‘Living well’ is an important concept across national dementia strategies. Qualitative research has contributed to understanding of living well for people with dementia. Longitudinal qualitative approaches, though fewer, can explore potential changes in accounts of living well, psychological coping and adapting to dementia, and if/how people with dementia maintain continuity in their lives. This longitudinal qualitative study aims to gauge what is important for ‘living well’ with mild-to-moderate dementia and whether this changes over time in a group of older people with mild-to-moderate dementia living at home. Semi-structured, qualitative interviews with 20 people with dementia from the IDEAL cohort study were conducted in 2017 and again one year later then thematically analysed. The overarching narrative was largely that of continuity and adaptation, with incremental not disruptive change. Continuing participation and meaningful occupation were important to maintaining living well over time; individuals pursued new as well as previous interests. As a key psychological coping strategy to support continuity in their lives, individuals emphasised their capabilities to maintain activities in spite of dementia, compartmentalising areas that had become more challenging. Maintaining social networks and accommodating changes in social relationships were also central to living well, including managing the psychological impacts of changes in spousal relationships. People in the earlier stages of dementia emphasise continuity and their capabilities, reporting change over time only in certain aspects of their lives. However, small, incremental changes in their social relationships and opportunities for meaningful occupation may still afford key areas for supporting capability to ‘live well’.

We prove that certain families of homogenous affine iterated function systems in $\mathbb {R}^{d}$ have the property that the open set condition and the existence of exact overlaps both occur densely in the space of translation parameters. These examples demonstrate that in the theorems of Falconer and Jordan–Pollicott–Simon on the almost sure dimensions of self-affine sets and measures, the set of exceptional translation parameters can be a dense set. The proof combines results from the literature on self-affine tilings of $\mathbb {R}^{d}$ with an adaptation of a classic argument of Erdős on the singularity of certain Bernoulli convolutions. This result encompasses a one-dimensional example due to Kenyon which arises as a special case.

There are many pressures on elite footballers. They work in a meritocracy, where only the best are selected and play at the highest levels. From the moment they enter an academy to their retirement there is a fear of deselection and rejection. Elite players need to contend with criticisms from fans and via social media; team and management dynamics can be stressful. Fears of injury are major concerns. In addition, the players are likely to face everyday difficulties experienced by the rest of society, such as relationship, family and financial problems. There is a great deal of stigma associated with mental health problems in footballers, hence approaches are required that are destigmatising. This article presents two frameworks conceptualising stress in footballers: the Power Threat Meaning Framework, which describes stress in non-diagnostic terms; and the Yerkes–Dodson curve, which describes how stress can affect footballers’ mental and physical performances on the pitch. Both frameworks can combine to enable therapists to understand players’ distress and its impact and to guide towards appropriate treatments, as we show in a fictitious case study.

A classical theorem of Hutchinson asserts that if an iterated function system acts on $\mathbb {R}^{d}$ by similitudes and satisfies the open set condition then it admits a unique self-similar measure with Hausdorff dimension equal to the dimension of the attractor. In the class of measures on the attractor, which arise as the projections of shift-invariant measures on the coding space, this self-similar measure is the unique measure of maximal dimension. In the context of affine iterated function systems it is known that there may be multiple shift-invariant measures of maximal dimension if the linear parts of the affinities share a common invariant subspace, or more generally if they preserve a finite union of proper subspaces of $\mathbb {R}^{d}$. In this paper we give an example where multiple invariant measures of maximal dimension exist even though the linear parts of the affinities do not preserve a finite union of proper subspaces.

Current policy emphasises the importance of ‘living well’ with dementia, but there has been no comprehensive synthesis of the factors related to quality of life (QoL), subjective well-being or life satisfaction in people with dementia. We examined the available evidence in a systematic review and meta-analysis. We searched electronic databases until 7 January 2016 for observational studies investigating factors associated with QoL, well-being and life satisfaction in people with dementia. Articles had to provide quantitative data and include ⩾75% people with dementia of any type or severity. We included 198 QoL studies taken from 272 articles in the meta-analysis. The analysis focused on 43 factors with sufficient data, relating to 37639 people with dementia. Generally, these factors were significantly associated with QoL, but effect sizes were often small (0.1–0.29) or negligible (<0.09). Factors reflecting relationships, social engagement and functional ability were associated with better QoL. Factors indicative of poorer physical and mental health (including depression and other neuropsychiatric symptoms) and poorer carer well-being were associated with poorer QoL. Longitudinal evidence about predictors of QoL was limited. There was a considerable between-study heterogeneity. The pattern of numerous predominantly small associations with QoL suggests a need to reconsider approaches to understanding and assessing living well with dementia.

Nanoenergetic composites are of overwhelming interest to the Department of Defense because of the higher power output and the ability to finely tune the ignition thresholds of these composites. Recently, several variants of a nanoaluminum-poly(perfluorinated methacrylate) (AlFA) have been synthesized and optimized for a variety of applications including reactive warhead liners and bullet spotters. While conventional techniques such as thermal analysis and bomb calorimetry can be used to characterize the reaction mechanism and energy output of AlFA composites, characterizing their dynamic behaviour is more challenging. Bullet spotter applications require a material to be impact sensitive at very low velocities, yet be adequately insensitive. Several live-fire tests were conducted which revealed the AlFA50 material reacted consistently upon target impact at high velocities, but unreliably at very low velocities. In an effort to better understand the fundamental impact ignition mechanism and to determine the impact velocity threshold of AlFA50 a series of Taylor gas gun experiments were conducted. It was determined that the light-initiation mechanism was consistent with a pinch mechanism, and that the ignition velocity threshold was near 74 m/s. Based on these results, it was hypothesized that the addition of a filler material could be used to sensitize the AlFA50, and that Asay shear impact testing could be used to determine a more optimal shape of such inclusions. Experiments performed using the Asay shear impact test setup confirmed the pinch ignition mechanism, but observations also revealed that the size of the pinch point was important. Finally, it was shown that the addition of large glass beads (> 1mm in diameter) was effective at sensitizing the AlFA50 material at high and low velocities, with ignition observed at impact velocities as low as 35 m/s.

