Phase Space Structure of Generalized Gaussian Cat States

We analyze generalized Gaussian cat states obtained by superposing arbitrary Gaussian states, e.g., a coherent state and a squeezed state. The Wigner functions of such states exhibit the typical pair of Gaussian hills plus an interference term which presents a novel structure, as compared with the standard superposition of coherent states (degenerate case). We prove that, in any dimensions, the structure of the interference term is characterized by a particular quadratic form; in one degree of freedom the phase is hyperbolic. This phase-space structure survives the action of a thermal reservoir. We also discuss certain superpositions of {\em mixed} Gaussian states generated by conditional Gaussian operations or Kerr-type dynamics on thermal states.Comment: 12 pages, 6 figures, submitted to Physical Review

Measurement of the copy number of the master quorum-sensing regulator of a bacterial cell

Quorum sensing is the mechanism by which bacteria communicate and synchronize group behaviors. Quantitative information on parameters such as the copy number of particular quorum-sensing proteins should contribute strongly to understanding how the quorum-sensing network functions. Here we show that the copy number of the master regulator protein LuxR in Vibrio harveyi, can be determined in vivo by exploiting small-number fluctuations of the protein distribution when cells undergo division. When a cell divides, both its volume and LuxR protein copy number N are partitioned with slight asymmetries. We have measured the distribution functions describing the partitioning of the protein fluorescence and the cell volume. The fluorescence distribution is found to narrow systematically as the LuxR population increases while the volume partitioning is unchanged. Analyzing these changes statistically, we have determined that N = 80-135 dimers at low cell density and 575 dimers at high cell density. In addition, we have measured the static distribution of LuxR over a large (3,000) clonal population. Combining the static and time-lapse experiments, we determine the magnitude of the Fano factor of the distribution. This technique has broad applicability as a general, in vivo technique for measuring protein copy number and burst size.Comment: Main text 23 pages, 5 figures. Supporting material 19 pages, 7 figures. In new version, text revised, one figure reformatte

Towards an understanding of neuroscience for science educators

Advances in neuroscience have brought new insights to the development of cognitive functions. These data are of considerable interest to educators concerned with how students learn. This review documents some of the recent findings in neuroscience, which is richer in describing cognitive functions than affective aspects of learning. A brief overview is presented here of the techniques used to generate data from imaging and how these findings have the possibility to inform educators. There are implications for considering the impact of neuroscience at all levels of education – from the classroom teacher and practitioner to policy. This relatively new cross-disciplinary area of research implies a need for educators and scientists to engage with each other. What questions are emerging through such dialogues between educators and scientists are likely to shed light on, for example, reward, motivation, working memory, learning difficulties, bilingualism and child development. The sciences of learning are entering a new paradigm

Sequences of stable bundles over compact complex surfaces

When identified with sequences of irreducible Hermitian-Einstein connections, sequences of stable holomorphic bundles of fixed topological type and bounded degree on a compact complex surface equipped with a Gauduchon metric are shown to have strongly convergent subsequences after blowing-up and pulling-back sufficiently many times.Nicholas P. Buchdah