Toda Fields on Riemann Surfaces: remarks on the Miura transformation

We point out that the Miura transformation is related to a holomorphic foliation in a relative flag manifold over a Riemann Surface. Certain differential operators corresponding to a free field description of $W$--algebras are thus interpreted as partial connections associated to the foliation.Comment: AmsLatex 1.1, 10 page

Boundary states for a free boson defined on finite geometries

Langlands recently constructed a map that factorizes the partition function of a free boson on a cylinder with boundary condition given by two arbitrary functions in the form of a scalar product of boundary states. We rewrite these boundary states in a compact form, getting rid of technical assumptions necessary in his construction. This simpler form allows us to show explicitly that the map between boundary conditions and states commutes with conformal transformations preserving the boundary and the reality condition on the scalar field.Comment: 16 pages, LaTeX (uses AMS components). Revised version; an analogy with string theory computations is discussed and references adde

Recursion Relations in Liouville Gravity coupled to Ising Model satisfying Fusion Rules

The recursion relations of 2D quantum gravity coupled to the Ising model discussed by the author previously are reexamined. We study the case in which the matter sector satisfies the fusion rules and only the primary operators inside the Kac table contribute. The theory involves unregularized divergences in some of correlators. We obtain the recursion relations which form a closed set among well-defined correlators on sphere, but they do not have a beautiful structure that the bosonized theory has and also give an inconsistent result when they include an ill-defined correlator with the divergence. We solve them and compute the several normalization independent ratios of the well-defined correlators, which agree with the matrix model results.Comment: Latex, 22 page

Efficient Numerical Schemes for Computing Cardiac Electrical Activation over Realistic Purkinje Networks: Method and Verification

We present a numerical solver for the fast conduction system in the heart using both a CPU and a hybrid CPU/GPU implementation. To verify both implementations, we construct analytical solutions and show that the L2-error is similar in both implementations and decreases linearly with the spatial step size. Finally, we test the performance of the implementations with networks of varying complexity, where the hybrid implementation is, on average, 5.8 times faster

The Number of Incipient Spanning Clusters in Two-Dimensional Percolation

Using methods of conformal field theory, we conjecture an exact form for the probability that n distinct clusters span a large rectangle or open cylinder of aspect ratio k, in the limit when k is large.Comment: 9 pages, LaTeX, 1 eps figure. Additional references and comparison with existing numerical results include

Perturbation Theory in Two Dimensional Open String Field Theory

In this paper we develop the covariant string field theory approach to open 2d strings. Upon constructing the vertices, we apply the formalism to calculate the lowest order contributions to the 4- and 5- point tachyon--tachyon tree amplitudes. Our results are shown to match the `bulk' amplitude calculations of Bershadsky and Kutasov. In the present approach the pole structure of the amplitudes becomes manifest and their origin as coming from the higher string modes transparent.Comment: 26 page

Critical interfaces of the Ashkin-Teller model at the parafermionic point

We present an extensive study of interfaces defined in the Z_4 spin lattice representation of the Ashkin-Teller (AT) model. In particular, we numerically compute the fractal dimensions of boundary and bulk interfaces at the Fateev-Zamolodchikov point. This point is a special point on the self-dual critical line of the AT model and it is described in the continuum limit by the Z_4 parafermionic theory. Extending on previous analytical and numerical studies [10,12], we point out the existence of three different values of fractal dimensions which characterize different kind of interfaces. We argue that this result may be related to the classification of primary operators of the parafermionic algebra. The scenario emerging from the studies presented here is expected to unveil general aspects of geometrical objects of critical AT model, and thus of c=1 critical theories in general.Comment: 15 pages, 3 figure

The Spitzer Survey of Interstellar Clouds in the Gould Belt. VI. The Auriga-California Molecular Cloud observed with IRAC and MIPS

