1,492 research outputs found
Trotter-Kato product formulae in Dixmier ideal
It is shown that for a certain class of the Kato functions the Trotter-Kato
product formulae converge in Dixmier ideal C 1, in topology, which is
defined by the 1,-norm. Moreover, the rate of convergence in
this topology inherits the error-bound estimate for the corresponding
operator-norm convergence. 1 since [24], [14]. Note that a subtle point of this
program is the question about the rate of convergence in the corresponding
topology. Since the limit of the Trotter-Kato product formula is a strongly
continuous semigroup, for the von Neumann-Schatten ideals this topology is the
trace-norm 1 on the trace-class ideal C 1 (H). In this case the limit
is a Gibbs semigroup [25]. For self-adjoint Gibbs semigroups the rate of
convergence was estimated for the first time in [7] and [9]. The authors
considered the case of the Gibbs-Schr{\"o}dinger semigroups. They scrutinised
in these papers a dependence of the rate of convergence for the (exponential)
Trotter formula on the smoothness of the potential in the Schr{\"o}dinger
generator. The first abstract result in this direction was due to [19]. In this
paper a general scheme of lifting the operator-norm rate convergence for the
Trotter-Kato product formulae was proposed and advocated for estimation the
rate of the trace-nor
Scattering Theory for Open Quantum Systems
Quantum systems which interact with their environment are often modeled by
maximal dissipative operators or so-called Pseudo-Hamiltonians. In this paper
the scattering theory for such open systems is considered. First it is assumed
that a single maximal dissipative operator in a Hilbert space \sH is
used to describe an open quantum system. In this case the minimal self-adjoint
dilation of can be regarded as the Hamiltonian of a closed
system which contains the open system \{A_D,\sH\}, but since
is necessarily not semibounded from below, this model is difficult to interpret
from a physical point of view. In the second part of the paper an open quantum
system is modeled with a family of maximal dissipative operators
depending on energy , and it is shown that the open system can be embedded
into a closed system where the Hamiltonian is semibounded. Surprisingly it
turns out that the corresponding scattering matrix can be completely recovered
from scattering matrices of single Pseudo-Hamiltonians as in the first part of
the paper. The general results are applied to a class of Sturm-Liouville
operators arising in dissipative and quantum transmitting
Schr\"{o}dinger-Poisson systems
Mean field approaches to the totally asymmetric exclusion process with quenched disorder and large particles
The process of protein synthesis in biological systems resembles a one
dimensional driven lattice gas in which the particles (ribosomes) have spatial
extent, covering more than one lattice site. Realistic, nonuniform gene
sequences lead to quenched disorder in the particle hopping rates. We study the
totally asymmetric exclusion process with large particles and quenched disorder
via several mean field approaches and compare the mean field results with Monte
Carlo simulations. Mean field equations obtained from the literature are found
to be reasonably effective in describing this system. A numerical technique is
developed for computing the particle current rapidly. The mean field approach
is extended to include two-point correlations between adjacent sites. The
two-point results are found to match Monte Carlo simulations more closely
The molecular basis of human retinal and vitreoretinal diseases
During the last two to three decades, a large body of work has revealed the molecular basis of many human disorders, including retinal and vitreoretinal degenerations and dysfunctions. Although belonging to the group of orphan diseases, they affect probably more than two million people worldwide. Most excitingly, treatment of a particular form of congenital retinal degeneration is now possible. A major advantage for treatment is the unique structure and accessibility of the eye and its different components, including the vitreous and retina. Knowledge of the many different eye diseases affecting retinal structure and function (night and color blindness, retinitis pigmentosa, cone and cone rod dystrophies, photoreceptor dysfunctions, as well as vitreoretinal traits) is critical for future therapeutic development. We have attempted to present a comprehensive picture of these disorders, including clinical, genetic and molecular information. The structural organization of the review leads the reader through non-syndromic and syndromic forms of (i) rod dominated diseases, (ii) cone dominated diseases, (iii) generalized retinal degenerations and (iv) vitreoretinal disorders, caused by mutations in more than 165 genes. Clinical variability and genetic heterogeneity have an important impact on genetic testing and counselling of affected families. As phenotypes do not always correlate with the respective genotypes, it is of utmost importance that clinicians, geneticists, counsellors, diagnostic laboratories and basic researchers understand the relationships between phenotypic manifestations and specific genes, as well as mutations and pathophysiologic mechanisms. We discuss future perspectives
