A simplicial gauge theory

We provide an action for gauge theories discretized on simplicial meshes, inspired by finite element methods. The action is discretely gauge invariant and we give a proof of consistency. A discrete Noether's theorem that can be applied to our setting, is also proved.Comment: 24 pages. v2: New version includes a longer introduction and a discrete Noether's theorem. v3: Section 4 on Noether's theorem has been expanded with Proposition 8, section 2 has been expanded with a paragraph on standard LGT. v4: Thorough revision with new introduction and more background materia

Risk of fractures in half a million survivors of 20 cancers: a population-based matched cohort study using linked English electronic health records.

BACKGROUND: A history of multiple myeloma, prostate cancer, and breast cancer has been associated with adverse bone health, but associations across a broader range of cancers are unclear. We aimed to compare the risk of any bone fracture and major osteoporotic fractures in survivors of a wide range of cancers versus cancer-free individuals. METHODS: In this population-based matched cohort study, we used electronic health records from the UK Clinical Practice Research Datalink linked to hospital data. We included adults (aged ≥18 years) eligible for linkage, and we restricted the study start to Jan 2, 1998, onwards and applied administrative censoring on Jan 31, 2020. The cancer survivor group included survivors of the 20 most common cancers. Each individual with cancer was matched (age, sex, and general practice) to up to five controls (1:5) who were cancer-free. The primary outcomes were any bone fracture and any major osteoporotic fracture (pelvic, hip, wrist, spine, or proximal humeral fractures) occurring more than 1 year after index date (ie, the diagnosis date of the matched individual with cancer). We used Cox regression models, adjusted for shared risk factors, to estimate associations between cancer survivorship and bone fractures. FINDINGS: 578 160 adults with cancer diagnosed in 1998-2020 were matched to 3 226 404 cancer-free individuals. Crude incidence rates of fractures in cancer survivors ranged between 8·39 cases (95% CI 7·45-9·46) per 1000 person-years for thyroid cancer and 21·62 cases (20·18-23·18) per 1000 person-years for multiple myeloma. Compared with cancer-free individuals, the risk of any bone fracture was increased in 15 of 20 cancers, and of major osteoporotic fractures in 17 of 20 cancers. Effect sizes varied: adjusted hazard ratios (HRs) were largest for multiple myeloma (1·94, 95% CI 1·77-2·13) and prostate cancer (1·43, 1·39-1·47); HRs in the range 1·20-1·50 were seen for stomach, liver, pancreas, lung, breast, kidney, and CNS cancers; smaller associations (HR <1·20) were observed for malignant melanoma, non-Hodgkin lymphoma, leukaemia, and oesophageal, colorectal, and cervical cancers. Increased risks of major osteoporotic fracture were noted most substantially in multiple myeloma (2·25, 1·96-2·58) and CNS (2·12, 1·56-2·87), liver (1·62, 1·01-2·61), prostate (1·60, 1·53-1·67), and lung cancers (1·60, 1·44-1·77). Effect sizes tended to reduce over time since diagnosis but remained elevated for more than 5 years in several cancers, such as multiple myeloma and stomach, lung, breast, prostate, and CNS cancers. INTERPRETATION: Survivors of most types of cancer were at increased risk of bone fracture for several years after cancer, with variation by cancer type. These findings can help to inform mitigation and prevention strategies. FUNDING: Wellcome Trust

Curvature condensation and bifurcation in an elastic shell

We study the formation and evolution of localized geometrical defects in an indented cylindrical elastic shell using a combination of experiment and numerical simulation. We find that as a symmetric localized indentation on a semi-cylindrical shell increases, there is a transition from a global mode of deformation to a localized one which leads to the condensation of curvature along a symmetric parabolic crease. This process introduces a soft mode in the system, converting a load-bearing structure into a hinged, kinematic mechanism. Further indentation leads to twinning wherein the parabolic crease bifurcates into two creases that move apart on either side of the line of symmetry. A qualitative theory captures the main features of the phenomena and leads to sharper questions about the nucleation of these defects.Comment: 4 pages, 5 figures, submitted to Physical Review Letter

Rim curvature anomaly in thin conical sheets revisited

This paper revisits one of the puzzling behaviors in a developable cone (d-cone), the shape obtained by pushing a thin sheet into a circular container of radius $R$ by a distance $\eta$ [E. Cerda, S. Chaieb, F. Melo, and L. Mahadevan, {\sl Nature} {\bf 401}, 46 (1999)]. The mean curvature was reported to vanish at the rim where the d-cone is supported [T. Liang and T. A. Witten, {\sl Phys. Rev. E} {\bf 73}, 046604 (2006)]. We investigate the ratio of the two principal curvatures versus sheet thickness $h$ over a wider dynamic range than was used previously, holding $R$ and $\eta$ fixed. Instead of tending towards 1 as suggested by previous work, the ratio scales as $(h/R)^{1/3}$. Thus the mean curvature does not vanish for very thin sheets as previously claimed. Moreover, we find that the normalized rim profile of radial curvature in a d-cone is identical to that in a "c-cone" which is made by pushing a regular cone into a circular container. In both c-cones and d-cones, the ratio of the principal curvatures at the rim scales as $(R/h)^{5/2}F/(YR^{2})$, where $F$ is the pushing force and $Y$ is the Young's modulus. Scaling arguments and analytical solutions confirm the numerical results.Comment: 25 pages, 12 figures. Added references. Corrected typos. Results unchange

