Very small deletions within the NESP55 gene in pseudohypoparathyroidism type 1b

Pseudohypoparathyroidism (PHP) is caused by reduced expression of genes within the GNAS cluster, resulting in parathormone resistance. The cluster contains multiple imprinted transcripts, including the stimulatory G protein α subunit (Gs-α) and NESP55 transcript preferentially expressed from the maternal allele, and the paternally expressed XLas, A/B and antisense transcripts. PHP1b can be caused by loss of imprinting affecting GNAS A/B alone (associated with STX16 deletion), or the entire GNAS cluster (associated with deletions of NESP55 in a minority of cases). We performed targeted genomic next-generation sequencing (NGS) of the GNAS cluster to seek variants and indels underlying PHP1b. Seven patients were sequenced by hybridisation-based capture and fourteen more by long-range PCR and transposon-mediated insertion and sequencing. A bioinformatic pipeline was developed for variant and indel detection. In one family with two affected siblings, and in a second family with a single affected individual, we detected maternally inherited deletions of 40 and 33 bp, respectively, within the deletion previously reported in rare families with PHP1b. All three affected individuals presented with atypically severe PHP1b; interestingly, the unaffected mother in one family had the detected deletion on her maternally inherited allele. Targeted NGS can reveal sequence changes undetectable by current diagnostic methods. Identification of genetic mutations underlying epigenetic changes can facilitate accurate diagnosis and counselling, and potentially highlight genetic elements critical for normal imprint settin

The SO(N) principal chiral field on a half-line

We investigate the integrability of the SO(N) principal chiral model on a half-line, and find that mixed Dirichlet/Neumann boundary conditions (as well as pure Dirichlet or Neumann) lead to infinitely many conserved charges classically in involution. We use an anomaly-counting method to show that at least one non-trivial example survives quantization, compare our results with the proposed reflection matrices, and, based on these, make some preliminary remarks about expected boundary bound-states.Comment: 7 pages, Late

The Entropy of a Binary Hidden Markov Process

The entropy of a binary symmetric Hidden Markov Process is calculated as an expansion in the noise parameter epsilon. We map the problem onto a one-dimensional Ising model in a large field of random signs and calculate the expansion coefficients up to second order in epsilon. Using a conjecture we extend the calculation to 11th order and discuss the convergence of the resulting series

Statistical mechanical aspects of joint source-channel coding

An MN-Gallager Code over Galois fields, $q$, based on the Dynamical Block Posterior probabilities (DBP) for messages with a given set of autocorrelations is presented with the following main results: (a) for a binary symmetric channel the threshold, $f_c$, is extrapolated for infinite messages using the scaling relation for the median convergence time, $t_{med} \propto 1/(f_c-f)$; (b) a degradation in the threshold is observed as the correlations are enhanced; (c) for a given set of autocorrelations the performance is enhanced as $q$ is increased; (d) the efficiency of the DBP joint source-channel coding is slightly better than the standard gzip compression method; (e) for a given entropy, the performance of the DBP algorithm is a function of the decay of the correlation function over large distances.Comment: 6 page

The Statistical Physics of Regular Low-Density Parity-Check Error-Correcting Codes

A variation of Gallager error-correcting codes is investigated using statistical mechanics. In codes of this type, a given message is encoded into a codeword which comprises Boolean sums of message bits selected by two randomly constructed sparse matrices. The similarity of these codes to Ising spin systems with random interaction makes it possible to assess their typical performance by analytical methods developed in the study of disordered systems. The typical case solutions obtained via the replica method are consistent with those obtained in simulations using belief propagation (BP) decoding. We discuss the practical implications of the results obtained and suggest a computationally efficient construction for one of the more practical configurations.Comment: 35 pages, 4 figure

Dynamic froth stability of copper flotation tailings

In this work, dynamic froth stability is used for the first time to investigate the flotation behaviour of copper tailings. Reprocessing of material from tailings dams is not only environmentally desirable, but also increasingly economically feasible as head grades can be high compared to new deposits. Flotation tailings, however, usually contain a large proportion of fine (10–50 m) and ultra fine (< ) material and the effect of these particle sizes on froth stability is not yet fully understood. For this study, samples were obtained from the overflow and underflow streams of the primary hydrocyclone at a concentrator that reprocesses copper flotation tailings. These samples were combined in different ratios to assess the dynamic froth stabilities at a wide range of particle size distributions and superficial gas velocities. The findings have shown that the effect of particle size on dynamic froth stability can be more complex than previously thought, with a local maximum in dynamic froth stability found at each air rate. Moreover, batch tests suggest that a local maximum in stability can be linked to improvements in flotation performance. Thus this work demonstrates that the dynamic froth stability can be used to find an optimum particle size distribution required to enhance flotation. This also has important implications for the reprocessing of copper tailings as it could inform the selection of the cut size for the hydrocyclones

