on a favourite theme along the Dutch painters of the Golden Age, The doctor’s visit or The lovesick maiden, especially in the Leiden artist’s production, Jan Steen (1626-1679).