133 research outputs found
A de Finetti Representation Theorem for Quantum Process Tomography
In quantum process tomography, it is possible to express the experimenter's
prior information as a sequence of quantum operations, i.e., trace-preserving
completely positive maps. In analogy to de Finetti's concept of exchangeability
for probability distributions, we give a definition of exchangeability for
sequences of quantum operations. We then state and prove a representation
theorem for such exchangeable sequences. The theorem leads to a simple
characterization of admissible priors for quantum process tomography and solves
to a Bayesian's satisfaction the problem of an unknown quantum operation.Comment: 10 page
Complete characterization of convergence to equilibrium for an inelastic Kac model
Pulvirenti and Toscani introduced an equation which extends the Kac
caricature of a Maxwellian gas to inelastic particles. We show that the
probability distribution, solution of the relative Cauchy problem, converges
weakly to a probability distribution if and only if the symmetrized initial
distribution belongs to the standard domain of attraction of a symmetric stable
law, whose index is determined by the so-called degree of
inelasticity, , of the particles: . This result is
then used: (1) To state that the class of all stationary solutions coincides
with that of all symmetric stable laws with index . (2) To determine
the solution of a well-known stochastic functional equation in the absence of
extra-conditions usually adopted
Probabilistic study of the speed of approach to equilibrium for an inelastic Kac model
This paper deals with a one--dimensional model for granular materials, which
boils down to an inelastic version of the Kac kinetic equation, with
inelasticity parameter . In particular, the paper provides bounds for
certain distances -- such as specific weighted --distances and the
Kolmogorov distance -- between the solution of that equation and the limit. It
is assumed that the even part of the initial datum (which determines the
asymptotic properties of the solution) belongs to the domain of normal
attraction of a symmetric stable distribution with characteristic exponent
\a=2/(1+p). With such initial data, it turns out that the limit exists and is
just the aforementioned stable distribution. A necessary condition for the
relaxation to equilibrium is also proved. Some bounds are obtained without
introducing any extra--condition. Sharper bounds, of an exponential type, are
exhibited in the presence of additional assumptions concerning either the
behaviour, near to the origin, of the initial characteristic function, or the
behaviour, at infinity, of the initial probability distribution function
Boundary driven zero-range processes in random media
The stationary states of boundary driven zero-range processes in random media
with quenched disorder are examined, and the motion of a tagged particle is
analyzed. For symmetric transition rates, also known as the random barrier
model, the stationary state is found to be trivial in absence of boundary
drive. Out of equilibrium, two further cases are distinguished according to the
tail of the disorder distribution. For strong disorder, the fugacity profiles
are found to be governed by the paths of normalized -stable
subordinators. The expectations of integrated functions of the tagged particle
position are calculated for three types of routes.Comment: 23 page
Polyandry Is a Common Event in Wild Populations of the Tsetse Fly Glossina fuscipes fuscipes and May Impact Population Reduction Measures
Glossina fuscipes fuscipes is the most common tsetse species in Uganda where it is responsible for transmitting Trypanosoma brucei rhodensiense and Trypanosoma brucei gambiense parasites causing sleeping sickness in humans in addition to related trypanosomes that cause Nagana in cattle. An understanding of the reproductive biology of this vector is essential for the application of sustainable control/eradication methods such as Sterile Insect Technique (SIT). We have analysed the number of times a female mates in the wild as this aspect of the reproductive behaviour may affect the stability and size of populations. We provide evidence that remating is a common event in the wild and females store sperm from multiple males, which may potentially be used for insemination. In vector eradication programmes, re-infestation of cleared areas and/or in cases of residual populations, the occurrence of remating may unfortunately enhance the reproductive potential of the re-invading propagules. We suggest that population age structure may influence remating frequency. Considering the seasonal demographic changes that this fly undergoes during the dry and wet seasons, control programmes based on SIT should release large numbers of sterile males, even in residual surviving target populations, in the dry season
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