Rigidity and volume preserving deformation on degenerate simplices

Given a degenerate $(n+1)$-simplex in a $d$-dimensional space $M^d$ (Euclidean, spherical or hyperbolic space, and $d\geq n$), for each $k$, $1\leq k\leq n$, Radon's theorem induces a partition of the set of $k$-faces into two subsets. We prove that if the vertices of the simplex vary smoothly in $M^d$ for $d=n$, and the volumes of $k$-faces in one subset are constrained only to decrease while in the other subset only to increase, then any sufficiently small motion must preserve the volumes of all $k$-faces; and this property still holds in $M^d$ for $d\geq n+1$ if an invariant $c_{k-1}(\alpha^{k-1})$ of the degenerate simplex has the desired sign. This answers a question posed by the author, and the proof relies on an invariant $c_k(\omega)$ we discovered for any $k$-stress $\omega$ on a cell complex in $M^d$. We introduce a characteristic polynomial of the degenerate simplex by defining $f(x)=\sum_{i=0}^{n+1}(-1)^{i}c_i(\alpha^i)x^{n+1-i}$, and prove that the roots of $f(x)$ are real for the Euclidean case. Some evidence suggests the same conjecture for the hyperbolic case.Comment: 27 pages, 2 figures. To appear in Discrete & Computational Geometr

The Influence of Hormones and Other Substances on Lens Regeneration in vitro

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73216/1/j.1432-0436.1980.tb01062.x.pd

Dissipative surface solitons in periodic structures

We report dissipative surface solitons forming at the interface between a semi-infinite lattice and a homogeneous Kerr medium. The solitons exist due to balance between amplification in the near-surface lattice channel and two-photon absorption. The stable dissipative surface solitons exist in both focusing and defocusing media, when propagation constants of corresponding states fall into a total semi-infinite and or into one of total finite gaps of the spectrum (i.e. in a domain where propagation of linear waves is inhibited for the both media). In a general situation, the surface solitons form when amplification coefficient exceeds threshold value. When a soliton is formed in a total finite gap there exists also the upper limit for the linear gain.Comment: 5 pages, 3 figures, to appear in Europhysics Letter

Only connect: addressing the emotional needs of Scotland's children and young people

A report on the SNAP (Scottish Needs Assessment Programme) Child and Adolescent Mental Health Phase Two survey. It describes a survey of a wide range of professionals working with children and young people in Scotland, and deals with professional perspectives on emotional, behavioural and psychological problems. Conclusions and recommendations are presented

Characterizing the universal rigidity of generic frameworks

A framework is a graph and a map from its vertices to E^d (for some d). A framework is universally rigid if any framework in any dimension with the same graph and edge lengths is a Euclidean image of it. We show that a generic universally rigid framework has a positive semi-definite stress matrix of maximal rank. Connelly showed that the existence of such a positive semi-definite stress matrix is sufficient for universal rigidity, so this provides a characterization of universal rigidity for generic frameworks. We also extend our argument to give a new result on the genericity of strict complementarity in semidefinite programming.Comment: 18 pages, v2: updates throughout; v3: published versio

Bioreactor scalability: laboratory-scale bioreactor design influences performance, ecology, and community physiology in expanded granular sludge bed bioreactors

Studies investigating the feasibility of new, or improved, biotechnologies, such as wastewater treatment digesters, inevitably start with laboratory-scale trials. However, it is rarely determined whether laboratory-scale results reflect full-scale performance or microbial ecology. The Expanded Granular Sludge Bed (EGSB) bioreactor, which is a high-rate anaerobic digester configuration, was used as a model to address that knowledge gap in this study. Two laboratory-scale idealizations of the EGSB—a one-dimensional and a three- dimensional scale-down of a full-scale design—were built and operated in triplicate under near-identical conditions to a full-scale EGSB. The laboratory-scale bioreactors were seeded using biomass obtained from the full-scale bioreactor, and, spent water from the distillation of whisky from maize was applied as substrate at both scales. Over 70 days, bioreactor performance, microbial ecology, and microbial community physiology were monitored at various depths in the sludge-beds using 16S rRNA gene sequencing (V4 region), specific methanogenic activity (SMA) assays, and a range of physical and chemical monitoring methods. SMA assays indicated dominance of the hydrogenotrophic pathway at full-scale whilst a more balanced activity profile developed during the laboratory-scale trials. At each scale, Methanobacterium was the dominant methanogenic genus present. Bioreactor performance overall was better at laboratory-scale than full-scale. We observed that bioreactor design at laboratory-scale significantly influenced spatial distribution of microbial community physiology and taxonomy in the bioreactor sludge-bed, with 1-D bioreactor types promoting stratification of each. In the 1-D laboratory bioreactors, increased abundance of Firmicutes was associated with both granule position in the sludge bed and increased activity against acetate and ethanol as substrates. We further observed that stratification in the sludge-bed in 1-D laboratory-scale bioreactors was associated with increased richness in the underlying microbial community at species (OTU) level and improved overall performance

Considerations for the design of an onboard air traffic situation display

The basic concept of remoting information to the cockpit is used to design and develop a computerized airborne traffic situation display device that automatically selects and presents segments of a controller's scope to the aircraft pilot via a narrow band digital data link. These data are integrated with aircraft heading and navigation information to provide a display useful in congested air space. The display can include alphanumerical symbols, air route maps, and controller instructions

Do music festival communities address environmental sustainability and how? A Scottish case study

© 2019 Cambridge University Press. This article discusses the findings of an Arts and Humanities Research Council project researching how music festival communities in Scotland can address issues of environmental sustainability and climate change. It investigates how music festival communities are constructed with a focus on what role, if any, they might play in responding to the global challenge of environmental sustainability. Using music festivals in Scotland as a case study, we employed a variety of research methods to interrogate different constituents in music festival communities about their views and behaviours regarding climate change and environmental sustainability. These included festival audiences via onsite questionnaires; festival organisers and promoters via interviews and focus groups; and musicians via creative practice-led research. We conclude that rather than necessarily being a site for progressive or utopian socio-cultural experimentation (as they are occasionally portrayed in festival literature), music festival communities engage in complex and often contradictory behaviours when it comes to responding to - and making sense of - their own complicity in social challenges such as climate change