Boundary condition at the junction

The quantum graph plays the role of a solvable model for a two-dimensional network. Here fitting parameters of the quantum graph for modelling the junction is discussed, using previous results of the second author.Comment: Replaces unpublished draft on related researc

New paradoxical games based on Brownian ratchets

Based on Brownian ratchets, a counter-intuitive phenomenon has recently emerged -- namely, that two losing games can yield, when combined, a paradoxical tendency to win. A restriction of this phenomenon is that the rules depend on the current capital of the player. Here we present new games where all the rules depend only on the history of the game and not on the capital. This new history-dependent structure significantly increases the parameter space for which the effect operates.Comment: 4 pages, 3 eps figures, revte

Minimal Brownian Ratchet: An Exactly Solvable Model

We develop an exactly-solvable three-state discrete-time minimal Brownian ratchet (MBR), where the transition probabilities between states are asymmetric. By solving the master equations we obtain the steady-state probabilities. Generally the steady-state solution does not display detailed balance, giving rise to an induced directional motion in the MBR. For a reduced two-dimensional parameter space we find the null-curve on which the net current vanishes and detailed balance holds. A system on this curve is said to be balanced. On the null-curve, an additional source of external random noise is introduced to show that a directional motion can be induced under the zero overall driving force. We also indicate the off-balance behavior with biased random noise.Comment: 4 pages, 4 figures, RevTex source, General solution added. To be appeared in Phys. Rev. Let

Non-Weyl asymptotics for quantum graphs with general coupling conditions

Inspired by a recent result of Davies and Pushnitski, we study resonance asymptotics of quantum graphs with general coupling conditions at the vertices. We derive a criterion for the asymptotics to be of a non-Weyl character. We show that for balanced vertices with permutation-invariant couplings the asymptotics is non-Weyl only in case of Kirchhoff or anti-Kirchhoff conditions, while for graphs without permutation numerous examples of non-Weyl behaviour can be constructed. Furthermore, we present an insight helping to understand what makes the Kirchhoff/anti-Kirchhoff coupling particular from the resonance point of view. Finally, we demonstrate a generalization to quantum graphs with nonequal edge weights.Comment: minor changes, to appear in Pierre Duclos memorial issue of J. Phys. A: Math. Theo

Quantum field theory on quantum graphs and application to their conductance

We construct a bosonic quantum field on a general quantum graph. Consistency of the construction leads to the calculation of the total scattering matrix of the graph. This matrix is equivalent to the one already proposed using generalized star product approach. We give several examples and show how they generalize some of the scattering matrices computed in the mathematical or condensed matter physics litterature. Then, we apply the construction for the calculation of the conductance of graphs, within a small distance approximation. The consistency of the approximation is proved by direct comparison with the exact calculation for the `tadpole' graph.Comment: 32 pages; misprints in tree graph corrected; proofs of consistency and unitarity adde

Bosonization and Scale Invariance on Quantum Wires

We develop a systematic approach to bosonization and vertex algebras on quantum wires of the form of star graphs. The related bosonic fields propagate freely in the bulk of the graph, but interact at its vertex. Our framework covers all possible interactions preserving unitarity. Special attention is devoted to the scale invariant interactions, which determine the critical properties of the system. Using the associated scattering matrices, we give a complete classification of the critical points on a star graph with any number of edges. Critical points where the system is not invariant under wire permutations are discovered. By means of an appropriate vertex algebra we perform the bosonization of fermions and solve the massless Thirring model. In this context we derive an explicit expression for the conductance and investigate its behavior at the critical points. A simple relation between the conductance and the Casimir energy density is pointed out.Comment: LaTex 31+1 pages, 2 figures. Section 3.6 and two references added. To appear in J. Phys. A: Mathematical and Theoretica

In situ monolayer patch clamp of acutely stimulated human iPSC-derived cardiomyocytes promotes consistent electrophysiological responses to SK channel inhibition

