Strain-stiffening in random packings of entangled granular chains

Random packings of granular chains are presented as a model polymer system to investigate the contribution of entanglements to strain-stiffening in the absence of Brownian motion. The chain packings are sheared in triaxial compression experiments. For short chain lengths, these packings yield when the shear stress exceeds a the scale of the confining pressure, similar to packings of spherical particles. In contrast, packings of chains which are long enough to form loops exhibit strain-stiffening, in which the effective stiffness of the material increases with strain, similar to many polymer materials. The latter packings can sustain stresses orders-of-magnitude greater than the confining pressure, and do not yield until the chain links break. X-ray tomography measurements reveal that the strain-stiffening packings contain system-spanning clusters of entangled chains.Comment: 4 pages, 4 figures. submitted to Physical Review Letter

Cellular Skeletons: A New Approach to Topological Skeletons with Geometric Features

This paper introduces a new kind of skeleton for binary volumes called the cellular skeleton. This skeleton is not a subset of voxels of a volume nor a subcomplex of a cubical complex: it is a chain complex together with a reduction from the original complex. Starting from the binary volume we build a cubical complex which represents it regarding 6 or 26-connectivity. Then the complex is thinned using the proposed method based on elementary collapses, which preserves significant geometric features. The final step reduces the number of cells using Discrete Morse Theory. The resulting skeleton is a reduction which preserves the homology of the original complex and the geometrical information of the output of the previous step. The result of this method, besides its skeletonization content, can be used for computing the homology of the original complex, which usually provides well shaped homology generators

Quantum-sl(2) action on a divided-power quantum plane at even roots of unity

We describe a nonstandard version of the quantum plane, the one in the basis of divided powers at an even root of unity $q=e^{i\pi/p}$. It can be regarded as an extension of the "nearly commutative" algebra $C[X,Y]$ with $X Y =(-1)^p Y X$ by nilpotents. For this quantum plane, we construct a Wess--Zumino-type de Rham complex and find its decomposition into representations of the $2p^3$-dimensional quantum group $U_q sl(2)$ and its Lusztig extension; the quantum group action is also defined on the algebra of quantum differential operators on the quantum plane.Comment: 18 pages, amsart++, xy, times. V2: a reference and related comments adde

A differential U-module algebra for U=U_q sl(2) at an even root of unity

We show that the full matrix algebra Mat_p(C) is a U-module algebra for U = U_q sl(2), a 2p^3-dimensional quantum sl(2) group at the 2p-th root of unity. Mat_p(C) decomposes into a direct sum of projective U-modules P^+_n with all odd n, 1<=n<=p. In terms of generators and relations, this U-module algebra is described as the algebra of q-differential operators "in one variable" with the relations D z = q - q^{-1} + q^{-2} z D and z^p = D^p = 0. These relations define a "parafermionic" statistics that generalizes the fermionic commutation relations. By the Kazhdan--Lusztig duality, it is to be realized in a manifestly quantum-group-symmetric description of (p,1) logarithmic conformal field models. We extend the Kazhdan--Lusztig duality between U and the (p,1) logarithmic models by constructing a quantum de Rham complex of the new U-module algebra.Comment: 29 pages, amsart++, xypics. V3: The differential U-module algebra was claimed quantum commutative erroneously. This is now corrected, the other results unaffecte

Serum Calcium and the Risk of Breast Cancer: Findings from the Swedish AMORIS Study and a Meta-Analysis of Prospective Studies

To investigate the association between serum calcium and risk of breast cancer using a large cohort and a systematic review with meta-analysis. From the Swedish Apolipoprotein Mortality Risk (AMORIS) Study we included 229,674 women who had baseline measurements of serum total calcium and albumin. Multivariable Cox regression was used to assess the association between total and albumin-corrected calcium and breast cancer risk. For the systematic review, an electronic search of MEDLINE and EMBASE databases was performed to identify other prospective cohorts assessing the relationship between serum calcium and breast cancer risk. We pooled the results of our AMORIS cohort with other eligible studies in a meta-analysis using a random effects model. I² test was used to assess heterogeneity. In the AMORIS study, 10,863 women were diagnosed with breast cancer (mean follow-up: 19 years). We found an inverse association between total serum calcium and breast cancer when comparing the fourth quartile to the first quartile (HR: 0.94, 95% CI: 0.88-0.99, p value for trend 0.04) and similar results using albumin-corrected calcium. In the systematic review, we identified another two prospective cohorts evaluating pre-diagnostic serum total calcium and breast cancer. Combining these studies and our findings in AMORIS in a meta-analysis showed a protective effect of serum calcium against breast cancer, with a summary RR of 0.80 (95% CI: 0.66-0.97). No substantial heterogeneity was observed. Our findings in AMORIS and the meta-analysis support an inverse association between serum calcium and breast cancer risk, which warrants mechanistic investigations

