Rolling of Coxeter polyhedra along mirrors

The topic of the paper are developments of $n$-dimensional Coxeter polyhedra. We show that the surface of such polyhedron admits a canonical cutting such that each piece can be covered by a Coxeter $(n-1)$-dimensional domain.Comment: 20pages, 15 figure

Deriving accurate peculiar velocities (even at high redshift)

The way that peculiar velocities are often inferred from measurements of distances and redshifts makes an approximation, v_p = cz-H_0 D, that gives significant errors even at relatively low redshifts (overestimates peculiar velocity by ~ 100 km/s at z~0.04). Here we demonstrate where the approximation breaks down, the systematic offset it introduces, and how the exact calculation should be implemented.Comment: 6 pages, 4 figures, accepted by MNRAS; revision adds footnote 3, a couple of references, and some minor tweaks to tex

Integrity bases for local invariants of composite quantum systems

Unitary group branchings appropriate to the calculation of local invariants of density matrices of composite quantum systems are formulated using the method of $S$-function plethysms. From this, the generating function for the number of invariants at each degree in the density matrix can be computed. For the case of two two-level systems the generating function is $F(q) = 1 + q + 4q^{2} + 6 q^{3} + 16 q^{4} + 23 q^{5} + 52 q^{6} + 77 q^{7} + 150 q^{8} + 224 q^{9} + 396 q^{10} + 583 q^{11}+ O(q^{12})$. Factorisation of such series leads in principle to the identification of an integrity basis of algebraically independent invariants. This note replaces Appendix B of our paper\cite{us} J Phys {\bf A33} (2000) 1895-1914 (\texttt{quant-ph/0001076}) which is incorrect.Comment: Latex, 4 pages, correcting Appendix B of quant-ph/0001076 Error in $F(q)$ corrected and conclusions modified accordingl

RAGE Signaling in Skeletal Biology

PURPOSE OF REVIEW: The receptor for advanced glycation end products (RAGE) and several of its ligands have been implicated in the onset and progression of pathologies associated with aging, chronic inflammation, and cellular stress. In particular, the role of RAGE and its ligands in bone tissue during both physiological and pathological conditions has been investigated. However, the extent to which RAGE signaling regulates bone homeostasis and disease onset remains unclear. Further, RAGE effects in the different bone cells and whether these effects are cell-type specific is unknown. The objective of the current review is to describe the literature over RAGE signaling in skeletal biology as well as discuss the clinical potential of RAGE as a diagnostic and/or therapeutic target in bone disease. RECENT FINDINGS: The role of RAGE and its ligands during skeletal homeostasis, tissue repair, and disease onset/progression is beginning to be uncovered. For example, detrimental effects of the RAGE ligands, advanced glycation end products (AGEs), have been identified for osteoblast viability/activity, while others have observed that low level AGE exposure stimulates osteoblast autophagy, which subsequently promotes viability and function. Similar findings have been reported with HMGB1, another RAGE ligand, in which high levels of the ligand are associated with osteoblast/osteocyte apoptosis, whereas low level/short-term administration stimulates osteoblast differentiation/bone formation and promotes fracture healing. Additionally, elevated levels of several RAGE ligands (AGEs, HMGB1, S100 proteins) induce osteoblast/osteocyte apoptosis and stimulate cytokine production, which is associated with increased osteoclast differentiation/activity. Conversely, direct RAGE-ligand exposure in osteoclasts may have inhibitory effects. These observations support a conclusion that elevated bone resorption observed in conditions of high circulating ligands and RAGE expression are due to actions on osteoblasts/osteocytes rather than direct actions on osteoclasts, although additional work is required to substantiate the observations. Recent studies have demonstrated that RAGE and its ligands play an important physiological role in the regulation of skeletal development, homeostasis, and repair/regeneration. Conversely, elevated levels of RAGE and its ligands are clearly related with various diseases associated with increased bone loss and fragility. However, despite the recent advancements in the field, many questions regarding RAGE and its ligands in skeletal biology remain unanswered

Research and development of high temperature resistant polymeric film forming material final summary report, 1 mar. 1961 - 17 apr. 1962

Preparation of poly-organometallosiloxane polymers from reactions between bis-dialkylamino metal derivatives and silanediol

