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 $\alpha$ is determined by the so-called degree of inelasticity, $p>0$, of the particles: $\alpha=\frac{2}{1+p}$. 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 $\alpha$. (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 $p>0$. In particular, the paper provides bounds for certain distances -- such as specific weighted $\chi$--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 $\alpha$-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