Phase Segregation Dynamics in Particle Systems with Long Range Interactions I: Macroscopic Limits

We present and discuss the derivation of a nonlinear non-local integro-differential equation for the macroscopic time evolution of the conserved order parameter of a binary alloy undergoing phase segregation. Our model is a d-dimensional lattice gas evolving via Kawasaki exchange dynamics, i.e. a (Poisson) nearest-neighbor exchange process, reversible with respect to the Gibbs measure for a Hamiltonian which includes both short range (local) and long range (nonlocal) interactions. A rigorous derivation is presented in the case in which there is no local interaction. In a subsequent paper (part II), we discuss the phase segregation phenomena in the model. In particular we argue that the phase boundary evolutions, arising as sharp interface limits of the family of equations derived in this paper, are the same as the ones obtained from the corresponding limits for the Cahn-Hilliard equation.Comment: amstex with macros (included in the file), tex twice, 20 page

Absolute-Frequency Measurement of the Iodine-Based Length Standard at 514.67 nm

The absolute frequency of the length standard at 514.67 nm based on the molecular iodine (127I 2) transition of the P(13) 43-0 component a3 is measured using a self-referenced femtosecond optical comb. This frequency-based technique improves measurement precision more than 100 times compared with previous wavelength-based results. Power- and pressure-related frequency shifts have been carefully studied. The measured absolute frequency is 71.8±1.5 kHz higher than the internationally accepted value of 582490603.37±0.15 MHz, adopted by the Comité International des Poids et Mesures (CIPM) in 1997

Manin products, Koszul duality, Loday algebras and Deligne conjecture

In this article we give a conceptual definition of Manin products in any category endowed with two coherent monoidal products. This construction can be applied to associative algebras, non-symmetric operads, operads, colored operads, and properads presented by generators and relations. These two products, called black and white, are dual to each other under Koszul duality functor. We study their properties and compute several examples of black and white products for operads. These products allow us to define natural operations on the chain complex defining cohomology theories. With these operations, we are able to prove that Deligne's conjecture holds for a general class of operads and is not specific to the case of associative algebras. Finally, we prove generalized versions of a few conjectures raised by M. Aguiar and J.-L. Loday related to the Koszul property of operads defined by black products. These operads provide infinitely many examples for this generalized Deligne's conjecture.Comment: Final version, a few references adde

Feed-Forward Chains of Recurrent Attractor Neural Networks Near Saturation

We perform a stationary state replica analysis for a layered network of Ising spin neurons, with recurrent Hebbian interactions within each layer, in combination with strictly feed-forward Hebbian interactions between successive layers. This model interpolates between the fully recurrent and symmetric attractor network studied by Amit el al, and the strictly feed-forward attractor network studied by Domany et al. Due to the absence of detailed balance, it is as yet solvable only in the zero temperature limit. The built-in competition between two qualitatively different modes of operation, feed-forward (ergodic within layers) versus recurrent (non- ergodic within layers), is found to induce interesting phase transitions.Comment: 14 pages LaTex with 4 postscript figures submitted to J. Phys.

A phase 1 dose-escalating study of pegylated recombinant human arginase 1 (Peg-rhArg1) in patients with advanced hepatocellular carcinoma

Background Hepatocellular carcinoma (HCC) cells are auxotrophic for arginine, depletion of which leads to tumour regression. The current study evaluated safety, pharmacokinetics (PK)/ pharmacodynamics (PD) parameters, and potential anti-tumor activity of pegylated recombinant human arginase 1 (peg-rhArg1) in advanced HCC patients. Methods Eligibility criteria included advanced HCC with measurable lesions, Child-Pugh A or B, and adequate organ function. Initial single IV bolus was followed by weekly doses of peg-rhArgI escalated from 500 U/kg to 2500 U/kg in a 3 + 3 design. Results Fifteen patients were enrolled at weekly doses of 500 U/kg (n = 3), 1000 U/kg (n = 3), 1600 U/kg (n = 3) and 2500 U/kg (n = 6). The median age was 57 years (33-74); 87% were hepatitis B carriers and 47% had prior systemic treatment. The most commonly reported drug-related non-haematological adverse events (AEs) were diarrhea (13.3%), abdominal discomfort (6.7%) and nausea (6.7%). No drug-related haematological AEs were seen. Only 1 of the six patients that received 2500U/kg peg-rhArg1 experienced DLT (grade 4 bilirubin elevation) and thus the maximum tolerated dose was 2500 U/kg. PK and PD analysis indicated that peg-rhArg1 was efficacious in inducing arginine depletion in a dose-dependent manner. Adequate arginine depletion dose was achieved in the 1,600-2,500 U/kg range and therefore the optimal biological dose was at 1600 U/kg, which was chosen as the recommended dose. The best response was stable disease for >8 weeks in 26.7% of the enrolled patients. Conclusion Peg-rhArg1 has manageable safety profile and preliminary evidence of activity in advanced HCC patients.published_or_final_versio

Spherical Spectral Synthesis and Two-Radius Theorems on Damek-Ricci Spaces

We prove that spherical spectral analysis and synthesis hold in Damek-Ricci spaces and derive two-radius theorems

Existence of Ricci flows of incomplete surfaces

We prove a general existence result for instantaneously complete Ricci flows starting at an arbitrary Riemannian surface which may be incomplete and may have unbounded curvature. We give an explicit formula for the maximal existence time, and describe the asymptotic behaviour in most cases.Comment: 20 pages; updated to reflect galley proof correction

Exclusion processes with degenerate rates: convergence to equilibrium and tagged particle

Stochastic lattice gases with degenerate rates, namely conservative particle systems where the exchange rates vanish for some configurations, have been introduced as simplified models for glassy dynamics. We introduce two particular models and consider them in a finite volume of size $\ell$ in contact with particle reservoirs at the boundary. We prove that, as for non--degenerate rates, the inverse of the spectral gap and the logarithmic Sobolev constant grow as $\ell^2$. It is also shown how one can obtain, via a scaling limit from the logarithmic Sobolev inequality, the exponential decay of a macroscopic entropy associated to a degenerate parabolic differential equation (porous media equation). We analyze finally the tagged particle displacement for the stationary process in infinite volume. In dimension larger than two we prove that, in the diffusive scaling limit, it converges to a Brownian motion with non--degenerate diffusion coefficient.Comment: 25 pages, 3 figure