Full-revivals in 2-D Quantum Walks

Recurrence of a random walk is described by the Polya number. For quantum walks, recurrence is understood as the return of the walker to the origin, rather than the full-revival of its quantum state. Localization for two dimensional quantum walks is known to exist in the sense of non-vanishing probability distribution in the asymptotic limit. We show on the example of the 2-D Grover walk that one can exploit the effect of localization to construct stationary solutions. Moreover, we find full-revivals of a quantum state with a period of two steps. We prove that there cannot be longer cycles for a four-state quantum walk. Stationary states and revivals result from interference which has no counterpart in classical random walks

Renormalization of Quantum Anosov Maps: Reduction to Fixed Boundary Conditions

A renormalization scheme is introduced to study quantum Anosov maps (QAMs) on a torus for general boundary conditions (BCs), whose number ($k$) is always finite. It is shown that the quasienergy eigenvalue problem of a QAM for {\em all} $k$ BCs is exactly equivalent to that of the renormalized QAM (with Planck's constant $\hbar ^{\prime}=\hbar /k$) at some {\em fixed} BCs that can be of four types. The quantum cat maps are, up to time reversal, fixed points of the renormalization transformation. Several results at fixed BCs, in particular the existence of a complete basis of ``crystalline'' eigenstates in a classical limit, can then be derived and understood in a simple and transparent way in the general-BCs framework.Comment: REVTEX, 12 pages, 1 table. To appear in Physical Review Letter

The stability of capillary waves on fluid sheets

The linear stability of finite amplitude capillary waves on inviscid sheets of fluid is investigated. A method similar to that recently used by Tiron & Choi (2012) to determine the stability of Crapper waves on fluid of infinite depth is developed by extending the conformal mapping technique of Dyachenko et al. (1996a) to a form capable of capturing general periodic waves on both the upper and the lower surface of the sheet, including the symmetric and antisymmetric waves studied by Kinnersley (1976). The primary, surprising result is that both symmetric and antisymmetric Kinnersley waves are unstable to small superharmonic disturbances. The waves are also unstable to subharmonic perturbations. Growth rates are computed for a range of steady waves in the Kinnersley family, and also waves found along the bifurcation branches identified by Blyth & Vanden-Broeck (2004). The instability results are corroborated by time integration of the fully nonlinear unsteady equations. Evidence is presented for superharmonic instability of nonlinear waves via a collision of eigenvalues on the imaginary axis which appear to have the same Krein signature

``Critical'' phonons of the supercritical Frenkel-Kontorova model: renormalization bifurcation diagrams

The phonon modes of the Frenkel-Kontorova model are studied both at the pinning transition as well as in the pinned (cantorus) phase. We focus on the minimal frequency of the phonon spectrum and the corresponding generalized eigenfunction. Using an exact decimation scheme, the eigenfunctions are shown to have nontrivial scaling properties not only at the pinning transition point but also in the cantorus regime. Therefore the phonons defy localization and remain critical even where the associated area-preserving map has a positive Lyapunov exponent. In this region, the critical scaling properties vary continuously and are described by a line of renormalization limit cycles. Interesting renormalization bifurcation diagrams are obtained by monitoring the cycles as the parameters of the system are varied from an integrable case to the anti-integrable limit. Both of these limits are described by a trivial decimation fixed point. Very surprisingly we find additional special parameter values in the cantorus regime where the renormalization limit cycle degenerates into the above trivial fixed point. At these ``degeneracy points'' the phonon hull is represented by an infinite series of step functions. This novel behavior persists in the extended version of the model containing two harmonics. Additional richnesses of this extended model are the one to two-hole transition line, characterized by a divergence in the renormalization cycles, nonexponentially localized phonons, and the preservation of critical behavior all the way upto the anti-integrable limit.Comment: 10 pages, RevTeX, 9 Postscript figure