Integrals of Motion for Critical Dense Polymers and Symplectic Fermions

We consider critical dense polymers ${\cal L}(1,2)$. We obtain for this model the eigenvalues of the local integrals of motion of the underlying Conformal Field Theory by means of Thermodynamic Bethe Ansatz. We give a detailed description of the relation between this model and Symplectic Fermions including the indecomposable structure of the transfer matrix. Integrals of motion are defined directly on the lattice in terms of the Temperley Lieb Algebra and their eigenvalues are obtained and expressed as an infinite sum of the eigenvalues of the continuum integrals of motion. An elegant decomposition of the transfer matrix in terms of a finite number of lattice integrals of motion is obtained thus providing a reason for their introduction.Comment: 53 pages, version accepted for publishing on JSTA

Learning Distributed Representations for Multiple-Viewpoint Melodic Prediction

The analysis of sequences is important for extracting in- formation from music owing to its fundamentally temporal nature. In this paper, we present a distributed model based on the Restricted Boltzmann Machine (RBM) for learning melodic sequences. The model is similar to a previous suc- cessful neural network model for natural language [2]. It is first trained to predict the next pitch in a given pitch se- quence, and then extended to also make use of information in sequences of note-durations in monophonic melodies on the same task. In doing so, we also propose an efficient way of representing this additional information that takes advantage of the RBM’s structure. Results show that this RBM-based prediction model performs better than previ- ously evaluated n-gram models and also outperforms them in certain cases. It is able to make use of information present in longer sequences more effectively than n-gram models, while scaling linearly in the number of free pa- rameters required

Simulation of associative learning with the replaced elements model

Associative learning theories can be categorised according to whether they treat the representation of stimulus compounds in an elemental or configural manner. Since it is clear that a simple elemental approach to stimulus representation is inadequate there have been several attempts to produce more elaborate elemental models. One recent approach, the Replaced Elements Model (Wagner, 2003), reproduces many results that have until recently been uniquely predicted by Pearce’s Configural Theory (Pearce, 1994). Although it is possible to simulate the Replaced Elements Model using “standard” simulation programs the generation of the correct stimulus representation is complex. The current paper describes a method for simulation of the Replaced Elements Model and presents the results of two example simulations that show differential predictions of Replaced Elements and Pearce’s Configural Theor

Palladium, platinum, and gold distribution in serpentinite seamounts in the Mariana and Izu-Bonin forearcs: evidence from Leg 125 fluids and serpentinites

Palladium, platinum, and gold were analyzed for 20 interstitial water samples from Leg 125. No Pd or Pt was detected in fluids from serpentinite muds from Conical Seamount in the Mariana forearc, indicating that low-temperature seawater-peridotite interaction does not mobilize these elements into the serpentinizing fluids to levels above 0.10 parts per billion (ppb) in solution. However, Au may be mobilized in high pH solutions. In contrast, fluids from vitric-rich clays on the flanks of the Torishima Seamount in the Izu-Bonin forearc have Pd values of between 4.0 and 11.8 nmol/L, Pt values between 2.3 and 5.0 nmol/L and Au values between 126.9 and 1116.9 pmol/L. The precious metals are mobilized, and possibly adsorbed onto clay mineral surfaces, during diagenesis and burial of the volcanic-rich clays. Desorption during squeezing of the sediments may produce the enhanced precious metal concentrations in the analyzed fluids. The metals are mobilized in the fluids probably as neutral hydroxide, bisulfide, and ammonia complexes. Pt/Pd ratios are between 0.42 and 2.33, which is much lower than many of the potential sources for Pt and Pd but is consistent with the greater solubility of Pd compared with Pt in most natural low-temperature fluids

Hydra: An Adaptive--Mesh Implementation of PPPM--SPH

We present an implementation of Smoothed Particle Hydrodynamics (SPH) in an adaptive-mesh PPPM algorithm. The code evolves a mixture of purely gravitational particles and gas particles. The code retains the desirable properties of previous PPPM--SPH implementations; speed under light clustering, naturally periodic boundary conditions and accurate pairwise forces. Under heavy clustering the cycle time of the new code is only 2--3 times slower than for a uniform particle distribution, overcoming the principal disadvantage of previous implementations\dash a dramatic loss of efficiency as clustering develops. A 1000 step simulation with 65,536 particles (half dark, half gas) runs in one day on a Sun Sparc10 workstation. The choice of time integration scheme is investigated in detail. A simple single-step Predictor--Corrector type integrator is most efficient. A method for generating an initial distribution of particles by allowing a a uniform temperature gas of SPH particles to relax within a periodic box is presented. The average SPH density that results varies by $\sim\pm1.3$\%. We present a modified form of the Layzer--Irvine equation which includes the thermal contribution of the gas together with radiative cooling. Tests of sound waves, shocks, spherical infall and collapse are presented. Appropriate timestep constraints sufficient to ensure both energy and entropy conservation are discussed. A cluster simulation, repeating Thomas andComment: 29 pp, uuencoded Postscrip

Optimal traps in graphene

We transform the two-dimensional Dirac-Weyl equation, which governs the charge carriers in graphene, into a non-linear first-order differential equation for scattering phase shift, using the so-called variable phase method. This allows us to utilize the Levinson Theorem to find zero-energy bound states created electrostatically in realistic structures. These confined states are formed at critical potential strengths, which leads to us posit the use of `optimal traps' to combat the chiral tunneling found in graphene, which could be explored experimentally with an artificial network of point charges held above the graphene layer. We also discuss scattering on these states and find the zero angular momentum states create a dominant peak in scattering cross-section as energy tends towards the Dirac point energy, suggesting a dominant contribution to resistivity.Comment: 11 pages, 5 figure

Palladium, platinum, and gold distribution in serpentinite seamounts in the Mariana and Izu-Bonin forearcs: evidence from Leg 125 fluids and serpentinites

Palladium, platinum, and gold were analyzed for 20 interstitial water samples from Leg 125. No Pd or Pt was detected in fluids from serpentinite muds from Conical Seamount in the Mariana forearc, indicating that low-temperature seawater-peridotite interaction does not mobilize these elements into the serpentinizing fluids to levels above 0.10 parts per billion (ppb) in solution. However, Au may be mobilized in high pH solutions. In contrast, fluids from vitric-rich clays on the flanks of the Torishima Seamount in the Izu-Bonin forearc have Pd values of between 4.0 and 11.8 nmol/L, Pt values between 2.3 and 5.0 nmol/L and Au values between 126.9 and 1116.9 pmol/L. The precious metals are mobilized, and possibly adsorbed onto clay mineral surfaces, during diagenesis and burial of the volcanic-rich clays. Desorption during squeezing of the sediments may produce the enhanced precious metal concentrations in the analyzed fluids. The metals are mobilized in the fluids probably as neutral hydroxide, bisulfide, and ammonia complexes. Pt/Pd ratios are between 0.42 and 2.33, which is much lower than many of the potential sources for Pt and Pd but is consistent with the greater solubility of Pd compared with Pt in most natural low-temperature fluids

Three-leg correlations in the two component spanning tree on the upper half-plane

We present a detailed asymptotic analysis of correlation functions for the two component spanning tree on the two-dimensional lattice when one component contains three paths connecting vicinities of two fixed lattice sites at large distance $s$ apart. We extend the known result for correlations on the plane to the case of the upper half-plane with closed and open boundary conditions. We found asymptotics of correlations for distance $r$ from the boundary to one of the fixed lattice sites for the cases $r\gg s \gg 1$ and $s \gg r \gg 1$.Comment: 16 pages, 5 figure