Approximation of Z2-cocycles and shift dynamical systems

Let G = G{n,, n, 1 n,+,, t >- 0} be a subgroup of all roots of unity generated by exp(21ri/n, ), t >- 0, and le_t r: (X, B, ji) C) be an ergodic transformation with pure point spectrum G. Given a cocycle P , SO:Xza , admitting an approximation with speed 0(l/nl+', e > 0) there exista a Morse cocycle 0 such that the corresponding transformations r and -ro are relatively isomorphic. An effective way of a construction of the Morse cocycle 0 is given. There is a cocycle p oddly approximated with an arbitrarily high speed and without roots. This note delivers examples of <p's admitting an arbitrarily high speed of approximation and such that the power multiplicity function of rn is equal to one and the power rank function is oscillatory. Finally, we also prove that if (p is a Morse cocycle then each proper factor of r,p is rigid. In particular continuous substitutions on two symbols cannot be factors of Morse dynamical systems

Embo: a Python package for empirical data analysis using the Information Bottleneck

We present embo, a Python package to analyze empirical data using the Information Bottleneck (IB) method and its variants, such as the Deterministic Information Bottleneck (DIB). Given two random variables X and Y, the IB finds the stochastic mapping M of X that encodes the most information about Y, subject to a constraint on the information that M is allowed to retain about X. Despite the popularity of the IB, an accessible implementation of the reference algorithm oriented towards ease of use on empirical data was missing. Embo is optimized for the common case of discrete, lowdimensional data. Embo is fast, provides a standard data-processing pipeline, offers a parallel implementation of key computational steps, and includes reasonable defaults for the method parameters. Embo is broadly applicable to different problem domains, as it can be employed with any dataset consisting in joint observations of two discrete variables. It is available from the Python Package Index (PyPI), Zenodo and GitLab

Dynamics, correlations and phases of the micromaser

The micromaser possesses a variety of dynamical phase transitions parametrized by the flux of atoms and the time-of-flight of the atom within the cavity. We discuss how these phases may be revealed to an observer outside the cavity using the long-time correlation length in the atomic beam. Some of the phase transitions are not reflected in the average excitation level of the outgoing atom, which is the commonly used observable. The correlation length is directly related to the leading eigenvalue of the time evolution operator, which we study in order to elucidate the phase structure. We find that as a function of the time-of-flight the transition from the thermal to the maser phase is characterized by a sharp peak in the correlation length. For longer times-of-flight there is a transition to a phase where the correlation length grows exponentially with the flux. We present a detailed numerical and analytical treatment of the different phases and discuss the physics behind them.Comment: 60 pages, 18 figure files, Latex + \special{} for the figures, (some redundant figures are eliminated and others are changed

Revival-collapse phenomenon in the fluctuations of quadrature field components of the multiphoton Jaynes-Cummings model

In this paper we consider a system consisting of a two-level atom, initially prepared in a coherent superposition of upper and lower levels, interacting with a radiation field prepared in generalized quantum states in the framework of multiphoton Jaynes-Cummings model. For this system we show that there is a class of states for which the fluctuation factors can exhibit revival-collapse phenomenon (RCP) similar to that exhibited in the corresponding atomic inversion. This is shown not only for normal fluctuations but also for amplitude-squared fluctuations. Furthermore, apart from this class of states we generally demonstrate that the fluctuation factors associated with three-photon transition can provide RCP similar to that occurring in the atomic inversion of the one-photon transition. These are novel results and their consequence is that RCP occurred in the atomic inversion can be measured via a homodyne detector. Furthermore, we discuss the influence of the atomic relative phases on such phenomenon.Comment: 17 pages, 4 figure

Trapped ions in the strong excitation regime: ion interferometry and non--classical states

The interaction of a trapped ion with a laser beam in the strong excitation regime is analyzed. In this regime, a variety of non--classical states of motion can be prepared either by using laser pulses of well defined area, or by an adiabatic passage scheme based on the variation of the laser frequency. We show how these states can be used to investigate fundamental properties of quantum mechanics. We also study possible applications of this system to build an ion interferometer.Comment: 9 pages, Revtex format, 5 compressed postscript figure

Dark States and Interferences in Cascade Transitions of Ultra-Cold Atoms in a Cavity

We examine the competition among one- and two-photon processes in an ultra-cold, three-level atom undergoing cascade transitions as a result of its interaction with a bimodal cavity. We show parameter domains where two-photon transitions are dominant and also study the effect of two-photon emission on the mazer action in the cavity. The two-photon emission leads to the loss of detailed balance and therefore we obtain the photon statistics of the cavity field by the numerical integration of the master equation. The photon distribution in each cavity mode exhibits sub- and super- Poissonian behaviors depending on the strength of atom-field coupling. The photon distribution becomes identical to a Poisson distribution when the atom-field coupling strengths of the modes are equal.Comment: 15 pages including 7 figures in Revtex, submitted to PR

An algebraic approach to the Tavis-Cummings problem

An algebraic method is introduced for an analytical solution of the eigenvalue problem of the Tavis-Cummings (TC) Hamiltonian, based on polynomially deformed su(2), i.e. su_n(2), algebras. In this method the eigenvalue problem is solved in terms of a specific perturbation theory, developed here up to third order. Generalization to the N-atom case of the Rabi frequency and dressed states is also provided. A remarkable enhancement of spontaneous emission of N atoms in a resonator is found to result from collective effects.Comment: 13 pages, 7 figure

