Solution of the pulse width modulation problem using orthogonal polynomials and Korteweg-de Vries equations

The mathematical underpinning of the pulse width modulation (PWM) technique lies in the attempt to represent “accurately” harmonic waveforms using only square forms of a fixed height. The accuracy can be measured using many norms, but the quality of the approximation of the analog signal (a harmonic form) by a digital one (simple pulses of a fixed high voltage level) requires the elimination of high order harmonics in the error term. The most important practical problem is in “accurate” reproduction of sine-wave using the same number of pulses as the number of high harmonics eliminated. We describe in this paper a complete solution of the PWM problem using Padé approximations, orthogonal polynomials, and solitons. The main result of the paper is the characterization of discrete pulses answering the general PWM problem in terms of the manifold of all rational solutions to Korteweg-de Vries equations.

Composite fermions and bosons: An invitation to electron masquerade in Quantum Hall

The two-dimensional electron gas formed at the semiconductor heterointerface is a theater for many intriguing plays of physics. The fractional quantum Hall effect (FQHE), which occurs in strong magnetic fields and low temperatures, is the most fascinating of them. The concept of composite fermions and bosons not only is beautiful by itself but also has proved highly successful in providing pictorial interpretation of the phenomena associated with the FQHE.

Visualization of Cavitated Vessels in Winter and Refilled Vessels in Spring in Diffuse-Porous Trees by Cryo-Scanning Electron Microscopy1

Xylem cavitation in winter and recovery from cavitation in the spring were visualized in two species of diffuse-porous trees, Betula platyphylla var. japonica Hara and Salix sachalinensis Fr. Schm., by cryo-scanning electron microscopy after freeze-fixation of living twigs. Water in the vessel lumina of the outer three annual rings of twigs of B. platyphylla var. japonica and of S. sachalinensis gradually disappeared during the period from January to March, an indication that cavitation occurs gradually in these species during the winter. In April, when no leaves had yet expanded, the lumina of most of the vessels of both species were filled with water. Many vessel lumina in twigs of both species were filled with water during the period from the subsequent growth season to the beginning of the next winter. These observations indicate that recovery in spring occurs before the onset of transpiration and that water transport through twigs occurs during the subsequent growing season. We found, moreover, that vessels repeat an annual cycle of winter cavitation and spring recovery from cavitation for several years until irreversible cavitation occurs.

High resolution ultrastructural mapping of total calcium: electron spectroscopic imaging/electron energy loss spectroscopy analysis of a physically/chemically processed nerve-muscle preparation.

We report on a procedure for tissue preparation that combines thoroughly controlled physical and chemical treatments: quick-freezing and freeze-drying followed by fixation with OsO4 vapors and embedding by direct resin infiltration. Specimens of frog cutaneous pectoris muscle thus prepared were analyzed for total calcium using electron spectroscopic imaging/electron energy loss spectroscopy (ESI/EELS) approach. The preservation of the ultrastructure was excellent, with positive K/Na ratios revealed in the fibers by x-ray microanalysis. Clear, high-resolution EELS/ESI calcium signals were recorded from the lumen of terminal cisternae of the sarcoplasmic reticulum but not from longitudinal cisternae, as expected from previous studies carried out with different techniques. In many mitochondria, calcium was below detection whereas in others it was appreciable although at variable level. Within the motor nerve terminals, synaptic vesicles as well as some cisternae of the smooth endoplasmic reticulum yielded positive signals at variance with mitochondria, that were most often below detection. Taken as a whole, the present study reveals the potential of our experimental approach to map with high spatial resolution the total calcium within individual intracellular organelles identified by their established ultrastructure, but only where the element is present at high levels.

The old problems of glass and the glass transition, and the many new twists.

In this paper I review the ways in which the glassy state is obtained both in nature and in materials science and highlight a "new twist"--the recent recognition of polymorphism within the glassy state. The formation of glass by continuous cooling (viscous slowdown) is then examined, the strong/fragile liquids classification is reviewed, and a new twist-the possibility that the slowdown is a result of an avoided critical point-is noted. The three canonical characteristics of relaxing liquids are correlated through the fragility. As a further new twist, the conversion of strong liquids to fragile liquids by pressure-induced coordination number increases is demonstrated. It is then shown that, for comparable systems, it is possible to have the same conversion accomplished via a first-order transition within the liquid state during quenching. This occurs in the systems in which "polyamorphism" (polymorphism in the glassy state) is observed, and the whole phenomenology is accounted for by Poole's bond-modified van der Waals model. The sudden loss of some liquid degrees of freedom through such weak first-order transitions is then related to the polyamorphic transition between native and denatured hydrated proteins, since the latter are also glass-forming systems--water-plasticized, hydrogen bond-cross-linked chain polymers (and single molecule glass formers). The circle is closed with a final new twist by noting that a short time scale phenomenon much studied by protein physicists-namely, the onset of a sharp change in d/dT ( is the Debye-Waller factor)--is general for glass-forming liquids, including computer-simulated strong and fragile ionic liquids, and is closely correlated with the experimental glass transition temperature. The latter thus originates in strong anharmonicity in certain components of the vibrational density of states, which permits the system to access the multiple minima of its configuration space. The connection between the anharmonicity in these modes, vibrational localization, the Kauzmann temperature, and the fragility of the liquid is proposed as the key problem in glass science.

A multimer model for P680, the primary electron donor of photosystem II.

We consider a model of the photosystem II (PS II) reaction center in which its spectral properties result from weak (approximately 100 cm-1) excitonic interactions between the majority of reaction center chlorins. Such a model is consistent with a structure similar to that of the reaction center of purple bacteria but with a reduced coupling of the chlorophyll special pair. We find that this model is consistent with many experimental studies of PS II. The similarity in magnitude of the exciton coupling and energetic disorder in PS II results in the exciton states being structurally highly heterogeneous. This model suggests that P680, the primary electron donor of PS II, should not be considered a dimer but a multimer of several weakly coupled pigments, including the pheophytin electron acceptor. We thus conclude that even if the reaction center of PS II is structurally similar to that of purple bacteria, its spectroscopy and primary photochemistry may be very different.

Types of evolutionary stability and the problem of cooperation.

The evolutionary stability of cooperation is a problem of fundamental importance for the biological and social sciences. Different claims have been made about this issue: whereas Axelrod and Hamilton's [Axelrod, R. & Hamilton, W. (1981) Science 211, 1390-1398] widely recognized conclusion is that cooperative rules such as "tit for tat" are evolutionarily stable strategies in the iterated prisoner's dilemma (IPD), Boyd and Lorberbaum [Boyd, R. & Lorberbaum, J. (1987) Nature (London) 327, 58-59] have claimed that no pure strategy is evolutionarily stable in this game. Here we explain why these claims are not contradictory by showing in what sense strategies in the IPD can and cannot be stable and by creating a conceptual framework that yields the type of evolutionary stability attainable in the IPD and in repeated games in general. Having established the relevant concept of stability, we report theorems on some basic properties of strategies that are stable in this sense. We first show that the IPD has "too many" such strategies, so that being stable does not discriminate among behavioral rules. Stable strategies differ, however, on a property that is crucial for their evolutionary survival--the size of the invasion they can resist. This property can be interpreted as a strategy's evolutionary robustness. Conditionally cooperative strategies such as tit for tat are the most robust. Cooperative behavior supported by these strategies is the most robust evolutionary equilibrium: the easiest to attain, and the hardest to disrupt.