36,788 research outputs found
An introduction to regular splines and their application for initial value problems of ordinary differential equations
This report describes an application of the general method of integrating initial value problems by means of regular splines for equations with movable singularities. By defining the families of functions that make up the regular splines such that they closely resemble the behaviour of the solutions of the differential equation, it is possible to trace the location of the singularities very precisely.
To demonstrate this we treat Riccati differential equations. These are known to possess solutions with poles, usually of the first order. This type of differential equation or system arises in describing chemical or biological processes or more general control processes.
To make the report self contained it starts with an introduction to regular splines and develops the algebraic tools for the manipulation of rational splines. After the description of the integration procedure, the asymptotic behaviour of the systematic error is investigated. An example exhibits the results obtained from the program given in Appendix A. Then Riccati equations are introduced and methods for the determination of the singularities are developed. These methods are tested numerically with several examples. The results are given in Appendix B
Double Checking the Doctor’s Credentials: The New Medical Expert Qualification Statute of MCARE
The problem of rapidly escalating premiums paid by doctors for medical malpractice insurance has plagued Pennsylvania in the last decade. These rates have uprooted Pennsylvania doctors from their local practices and hospitals in favor of out-of-state locations with lower rates. Furthermore, some Pennsylvania doctors and hospitals specializing in high-risk procedures have refused to perform high-risk surgeries or have limited their practice to more routine procedures
Quantum cryptography as a retrodiction problem
We propose a quantum key distribution protocol based on a quantum
retrodiction protocol, known as the Mean King problem. The protocol uses a two
way quantum channel. We show security against coherent attacks in a
transmission error free scenario, even if Eve is allowed to attack both
transmissions. This establishes a connection between retrodiction and key
distribution.Comment: 5 pages, 1 figur
Quark-Gluon-Plasma Formation at SPS Energies?
By colliding ultrarelativistic ions, one achieves presently energy densities
close to the critical value, concerning the formation of a quark-gluon-plasma.
This indicates the importance of fluctuations and the necessity to go beyond
the investigation of average events. Therefore, we introduce a percolation
approach to model the final stage ( fm/c) of ion-ion collisions, the
initial stage being treated by well-established methods, based on strings and
Pomerons. The percolation approach amounts to finding high density domains, and
treating them as quark-matter droplets. In this way, we have a {\bf realistic,
microscopic, and Monte--Carlo based model which allows for the formation of
quark matter.} We find that even at SPS energies large quark-matter droplets
are formed -- at a low rate though. In other words: large quark-matter droplets
are formed due to geometrical fluctuation, but not in the average event.Comment: 7 Pages, HD-TVP-94-6 (1 uuencoded figure
Empirical risk minimization as parameter choice rule for general linear regularization methods.
We consider the statistical inverse problem to recover f from noisy measurements Y = Tf + sigma xi where xi is Gaussian white noise and T a compact operator between Hilbert spaces. Considering general reconstruction methods of the form (f) over cap (alpha) = q(alpha) (T*T)T*Y with an ordered filter q(alpha), we investigate the choice of the regularization parameter alpha by minimizing an unbiased estiate of the predictive risk E[parallel to T f - T (f) over cap (alpha)parallel to(2)]. The corresponding parameter alpha(pred) and its usage are well-known in the literature, but oracle inequalities and optimality results in this general setting are unknown. We prove a (generalized) oracle inequality, which relates the direct risk E[parallel to f - (f) over cap (alpha pred)parallel to(2)] with the oracle prediction risk inf(alpha>0) E[parallel to T f - T (f) over cap (alpha)parallel to(2)]. From this oracle inequality we are then able to conclude that the investigated parameter choice rule is of optimal order in the minimax sense. Finally we also present numerical simulations, which support the order optimality of the method and the quality of the parameter choice in finite sample situations
Photo-induced states in a Mott insulator
We investigate the properties of the metallic state obtained by photo-doping
carriers into a Mott insulator. In a strongly interacting system, these
carriers have a long life-time, so that they can dissipate their kinetic energy
to a phonon bath. In the relaxed state, the scattering rate saturates at a
non-zero temperature-independent value, and the momentum-resolved spectral
function features broad bands which differ from the well-defined quasi-particle
bands of a chemically doped system. Our results indicate that a photo-doped
Mott insulator behaves as a bad metal, in which strong scattering between
doublons and holes inhibits Fermi-liquid behavior down to low temperature.Comment: 5 page
Thermalization of a pump-excited Mott insulator
We use nonequilibrium dynamical mean-field theory in combination with a
recently implemented strong-coupling impurity solver to investigate the
relaxation of a Mott insulator after a laser excitation with frequency
comparable to the Hubbard gap. The time evolution of the double occupancy
exhibits a crossover from a strongly damped transient at short times towards an
exponential thermalization at long times. In the limit of strong interactions,
the thermalization time is consistent with the exponentially small decay rate
for artificially created doublons, which was measured in ultracold atomic
gases. When the interaction is comparable to the bandwidth, on the other hand,
the double occupancy thermalizes within a few times the inverse bandwidth along
a rapid thermalization path in which the exponential tail is absent. Similar
behavior can be observed in time-resolved photoemission spectroscopy. Our
results show that a simple quasi-equilibrium description of the electronic
state breaks down for pump-excited Mott insulators characterized by strong
interactions.Comment: 8 pages, 4 figure
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