Virale und nichtvirale Gentherapieansätze zur Behandlung von Netzhauterkrankungen
Zusammenfassung: Für die Behandlung von Netzhauterkrankungen eröffnet der Einsatz der Gentherapie neue Perspektiven. Die Verwendung von verschiedenartigen Oligonukleotiden oder viralen Expressionsvektoren erlaubt die Entwicklung von neuen Heilungsstrategien für Neovaskularisierungskrankheiten und retinale Degeneration. Therapeutische Oligonukleotide ("Antisense"-Oligonukleotide, Aptamere und siRNA) können den gezielten Abbau von Transkripten und damit die Konzentrationsabnahme eines an der Pathogenese beteiligten Proteins induzieren. Dagegen wird mit viralen Vektoren (rAAV und Lentivirus) häufig die Funktion eines defekten Gens durch die eines gesunden ersetzt und so die Ursache der Krankheit bekämpft. Die an Tiermodellen erfolgreich angewandten Gentherapien führten bereits zur Entwicklung von Medikamenten, und weitere werden zurzeit klinisch erprob
Circuit architecture explains functional similarity of bacterial heat shock responses
Heat shock response is a stress response to temperature changes and a
consecutive increase in amounts of unfolded proteins. To restore homeostasis,
cells upregulate chaperones facilitating protein folding by means of
transcription factors (TF). We here investigate two heat shock systems: one
characteristic to gram negative bacteria, mediated by transcriptional activator
sigma32 in E. coli, and another characteristic to gram positive bacteria,
mediated by transcriptional repressor HrcA in L. lactis. We construct simple
mathematical model of the two systems focusing on the negative feedbacks, where
free chaperons suppress sigma32 activation in the former, while they activate
HrcA repression in the latter. We demonstrate that both systems, in spite of
the difference at the TF regulation level, are capable of showing very similar
heat shock dynamics. We find that differences in regulation impose distinct
constrains on chaperone-TF binding affinities: the binding constant of free
sigma32 to chaperon DnaK, known to be in 100 nM range, set the lower limit of
amount of free chaperon that the system can sense the change at the heat shock,
while the binding affinity of HrcA to chaperon GroE set the upper limit and
have to be rather large extending into the micromolar range.Comment: 17 pages, 5 figure
Sufficient conditions for the anti-Zeno effect
The ideal anti-Zeno effect means that a perpetual observation leads to an
immediate disappearance of the unstable system. We present a straightforward
way to derive sufficient conditions under which such a situation occurs
expressed in terms of the decaying states and spectral properties of the
Hamiltonian. They show, in particular, that the gap between Zeno and anti-Zeno
effects is in fact very narrow.Comment: LatEx2e, 9 pages; a revised text, to appear in J. Phys. A: Math. Ge
A Markov Chain based method for generating long-range dependence
This paper describes a model for generating time series which exhibit the
statistical phenomenon known as long-range dependence (LRD). A Markov Modulated
Process based upon an infinite Markov chain is described. The work described is
motivated by applications in telecommunications where LRD is a known property
of time-series measured on the internet. The process can generate a time series
exhibiting LRD with known parameters and is particularly suitable for modelling
internet traffic since the time series is in terms of ones and zeros which can
be interpreted as data packets and inter-packet gaps. The method is extremely
simple computationally and analytically and could prove more tractable than
other methods described in the literatureComment: 8 pages, 2 figure
Instabilities in complex mixtures with a large number of components
Inside living cells are complex mixtures of thousands of components. It is
hopeless to try to characterise all the individual interactions in these
mixtures. Thus, we develop a statistical approach to approximating them, and
examine the conditions under which the mixtures phase separate. The approach
approximates the matrix of second virial coefficients of the mixture by a
random matrix, and determines the stability of the mixture from the spectrum of
such random matrices.Comment: 4 pages, uses RevTeX 4.
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