A Phase transition in zero count probability for Stationary Gaussian Processes

We study the probability that a real stationary Gaussian process has at least $\eta T$ zeros in $[0,T]$ (overcrowding), or at most this number (undercrowding). We show that if the spectral measure of the process is supported on $\pm[B,A]$, overcrowding probability transitions from exponential decay to Gaussian decay at $\eta=\tfrac{A}{\pi}$, while undercrowding probability undergoes the reverse transition at $\eta=\tfrac{B}{\pi}$.Comment: 17 page

Zeroes of Gaussian Analytic Functions with Translation-Invariant Distribution

We study zeroes of Gaussian analytic functions in a strip in the complex plane, with translation-invariant distribution. We prove that the a limiting horizontal mean counting-measure of the zeroes exists almost surely, and that it is non-random if and only if the spectral measure is continuous (or degenerate). In this case, the mean zero-counting measure is computed in terms of the spectral measure. We compare the behavior with Gaussian analytic function with symmetry around the real axis. These results extend a work by Norbert Wiener.Comment: 24 pages, 1 figure. Some corrections were made and presentation was improve

The sharks and rays at Singapore's fishery ports

The status of elasmobranchs in Southeast Asia has been highlighted as a serious concern, yet there are limited data to assess stocks and develop appropriate management plans. Surveys of elasmobranchs at two fishery ports in Singapore were conducted between 2017 and 2020. These fishery ports receive fresh, whole imports of seafood from the region as well as seafood caught in Singapore waters. Data were collected on 13,817 rays, 2,480 sharks, and 1,297 wedgefishes and giant guitarfishes over 102 surveys. The majority of elasmobranchs were imported from Indonesia or Malaysia, and only a few individuals (six sharks and 278 rays) were reportedly caught within Singapore waters. In Singapore, elasmobranchs are predominantly used for their meat, and wedgefish snouts are also commonly used in collagen soup. The data collected highlights potential conservation concerns, particularly surrounding the large volumes of Maculabatis gerrardi and Maculabatis macrura rays (categorized as Vulnerable and Not Assessed by the IUCN) that are imported, and the high proportions of immature individuals of Carcharhinus sorrah and Carcharhinus sealei sharks. During this study, a single Rhynchobatus cooki was discovered – the first reported sighting in over 20 years