We provide conditions under which a generalized shift-invariant (GSI) system can be approximated by a GSI system for which the generators have compact support in the Fourier domain. The approximation quality will be measured in terms of the Bessel bound (upper frame bound) for the difference between the two GSI systems. In particular, this leads to easily verifiable conditions for a perturbation of a GSI system to preserve the frame property.

The International Design Engineering Annual (IDEA) Challenge is a virtually hosted hackathon for Engineering Design researchers with aims of: i) generating open access datasets; ii) fostering community between researchers; and, iii) applying great design minds to develop solutions to real design problems. This paper presents the 2022 IDEA challenge and elements of the captured dataset with the aim of providing insights into prototyping behaviours at virtually hosted hackathons, comparing it with the 2021 challenge dataset and providing reflections and learnings from two years of running the challenge. The dataset is shown to provide valuable insights into how designers spend their time at hackathon events and how, why and when prototypes are used during their design processes. The dataset also corroborates the findings from the 2021 dataset, demonstrating the complementarity of physical and sketch prototypes. With this paper, we also invite the wider community to contribute to the IDEA Challenge in future years, either as participants or in using the platform to run their own design studies.

A sequence $\left \{g_k\right \}_{k=1}^{\infty }$ in a Hilbert space ${\cal H}$ has the expansion property if each $f\in \overline {\text {span}} \left \{g_k\right \}_{k=1}^{\infty }$ has a representation $f=\sum _{k=1}^{\infty } c_k g_k$ for some scalar coefficients $c_k.$ In this paper, we analyze the question whether there exist small norm-perturbations of $\left \{g_k\right \}_{k=1}^{\infty }$ which allow to represent all $f\in {\cal H};$ the answer turns out to be yes for frame sequences and Riesz sequences, but no for general basic sequences. The insight gained from the analysis is used to address a somewhat dual question, namely, whether it is possible to remove redundancy from a sequence with the expansion property via small norm-perturbations; we prove that the answer is yes for frames $\left \{g_k\right \}_{k=1}^{\infty }$ such that $g_k\to 0$ as $k\to \infty ,$ as well as for frames with finite excess. This particular question is motivated by recent progress in dynamical sampling.

Nioghalvfjerdsfjorden glacier is a >60 km long and 20 km wide floating outlet glacier located at 79°30’ N, 22° W, draining a large area of the northeast Greenland ice sheet. Climate, mass-balance and dynamics studies were carried out on the glacier in three field seasons in 1996, 1997 and 1998. As part of this work, tidal-movement observations were carried out by simultaneous differential global positioning system (GPS) measurements at several locations distributed on the glacier surface. The GPS observations were performed continuously over several tidal cycles. At the same time, tiltmeter measurements were carried out in the grounding zones along the glacier margins and upstream, where the glacier leaves the main ice sheet A tide gauge installed in the sea immediately in front of the glacier front recorded the tide in the open sea during the field seasons. The observations show that the main part of the glacier tongue responds as a freely floating plate to the phase and amplitude of the local tide in the sea. However, kilometre-wide flexure zones exist along the marginal and upstream grounding lines. Attempts to model the observed tidal deflection and tilt patterns in the flexure zone by elastic-beam theory are unsuccessful, in contrast to previous findings by other investigators. The strongest disagreement between our measurements and results derived from elastic-beam theory is a significant variation of the phase of the tidal records with distance from the grounding line (most clearly displayed by the tilt records). We suggest that the viscous properties of glacier ice must be taken into account, and consequently that a viscoelastic-beam model must be used to adequately describe tidal bending of floating glaciers.

In theoretical treatments of tidal bending of floating glaciers, the glacier is usually modelled as an elastic beam with uniform thickness, resting on an elastic foundation. With a few exceptions, values of the elastic (Young’s) modulus E of ice derived from tidal deflection records of floating glaciers are in the range 0.9–3 GPa. It has therefore been suggested that the elastic-beam model with a single value of E ≈ 1GPa adequately describes tidal bending of glaciers. In contrast, laboratory experiments with ice give E = 9.3 GPa, i.e. 3–10 times higher than the glacier-derived values. This suggests that ice creep may have a significant influence on tidal bending of glaciers. Moreover, detailed tidal-deflection and tilt data from Nioghalvfjerdsfjorden glacier, northeast Greenland, cannot be explained by elastic-beam theory. We present a theory of tidal bending of glaciers based on linear viscoelastic-beam theory. A four-element, linear viscoelastic model for glacier ice with a reasonable choice of model parameters can explain the observed tidal flexure data. Implications of the viscoelastic response of glaciers to tidal forcing are discussed briefly.