The Pure Virtual Braid Group Is Quadratic

If an augmented algebra K over Q is filtered by powers of its augmentation ideal I, the associated graded algebra grK need not in general be quadratic: although it is generated in degree 1, its relations may not be generated by homogeneous relations of degree 2. In this paper we give a sufficient criterion (called the PVH Criterion) for grK to be quadratic. When K is the group algebra of a group G, quadraticity is known to be equivalent to the existence of a (not necessarily homomorphic) universal finite type invariant for G. Thus the PVH Criterion also implies the existence of such a universal finite type invariant for the group G. We apply the PVH Criterion to the group algebra of the pure virtual braid group (also known as the quasi-triangular group), and show that the corresponding associated graded algebra is quadratic, and hence that these groups have a (not necessarily homomorphic) universal finite type invariant.Comment: 53 pages, 15 figures. Some clarifications added and inaccuracies corrected, reflecting suggestions made by the referee of the published version of the pape

Development, feasibility, and acceptability of an intervention to improve care for agitation in people living in nursing homes with dementia nearing the end-of-life

OBJECTIVES: To develop a staff training intervention for agitation in people with severe dementia, reaching end-of-life, residing in nursing homes (NHs), test feasibility, acceptability, and whether a trial is warranted. DESIGN: Feasibility study with pre- and post-intervention data collection, qualitative interviews, and focus groups. SETTING: Three NHs in South East England with dementia units, diverse in terms of size, ownership status, and location. PARTICIPANTS: Residents with a dementia diagnosis or scoring ≥2 on the Noticeable Problems Checklist, rated as "severe" on Clinical Dementia Rating Scale, family carers, and staff (healthcare assistants and nurses). INTERVENTION: Manualized training, delivered by nonclinical psychology graduates focusing on agitation in severe dementia, underpinned by a palliative care framework. MEASUREMENTS: Main outcomes were feasibility of recruitment, data collection, follow-up, and intervention acceptability. We collected resident, family carer, and staff demographics. Staff provided data on resident's agitation, pain, quality of life, and service receipt. Staff reported their sense of competence in dementia care. Family carers reported on satisfaction with end-of-life care. In qualitative interviews, we explored staff and family carers' views on the intervention. RESULTS: The target three NHs participated: 28 (49%) residents, 53 (74%) staff, and 11 (85%) family carers who were eligible to participate consented. Eight-four percent of staff attended ≥3 sessions, and we achieved 93% follow-up. We were able to complete quantitative interviews. Staff and family carers reported the intervention and delivery were acceptable and helpful. CONCLUSIONS: The intervention was feasible and acceptable indicating a larger trial for effectiveness may be warranted

Periodic and Aperiodic Bunching in the Addition Spectra of Quantum Dot

We study electron addition spectra of quantum dots in a broad range of electron occupancies starting from the first electron. Spectra for dots containing <200 electrons reveal a surprising feature. Electron additions are not evenly spaced in gate voltage. Rather, they group into bunches. With increasing electron number the bunching evolves from occurring randomly to periodically at about every fifth electron. The periodicity of the bunching and features in electron tunneling rates suggest that the bunching is associated with electron additions into spatially distinct regions within the dots.Comment: 4 pages, 2 figures. Submitted to PR

Hyperemesis gravidarum and subsequent breast cancer risk

Both parity and a young age at first pregnancy are associated with a reduction in breast cancer risk. The hormones involved in this process are not fully investigated. Human chorionic gonadotropin is a placental hormone, which in rats and in human breast cells in vitro has been shown to prevent against breast cancer. Hyperemesis, a severe nausea combined with vomiting during pregnancy, is associated with increased levels of human chorionic gonadotropin. We investigated the possible relationship between hyperemesis and subsequent breast cancer risk in a case–control study based on registry data. Among 13 079 breast cancer cases and 34 348 individually matched controls we found 148 cases and 405 controls who had been hospitalised for hyperemesis. Hyperemesis was not associated with breast cancer risk (adjusted odds ratio 1.05, 95% confidence interval 0.86–1.27), and similar risks were observed regardless of age at diagnosis, number of hospitalisations for hyperemesis or time of follow-up. Our results do not support the hypothesis that human chorionic gonadotropin is responsible for the protective effect of pregnancies upon breast cancer risk

Automorphism groups of polycyclic-by-finite groups and arithmetic groups

We show that the outer automorphism group of a polycyclic-by-finite group is an arithmetic group. This result follows from a detailed structural analysis of the automorphism groups of such groups. We use an extended version of the theory of the algebraic hull functor initiated by Mostow. We thus make applicable refined methods from the theory of algebraic and arithmetic groups. We also construct examples of polycyclic-by-finite groups which have an automorphism group which does not contain an arithmetic group of finite index. Finally we discuss applications of our results to the groups of homotopy self-equivalences of K(\Gamma, 1)-spaces and obtain an extension of arithmeticity results of Sullivan in rational homotopy theory