Human induced pluripotent stem cell-derived cardiomyocytes (iPSC-CMs) represent an in vitro model of cardiac function. Isolated iPSC-CMs, however, exhibit electrophysiological heterogeneity which hinders their utility in the study of certain cardiac currents. In the healthy adult heart, the current mediated by small conductance, calcium-activated potassium (SK) channels (ISK) is atrial-selective. Functional expression of ISK within atrial-like iPSC-CMs has not been explored thoroughly. The present study therefore aimed to investigate atrial-like iPSC-CMs as a model system for the study of ISK. iPSCs were differentiated using retinoic acid (RA) to produce iPSC-CMs which exhibited an atrial-like phenotype (RA-iPSC-CMs). Only 18% of isolated RA-iPSC-CMs responded to SK channel inhibition by UCL1684 and isolated iPSC-CMs exhibited substantial cell-to-cell electrophysiological heterogeneity. This variability was significantly reduced by patch clamp of RA-iPSC-CMs in situ as a monolayer (iPSC-ML). A novel method of electrical stimulation was developed to facilitate recording from iPSC-MLs via In situ Monolayer Patch clamp of Acutely Stimulated iPSC-CMs (IMPASC). Using IMPASC, &gt; 95% of iPSC-MLs could be paced at a 1 Hz. In contrast to isolated RA-iPSC-CMs, 100% of RA-iPSC-MLs responded to UCL1684, with APD50 being prolonged by 16.0 ± 2.0 ms (p &lt; 0.0001; n = 12). These data demonstrate that in conjunction with IMPASC, RA-iPSC-MLs represent an improved model for the study of ISK. IMPASC may be of wider value in the study of other ion channels that are inconsistently expressed in isolated iPSC-CMs and in pharmacological studies.<br/

Quantum Fields on Star Graphs

We construct canonical quantum fields which propagate on a star graph modeling a quantum wire. The construction uses a deformation of the algebra of canonical commutation relations, encoding the interaction in the vertex of the graph. We discuss in this framework the Casimir effect and derive the correction to the Stefan-Boltzmann law induced by the vertex interaction. We also generalize the algebraic setting for covering systems with integrable bulk interactions and solve the quantum non-linear Schroedinger model on a star graph.Comment: LaTex 23+1 pages, 4 figure

Drug screening to identify compounds to act as co-therapies for the treatment of Burkholderia species

Burkholderia pseudomallei is a soil-dwelling organism present throughout the tropics. It is the causative agent of melioidosis, a disease that is believed to kill 89,000 people per year. It is naturally resistant to many antibiotics, requiring at least two weeks of intravenous treatment with ceftazidime, imipenem or meropenem followed by 6 months of orally delivered co-trimoxazole. This places a large treatment burden on the predominantly middle-income nations where the majority of disease occurs. We have established a high-throughput assay for compounds that could be used as a co-therapy to potentiate the effect of ceftazidime, using the related non-pathogenic bacterium Burkholderia thailandensis as a surrogate. Optimization of the assay gave a Z' factor of 0.68. We screened a library of 61,250 compounds and identified 29 compounds with a pIC50 (-log10(IC50)) greater than five. Detailed investigation allowed us to down select to six "best in class" compounds, which included the licensed drug chloroxine. Co-treatment of B. thailandensis with ceftazidime and chloroxine reduced culturable cell numbers by two orders of magnitude over 48 hours, compared to treatment with ceftazidime alone. Hit expansion around chloroxine was performed using commercially available compounds. Minor modifications to the structure abolished activity, suggesting that chloroxine likely acts against a specific target. Finally, an initial study demonstrates the utility of chloroxine to act as a co-therapy to potentiate the effect of ceftazidime against B. pseudomallei. This approach successfully identified potential co-therapies for a recalcitrant Gram-negative bacterial species. Our assay could be used more widely to aid in chemotherapy to treat infections caused by these bacteria

Intermediate statistics for a system with symplectic symmetry: the Dirac rose graph

We study the spectral statistics of the Dirac operator on a rose-shaped graph---a graph with a single vertex and all bonds connected at both ends to the vertex. We formulate a secular equation that generically determines the eigenvalues of the Dirac rose graph, which is seen to generalise the secular equation for a star graph with Neumann boundary conditions. We derive approximations to the spectral pair correlation function at large and small values of spectral spacings, in the limit as the number of bonds approaches infinity, and compare these predictions with results of numerical calculations. Our results represent the first example of intermediate statistics from the symplectic symmetry class.Comment: 26 pages, references adde