Since the 1970s there has been a rich theory of equilibrium states over shift spaces associated to Hölder-continuous real-valued potentials. The construction of equilibrium states associated to matrix-valued potentials is much more recent, with a complete description of such equilibrium states being achieved by Feng and Käenmäki [Equilibrium states of the pressure function for products of matrices. Discrete Contin. Dyn. Syst.30(3) (2011), 699–708]. In a recent article [Ergodic properties of matrix equilibrium states. Ergod. Th. & Dynam. Sys. (2017), to appear] the author investigated the ergodic-theoretic properties of these matrix equilibrium states, attempting in particular to give necessary and sufficient conditions for mixing, positive entropy, and the property of being a Bernoulli measure with respect to the natural partition, in terms of the algebraic properties of the semigroup generated by the matrices. Necessary and sufficient conditions were successfully established for the latter two properties, but only a sufficient condition for mixing was given. The purpose of this note is to complete that investigation by giving a necessary and sufficient condition for a matrix equilibrium state to be mixing.

Motivated by recent investigations of ergodic optimization for matrix cocycles, we study the measures of the maximum top Lyapunov exponent for pairs of bounded weighted shift operators on a separable Hilbert space. We prove that, for generic pairs of weighted shift operators, the Lyapunov-maximizing measure is unique, and show that there exist pairs of operators whose unique Lyapunov-maximizing measure takes any prescribed value less than $\log 2$ for its metric entropy. We also show that, in contrast to the matrix case, the Lyapunov-maximizing measures of pairs of bounded operators are, in general, not characterized by their supports: we construct explicitly a pair of operators and a pair of ergodic measures on the 2-shift with identical supports, such that one of the two measures is Lyapunov-maximizing for the pair of operators and the other measure is not. Our proofs make use of the Ornstein $\overline{d}$-metric to estimate differences in the top Lyapunov exponent of a pair of weighted shift operators as the underlying measure is varied.

Given a finite irreducible set of real $d\times d$ matrices $A_{1},\ldots ,A_{M}$ and a real parameter $s>0$, there exists a unique shift-invariant equilibrium state on $\{1,\ldots ,M\}^{\mathbb{N}}$ associated to $(A_{1},\ldots ,A_{M},s)$. In this paper we characterize the ergodic properties of such equilibrium states in terms of the algebraic properties of the semigroup generated by the associated matrices. We completely characterize when the equilibrium state has zero entropy, when it gives distinct Lyapunov exponents to the natural cocycle generated by $A_{1},\ldots ,A_{M}$, and when it is a Bernoulli measure. We also give a general sufficient condition for the equilibrium state to be mixing, and give an example where the equilibrium state is ergodic but not totally ergodic. Connections with a class of measures investigated by Kusuoka are explored in an appendix.

The joint spectral radius of a bounded set of d × d real matrices is defined to be the maximum possible exponential growth rate of products of matrices drawn from that set. For a fixed set of matrices, a sequence of matrices drawn from that set is called extremal if the associated sequence of partial products achieves this maximal rate of growth. An influential conjecture of J. Lagarias and Y. Wang asked whether every finite set of matrices admits an extremal sequence which is periodic. This is equivalent to the assertion that every finite set of matrices admits an extremal sequence with bounded subword complexity. Counterexamples were subsequently constructed which have the property that every extremal sequence has at least linear subword complexity. In this paper we extend this result to show that for each integer p ≥ 1, there exists a pair of square matrices of dimension 2p(2p+1 − 1) for which every extremal sequence has subword complexity at least 2−p2np.

A single nucleotide polymorphism rs12807809 located upstream of the neurogranin (NRGN) gene has been identified as a risk variant for schizophrenia in recent genome-wide association studies. To date, there has been little investigation of the endophenotypic consequences of this variant, and our own investigations have suggested that the effects of this gene are not apparent at the level of cognitive function in patients or controls. Because the impact of risk variants may be more apparent at the level of brain, the aim of this investigation was to delineate whether NRGN genotype predicted variability in brain structure and/or function. Healthy individuals participated in structural (N = 140) and/or functional (N = 36) magnetic resonance imaging (s/fMRI). Voxel-based morphometry was used to compare gray and white matter volumes between carriers of the non-risk C allele (i.e., CC/CT) and those who were homozygous for the risk T allele. Functional imaging data were acquired during the performance of a spatial working memory task, and were also analyzed with respect to the difference between C carriers and T homozygotes. There was no effect of the NRGN variant rs12807809 on behavioral performance or brain structure. However, there was a main effect of genotype on brain activity during performance of the working memory task, such that while C carriers exhibited a load-independent decrease in left superior frontal gyrus/BA10, TT individuals failed to show a similar decrease in activity. The failure to disengage this ventromedial prefrontal region, despite preserved performance, may be indicative of a reduction in processing efficiency in healthy TT carriers. Although it remains to be established whether this holds true in larger samples and in patient cohorts, if valid, this suggests a potential mechanism by which NRGN variability might contribute to schizophrenia risk.