Quantum deformation of quantum gravity

We describe a deformation of the observable algebra of quantum gravity in which the loop algebra is extended to framed loops. This allows an alternative nonperturbative quantization which is suitable for describing a phase of quantum gravity characterized by states which are normalizable in the measure of Chern-Simons theory. The deformation parameter, q, depends on the cosmological constant. The Mandelstam identities are extended to a set of relations which are governed by the Kauffman bracket so that the spin network basis is deformed to a basis of SU(2)q spin networks. Corrections to the actions of operators in non-perturbative quantum gravity may be readily computed using recoupling theory; the example of the area observable is treated here. Finally, eigenstates of the q-deformed Wilson loops are constructed, which may make possible the construction of a q-deformed connection representation through an inverse transform.Comment: 12 pages, many figure

Electron Tunneling in Single Crystals of Pseudomonas aeruginosa Azurins

Rates of reduction of Os(III), Ru(III), and Re(I)^* by Cu(I) in His83-modified Pseudomonas aeruginosa azurins (M−Cu distance ∼17 Å) have been measured in single crystals, where protein conformation and surface solvation are precisely defined by high-resolution X-ray structure determinations:  1.7(8) × 10^6 s^(-1) (298 K), 1.8(8) × 10^6 s^(-1) (140 K), [Ru(bpy)_2(im)^(3+)-]; 3.0(15) × 10^6 s^(-1) (298 K), [Ru(tpy)(bpy)^(3+)-]; 3.0(15) × 10^6 s^(-1) (298 K), [Ru(tpy)(phen)^(3+)-]; 9.0(50) × 10^2 s^(-1) (298 K), [Os(bpy)2(im)^(3+)-]; 4.4(20) × 10^6 s^(-1) (298 K), [Re(CO)_3(phen)^(+*)] (bpy = 2,2‘-bipyridine; im = imidazole; tpy = 2,2‘:6‘,2‘ ‘-terpyridine; phen = 1,10-phenanthroline). The time constants for electron tunneling in crystals are roughly the same as those measured in solution, indicating very similar protein structures in the two states. High-resolution structures of the oxidized (1.5 Å) and reduced (1.4 Å) states of Ru(II)(tpy)(phen)(His83)Az establish that very small changes in copper coordination accompany reduction but reveal a shorter axial interaction between copper and the Gly45 peptide carbonyl oxygen [2.6 Å for Cu(II)] than had been recognized previously. Although Ru(bpy)_2(im)(His83)Az is less solvated in the crystal, the reorganization energy for Cu(I) → Ru(III) electron transfer falls in the range (0.6−0.8 eV) determined experimentally for the reaction in solution. Our work suggests that outer-sphere protein reorganization is the dominant activation component required for electron tunneling

Relaxation Dynamics of Pseudomonas aeruginosa Re^I(C)O_3(α-diimine)(HisX)^+ (X=83, 107, 109, 124, 126)Cu-^(II) Azurins

Photoinduced relaxation processes of five structurally characterized Pseudomonas aeruginosa Re^I(CO)_3(α-diimine)(HisX) (X = 83, 107, 109, 124, 126)Cu^(II) azurins have been investigated by time-resolved (ps−ns) IR spectroscopy and emission spectroscopy. Crystal structures reveal the presence of Re-azurin dimers and trimers that in two cases (X = 107, 124) involve van der Waals interactions between interdigitated diimine aromatic rings. Time-dependent emission anisotropy measurements confirm that the proteins aggregate in mM solutions (D2O, KPi buffer, pD = 7.1). Excited-state DFT calculations show that extensive charge redistribution in the ReI(CO)_3 → diimine ^3MLCT state occurs: excitation of this ^3MLCT state triggers several relaxation processes in Re-azurins whose kinetics strongly depend on the location of the metallolabel on the protein surface. Relaxation is manifested by dynamic blue shifts of excited-state ν(CO) IR bands that occur with triexponential kinetics: intramolecular vibrational redistribution together with vibrational and solvent relaxation give rise to subps, 2, and 8−20 ps components, while the ~10^2 ps kinetics are attributed to displacement (reorientation) of the Re^I(CO)_3(phen)(im) unit relative to the peptide chain, which optimizes Coulombic interactions of the Re^I excited-state electron density with solvated peptide groups. Evidence also suggests that additional segmental movements of Re-bearing β-strands occur without perturbing the reaction field or interactions with the peptide. Our work demonstrates that time-resolved IR spectroscopy and emission anisotropy of Re^I carbonyl−diimine complexes are powerful probes of molecular dynamics at or around the surfaces of proteins and protein−protein interfacial regions

