Nonclassical Degrees of Freedom in the Riemann Hamiltonian

The Hilbert-Polya conjecture states that the imaginary parts of the zeros of the Riemann zeta function are eigenvalues of a quantum hamiltonian. If so, conjectures by Katz and Sarnak put this hamiltonian in Altland and Zirnbauer's universality class C. This implies that the system must have a nonclassical two-valued degree of freedom. In such a system, the dominant primitive periodic orbits contribute to the density of states with a phase factor of -1. This resolves a previously mysterious sign problem with the oscillatory contributions to the density of the Riemann zeros.Comment: 4 pages, no figures; v3-6 have minor corrections to v2, v2 has a more complete solution of the sign problem than v

Aberration-like cusped focusing in the post-paraxial Talbot effect

We present an analysis of self-imaging in a regime beyond the paraxial, where deviation from simple paraxial propagation causes apparent self-imaging aberrations. The resulting structures are examples of aberration without rays and are described analytically using post-paraxial theory. They are shown to relate to, but surprisingly do not precisely replicate, a standard integral representation of a diffraction cusp. Beyond the Talbot effect, this result is significant as it illustrates that the effect of aberration -- as manifested in the replacement of a perfect focus with a cusp-like pattern -- can occur as a consequence of improving the paraxial approximation, rather than due to imperfections in the optical system.Comment: 8 pages, 3 figures, IoP styl

Dynamic communities in multichannel data: An application to the foreign exchange market during the 2007--2008 credit crisis

We study the cluster dynamics of multichannel (multivariate) time series by representing their correlations as time-dependent networks and investigating the evolution of network communities. We employ a node-centric approach that allows us to track the effects of the community evolution on the functional roles of individual nodes without having to track entire communities. As an example, we consider a foreign exchange market network in which each node represents an exchange rate and each edge represents a time-dependent correlation between the rates. We study the period 2005-2008, which includes the recent credit and liquidity crisis. Using dynamical community detection, we find that exchange rates that are strongly attached to their community are persistently grouped with the same set of rates, whereas exchange rates that are important for the transfer of information tend to be positioned on the edges of communities. Our analysis successfully uncovers major trading changes that occurred in the market during the credit crisis.Comment: 8 pages, 6 figures, accepted for publication in Chao

Chaos and Quantum Thermalization

We show that a bounded, isolated quantum system of many particles in a specific initial state will approach thermal equilibrium if the energy eigenfunctions which are superposed to form that state obey {\it Berry's conjecture}. Berry's conjecture is expected to hold only if the corresponding classical system is chaotic, and essentially states that the energy eigenfunctions behave as if they were gaussian random variables. We review the existing evidence, and show that previously neglected effects substantially strengthen the case for Berry's conjecture. We study a rarefied hard-sphere gas as an explicit example of a many-body system which is known to be classically chaotic, and show that an energy eigenstate which obeys Berry's conjecture predicts a Maxwell--Boltzmann, Bose--Einstein, or Fermi--Dirac distribution for the momentum of each constituent particle, depending on whether the wave functions are taken to be nonsymmetric, completely symmetric, or completely antisymmetric functions of the positions of the particles. We call this phenomenon {\it eigenstate thermalization}. We show that a generic initial state will approach thermal equilibrium at least as fast as $O(\hbar/\Delta)t^{-1}$, where $\Delta$ is the uncertainty in the total energy of the gas. This result holds for an individual initial state; in contrast to the classical theory, no averaging over an ensemble of initial states is needed. We argue that these results constitute a new foundation for quantum statistical mechanics.Comment: 28 pages in Plain TeX plus 2 uuencoded PS figures (included); minor corrections only, this version will be published in Phys. Rev. E; UCSB-TH-94-1

Cardiac magnetic resonance findings predict increased resource utilization in elective coronary artery bypass grafting

Morbidity following CABG (coronary artery bypass grafting) is difficult to predict and leads to increased healthcare costs. We hypothesized that pre-operative CMR (cardiac magnetic resonance) findings would predict resource utilization in elective CABG. Over a 12-month period, patients requiring elective CABG were invited to undergo CMR 1 day prior to CABG. Gadolinium-enhanced CMR was performed using a trueFISP inversion recovery sequence on a 1.5 tesla scanner (Sonata; Siemens). Clinical data were collected prospectively. Admission costs were quantified based on standardized actual cost/day. Admission cost greater than the median was defined as 'increased'. Of 458 elective CABG cases, 45 (10%) underwent pre-operative CMR. Pre-operative characteristics [mean (S.D.) age, 64 (9) years, mortality (1%) and median (interquartile range) admission duration, 7 (6–8) days] were similar in patients who did or did not undergo CMR. In the patients undergoing CMR, eight (18%) and 11 (24%) patients had reduced LV (left ventricular) systolic function by CMR [LVEF (LV ejection fraction) <55%] and echocardiography respectively. LE (late enhancement) with gadolinium was detected in 17 (38%) patients. The average cost/day was $2723. The median (interquartile range) admission cost was$19059 ($10891–157917). CMR LVEF {OR (odds ratio), 0.93 [95% CI (confidence interval), 0.87–0.99]; P=0.03} and SV (stroke volume) index [OR 1.07 (95% CI, 1.00–1.14); P=0.02] predicted increased admission cost. CMR LVEF (P=0.08) and EuroScore tended to predict actual admission cost (P=0.09), but SV by CMR (P=0.16) and LV function by echocardiography (P=0.95) did not. In conclusion, in this exploratory investigation, pre-operative CMR findings predicted admission duration and increased admission cost in elective CABG surgery. The cost-effectiveness of CMR in risk stratification in elective CABG surgery merits prospective assessment

