Stability of Spectral Types for Jacobi Matrices Under Decaying Random Perturbations

We study stability of spectral types for semi-infinite self-adjoint tridiagonal matrices under random decaying perturbations. We show that absolutely continuous spectrum associated with bounded eigenfunctions is stable under Hilbert-Schmidt random perturbations. We also obtain some results for singular spectral types

Eigenvalue Spacings and Dynamical Upper Bounds for Discrete One-Dimensional Schroedinger Operators

We prove dynamical upper bounds for discrete one-dimensional Schroedinger operators in terms of various spacing properties of the eigenvalues of finite volume approximations. We demonstrate the applicability of our approach by a study of the Fibonacci Hamiltonian

The Nevai Condition

We study Nevai's condition that for orthogonal polynomials on the real line, $K_n(x,x_0)^2 K_n(x_0,x_0)^{-1} d\rho (x)\to\delta_{x_0}$ where $K_n$ is the CD kernel. We prove that it holds for the Nevai class of a finite gap set uniformly on the spectrum and we provide an example of a regular measure on $[-2,2]$ where it fails on an interval

Loss of buoyancy control in the copepod Calanus finmarchicus

A mechanism is demonstrated that could explain large-scale aggregations of lipid-rich copepods in the surface waters of marine environments. Laboratory experiments establish that changes in salinity and temperature induce lipid-mediated buoyancy instability that entrains copepods in surface waters. Reduced hydrostatic pressure associated with forced ascent of copepods at fjordic sills, shelf breaks and seamounts would also reduce the density of the lipid reserves, forcing copepods and particularly those in diapause to the surface. We propose that salinity, temperature and hydrodynamics of the physical environment, in conjunction with the biophysical properties of lipids, explain periodic high abundances of lipid-rich copepods in surface waters

Singular Continuous Spectrum for the Laplacian on Certain Sparse Trees

We present examples of rooted tree graphs for which the Laplacian has singular continuous spectral measures. For some of these examples we further establish fractional Hausdorff dimensions. The singular continuous components, in these models, have an interesting multiplicity structure. The results are obtained via a decomposition of the Laplacian into a direct sum of Jacobi matrices

Photoperiodism and overwintering in boreal and sub-Arctic Calanus finmarchicus populations

The copepod Calanus finmarchicus, a key species in the North Atlantic, generally spends the non-productive season by descending into deep waters and entering diapause, a physiological state characterized by reduced metabolism and arrested development. In the open ocean, overwintering depths are below 600 m, where temperature and light conditions are favourable to initiate diapause. However, C. finmarchicus has also been reported diapausing in areas with shallow water depth such as fjords, coastal waters and shelf seas. In these environments, the temperature and light conditions are different, and it has been hypothesized that under such conditions C. finmarchicus may remain active throughout winter. Here, we investigated changes in the swimming activity of C. finmarchicus from shallow fjords in the eastern North Atlantic during overwintering in response to ambient photoperiod. We conducted monthly experiments with populations from 2 fjords from different latitudes (sub-Arctic Ramfjord, 69°N and boreal Loch Etive, 56°N), measuring the locomotor activity of individual C. finmarchicus stage CVs exposed to a natural light:dark cycle. At both locations, peaks in activity in response to the light cycle were observed to shift from nocturnal during the early overwintering phase to diurnal during mid and late overwintering phase, with a minimal intensity observed during the mid-overwintering phase. In Ramfjord, activity and rhythmicity were generally lower than in Loch Etive. We conclude that C. finmarchicus remains active throughout its overwintering period when in shallow (<200 m) locations but down-regulates its locomotor activity during the main overwintering phase, which we describe as a winter resting state as distinct from classical diapause

Photophysiological cycles in Arctic krill are entrained by weak midday twilight during the Polar Night

Light plays a fundamental role in the ecology of organisms in nearly all habitats on Earth and is central for processes such as vision and the entrainment of the circadian clock. The poles represent extreme light regimes with an annual light cycle including periods of Midnight Sun and Polar Night. The Arctic Ocean extends to the North Pole, and marine light extremes reach their maximum extent in this habitat. During the Polar Night, traditional definitions of day and night and seasonal photoperiod become irrelevant since there are only “twilight” periods defined by the sun’s elevation below the horizon at midday; we term this “midday twilight.” Here, we characterize light across a latitudinal gradient (76.5° N to 81° N) during Polar Night in January. Our light measurements demonstrate that the classical solar diel light cycle dominant at lower latitudes is modulated during Arctic Polar Night by lunar and auroral components. We therefore question whether this particular ambient light environment is relevant to behavioral and visual processes. We reveal from acoustic field observations that the zooplankton community is undergoing diel vertical migration (DVM) behavior. Furthermore, using electroretinogram (ERG) recording under constant darkness, we show that the main migratory species, Arctic krill (Thysanoessa inermis) show endogenous increases in visual sensitivity during the subjective night. This change in sensitivity is comparable to that under exogenous dim light acclimations, although differences in speed of vision suggest separate mechanisms. We conclude that the extremely weak midday twilight experienced by krill at high latitudes during the darkest parts of the year has physiological and ecological relevance

Excavations at Catridge Farm, Lacock, Wiltshire.

This report describes the results of an excavation at the site of Catridge Farm, Lacock, Wiltshire, undertaken as part of the National Archaeological Identification Survey Pilot Project: West Wiltshire (A350 corridor), following an earthwork survey of settlement remains at the site. Overlying a medieval agricultural soil were the remains of an early postmedieval structure, probably a farm building, within which had been deposited a large dump of household refuse of 17th century date, including ceramics, glass vessels, metalwork, animal bone and charred plant remains. The report describes the excavated remains and the finds assemblages, including chemical analysis of the glass, and assesses the significance of the results in terms of our understanding of the settlement at Catridge and as a contribution to the archaeology of post-medieval rural households more generally