The reaction of stock markets to crashes: a comparison study between emerging and mature markets using wavelet transforms

We study here the behaviour of the first three eigenvalues (λ1, λ2, λ3) and their ratio [(λ1/λ2), (λ1/λ3), (λ2/λ3)] of the covariance matrices of the original return series and of those rebuilt from wavelet components for emerging and mature markets. It has been known for some time that the largest eigenvalue (λ1) contains information on the risk associated with the particular assets of which the covariance matrix is comprised. Here, we wish to ascertain whether the subdominant eigenvalues (λ2, λ3) hold information on the risk of the stock market and also to measure the recovery time for emerging and mature markets. To do this, we use the discrete wavelet transform which gives a clear picture of the movements in the return series by reconstructing them using each wavelet component. Our results appear to indicate that mature markets respond to crashes differently to emerging ones, in that emerging markets may take up to two months to recover while major markets take less than a month to do so. In addition, the results appears to show that the subdominant eigenvalues (λ2, λ3) give additional information on market movement, especially for emerging markets and that a study of the behaviour of the other eigenvalues may provide insight on crash dynamics

Two-loop Yang-Mills diagrams from superstring amplitudes

Starting from the superstring amplitude describing interactions among D-branes with a constant world-volume field strength, we present a detailed analysis of how the open string degeneration limits reproduce the corresponding field theory Feynman diagrams. A key ingredient in the string construction is represented by the twisted (Prym) super differentials, as their periods encode the information about the background field. We provide an efficient method to calculate perturbatively the determinant of the twisted period matrix in terms of sets of super-moduli appropriate to the degeneration limits. Using this result we show that there is a precise one-to-one correspondence between the degeneration of different factors in the superstring amplitudes and one-particle irreducible Feynman diagrams capturing the gauge theory effective action at the two-loop level.Comment: 42 pages plus appendices, 10 figure

Neutrino Oscillations in the Framework of Three-Generation Mixings with Mass Hierarchy

We have analyzed the results of reactor and accelerator neutrino oscillation experiments in the framework of a general model with mixing of three neutrino fields and a neutrino mass hierarchy that can accommodate the results of the solar neutrino experiments. It is shown that $\nu_\mu \leftrightarrows \nu_e$ oscillations with $0.6 \le \Delta m^2 \le 100 \, \mathrm{eV}^2$ and amplitude larger than $2 \times 10^{-3}$ are not compatible with the existing limits on neutrino oscillations if the non-diagonal elements of the mixing matrix $\left| U_{e3} \right|$ and $\left| U_{\mu3} \right|$ are small. Thus, if the excess of electron events recently observed in the LSND experiment is due to $\nu_\mu \leftrightarrows \nu_e$ oscillations, the mixing in the lepton sector is basically different from the CKM mixing of quarks. If this type of mixing is realized in nature, the observation of $\nu_\mu \leftrightarrows \nu_e$ oscillations would not influence $\nu_\mu \leftrightarrows \nu_\tau$ oscillations that are being searched for in the CHORUS and NOMAD experiments.Comment: Revtex file, 13 pages + 2 figures (included). The postscript file of text and figures is available at http://www.to.infn.it/teorici/giunti/papers.html or ftp://ftp.to.infn.it/pub/giunti/1995/dftt-25-95/dftt-25-95.ps.

