Concentration of Lipschitz Functionals of Determinantal and Other Strong Rayleigh Measures

Let {X1 , . . , Xn} be a collection of binary-valued random variables and let f : {0, 1}n → $\mathbb{R}$ be a Lipschitz function. Under a negative dependence hypothesis known as the strong Rayleigh condition, we show that f − ${\mathbb E}$f satisfies a concentration inequality. The class of strong Rayleigh measures includes determinantal measures, weighted uniform matroids and exclusion measures; some familiar examples from these classes are generalized negative binomials and spanning tree measures. For instance, any Lipschitz-1 function of the edges of a uniform spanning tree on vertex set V (e.g., the number of leaves) satisfies the Gaussian concentration inequality \begin{linenomath}$${{\mathbb P} (f - {\mathbb E} f \geq a) \leq \exp \biggl( - \frac{a^2}{8 \, |V|} \biggr) }.$$\end{linenomath} We also prove a continuous version for concentration of Lipschitz functionals of a determinantal point process.

A POSSIBLE DESCRIPTION OF MULTIPLICITY DISTRIBUTION AT HIGH ENERGIES

It is shown that the parameters of two negative binomials describing the multiplicity distribution of secondary charged particles are connected with the mechanisms of generations and decays of two-body resonances.

The association between larval parasitic water mites (Hydracarina) and Anopheles implexus (Theobald) (Diptera, Culicidae)

The parasitic larvae of two species of water mites were studied on resting and biting Anopheles implexus (Theo.) from the Zika Forest near Entebbe, Uganda. Details are given of the mites' morphology, positions of attachment, growth stages and visible effects on hosts. Living larvae of the more numerous mite species (designated as species F, Limnesiidae) were only moderately reliable indicators of the nulliparous state of female hosts, whereas those of the other species (species G, Arrenuridae) were more reliable nullipar indicators, evidently owing to their far more rapid development. The presence of living larvae of either species not completely full-grown denoted the nulliparous state of female hosts with certainty. Male mosquitoes showed consistently lower infestation rates than females from the same resting samples, but the incidence of the different growth classes of species F indicated that these mites departed from hosts of either sex with equal facility and therefore regardless of whether the hosts returned to oviposition sites or not. Frequency distributions of species F on each host sex fitted most closely to highly clumped negative binomials, and biological interpretation of patterns of decline in mite numbers on females in successive Sella's stage groups, and other data, provided evidence of there being at most a negligible amount of mite-mediated host mortality.The study confirms the usefulness as well as the limitations of the presence of parasitic water mites as a rapid means of age-grading female mosquitoes, and suggests several new applications.