Transition-State Interactions in a Promiscuous Enzyme: Sulfate and Phosphate Monoester Hydrolysis by Pseudomonas aeruginosa Arylsulfatase.

Pseudomonas aeruginosa arylsulfatase (PAS) hydrolyzes sulfate and, promiscuously, phosphate monoesters. Enzyme-catalyzed sulfate transfer is crucial to a wide variety of biological processes, but detailed studies of the mechanistic contributions to its catalysis are lacking. We present linear free energy relationships (LFERs) and kinetic isotope effects (KIEs) of PAS and analyses of active site mutants that suggest a key role for leaving group (LG) stabilization. In LFERs PASWT has a much less negative Brønsted coefficient (βleaving groupobs-Enz = -0.33) than the uncatalyzed reaction (βleaving groupobs = -1.81). This situation is diminished when cationic active site groups are exchanged for alanine. The considerable degree of bond breaking during the transition state (TS) is evidenced by an 18Obridge KIE of 1.0088. LFER and KIE data for several active site mutants point to leaving group stabilization by active site K375, in cooperation with H211. 15N KIEs and the increased sensitivity to leaving group ability of the sulfatase activity in neat D2O (Δβleaving groupH-D = +0.06) suggest that the mechanism for S-Obridge bond fission shifts, with decreasing leaving group ability, from charge compensation via Lewis acid interactions toward direct proton donation. 18Ononbridge KIEs indicate that the TS for PAS-catalyzed sulfate monoester hydrolysis has a significantly more associative character compared to the uncatalyzed reaction, while PAS-catalyzed phosphate monoester hydrolysis does not show this shift. This difference in enzyme-catalyzed TSs appears to be the major factor favoring specificity toward sulfate over phosphate esters by this promiscuous hydrolase, since other features are either too similar (uncatalyzed TS) or inherently favor phosphate (charge).BBSRC BB/I004327/1 EPSRC EP/E019390/1

Statistical Analysis of Magnetic Field Spectra

We have calculated and statistically analyzed the magnetic-field spectrum (the ``B-spectrum'') at fixed electron Fermi energy for two quantum dot systems with classically chaotic shape. This is a new problem which arises naturally in transport measurements where the incoming electron has a fixed energy while one tunes the magnetic field to obtain resonance conductance patterns. The ``B-spectrum'', defined as the collection of values ${B_i}$ at which conductance $g(B_i)$ takes extremal values, is determined by a quadratic eigenvalue equation, in distinct difference to the usual linear eigenvalue problem satisfied by the energy levels. We found that the lower part of the ``B-spectrum'' satisfies the distribution belonging to Gaussian Unitary Ensemble, while the higher part obeys a Poisson-like behavior. We also found that the ``B-spectrum'' fluctuations of the chaotic system are consistent with the results we obtained from random matrices

Stroke following percutaneous coronary intervention : type-specific incidence, outcomes and determinants seen by the British Cardiovascular Intervention Society 2007-12

Published on behalf of the European Society of Cardiology. All rights reserved. © The Author 2015. For permissions please email: [email protected] reviewedPostprin

Toward Fulfilling the Promise of Molecular Medicine in Fragile X

Fragile X syndrome (FXS) is the most common inherited form of mental retardation and a leading known cause of autism. It is caused by loss of expression of the fragile X mental retardation protein (FMRP), an RNA-binding protein that negatively regulates protein synthesis. In neurons, multiple lines of evidence suggest that protein synthesis at synapses is triggered by activation of group 1 metabotropic glutamate receptors (Gp1 mGluRs) and that many functional consequences of activating these receptors are altered in the absence of FMRP. These observations have led to the theory that exaggerated protein synthesis downstream of Gp1 mGluRs is a core pathogenic mechanism in FXS. This excess can be corrected by reducing signaling by Gp1 mGluRs, and numerous studies have shown that inhibition of mGluR5, in particular, can ameliorate multiple mutant phenotypes in animal models of FXS. Clinical trials based on this therapeutic strategy are currently under way. FXS is therefore poised to be the first neurobehavioral disorder in which corrective treatments have been developed from the bottom up: from gene identification to pathophysiology in animals to novel therapeutics in humans. The insights gained from FXS and other autism-related single-gene disorders may also assist in identifying molecular mechanisms and potential treatment approaches for idiopathic autism.Eunice Kennedy Shriver National Institute of Child Health and Human Development (U.S.)National Institute of Mental Health (U.S.)FRAXA Research Foundatio