We present observations of the Auriga-California Molecular Cloud (AMC) at 3.6, 4.5, 5.8, 8.0, 24, 70 and 160 micron observed with the IRAC and MIPS detectors as part of the Spitzer Gould Belt Legacy Survey. The total mapped areas are 2.5 sq-deg with IRAC and 10.47 sq-deg with MIPS. This giant molecular cloud is one of two in the nearby Gould Belt of star-forming regions, the other being the Orion A Molecular Cloud (OMC). We compare source counts, colors and magnitudes in our observed region to a subset of the SWIRE data that was processed through our pipeline. Using color-magnitude and color-color diagrams, we find evidence for a substantial population of 166 young stellar objects (YSOs) in the cloud, many of which were previously unknown. Most of this population is concentrated around the LkHalpha 101 cluster and the filament extending from it. We present a quantitative description of the degree of clustering and discuss the fraction of YSOs in the region with disks relative to an estimate of the diskless YSO population. Although the AMC is similar in mass, size and distance to the OMC, it is forming about 15 - 20 times fewer stars.Comment: (30 pages, 17 figures (2 multipage figures), accepted for publication in ApJ

Entropy flow in near-critical quantum circuits

Near-critical quantum circuits are ideal physical systems for asymptotically large-scale quantum computers, because their low energy collective excitations evolve reversibly, effectively isolated from the environment. The design of reversible computers is constrained by the laws governing entropy flow within the computer. In near-critical quantum circuits, entropy flows as a locally conserved quantum current, obeying circuit laws analogous to the electric circuit laws. The quantum entropy current is just the energy current divided by the temperature. A quantum circuit made from a near-critical system (of conventional type) is described by a relativistic 1+1 dimensional relativistic quantum field theory on the circuit. The universal properties of the energy-momentum tensor constrain the entropy flow characteristics of the circuit components: the entropic conductivity of the quantum wires and the entropic admittance of the quantum circuit junctions. For example, near-critical quantum wires are always resistanceless inductors for entropy. A universal formula is derived for the entropic conductivity: \sigma_S(\omega)=iv^{2}S/\omega T, where \omega is the frequency, T the temperature, S the equilibrium entropy density and v the velocity of `light'. The thermal conductivity is Real(T\sigma_S(\omega))=\pi v^{2}S\delta(\omega). The thermal Drude weight is, universally, v^{2}S. This gives a way to measure the entropy density directly.Comment: 2005 paper published 2017 in Kadanoff memorial issue of J Stat Phys with revisions for clarity following referee's suggestions, arguments and results unchanged, cross-posting now to quant-ph, 27 page

State-Dependent Accessibility of the P-S6 Linker of Pacemaker (HCN) Channels Supports a Dynamic Pore-to-Gate Coupling Model

The hyperpolarization-activated cyclic nucleotide-modulated channel gene family (HCN1-4) encodes the membrane depolarizing current that underlies pacemaking. Although the topology of HCN resembles Kv channels, much less is known about their structure-function correlation. Previously, we identified several pore residues in the S5-P linker and P-loop that are externally accessible and/or influence HCN gating, and proposed an evolutionarily conserved pore-to-gate mechanism. Here we sought dynamic evidence by assessing the functional consequences of Cys-scanning substitutions in the unexplored P-S6 linker (residues 352–359), the HCN1-R background (that is, resistant to sulfhydryl-reactive agents). None of A352C, Q353C, A354C, P355C, V356C, S357C, M358C, or S359C produced functional currents; the loss-of-function of Q353C, A354C, S357C, and M358C could be rescued by the reducing agent dithiothreitol. Q353C, A354C, and S357C, but not M358C and HCN1-R, were sensitive to Cd2+ blockade (IC50 = 3–12 μM vs. >1 mM). External application of the positively charged covalent sulfhydryl modifier MTSET irreversibly reduced I−140mV of Q353C and A354C to 27.9 ± 3.4% and 58.2 ± 13.1% of the control, respectively, and caused significant steady-state activation shifts (∆V1/2 = –21.1 ± 1.6 for Q353C and −10.0 ± 2.9 mV for A354C). Interestingly, MTSET reactivity was also state dependent. MTSET, however, affected neither S357C nor M358C, indicating site specificity. Collectively, we have identified novel P-S6 residues whose extracellular accessibility was sterically and state dependent and have provided the first functional evidence consistent with a dynamic HCN pore-to-gate model