Disjoint mixing operators

Chan and Shapiro showed that each (non-trivial) translation operator acting on the Fréchet space of entire functions endowed with the topology of locally uniform convergence supports a universal function of exponential type zero. We show the existence of d-universal functions of exponential type zero for arbitrary finite tuples of pairwise distinct translation operators. We also show that every separable infinite-dimensional Fréchet space supports an arbitrarily large finite and commuting disjoint mixing collection of operators. When this space is a Banach space, it supports an arbitrarily large finite disjoint mixing collection of C0-semigroups. We also provide an easy proof of the result of Salas that every infinite-dimensional Banach space supports arbitrarily large tuples of dual d-hypercyclic operators, and construct an example of a mixing Hilbert space operator T so that (T,T2) is not d-mixing.

Hypercyclic tuples of operators on $C^n$ and $R^n$

A tuple $(T_1,\dots,T_n)$ of continuous linear operators on a topological vector space $X$ is called hypercyclic if there is $x\in X$ such that the the orbit of $x$ under the action of the semigroup generated by $T_1,\dots,T_n$ is dense in $X$. This concept was introduced by N.~Feldman, who have raised 7 questions on hypercyclic tuples. We answer those 4 of them, which can be dealt with on the level of operators on finite dimensional spaces. In
particular, we prove that the minimal cardinality of a hypercyclic tuple of operators on $\C^n$ (respectively, on $\R^n$) is $n+1$ (respectively, $\frac n2+\frac{5+(-1)^n}{4}$), that there are non-diagonalizable tuples of operators on $\R^2$ which possess an orbit being neither dense nor nowhere dense and construct a hypercyclic 6-tuple of operators on $\C^3$ such that every operator commuting with each member of the tuple is non-cyclic.

Assessing the Nonequilibrium Thermodynamics in a Quenched Quantum Many-Body System via Single Projective Measurements

We analyze the nature of the statistics of the work done on or by a quantum many-body system brought out of equilibrium. We show that, for the sudden quench and for an initial state that commutes with the initial Hamiltonian, it is possible to retrieve the whole nonequilibrium thermodynamics via single projective measurements of observables. We highlight, in a physically clear way, the qualitative implications for the statistics of work coming from considering processes described by operators that either commute or do not commute with the unperturbed Hamiltonian of a given system. We consider a quantum many-body system and derive an expression that allows us to give a physical interpretation, for a thermal initial state, to all of the cumulants of the work in the case of quenched operators commuting with the unperturbed Hamiltonian. In the commuting case, the observables that we need to measure have an intuitive physical meaning. Conversely, in the noncommuting case, we show that, although it is possible to operate fully within the single-measurement framework irrespectively of the size of the quench, some difficulties are faced in providing a clear-cut physical interpretation to the cumulants. This circumstance makes the study of the physics of the system nontrivial and highlights the nonintuitive phenomenology of the emergence of thermodynamics from the fully quantum microscopic description. We illustrate our ideas with the example of the Ising model in a transverse field showing the interesting behavior of the high-order statistical moments of the work distribution for a generic thermal state and linking them to the critical nature of the model itself.

Individual Characteristics Associated with Mismatches between Self-Reported and Accelerometer-Measured Physical Activity

Background: Accurate assessment tools are required for the surveillance of physical activity (PA) levels and the assessment of the effect of interventions. In addition, increasing awareness of PA is often used as the first step in pragmatic behavioural interventions, as discrepancies between the amount of activity an individual perceives they do and the amount actually undertaken may act as a barrier to change. Previous research has demonstrated differences in the amount of activity individuals report doing, compared to their level of physical activity when measured with an accelerometer. Understanding the characteristics of those whose PA level is ranked differently when measured with either self-report or accelerometry is important as it may inform the choice of instrument for future research. The aim of this project was to determine which individual characteristics are associated with differences between self-reported and accelerometer measured physical activity.

Methods: Participant data from the 2009 wave of the Commuting and Health in Cambridge study were used. Quartiles of self-reported and accelerometer measured PA were derived by ranking each measure from lowest to highest. These quartiles were compared to determine whether individuals’ physical activity was ranked higher by either method. Multinomial logistic regression models were used to investigate the individual characteristics associated with different categories of mismatch.

Results: Data from 486 participants (70% female) were included in the analysis. In adjusted analyses, the physical activity of overweight or obese individuals was significantly more likely to be ranked higher by self-report than by accelerometer than that of normal-weight individuals (OR = 2.07, 95%CI = 1.28–3.34), particularly among women (OR = 3.97, 95%CI = 2.11–7.47).

Conclusions: There was a greater likelihood of mismatch between self-reported and accelerometer measured physical activity levels in overweight or obese adults. Future studies in overweight or obese adults should consider employing both methods of measurement.

Could occupational physical activity mitigate the link between moderate kidney dysfunction and coronary heart disease?

