Generic f(R) theories and classicality of their scalarons

We study quantum stability bound on the mass of scalaron in generic theories of $f(R)$ gravity. We show that in these scenarios, the scalaron mass increases faster with local density of the environment than one loop quantum correction to it thereby leading to violation of quantum bound on the chameleon mass. The introduction of quadratic curvature corrections in the action are shown to stabilize the model.Comment: 7 pages, no figures, typos corrected, to match with the PLB published versio

On limit periodicity of discrete time stochastic processes

We consider a discrete time dynamic system described by a difference equation with periodic coefficients and with additive stochastic noise. We investigate the possibility of the periodicity of the solution. In particular, we established sufficient conditions for convergence of the solution in mean square or almost surely to some stochastic periodic process

From SICs and MUBs to Eddington

This is a survey of some very old knowledge about Mutually Unbiased Bases (MUB) and Symmetric Informationally Complete POVMs (SIC). In prime dimensions the former are closely tied to an elliptic normal curve symmetric under the Heisenberg group, while the latter are believed to be orbits under the Heisenberg group in all dimensions. In dimensions 3 and 4 the SICs are understandable in terms of elliptic curves, but a general statement escapes us. The geometry of the SICs in 3 and 4 dimensions is discussed in some detail.Comment: 12 pages; from the Festschrift for Tony Sudber

Mutually unbiased bases: tomography of spin states and star-product scheme

Mutually unbiased bases (MUBs) are considered within the framework of a generic star-product scheme. We rederive that a full set of MUBs is adequate for a spin tomography, i.e. knowledge of all probabilities to find a system in each MUB-state is enough for a state reconstruction. Extending the ideas of the tomographic-probability representation and the star-product scheme to MUB-tomography, dequantizer and quantizer operators for MUB-symbols of spin states and operators are introduced, ordinary and dual star-product kernels are found. Since MUB-projectors are to obey specific rules of the star-product scheme, we reveal the Lie algebraic structure of MUB-projectors and derive new relations on triple- and four-products of MUB-projectors. Example of qubits is considered in detail. MUB-tomography by means of Stern-Gerlach apparatus is discussed.Comment: 11 pages, 1 table, partially presented at the 17th Central European Workshop on Quantum Optics (CEWQO'2010), June 6-11, 2010, St. Andrews, Scotland, U

SIC~POVMs and Clifford groups in prime dimensions

We show that in prime dimensions not equal to three, each group covariant symmetric informationally complete positive operator valued measure (SIC~POVM) is covariant with respect to a unique Heisenberg--Weyl (HW) group. Moreover, the symmetry group of the SIC~POVM is a subgroup of the Clifford group. Hence, two SIC~POVMs covariant with respect to the HW group are unitarily or antiunitarily equivalent if and only if they are on the same orbit of the extended Clifford group. In dimension three, each group covariant SIC~POVM may be covariant with respect to three or nine HW groups, and the symmetry group of the SIC~POVM is a subgroup of at least one of the Clifford groups of these HW groups respectively. There may exist two or three orbits of equivalent SIC~POVMs for each group covariant SIC~POVM, depending on the order of its symmetry group. We then establish a complete equivalence relation among group covariant SIC~POVMs in dimension three, and classify inequivalent ones according to the geometric phases associated with fiducial vectors. Finally, we uncover additional SIC~POVMs by regrouping of the fiducial vectors from different SIC~POVMs which may or may not be on the same orbit of the extended Clifford group.Comment: 30 pages, 1 figure, section 4 revised and extended, published in J. Phys. A: Math. Theor. 43, 305305 (2010

Generalized Brans-Dicke theories

In Brans-Dicke theory a non-linear self interaction of a scalar field allows a possibility of realizing the late-time cosmic acceleration, while recovering the General Relativistic behavior at early cosmological epochs. We extend this to more general modified gravitational theories in which a de Sitter solution for dark energy exists without using a field potential. We derive a condition for the stability of the de Sitter point and study the background cosmological dynamics of such theories. We also restrict the allowed region of model parameters from the demand for the avoidance of ghosts and instabilities. A peculiar evolution of the field propagation speed allows us to distinguish those theories from the LCDM model.Comment: 14 pages, 4 figures, version to appear in JCA

Cancer incidence in British vegetarians

Background: Few prospective studies have examined cancer incidence among vegetarians. Methods: We studied 61 566 British men and women, comprising 32 403 meat eaters, 8562 non-meat eaters who did eat fish ('fish eaters') and 20 601 vegetarians. After an average follow-up of 12.2 years, there were 3350 incident cancers of which 2204 were among meat eaters, 317 among fish eaters and 829 among vegetarians. Relative risks (RRs) were estimated by Cox regression, stratified by sex and recruitment protocol and adjusted for age, smoking, alcohol, body mass index, physical activity level and, for women only, parity and oral contraceptive use. Results: There was significant heterogeneity in cancer risk between groups for the following four cancer sites: stomach cancer, RRs (compared with meat eaters) of 0.29 (95% CI: 0.07–1.20) in fish eaters and 0.36 (0.16–0.78) in vegetarians, P for heterogeneity=0.007; ovarian cancer, RRs of 0.37 (0.18–0.77) in fish eaters and 0.69 (0.45–1.07) in vegetarians, P for heterogeneity=0.007; bladder cancer, RRs of 0.81 (0.36–1.81) in fish eaters and 0.47 (0.25–0.89) in vegetarians, P for heterogeneity=0.05; and cancers of the lymphatic and haematopoietic tissues, RRs of 0.85 (0.56–1.29) in fish eaters and 0.55 (0.39–0.78) in vegetarians, P for heterogeneity=0.002. The RRs for all malignant neoplasms were 0.82 (0.73–0.93) in fish eaters and 0.88 (0.81–0.96) in vegetarians (P for heterogeneity=0.001). Conclusion: The incidence of some cancers may be lower in fish eaters and vegetarians than in meat eaters

Racial and Ethnic Differences in Individuals with Sporadic Creutzfeldt-Jakob Disease in the United States of America

BACKGROUND: Little is known about racial and ethnic differences in individuals with sporadic Creutzfeldt-Jakob disease (sCJD). The authors sought to examine potential clinical, diagnostic, genetic, and neuropathological differences in sCJD patients of different races/ethnicities. METHODOLOGY/PRINCIPAL FINDINGS: A retrospective study of 116 definite and probable sCJD cases from Johns Hopkins and the Department of Veterans Affairs Healthcare Systems was conducted that examined differences in demographic, clinical, diagnostic, genetic, and neuropathological characteristics among racial/ethnic groups. Age at disease onset differed among racial/ethnic groups. Non-Hispanic Whites had a significantly older age at disease onset compared to the other groups (65 vs. 60, p = 0.036). Non-Whites were accurately diagnosed more rapidly than Whites (p = 0.008) and non-Hispanic Whites were more likely to have normal appearing basal ganglia on brain magnetic resonance imaging (MRI) compared to minorities (p = 0.02). Whites were also more likely to undergo post-mortem evaluation compared to non-Whites (p = 0.02). CONCLUSIONS/SIGNIFICANCE: Racial/ethnic groups affected by sCJD demonstrated differences in age at disease onset, time to correct diagnosis, clinical presentation, and diagnostic test results. Whites were more likely to undergo autopsy compared to non-Whites. These results have implications in regards to case ascertainment, diagnosis, and surveillance of sCJD and possibly other human prion diseases