Sewing sound quantum flesh onto classical bones

Semiclassical transformation theory implies an integral representation for stationary-state wave functions $\psi_m(q)$ in terms of angle-action variables ($\theta,J$). It is a particular solution of Schr\"{o}dinger's time-independent equation when terms of order $\hbar^2$ and higher are omitted, but the pre-exponential factor $A(q,\theta)$ in the integrand of this integral representation does not possess the correct dependence on $q$. The origin of the problem is identified: the standard unitarity condition invoked in semiclassical transformation theory does not fix adequately in $A(q,\theta)$ a factor which is a function of the action $J$ written in terms of $q$ and $\theta$. A prescription for an improved choice of this factor, based on succesfully reproducing the leading behaviour of wave functions in the vicinity of potential minima, is outlined. Exact evaluation of the modified integral representation via the Residue Theorem is possible. It yields wave functions which are not, in general, orthogonal. However, closed-form results obtained after Gram-Schmidt orthogonalization bear a striking resemblance to the exact analytical expressions for the stationary-state wave functions of the various potential models considered (namely, a P\"{o}schl-Teller oscillator and the Morse oscillator).Comment: RevTeX4, 6 page

Frustration, interaction strength and ground-state entanglement in complex quantum systems

Entanglement in the ground state of a many-body quantum system may arise when the local terms in the system Hamiltonian fail to commute with the interaction terms in the Hamiltonian. We quantify this phenomenon, demonstrating an analogy between ground-state entanglement and the phenomenon of frustration in spin systems. In particular, we prove that the amount of ground-state entanglement is bounded above by a measure of the extent to which interactions frustrate the local terms in the Hamiltonian. As a corollary, we show that the amount of ground-state entanglement is bounded above by a ratio between parameters characterizing the strength of interactions in the system, and the local energy scale. Finally, we prove a qualitatively similar result for other energy eigenstates of the system.Comment: 11 pages, 3 figure

The Deflection of the Two Interacting Coronal Mass Ejections of 2010 May 23-24 as Revealed by Combined In situ Measurements and Heliospheric Imaging

In 2010 May 23-24, SDO observed the launch of two successive coronal mass ejections (CMEs), which were subsequently tracked by the SECCHI suite onboard STEREO. Using the COR2 coronagraphs and the heliospheric imagers (HIs), the initial direction of both CMEs is determined to be slightly west of the Sun-Earth line. We derive the CME kinematics, including the evolution of the CME expansion until 0.4 AU. We find that, during the interaction, the second CME decelerates from a speed above 500 km/s to 380 km/s the speed of the leading edge of the first CME. STEREO observes a complex structure composed of two different bright tracks in HI2-A but only one bright track in HI2-B. In situ measurements from Wind show an "isolated" ICME, with the geometry of a flux rope preceded by a shock. Measurements in the sheath are consistent with draping around the transient. By combining remote-sensing and in situ measurements, we determine that this event shows a clear instance of deflection of two CMEs after their collision, and we estimate the deflection of the first CME to be about 10 degrees towards the Sun-Earth line. The arrival time, arrival speed and radius at Earth of the first CME are best predicted from remote-sensing observations taken before the collision of the CMEs. Due to the over-expansion of the CME after the collision, there are few, if any, signs of interaction in in situ measurements. This study illustrates that complex interactions during the Sun-to-Earth propagation may not be revealed by in situ measurements alone.Comment: 14 pages, 8 figures, 1 table, accepted to the Astrophysical Journa

Growth of fat slits and dispersionless KP hierarchy

A "fat slit" is a compact domain in the upper half plane bounded by a curve with endpoints on the real axis and a segment of the real axis between them. We consider conformal maps of the upper half plane to the exterior of a fat slit parameterized by harmonic moments of the latter and show that they obey an infinite set of Lax equations for the dispersionless KP hierarchy. Deformation of a fat slit under changing a particular harmonic moment can be treated as a growth process similar to the Laplacian growth of domains in the whole plane. This construction extends the well known link between solutions to the dispersionless KP hierarchy and conformal maps of slit domains in the upper half plane and provides a new, large family of solutions.Comment: 26 pages, 6 figures, typos correcte