High-Precision Entropy Values for Spanning Trees in Lattices

Shrock and Wu have given numerical values for the exponential growth rate of the number of spanning trees in Euclidean lattices. We give a new technique for numerical evaluation that gives much more precise values, together with rigorous bounds on the accuracy. In particular, the new values resolve one of their questions.Comment: 7 pages. Revision mentions alternative approach. Title changed slightly. 2nd revision corrects first displayed equatio

G-Brownian Motion as Rough Paths and Differential Equations Driven by G-Brownian Motion

The present paper is devoted to the study of sample paths of G-Brownian motion and stochastic differential equations (SDEs) driven by G-Brownian motion from the view of rough path theory. As the starting point, we show that quasi-surely, sample paths of G-Brownian motion can be enhanced to the second level in a canonical way so that they become geometric rough paths of roughness 2 < p < 3. This result enables us to introduce the notion of rough differential equations (RDEs) driven by G-Brownian motion in the pathwise sense under the general framework of rough paths. Next we establish the fundamental relation between SDEs and RDEs driven by G-Brownian motion. As an application, we introduce the notion of SDEs on a differentiable manifold driven by GBrownian motion and construct solutions from the RDE point of view by using pathwise localization technique. This is the starting point of introducing G-Brownian motion on a Riemannian manifold, based on the idea of Eells-Elworthy-Malliavin. The last part of this paper is devoted to such construction for a wide and interesting class of G-functions whose invariant group is the orthogonal group. We also develop the Euler-Maruyama approximation for SDEs driven by G-Brownian motion of independent interest

Flows driven by Banach space-valued rough paths

We show in this note how the machinery of C^1-approximate flows devised in the work "Flows driven by rough paths", and applied there to reprove and extend most of the results on Banach space-valued rough differential equations driven by a finite dimensional rough path, can be used to deal with rough differential equations driven by an infinite dimensional Banach space-valued weak geometric Holder p-rough paths, for any p>2, giving back Lyons' theory in its full force in a simple way.Comment: 8 page

DNA adducts in fish following an oil spill exposure

On 12 December 1999, one third of the load of the Erika tanker, amounting to about 10,000 t crude oil flowed into sea waters close to the French Atlantic Coast. This oil contained polycyclic aromatic compounds (PAC) that are known to be genotoxic. Genotoxic effects induce DNA adducts formation, which can thus be used as pollution biomarkers. Here, we assessed the genotoxic impact of the “Erika” oil spill by DNA adducts detection in the liver of immature fishes (Solea solea) from four locations of the French Brittany coasts. Two months after the spill, a high amount of DNA adducts was found in samples from all locations, amounting to 92–290 DNA adduct per 109 nucleotides. Then total DNA adduct levels decreased to reach about 50 adducts per 109 nucleotides nine months after the spill. In vitro experiments using human cell cultures and fish liver microsomes evidence the genotoxicity of the Erika fuel. They also prove the formation of reactive species able to create DNA adducts. Furthermore, in vitro and in vivo DNA adducts fingerprints are similar, thus confirming that DNA adducts are a result of the oil spill

Emergence of long memory in stock volatility from a modified Mike-Farmer model

The Mike-Farmer (MF) model was constructed empirically based on the continuous double auction mechanism in an order-driven market, which can successfully reproduce the cubic law of returns and the diffusive behavior of stock prices at the transaction level. However, the volatility (defined by absolute return) in the MF model does not show sound long memory. We propose a modified version of the MF model by including a new ingredient, that is, long memory in the aggressiveness (quantified by the relative prices) of incoming orders, which is an important stylized fact identified by analyzing the order flows of 23 liquid Chinese stocks. Long memory emerges in the volatility synthesized from the modified MF model with the DFA scaling exponent close to 0.76, and the cubic law of returns and the diffusive behavior of prices are also produced at the same time. We also find that the long memory of order signs has no impact on the long memory property of volatility, and the memory effect of order aggressiveness has little impact on the diffusiveness of stock prices.Comment: 6 pages, 6 figures and 1 tabl