Sustainability standards are important governance tools for addressing social and environmental challenges. Yet, such tools are often criticized for being either too open-ended or too restrictive, thereby failing to contribute significantly to the development of sustainable practices. Both dimensions of the critique, however, miss the point. While all standards in principle combine elements of openness and closure, both of which are necessary to keep the sustainability agenda relevant and adaptive, sustainability standards often operate in contexts that favor closure. In this article, we draw on a research tradition that views communication as constitutive of organization to emphasize the significance of communicative mechanisms that stimulate organizational openness in the application of standards. With the notion of “license to critique,” we present a managerial philosophy designed to involve managers and employees, mobilize and develop their knowledge about sustainability and bring it forward for the benefit of both the organization and the environment.

Collections of functions forming a partition of unity play an important role in analysis. In this paper we characterise for any $N\in \mathbb{N}$ the entire functions $P$ for which the partition of unity condition $\sum _{\mathbf{n}\in \mathbb{Z}^{d}}P(\mathbf{x}+\mathbf{n})\unicode[STIX]{x1D712}_{[0,N]^{d}}(\mathbf{x}+\mathbf{n})=1$ holds for all $\mathbf{x}\in \mathbb{R}^{d}.$ The general characterisation leads to various easy ways of constructing such entire functions as well. We demonstrate the flexibility of the approach by showing that additional properties like continuity or differentiability of the functions $(P\unicode[STIX]{x1D712}_{[0,N]^{d}})(\cdot +\mathbf{n})$ can be controlled. In particular, this leads to easy ways of constructing entire functions $P$ such that the functions in the partition of unity belong to the Feichtinger algebra.

This article argues that the social construction of user participation policies includes both differences and similarities regarding three user groups: older people, disabled people and people with mental health problems. The article is based on a historical discourse analysis of national documents in Norway. It points at a democracy/social rights discourse, based on the idea of social citizenship, as a common and historically stable discourse for all three user groups and relates this to the specific characteristics of Norwegian welfare policies. A contrasting consumer discourse, stressing users’ consumer role and related to the impact of New Public Management reforms, is only evident in the case of older people and from the 1990s. A co-production/co-partnering discourse, stressing user/professional-partnership, is evident in the current policies directed at older people and those with mental health problems. Both the consumer and co-production discourse remain marginal in the case of disabled people.

Grafakos and Sansing [‘Gabor frames and directional time–frequency analysis’, Appl. Comput. Harmon. Anal.25 (2008), 47–67] have shown how to obtain directionally sensitive time–frequency decompositions in $L^{2}(\mathbb{R}^{n})$ based on Gabor systems in $L^{2}(\mathbb{R})$. The key tool is the ‘ridge idea’, which lifts a function of one variable to a function of several variables. We generalise their result in two steps: first by showing that similar results hold starting with general frames for $L^{2}(\mathbb{R}),$ in the settings of both discrete frames and continuous frames, and second by extending the representations to Sobolev spaces. The first step allows us to apply the theory to several other classes of frames, for example wavelet frames and shift-invariant systems, and the second one significantly extends the class of examples and applications. We consider applications to the Meyer wavelet and complex B-splines. In the special case of wavelet systems we show how to discretise the representations using ${\it\epsilon}$-nets.

The unitary extension principle $\left( \text{UEP} \right)$ by A. Ron and Z. Shen yields a sufficient condition for the construction of Parseval wavelet frames with multiple generators. In this paper we characterize the $\text{UEP}$ -type wavelet systems that can be extended to a Parseval wavelet frame by adding just one $\text{UEP}$ -type wavelet system. We derive a condition that is necessary for the extension of a UEP-type wavelet system to any Parseval wavelet frame with any number of generators and prove that this condition is also sufficient to ensure that an extension with just two generators is possible.

