Numerical evidence of the double-Griffiths phase of the random quantum Ashkin-Teller chain

The random quantum Ashkin-Teller chain is studied numerically by means of time-dependent Density-Matrix Renormalization Group. The critical lines are estimated as the location of the peaks of the integrated autocorrelation times, computed from spin-spin and polarization-polarization autocorrelation functions. Disorder fluctuations of magnetization and polarization are observed to be maximum on these critical lines. Entanglement entropy leads to the same phase diagram, though with larger Finite-Size effects. The decay of spin-spin and polarization-polarization autocorrelation functions provides numerical evidence of the existence of a double Griffiths phase when taking into account finite-size effects. The two associated dynamical exponents z increase rapidly as the critical lines are approached, in agreement with the recent conjecture of a divergence at the two transitions in the thermodynamic limit

Preferential duplication graphs

We consider a preferential duplication model for growing random graphs, extending previous models of duplication graphs by selecting the vertex to be duplicated with probability proportional to its degree. We show that a special case of this model can be analysed using the same stochastic approximation as for vertex-reinforced random walks, and show that 'trapping' behaviour can occur, such that the descendants of a particular group of initial vertices come to dominate the graph

Mutual information and conditional mean prediction error

This version: arXiv:1407.7165v1. Available from arXiv.org via the link in this recordMutual information is fundamentally important for measuring statistical dependence between variables and for quantifying information transfer by signaling and communication mechanisms. It can, however, be challenging to evaluate for physical models of such mechanisms and to estimate reliably from data. Furthermore, its relationship to better known statistical procedures is still poorly understood. Here we explore new connections between mutual information and regression-based dependence measures, $\nu^{-1}$, that utilise the determinant of the second-moment matrix of the conditional mean prediction error. We examine convergence properties as $\nu\rightarrow0$ and establish sharp lower bounds on mutual information and capacity of the form $\mathrm{log}(\nu^{-1/2})$. The bounds are tighter than lower bounds based on the Pearson correlation and ones derived using average mean square-error rate distortion arguments. Furthermore, their estimation is feasible using techniques from nonparametric regression. As an illustration we provide bootstrap confidence intervals for the lower bounds which, through use of a composite estimator, substantially improve upon inference about mutual information based on $k$-nearest neighbour estimators alone

Mutual information and conditional mean prediction error

This version: arXiv:1407.7165v1. Available from arXiv.org via the link in this recordMutual information is fundamentally important for measuring statistical dependence between variables and for quantifying information transfer by signaling and communication mechanisms. It can, however, be challenging to evaluate for physical models of such mechanisms and to estimate reliably from data. Furthermore, its relationship to better known statistical procedures is still poorly understood. Here we explore new connections between mutual information and regression-based dependence measures, $\nu^{-1}$, that utilise the determinant of the second-moment matrix of the conditional mean prediction error. We examine convergence properties as $\nu\rightarrow0$ and establish sharp lower bounds on mutual information and capacity of the form $\mathrm{log}(\nu^{-1/2})$. The bounds are tighter than lower bounds based on the Pearson correlation and ones derived using average mean square-error rate distortion arguments. Furthermore, their estimation is feasible using techniques from nonparametric regression. As an illustration we provide bootstrap confidence intervals for the lower bounds which, through use of a composite estimator, substantially improve upon inference about mutual information based on $k$-nearest neighbour estimators alone

The magnitude and colour of noise in genetic negative feedback systems

This is the final version of the article. Available from OUP via the DOI in this record.The comparative ability of transcriptional and small RNA-mediated negative feedback to control fluctuations or 'noise' in gene expression remains unexplored. Both autoregulatory mechanisms usually suppress the average (mean) of the protein level and its variability across cells. The variance of the number of proteins per molecule of mean expression is also typically reduced compared with the unregulated system, but is almost never below the value of one. This relative variance often substantially exceeds a recently obtained, theoretical lower limit for biochemical feedback systems. Adding the transcriptional or small RNA-mediated control has different effects. Transcriptional autorepression robustly reduces both the relative variance and persistence (lifetime) of fluctuations. Both benefits combine to reduce noise in downstream gene expression. Autorepression via small RNA can achieve more extreme noise reduction and typically has less effect on the mean expression level. However, it is often more costly to implement and is more sensitive to rate parameters. Theoretical lower limits on the relative variance are known to decrease slowly as a measure of the cost per molecule of mean expression increases. However, the proportional increase in cost to achieve substantial noise suppression can be different away from the optimal frontier-for transcriptional autorepression, it is frequently negligible.Funding for open access charge: MRC-EPSRC funded Fellowship in Bioinformatics (to C.G.B.)

Credit Risk and Discontinuous Effects of Monetary Reverse Transactions

A central bank possesses various instruments to provide liquidity. These are either outright monetary transactions (OMT) of securities or other refinancing facilities, primarily repos, which are executed with standard tenders. The eligible securities (i.e. bonds or equities) need to conform with certain credit risk criteria (i.e., satisfactory credit rating or low default probability). This paper introduces a monetary model to address the role of collateralized securities on the effectiveness of monetary policy. Our results suggest that credit rating downgrading may precipitate into a disproportionate credit contraction

Evidence of polariton induced transparency in a single organic quantum wire

The resonant interaction between quasi-one dimensional excitons and photons is investigated. For a single isolated organic quantum wire, embedded in its single crystal monomer matrix, the strong exciton-photon coupling regime is reached. This is evidenced by the suppression of the resonant excitonic absorption arising when the system eigenstate is a polariton. These observations demonstrate that the resonant excitonic absorption in a semiconductor can be understood in terms of a balance between the exciton coherence time and the Rabi period between exciton-like and photon-like states of the polariton.Comment: 9 pages and 4 figure