Influence of oxygen ordering kinetics on Raman and optical response in YBa_2Cu_3O_{6.4}

Kinetics of the optical and Raman response in YBa_2Cu_3O_{6.4} were studied during room temperature annealing following heat treatment. The superconducting T_c, dc resistivity, and low-energy optical conductivity recover slowly, implying a long relaxation time for the carrier density. Short relaxation times are observed for the B_{1g} Raman scattering -- magnetic, continuum, and phonon -- and the charge transfer band. Monte Carlo simulations suggest that these two relaxation rates are related to two length scales corresponding to local oxygen ordering (fast) and long chain and twin formation (slow).Comment: REVTeX, 3 pages + 4 PostScript (compressed) figure

The Origin of Time Asymmetry

It is argued that the observed Thermodynamic Arrow of Time must arise from the boundary conditions of the universe. We analyse the consequences of the no boundary proposal, the only reasonably complete set of boundary conditions that has been put forward. We study perturbations of a Friedmann model containing a massive scalar field but our results should be independent of the details of the matter content. We find that gravitational wave perturbations have an amplitude that remains in the linear regime at all times and is roughly time symmetric about the time of maximum expansion. Thus gravitational wave perturbations do not give rise to an Arrow of Time. However density perturbations behave very differently. They are small at one end of the universe's history, but grow larger and become non linear as the universe gets larger. Contrary to an earlier claim, the density perturbations do not get small again at the other end of the universe's history. They therefore give rise to a Thermodynamic Arrow of Time that points in a constant direction while the universe expands and contracts again. The Arrow of Time does not reverse at the point of maximum expansion. One has to appeal to the Weak Anthropic Principle to explain why we observe the Thermodynamic Arrow to agree with the Cosmological Arrow, the direction of time in which the universe is expanding.Comment: 41 pages, DAMTP R92/2

Two-magnon Raman scattering in insulating cuprates: Modifications of the effective Raman operator

Calculations of Raman scattering intensities in spin 1/2 square-lattice Heisenberg model, using the Fleury-Loudon-Elliott theory, have so far been unable to describe the broad line shape and asymmetry of the two magnon peak found experimentally in the cuprate materials. Even more notably, the polarization selection rules are violated with respect to the Fleury-Loudon-Elliott theory. There is comparable scattering in $B_{1g}$ and $A_{1g}$ geometries, whereas the theory would predict scattering in only $B_{1g}$ geometry. We review various suggestions for this discrepency and suggest that at least part of the problem can be addressed by modifying the effective Raman Hamiltonian, allowing for two-magnon states with arbitrary total momentum. Such an approach based on the Sawatzsky-Lorenzana theory of optical absorption assumes an important role of phonons as momentum sinks. It leaves the low energy physics of the Heisenberg model unchanged but substantially alters the Raman line-shape and selection rules, bringing the results closer to experiments.Comment: 7 pages, 6 figures, revtex. Contains some minor revisions from previous versio

Non-line-of-sight 3D imaging with a single-pixel camera

Real time, high resolution 3D reconstruction of scenes hidden from the direct field of view is a challenging field of research with applications in real-life situations related e.g. to surveillance, self-driving cars and rescue missions. Most current techniques recover the 3D structure of a non-lineof-sight (NLOS) static scene by detecting the return signal from the hidden object on a scattering observation area. Here, we demonstrate the full colour retrieval of the 3D shape of a hidden scene by coupling back-projection imaging algorithms with the high-resolution time-of-flight information provided by a single-pixel camera. By using a high effciency Single-Photon Avalanche Diode (SPAD) detector, this technique provides the advantage of imaging with no mechanical scanning parts, with acquisition times down to sub-seconds.Comment: 6 pages, 4 figure