Weak conditions for interpolation in holomorphic spaces

An analogue of the notion of uniformly separated sequences, expressed in terms of extremal functions, yields a necessary and sufficient condition for interpolation in Lp spaces of holomorphic functions of Paley-Wiener-type when 0 < p \leq 1, of Fock-type when 0 < p \leq 2, and of Bergman-type when 0 < p < \infty. Moreover, if a uniformly discrete sequence has a certain uniform non-uniqueness property with respect to any such Lp space ($0$lt; p &lt; \infty$), then it is an interpolation sequence for that space. The proofs of these results are based on an approximation theorem for subharmonic functions, Beurling's results concerning compactwise limits of sequences, and the description of interpolation sequences in terms of Beurling-type densities. Details are carried out only for Fock spaces, which represent the most difficult case

Reconstruction of Bandlimited Functions from Unsigned Samples

We consider the recovery of real-valued bandlimited functions from the absolute values of their samples, possibly spaced nonuniformly. We show that such a reconstruction is always possible if the function is sampled at more than twice its Nyquist rate, and may not necessarily be possible if the samples are taken at less than twice the Nyquist rate. In the case of uniform samples, we also describe an FFT-based algorithm to perform the reconstruction. We prove that it converges exponentially rapidly in the number of samples used and examine its numerical behavior on some test cases

Interpolation in non-positively curved K\"ahler manifolds

We extend to any simply connected K\"ahler manifold with non-positive sectional curvature some conditions for interpolation in $\mathbb{C}$ and in the unit disk given by Berndtsson, Ortega-Cerd\`a and Seip. The main tool is a comparison theorem for the Hessian in K\"ahler geometry due to Greene, Wu and Siu, Yau.Comment: 9 pages, Late

Comparison of seasonal habitat selection between threatened woodland caribou ecotypes in central British Columbia

Woodland caribou (Rangifer tarandus caribou) in British Columbia have been classified into ecotypes based on differences in use of habitat in winter. Although recovery planning focuses on ecotypes, habitat use and selection varies within ecotypes. Our objectives were to compare habitat use and selection among previously identified woodland caribou herds at the transition zone between northern (Moberly, Quintette, and Kennedy herds) and mountain (Parsnip herd) ecotypes in central British Columbia. We developed selection models for each herd in spring, calving, summer/fall, early and late winter. Topographic models best predicted selection by most herds in most seasons, but importance of vegetation-cover was highlighted by disproportionate use of specific vegetation-cover types by all caribou herds (e.g., in early winter, 75% of Kennedy locations were in pine-leading stands, 84% of Parsnip locations were in fir and fir-leading stands, and 87 and 96% of locations were in alpine for the Moberly and Quintette herds, respectively). Using a combination of GPS and VHF radio-collar locations, we documented some spatial overlap among herds within the year, but use of vegetation-cover types and selection of elevations, aspects, and vegetation-cover types differed among herds and within ecotypes in all seasons. Habitat use and selection were most similar between the two northern-ecotype herds residing on the eastern side of the Rocky Mountains. This research indicates that habitat use and selection by caribou herds in all seasons is more variable than ecotype classifications suggest and demonstrates the value of undertaking herd-specific mapping of critical habitat for woodland caribou

Who Punishes? Personality Traits Predict Individual Variation in Punitive Sentiment

Cross-culturally, participants in public goods games reward participants and punish defectors to a degree beyond that warranted by rational, profit-maximizing considerations. Costly punishment, where individuals impose costs on defectors at a cost to themselves, is thought to promote the maintenance of cooperation. However, despite substantial variation in the extent to which people punish, little is known about why some individuals, and not others, choose to pay these costs. Here, we test whether personality traits might contribute to variation in helping and punishment behavior. We first replicate a previous study using public goods scenarios to investigate effects of sex, relatedness and likelihood of future interaction on willingness to help a group member or to punish a transgressor. As in the previous study, we find that individuals are more willing to help related than unrelated needy others and that women are more likely to express desire to help than men. Desire to help was higher if the probability of future interaction is high, at least among women. In contrast, among these variables, only participant sex predicted some measures of punitive sentiment. Extending the replication, we found that punitive sentiment, but not willingness to help, was predicted by personality traits. Most notably, participants scoring lower on Agreeableness expressed more anger towards and greater desire to punish a transgressor, and were more willing to engage in costly punishment, at least in our scenario. Our results suggest that some personality traits may contribute to underpinning individual variation in social enforcement of cooperation

Cornerstones of Sampling of Operator Theory

This paper reviews some results on the identifiability of classes of operators whose Kohn-Nirenberg symbols are band-limited (called band-limited operators), which we refer to as sampling of operators. We trace the motivation and history of the subject back to the original work of the third-named author in the late 1950s and early 1960s, and to the innovations in spread-spectrum communications that preceded that work. We give a brief overview of the NOMAC (Noise Modulation and Correlation) and Rake receivers, which were early implementations of spread-spectrum multi-path wireless communication systems. We examine in detail the original proof of the third-named author characterizing identifiability of channels in terms of the maximum time and Doppler spread of the channel, and do the same for the subsequent generalization of that work by Bello. The mathematical limitations inherent in the proofs of Bello and the third author are removed by using mathematical tools unavailable at the time. We survey more recent advances in sampling of operators and discuss the implications of the use of periodically-weighted delta-trains as identifiers for operator classes that satisfy Bello's criterion for identifiability, leading to new insights into the theory of finite-dimensional Gabor systems. We present novel results on operator sampling in higher dimensions, and review implications and generalizations of the results to stochastic operators, MIMO systems, and operators with unknown spreading domains

Sustaining the Digital Humanities in the UK

The Sustaining Digital Humanities in the UK report is timely for the UK Digital Humanities (DH) landscape. The establishment of UK Research and Innovation (UKRI) has created an opportune moment for the strategic planning of research infrastructure between and across all the research areas. Led by Giles Bergel and Pip Willcox, this report is based on the findings of a workshop held at the University of Oxford’s e-Research Centre (OeRC) on 21 June 2018 and sponsored by the Software Sustainability Institute. The workshop was led by an advisory board of Digital Humanities practitioners, representing a range of career stages, roles, and disciplines. The workshop’s organisers and advisory board are the joint authors of this report, with contributions from workshop participants. The mission of the Software Sustainability Institute (SSI) is to cultivate better, more sustainable, research software to enable world-class research. Currently celebrating its 10th year, the SSI has achieved broadening engagement across academic communities including humanities – for example as a longstanding supporter of the Digital Humanities at Oxford Summer School (DHOxSS), and with SSI Fellows in the arts and humanities areas. This report was commissioned by the SSI with the aim of advancing its mission within the humanities. Digital Humanities, a broad intersection of models, methods, tools, materials, career paths and affiliations, in both established and novel disciplines was identified as the area within the humanities that most closely aligns with the SSI’s role

Analytic Representation of Finite Quantum Systems

A transform between functions in R and functions in Zd is used to define the analogue of number and coherent states in the context of finite d-dimensional quantum systems. The coherent states are used to define an analytic representation in terms of theta functions. All states are represented by entire functions with growth of order 2, which have exactly d zeros in each cell. The analytic function of a state is constructed from its zeros. Results about the completeness of finite sets of coherent states within a cell are derived

Bodegraven-noord: inrichting in het licht van zuiveloverschotten: bijlagen

Wetensch. publicatieInstitute of Environmental Science