Background

Chronic kidney disease is now regarded as a risk factor for cardiovascular disease. The impact of occupational or non-occupational physical activity (PA) on moderate decreases of renal function is uncertain.

We aimed to identify the potential association of PA (occupational and leisure-time) on early decline of estimated glomerular filtration rate (eGFR) and to determine the potential mediating effect of PA on the relationship between eGFR and heart disease.

From the PRIME study analyses were conducted in 1058 employed men. Energy expended during leisure, work and commuting was calculated. Linear regression analyses were used to determine the link between types of PA and moderate decrements of eGFR determined with the KDIGO guideline at the baseline assessment. Cox proportional hazards analyses were used to explore the potential effect of PA on the relationship between eGFR and heart disease, ascertained during follow-up over 10 years.

For these employed men, and after adjustment for known confounders of GFR change, more time spent sitting at work was associated with increased risk of moderate decline in kidney function, while carrying objects or being active at work was associated with decreased risk. In contrast, no significant link with leisure PA was apparent. No potential mediating effect of occupational PA was found for the relationship between eGFR and coronary heart disease.

Occupational PA (potential modifiable factors) could provide a dual role on early impairment of renal function, without influence on the relationship between early decrease of e-GFR and CHD risk.

Operator systems from discrete groups

We express various sets of quantum correlations studied in the theoretical physics literature in terms of different tensor products of operator systems of discrete groups. We thus recover earlier results of Tsirelson and formulate a new approach for the study of quantum correlations. To do this we formulate a general framework for the study of operator systems arising from discrete groups. We study in detail the operator system of the free group Fn on n generators, as well as the operator systems of the free products of finitely many copies of the two-element group Z2. We examine various tensor products of group operator systems, including the minimal, the maximal, and the commuting tensor products. We introduce a new tensor product in the category of operator systems and formulate necessary and sufficient conditions for its equality to the commuting tensor product in the case of group operator systems.

Designing Bare Essentials: Aldi, Lidle and the architectures of cheapness

They’re cheap. They’re in every settlement of significance in Britain, Ireland and elsewhere. We all use them but perhaps do not always admit to it. Especially, if we are architects.
Over the past decades Aldi/Lidl low cost supermarkets have escaped from middle Europe to take over large tracts of the English speaking world remaking them according to a formula of mass-produced sheds, buff-coloured cobble-lock car parks, logos in primary colours, bare-shelves and eclectic special offers. Response within architectural discourse to this phenomenon has been largely one of indifference and such places remain, perhaps reiterating Pevsner’s controversial insights into the bicycle shed, on the peripheries of what we might term architecture. This paper seeks to explore the spatial complexities of the discount supermarket and in doing so open up a discussion on the architecture of cheapness. As a road-map, it takes former managing director Dieter Brandes’ treatise on the Aldi formula, Bare Essentials: the Aldi Way to Retailing, and investigates the strategies through which economic exigencies manifest themselves in a series of spatial tactics which involve building. Central to this is the idea of architecture as system rather than form and, in Aldi/Lidl’s case, the result of a spatial network of flows. To understand the architecture of the supermarket, then, it is necessary to measure the times and spaces of supply across the scales of intersection between global and local.
Evaluating the energy, economy and precision of such systems challenges the liminal position of the commercial, the placeless and especially the cheap within architectural discourse. As is well known, architectures of mass-production and prefabrication and their origins exercised modernist thinkers such as Sigfried Giedion and Walter Gropius in the early twentieth century and has undergone a resurgence in recent times. Meanwhile, the mapping of the hitherto overlooked forms and iconography of commerce in Learning from Las Vegas (1971) was extended by Rem Koolhaas et al into an investigation of the technologies, systems and precedents of retail in the Harvard Design School Guide to Shopping, thirty years later in 2001. While obviously always a criteria for building, to find writings on architecture which explicitly celebrate cheapness as a design virtue or, indeed, even iterate the word cheap is more difficult. Walter Gropius’ essay ‘How can we build cheaper, better, more attractive houses?’ (1927), however, situates the cheap within the discussions – articulated, amongst others, by Karl Teige and Bruno Taut – surrounding the minimal dwelling and the moral benefits of absence of the 1920s and 30s.
In our contemporary age of heightened consumption, it is perhaps fitting that an architecture of bare essentials is defined in retail rather than in housing, a commercial existenzminimum where the Miesian paradox of ‘less is more’ is resold as a paradigm of ‘more for less’ in the ubiquitous yet overlooked architectures of the discount supermarket.