Structural investigation of Fe silicide films grown by pulsed laser deposition

Pulsed laser deposition was used to grow epitaxial β‐FeSi2 films on Si(111) (1×1) and Si(111) (7×7) with the following epitaxial orientations: β‐FeSi2(001)//Si(111) with β‐FeSi2[010]//Si〈110〉 and three rotational variants. Silicide growth was influenced by substrate temperature and deposition rate, but not by the structure of the starting surface. Films containing both β‐FeSi2 and FeSi were formed at low substrate temperatures and high deposition rates, while films containing only β‐FeSi2 were formed at higher substrate temperatures and lower deposition rates. FeSi grains had the following epitaxial relationship to the Si substrate, FeSi(111)//Si(111) with FeSi(110)//Si(112). The microstructure of the silicide films varied with film thickness, as did the roughness at the silicide/Si interface. These results suggest that an Fe‐rich environment was created during the growth of the silicide films.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70762/2/JAPIAU-76-4-2202-1.pd

Which activities threaten independent living of elderly when becoming problematic : inspiration for meaningful service robot functionality

Purpose: In light of the increasing elderly population and the growing demand for home care, the potential of robot support is given increasing attention. In this paper, an inventory of activities was made that threaten independent living of elderly when becoming problematic. Results will guide the further development of an existing service robot, the Care-O-bot®. Method: A systematic literature search of PubMed was performed, focused on the risk factors for institutionalization. Additionally, focus group sessions were conducted in the Netherlands, United Kingdom and France. In these focus group sessions, problematic activities threatening the independence of elderly people were discussed. Three separate target groups were included in the focus group sessions: (1) elderly persons (n = 41), (2) formal caregivers (n = 40) and (3) informal caregivers (n = 32). Results: Activities within the International Classification of Functioning domains mobility, self-care, and interpersonal interaction and relationships were found to be the most problematic. Conclusions: A distinct set of daily activities was identified that may threaten independent living, but no single activity could be selected as the main activity causing a loss of independence as it is often a combination of problematic activities that is person-specific. Supporting the problematic activities need not involve a robotic solution Read More: http://informahealthcare.com/doi/abs/10.3109/17483107.2013.840861Peer reviewe

Light-Cone Quantization of the Liouville Model

We present the quantization of the Liouville model defined in light-cone coordinates in (1,1) signature space. We take advantage of the representation of the Liouville field by the free field of the Backl\"{u}nd transformation and adapt the approch by Braaten, Curtright and Thorn. Quantum operators of the Liouville field $\partial_{+}\phi$, $\partial_{-}\phi$, $e^{g\phi}$, $e^{2g\phi}$ are constructed consistently in terms of the free field. The Liouville model field theory space is found to be restricted to the sector with field momentum $P_{+}=-P_{-}$, $P_{+}> 0$ , which is a closed subspace for the Liouville theory operator algebra.Comment: 16 p, EFI-92-6

Continuous melting of compact polymers

The competition between chain entropy and bending rigidity in compact polymers can be addressed within a lattice model introduced by P.J. Flory in 1956. It exhibits a transition between an entropy dominated disordered phase and an energetically favored crystalline phase. The nature of this order-disorder transition has been debated ever since the introduction of the model. Here we present exact results for the Flory model in two dimensions relevant for polymers on surfaces, such as DNA adsorbed on a lipid bilayer. We predict a continuous melting transition, and compute exact values of critical exponents at the transition point.Comment: 5 pages, 1 figur

Symmetry Reduction by Lifting for Maps

We study diffeomorphisms that have one-parameter families of continuous symmetries. For general maps, in contrast to the symplectic case, existence of a symmetry no longer implies existence of an invariant. Conversely, a map with an invariant need not have a symmetry. We show that when a symmetry flow has a global Poincar\'{e} section there are coordinates in which the map takes a reduced, skew-product form, and hence allows for reduction of dimensionality. We show that the reduction of a volume-preserving map again is volume preserving. Finally we sharpen the Noether theorem for symplectic maps. A number of illustrative examples are discussed and the method is compared with traditional reduction techniques.Comment: laTeX, 31 pages, 5 figure