Heterogeneity in the non-planarity and arterial curvature of arteriovenous fistulae in vivo

Objective: Native arteriovenous fistulae (AVF) for haemodialysis are susceptible to non-maturation. Adverse features of local blood flow have been implicated in the formation of peri-anastomotic neointimal hyperplasia which may underpin non-maturation. While computational fluid dynamic simulations of idealised models highlight the importance of geometry on fluid and vessel wall interactions, little is known in vivo about AVF geometry and its role in adverse clinical outcomes. This study set out to examine the three-dimensional geometry of native AVF and the geometric correlates of AVF failure. Methods: As part of an observational study between 2013 and 2016, patients underwent creation of an upper limb AVF according to current surgical best practice. Phase-contrast MRI was performed on the day of surgery to obtain luminal geometry along with ultrasound measurements of flow. MRI datasets were segmented and reconstructed for quantitative and qualitative analysis of local geometry. Clinical maturation was evaluated at six weeks. Results: 60 patients were successfully imaged on the day of surgery. Radiocephalic (n=17), brachiocephalic (n=40) and brachiobasilic (n=3) fistulae were all included in the study. Centrelines extracted from segmented vessel lumen exhibited significant heterogeneity in arterial non-planarity and curvature. Furthermore, these features are more marked in brachiocephalic as compared to radiocephalic fistulae. Across the cohort, the projected bifurcation angle was was 73° (±16°) mean (±sd). Geometry was preserved at two weeks in 20 patients who underwent repeat imaging. A greater degree of arterial non-planarity (log odds ratio (logOR) 0.95 per 0.1/vessel diameter (95% CI 0.22 to 1.90, P= .03)) along with a larger bifurcation angle (logOR 0.05 per degree (95% CI 0.01 to 0.09, P= .02)) are associated with a great rate of maturation, as is fistula location (upper vs lower arm) logOR -1.9 (95% CI -3.2 to 0.7, P = .002) . Conclusions: There is significant heterogeneity in the three-dimensional geometry of arteriovenous fistulae, in particular, arterial non-planarity and curvature. In this largest cohort of AVF geometry to date, the effect of individual geometric correlates on maturation is uncertain but supports the premise that future modelling studies will need to acknowledge the complex geometry of AVF

Spectroscopy and Reactivity of a Photogenerated Tryptophan Radical in a Structurally Defined Protein Environment

Near-UV irradiation of structurally characterized [Re(I)(CO)_3(1,10-phenanthroline)(Q107H)](W48F/Y72F/H83Q/Y108W)AzM(II) [Az = Pseudomonas aeruginosa azurin, M = Cu, Zn]/[Co(NH_3)_5Cl]Cl_2 produces a tryptophan radical (W108•) with unprecedented kinetic stability. After rapid formation (k = 2.8 × 10^6 s^(-1)), the radical persists for more than 5 h at room temperature in the folded ReAzM(II) structure. The absorption spectrum of ReAz(W108•)M(II) exhibits maxima at 512 and 536 nm. Oxidation of K_4[Mo(CN)_8] by ReAz(W108•)Zn(II) places the W108•/W108 reduction potential in the protein above 0.8 V vs NHE

Differential Equations for Periods and Flat Coordinates in Two Dimensionsional Topological Matter Theories

We derive directly from the N=2 LG superpotential the differential equations that determine the flat coordinates of arbitrary topological CFT's.Comment: 34

Structures of Ruthenium-modified Pseudomonas aeruginosa Azurin and [Ru(2,2’-bipyridine)_2(imidazole)_2)]SO_4•10H_2O

The crystal structure of Ru(2,2'-bipyridine)_2(imidazole)(His83)azurin (RuAz) has been determined to 2.3 Å ¬resolution by X-ray crystallography. The spectroscopic and thermodynamic properties of both the native protein and [Ru(2,2'-bipyridine)_2(imidazole)_2]^(2+) are maintained in the modified protein. Dark-green RuAz crystals grown from PEG 4000, LiNO_3, CuCl_2 and Tris buffer are monoclinic, belong to the space group C2 and have cell parameters a = 100.6, b = 35.4, c = 74.7 Å and β = 106.5°. In addition, [Ru(2,2'-bipyridine)_2(imidazole)_2]SO_4•10H_2O was synthesized, crystallized and structurally characterized by X-ray crystallography. Red-brown crystals of this complex are monoclinic, space group P2_1/n, unit-cell parameters a = 13.230 (2), b = 18.197 (4), c = 16.126 (4) Å, β = 108.65 (2)°. Stereochemical parameters for the refinement of Ru(2,2'-bipyridine)_2(imidazole)(His83) were taken from the atomic coordinates of [Ru(2,2'-bipyridine)_2(imidazole)_2]^(2+). The structure of RuAz confirms that His83 is the only site of chemical modification and that the native azurin structure is not perturbed significantly by the ruthenium label