Adaptation and Evaluation of the Neighborhood Environment Walkability Scale in India (NEWS-India)

Physical inactivity is the fourth leading risk factor for global mortality, with most of these deaths occurring in low and middle-income countries (LMICs) like India. Research from developed countries has consistently demonstrated associations between built environment features and physical activity levels of populations. The development of culturally sensitive and reliable measures of the built environment is a necessary first step for accurate analysis of environmental correlates of physical activity in LMICs. This study systematically adapted the Neighborhood Environment Walkability Scale (NEWS) for India and evaluated aspects of test-retest reliability of the adapted version among Indian adults. Cultural adaptation of the NEWS was conducted by Indian and international experts. Semi-structured interviews were conducted with local residents and key informants in the city of Chennai, India. At baseline, participants (N = 370; female = 47.2%) from Chennai completed the adapted NEWS-India surveys on perceived residential density, land use mix-diversity, land use mix-access, street connectivity, infrastructure and safety for walking and cycling, aesthetics, traffic safety, and safety from crime. NEWS-India was administered for a second time to consenting participants (N = 62; female = 53.2%) with a gap of 2–3 weeks between successive administrations. Qualitative findings demonstrated that built environment barriers and constraints to active commuting and physical activity behaviors intersected with social ecological systems. The adapted NEWS subscales had moderate to high test-retest reliability (ICC range 0.48–0.99). The NEWS-India demonstrated acceptable measurement properties among Indian adults and may be a useful tool for evaluation of built environment attributes in India. Further adaptation and evaluation in rural and suburban settings in India is essential to create a version that could be used throughout India.

Enhancing the Manufacturing Knowledge of Undergraduate Engineering Students: A Case Study of a Design-Build-Test Challenge Involving Folding Bicycles

Many engineers currently in professional practice will have gained a degree level qualification which involved studying a curriculum heavy with mathematics and engineering science. While this knowledge is vital to the engineering design process so also is manufacturing knowledge, if the resulting designs are to be both technically and commercially viable.
The methodology advanced by the CDIO Initiative aims to improve engineering education by teaching in the context of Conceiving, Designing, Implementing and Operating products, processes or systems. A key element of this approach is the use of Design-Built-Test (DBT) projects as the core of an integrated curriculum. This approach facilitates the development of professional skills as well as the application of technical knowledge and skills developed in other parts of the degree programme. This approach also changes the role of lecturer to that of facilitator / coach in an active learning environment in which students gain concrete experiences that support their development.
The case study herein describes Mechanical Engineering undergraduate student involvement in the manufacture and assembly of concept and functional prototypes of a folding bicycle.

The effect of changing the built environment on physical activity: a quantitative review of the risk of bias in natural experiments.

BACKGROUND:
Evidence regarding the association of the built environment with physical activity is influencing policy recommendations that advocate changing the built environment to increase population-level physical activity. However, to date there has been no rigorous appraisal of the quality of the evidence on the effects of changing the built environment. The aim of this review was to conduct a thorough quantitative appraisal of the risk of bias present in those natural experiments with the strongest experimental designs for assessing the causal effects of the built environment on physical activity.

METHODS:
Eligible studies had to evaluate the effects of changing the built environment on physical activity, include at least one measurement before and one measurement of physical activity after changes in the environment, and have at least one intervention site and non-intervention comparison site. Given the large number of systematic reviews in this area, studies were identified from three exemplar systematic reviews; these were published in the past five years and were selected to provide a range of different built environment interventions. The risk of bias in these studies was analysed using the Cochrane Risk of Bias Assessment Tool: for Non-Randomized Studies of Interventions (ACROBAT-NRSI).

RESULTS:
Twelve eligible natural experiments were identified. Risk of bias assessments were conducted for each physical activity outcome from all studies, resulting in a total of fifteen outcomes being analysed. Intervention sites included parks, urban greenways/trails, bicycle lanes, paths, vacant lots, and a senior citizen's centre. All outcomes had an overall critical (n = 12) or serious (n = 3) risk of bias. Domains with the highest risk of bias were confounding (due to inadequate control sites and poor control of confounding variables), measurement of outcomes, and selection of the reported result.

CONCLUSIONS:
The present review focused on the strongest natural experiments conducted to date. Given this, the failure of existing studies to adequately control for potential sources of bias highlights the need for more rigorous research to underpin policy recommendations for changing the built environment to increase physical activity. Suggestions are proposed for how future natural experiments in this area can be improved.

Estimating quantum chromatic numbers

We develop further the new versions of quantum chromatic numbers of graphs introduced by the first and fourth authors. We prove that the problem of computation of the commuting quantum chromatic number of a graph is solvable by an SDP algorithm and describe an hierarchy of variants of the commuting quantum chromatic number which converge to it. We introduce the tracial rank of a graph, a parameter that gives a lower bound for the commuting quantum chromatic number and parallels the projective rank, and prove that it is multiplicative. We describe the tracial rank, the projective rank and the fractional chromatic numbers in a unified manner that clarifies their connection with the commuting quantum chromatic number, the quantum chromatic number and the classical chromatic number, respectively. Finally, we present a new SDP algorithm that yields a parameter larger than the Lovász number and is yet a lower bound for the tracial rank of the graph. We determine the precise value of the tracial rank of an odd cycle.