Noncommutative Toda Chains, Hankel Quasideterminants And Painlev'e II Equation

We construct solutions of an infinite Toda system and an analogue of the Painlev'e II equation over noncommutative differential division rings in terms of quasideterminants of Hankel matrices.Comment: 16 pp; final revised version, will appear in J.Phys. A, minor changes (typos corrected following the Referee's List, aknowledgements and a new reference added

Building the field of health policy and systems research: framing the questions.

In the first of a series of articles addressing the current challenges and opportunities for the development of Health Policy & Systems Research (HPSR), Kabir Sheikh and colleagues lay out the main questions vexing the field

Quasideterminant solutions of a non-Abelian Hirota-Miwa equation

A non-Abelian version of the Hirota-Miwa equation is considered. In an earlier paper [Nimmo (2006) J. Phys. A: Math. Gen. \textbf{39}, 5053-5065] it was shown how solutions expressed as quasideterminants could be constructed for this system by means of Darboux transformations. In this paper we discuss these solutions from a different perspective and show that the solutions are quasi-Pl\"{u}cker coordinates and that the non-Abelian Hirota-Miwa equation may be written as a quasi-Pl\"{u}cker relation. The special case of the matrix Hirota-Miwa equation is also considered using a more traditional, bilinear approach and the techniques are compared

Matrix solutions of a noncommutative KP equation and a noncommutative mKP equation

Matrix solutions of a noncommutative KP and a noncommutative mKP equation which can be expressed as quasideterminants are discussed. In particular, we investigate interaction properties of two-soliton solutions.Comment: 2 figure

Substrate inhibition imposes fitness penalty at high protein stability

Proteins are only moderately stable. It has long been debated whether this narrow range of stabilities is solely a result of neutral drift towards lower stability or purifying selection against excess stability is also at work - for which no experimental evidence was found so far. Here we show that mutations outside the active site in the essential E. coli enzyme adenylate kinase result in stability-dependent increase in substrate inhibition by AMP, thereby impairing overall enzyme activity at high stability. Such inhibition caused substantial fitness defects not only in the presence of excess substrate but also under physiological conditions. In the latter case, substrate inhibition caused differential accumulation of AMP in the stationary phase for the inhibition prone mutants. Further, we show that changes in flux through Adk could accurately describe the variation in fitness effects. Taken together, these data suggest that selection against substrate inhibition and hence excess stability may have resulted in a narrow range of optimal stability observed for modern proteins.Comment: 30 pages, 6 figures, 1 table, Supplementary figures and tables - 6 page

Logarithmic behavior of degradation dynamics in metal--oxide semiconductor devices

In this paper the authors describe a theoretical simple statistical modelling of relaxation process in metal-oxide semiconductor devices that governs its degradation. Basically, starting from an initial state where a given number of traps are occupied, the dynamics of the relaxation process is measured calculating the density of occupied traps and its fluctuations (second moment) as function of time. Our theoretical results show a universal logarithmic law for the density of occupied traps $\bar{} \sim \phi (T,E_{F}) (A+B \ln t)$, i.e., the degradation is logarithmic and its amplitude depends on the temperature and Fermi Level of device. Our approach reduces the work to the averages determined by simple binomial sums that are corroborated by our Monte Carlo simulations and by experimental results from literature, which bear in mind enlightening elucidations about the physics of degradation of semiconductor devices of our modern life

Short-Pulse, Compressed Ion Beams at the Neutralized Drift Compression Experiment

We have commenced experiments with intense short pulses of ion beams on the Neutralized Drift Compression Experiment (NDCX-II) at Lawrence Berkeley National Laboratory, with 1-mm beam spot size within 2.5 ns full-width at half maximum. The ion kinetic energy is 1.2 MeV. To enable the short pulse duration and mm-scale focal spot radius, the beam is neutralized in a 1.5-meter-long drift compression section following the last accelerator cell. A short-focal-length solenoid focuses the beam in the presence of the volumetric plasma that is near the target. In the accelerator, the line-charge density increases due to the velocity ramp imparted on the beam bunch. The scientific topics to be explored are warm dense matter, the dynamics of radiation damage in materials, and intense beam and beam-plasma physics including select topics of relevance to the development of heavy-ion drivers for inertial fusion energy. Below the transition to melting, the short beam pulses offer an opportunity to study the multi-scale dynamics of radiation-induced damage in materials with pump-probe experiments, and to stabilize novel metastable phases of materials when short-pulse heating is followed by rapid quenching. First experiments used a lithium ion source; a new plasma-based helium ion source shows much greater charge delivered to the target.Comment: 4 pages, 2 figures, 1 table. Submitted to the proceedings for the Ninth International Conference on Inertial Fusion Sciences and Applications, IFSA 201

On a direct approach to quasideterminant solutions of a noncommutative KP equation

A noncommutative version of the KP equation and two families of its solutions expressed as quasideterminants are discussed. The origin of these solutions is explained by means of Darboux and binary Darboux transformations. Additionally, it is shown that these solutions may also be verified directly. This approach is reminiscent of the wronskian technique used for the Hirota bilinear form of the regular, commutative KP equation but, in the noncommutative case, no bilinearising transformation is available.Comment: 11 page