Vast amount of genetic marker information is being used to obtain insight into the genetic architecture of complex traits, for locating genomic regions (quantitative trait loci (QTL)) affecting disease and for enhancing the accuracy of prediction of genetic values in selection programmes. The genomic model commonly found in the literature, with marker effects affecting mean only, is extended to investigate putative effects at the level of the environmental variance. Two classes of models are proposed and their behaviour, studied using simulated data, indicates that they are capable of detecting genetic variation at the level of mean and variance. Implementation is via Markov chain Monte Carlo (McMC) algorithms. The models are compared in terms of a measure of global fit, in their ability to detect QTL effects and in terms of their predictive power. The models are subsequently fitted to back fat thickness data in pigs. The analysis of back fat thickness shows that the data support genomic models with effects on the mean but not on the variance. The relative sizes of experiment necessary to detect effects on mean and variance is discussed and an extension of the McMC algorithm is proposed.

Over recent years, statistical support for the presence of genetic factors operating at the level of the environmental variance has come from fitting a genetically structured heterogeneous variance model to field or experimental data in various species. Misleading results may arise due to skewness of the marginal distribution of the data. To investigate how the scale of measurement affects inferences, the genetically structured heterogeneous variance model is extended to accommodate the family of Box–Cox transformations. Litter size data in rabbits and pigs that had previously been analysed in the untransformed scale were reanalysed in a scale equal to the mode of the marginal posterior distribution of the Box–Cox parameter. In the rabbit data, the statistical evidence for a genetic component at the level of the environmental variance is considerably weaker than that resulting from an analysis in the original metric. In the pig data, the statistical evidence is stronger, but the coefficient of correlation between additive genetic effects affecting mean and variance changes sign, compared to the results in the untransformed scale. The study confirms that inferences on variances can be strongly affected by the presence of asymmetry in the distribution of data. We recommend that to avoid one important source of spurious inferences, future work seeking support for a genetic component acting on environmental variation using a parametric approach based on normality assumptions confirms that these are met.

Perturbation theory is a fundamental tool in Banach space theory. However, the applications of the classical results are limited by the fact that they force the perturbed sequence to be equivalent to the given sequence. We will develop amore general perturbation theory that does not force equivalence of the sequences.

Recent work of Ding and Huang shows that if we perturb a bounded operator (between Hilbert spaces) which has closed range, then the perturbed operator again has closed range. We extend this result by introducing a weaker perturbation condition, and our result is then used to prove a theorem about the stability of frames for a subspace.

A prospective multicenter study of 1,032 cesarean sections was performed to identify risk factors for postoperative wound infection. The overall rate of wound infection was 6.6% (3.8% in elective cases and 7.5% following nonelective operations), with considerable interhospital variation. Obesity was recognized as a patient-related risk factor, while risk factors inherent to the obstetric situation were duration of ruptured membranes prior to operation, fetal and labor monitoring by intrauterine devices, and omission of the use of plastic draping and redisinfection of the skin before closure. Logistic regression analysis was used to estimate the influence of these factors on the probability of wound infection. Certain risk factors associated with and overrepresented in nonelective operations would explain the increased infection rates in these, and the observed interhospital variations did not differ from the expected rates when the distribution of other risk factors was considered.

Cerebrospinal flud (CSF), thyrotropin releasing hormone (TRH), CSF-vasopressin (AVP), plasma-AVP, CSF-osmolality, plasma-osmolality, CSF-adrenaline (A) and -noradrenaline (NA) were measured in psychiatric patients and controls. Psychiatric patients were classified according to ICD-9 and grouped into endogenous depression, non-endogenous depression, mania and schizophrenia. The depressive groups were classified according to the Newcastle Rating Scale for Depression 1965. Severity of disease was quantified by BRMES, BRMS and BPRS. No difference in CSF-TRH levels was seen among the different diagnostic groups and controls. A positive correlation between CSF-TRH and CSF-A was demonstrated. CSF-AVP concentrations were significantly lowered in both endogenous and non-endogenous depression; no correlation with CSF-A or -NA was seen. Neither did any difference between plasma levels of AVP, plasma-osmolality or CSF-osmolality appear among the groups investigated.