Observations of Dispersion Cancellation of Entangled Photon Pairs

An experimental study of the dispersion cancellation occurring in frequency-entangled photon pairs is presented. The approach uses time-resolved up conversion of the pairs, which has temporal resolution at the fs level, and group-delay dispersion sensitivity of $\approx \ 20 \, \mathrm{fs}^2$ under experimental conditions. The cancellation is demonstrated with dispersion stronger than $\pm 10^3 \, \mathrm{fs}^2$ in the signal $(-)$ and idler $(+)$ modes. The observations represent the generation, compression, and characterization of ultrashort biphotons with correlation width as small as 6.8 times the degenerate optical period.Comment: 5 pages, 3 figure

Minimal Permutations and 2-Regular Skew Tableaux

Bouvel and Pergola introduced the notion of minimal permutations in the study of the whole genome duplication-random loss model for genome rearrangements. Let $\mathcal{F}_d(n)$ denote the set of minimal permutations of length $n$ with $d$ descents, and let $f_d(n)= |\mathcal{F}_d(n)|$. They derived that $f_{n-2}(n)=2^{n}-(n-1)n-2$ and $f_n(2n)=C_n$, where $C_n$ is the $n$-th Catalan number. Mansour and Yan proved that $f_{n+1}(2n+1)=2^{n-2}nC_{n+1}$. In this paper, we consider the problem of counting minimal permutations in $\mathcal{F}_d(n)$ with a prescribed set of ascents. We show that such structures are in one-to-one correspondence with a class of skew Young tableaux, which we call $2$-regular skew tableaux. Using the determinantal formula for the number of skew Young tableaux of a given shape, we find an explicit formula for $f_{n-3}(n)$. Furthermore, by using the Knuth equivalence, we give a combinatorial interpretation of a formula for a refinement of the number $f_{n+1}(2n+1)$.Comment: 19 page

Wild record of an apple snail in the Waikato River, Hamilton, New Zealand and their incidence in freshwater aquaria

We report the discovery of a single specimen of a live apple snail Pomacea diffusa Blume 1957 (Ampullariidae: Prosobranchia), from the Waikato River, Hamilton city, central North Island, New Zealand. This species, along with the congeneric P. insularum, is imported for the aquarium trade, and its occurrence in the river likely stemmed from an aquarium release. A survey of 55 aquaria belonging to 43 hobbyists revealed 27 apple snails, with one owner having 22 snails. Assessment of environmental tolerances and impacts of P. diffusa, based largely on studies of the closely related and commonly confused congener P. bridgesii, suggests that direct habitat impacts by this species are likely to be minor. However, there could be indirect influences on native biodiversity through predation on eggs or competition for food supplies with other detritivorous species if densities were to become high. Water temperatures in the Waikato River below Hamilton (10-23˚C in 2009) may enable released individuals to persist for an extended period, and over summer may exceed the threshold required to enable breeding. However, population establishment would be most likely in locations where water is heated through geothermal influences or industrial cooling water discharges