Regulation of neutrophil senescence by microRNAs

Neutrophils are rapidly recruited to sites of tissue injury or infection, where they protect against invading pathogens. Neutrophil functions are limited by a process of neutrophil senescence, which renders the cells unable to respond to chemoattractants, carry out respiratory burst, or degranulate. In parallel, aged neutrophils also undergo spontaneous apoptosis, which can be delayed by factors such as GMCSF. This is then followed by their subsequent removal by phagocytic cells such as macrophages, thereby preventing unwanted inflammation and tissue damage. Neutrophils translate mRNA to make new proteins that are important in maintaining functional longevity. We therefore hypothesised that neutrophil functions and lifespan might be regulated by microRNAs expressed within human neutrophils. Total RNA from highly purified neutrophils was prepared and subjected to microarray analysis using the Agilent human miRNA microarray V3. We found human neutrophils expressed a selected repertoire of 148 microRNAs and that 6 of these were significantly upregulated after a period of 4 hours in culture, at a time when the contribution of apoptosis is negligible. A list of predicted targets for these 6 microRNAs was generated from http://mirecords.biolead.org and compared to mRNA species downregulated over time, revealing 83 genes targeted by at least 2 out of the 6 regulated microRNAs. Pathway analysis of genes containing binding sites for these microRNAs identified the following pathways: chemokine and cytokine signalling, Ras pathway, and regulation of the actin cytoskeleton. Our data suggest that microRNAs may play a role in the regulation of neutrophil senescence and further suggest that manipulation of microRNAs might represent an area of future therapeutic interest for the treatment of inflammatory disease

MicroRNAs in cardiac arrhythmia: DNA sequence variation of MiR-1 and MiR-133A in long QT syndrome.

Long QT syndrome (LQTS) is a genetic cardiac condition associated with prolonged ventricular repolarization, primarily a result of perturbations in cardiac ion channels, which predisposes individuals to life-threatening arrhythmias. Using DNA screening and sequencing methods, over 700 different LQTS-causing mutations have been identified in 13 genes worldwide. Despite this, the genetic cause of 30-50% of LQTS is presently unknown. MicroRNAs (miRNAs) are small (∼ 22 nucleotides) noncoding RNAs which post-transcriptionally regulate gene expression by binding complementary sequences within messenger RNAs (mRNAs). The human genome encodes over 1800 miRNAs, which target about 60% of human genes. Consequently, miRNAs are likely to regulate many complex processes in the body, indeed aberrant expression of various miRNA species has been implicated in numerous disease states, including cardiovascular diseases. MiR-1 and MiR-133A are the most abundant miRNAs in the heart and have both been reported to regulate cardiac ion channels. We hypothesized that, as a consequence of their role in regulating cardiac ion channels, genetic variation in the genes which encode MiR-1 and MiR-133A might explain some cases of LQTS. Four miRNA genes (miR-1-1, miR-1-2, miR-133a-1 and miR-133a-2), which encode MiR-1 and MiR-133A, were sequenced in 125 LQTS probands. No genetic variants were identified in miR-1-1 or miR-133a-1; but in miR-1-2 we identified a single substitution (n.100A> G) and in miR-133a-2 we identified two substitutions (n.-19G> A and n.98C> T). None of the variants affect the mature miRNA products. Our findings indicate that sequence variants of miR-1-1, miR-1-2, miR-133a-1 and miR-133a-2 are not a cause of LQTS in this cohort

A mutation in a functional Sp1 binding site of the telomerase RNA gene (hTERC) promoter in a patient with Paroxysmal Nocturnal Haemoglobinuria

BACKGROUND: Mutations in the gene coding for the RNA component of telomerase, hTERC, have been found in autosomal dominant dyskeratosis congenita (DC) and aplastic anemia. Paroxysmal nocturnal hemoglobinuria (PNH) is a clonal blood disorder associated with aplastic anemia and characterized by the presence of one or more clones of blood cells lacking glycosylphosphatidylinositol (GPI) anchored proteins due to a somatic mutation in the PIGA gene. METHODS: We searched for mutations in DNA extracted from PNH patients by amplification of the hTERC gene and denaturing high performance liquid chromatography (dHPLC). After a mutation was found in a potential transcription factor binding site in one patient electrophoretic mobility shift assays were used to detect binding of transcription factors to that site. The effect of the mutation on the function of the promoter was tested by transient transfection constructs in which the promoter is used to drive a reporter gene. RESULTS: Here we report the finding of a novel promoter mutation (-99C->G) in the hTERC gene in a patient with PNH. The mutation disrupts an Sp1 binding site and destroys its ability to bind Sp1. Transient transfection assays show that mutations in this hTERC site including C-99G cause either up- or down-regulation of promoter activity and suggest that the site regulates core promoter activity in a context dependent manner in cancer cells. CONCLUSIONS: These data are the first report of an hTERC promoter mutation from a patient sample which can modulate core promoter activity in vitro, raising the possibility that the mutation may affect the transcription of the gene in hematopoietic stem cells in vivo, and that dysregulation of telomerase may play a role in the development of bone marrow failure and the evolution of PNH clones