280 research outputs found
Uniform asymptotics of the coefficients of unitary moment polynomials
Keating and Snaith showed that the absolute moment of the
characteristic polynomial of a random unitary matrix evaluated on the unit
circle is given by a polynomial of degree . In this article, uniform
asymptotics for the coefficients of that polynomial are derived, and a maximal
coefficient is located. Some of the asymptotics are given in explicit form.
Numerical data to support these calculations are presented. Some apparent
connections between random matrix theory and the Riemann zeta function are
discussed.Comment: 31 pages, 1 figure, 2 tables. A few minor misprints fixe
A quantum Bose-Hubbard model with evolving graph as toy model for emergent spacetime
We present a toy model for interacting matter and geometry that explores
quantum dynamics in a spin system as a precursor to a quantum theory of
gravity. The model has no a priori geometric properties, instead, locality is
inferred from the more fundamental notion of interaction between the matter
degrees of freedom. The interaction terms are themselves quantum degrees of
freedom so that the structure of interactions and hence the resulting local and
causal structures are dynamical. The system is a Hubbard model where the graph
of the interactions is a set of quantum evolving variables. We show
entanglement between spatial and matter degrees of freedom. We study
numerically the quantum system and analyze its entanglement dynamics. We
analyze the asymptotic behavior of the classical model. Finally, we discuss
analogues of trapped surfaces and gravitational attraction in this simple
model.Comment: 23 pages, 6 figures; updated to published versio
RNA-seq reveals the RNA binding proteins, Hfq and RsmA, play various roles in virulence, antibiotic production and genomic flux in Serratia sp. ATCC 39006.
Background: Serratia sp. ATCC 39006 (S39006) is a Gram-negative enterobacterium that is virulent in plant and animal models. It produces a red-pigmented trypyrrole secondary metabolite, prodigiosin (Pig), and a carbapenem antibiotic (Car), as well as the exoenzymes, pectate lyase and cellulase. Secondary metabolite production in this strain is controlled by a complex regulatory network involving quorum sensing (QS). Hfq and RsmA (two RNA binding proteins and major post-transcriptional regulators of gene expression) play opposing roles in the regulation of several key phenotypes within S39006. Prodigiosin and carbapenem production was abolished, and virulence attenuated, in an S39006 ∆hfq mutant, while the converse was observed in an S39006 rsmA transposon insertion mutant.Results: In order to define the complete regulon of Hfq and RsmA, deep sequencing of cDNA libraries (RNA-seq) was used to analyse the whole transcriptome of S39006 ∆hfq and rsmA::Tn mutants. Moreover, we investigated global changes in the proteome using an LC-MS/MS approach. Analysis of differential gene expression showed that Hfq and RsmA directly or indirectly regulate (at the level of RNA) 4% and 19% of the genome, respectively, with some correlation between RNA and protein expression. Pathways affected include those involved in antibiotic regulation, virulence, flagella synthesis, and surfactant production. Although Hfq and RsmA are reported to activate flagellum production in E. coli and an adherent-invasive E. coli hfq mutant was shown to have no flagella by electron microscopy, we found that flagellar production was increased in the S39006 rsmA and hfq mutants. Additionally, deletion of rsmA resulted in greater genomic flux with increased activity of two mobile genetic elements. This was confirmed by qPCR and analysis of rsmA culture supernatant revealed the presence of prophage DNA and phage particles. Finally, expression of a hypothetical protein containing DUF364 increased prodigiosin production and was controlled by a putative 5′ cis-acting regulatory RNA element. Conclusion: Using a combination of transcriptomics and proteomics this study provides a systems-level understanding of Hfq and RsmA regulation and identifies similarities and differences in the regulons of two major regulators. Additionally our study indicates that RsmA regulates both core and variable genome regions and contributes to genome stability
From Quantum Mechanics to Quantum Field Theory: The Hopf route
We show that the combinatorial numbers known as {\em Bell numbers} are
generic in quantum physics. This is because they arise in the procedure known
as {\em Normal ordering} of bosons, a procedure which is involved in the
evaluation of quantum functions such as the canonical partition function of
quantum statistical physics, {\it inter alia}. In fact, we shall show that an
evaluation of the non-interacting partition function for a single boson system
is identical to integrating the {\em exponential generating function} of the
Bell numbers, which is a device for encapsulating a combinatorial sequence in a
single function. We then introduce a remarkable equality, the Dobinski
relation, and use it to indicate why renormalisation is necessary in even the
simplest of perturbation expansions for a partition function. Finally we
introduce a global algebraic description of this simple model, giving a Hopf
algebra, which provides a starting point for extensions to more complex
physical systems
Entropy calculation for a toy black hole
In this note we carry out the counting of states for a black hole in loop
quantum gravity, however assuming an equidistant area spectrum. We find that
this toy-model is exactly solvable, and we show that its behavior is very
similar to that of the correct model. Thus this toy-model can be used as a nice
and simplifying `laboratory' for questions about the full theory.Comment: 18 pages, 4 figures. v2: Corrected mistake in bibliography, added
appendix with further result
Stationary Distribution and Eigenvalues for a de Bruijn Process
We define a de Bruijn process with parameters n and L as a certain
continuous-time Markov chain on the de Bruijn graph with words of length L over
an n-letter alphabet as vertices. We determine explicitly its steady state
distribution and its characteristic polynomial, which turns out to decompose
into linear factors. In addition, we examine the stationary state of two
specializations in detail. In the first one, the de Bruijn-Bernoulli process,
this is a product measure. In the second one, the Skin-deep de Bruin process,
the distribution has constant density but nontrivial correlation functions. The
two point correlation function is determined using generating function
techniques.Comment: Dedicated to Herb Wilf on the occasion of his 80th birthda
Quantum Physics and Computers
Recent theoretical results confirm that quantum theory provides the
possibility of new ways of performing efficient calculations. The most striking
example is the factoring problem. It has recently been shown that computers
that exploit quantum features could factor large composite integers. This task
is believed to be out of reach of classical computers as soon as the number of
digits in the number to factor exceeds a certain limit. The additional power of
quantum computers comes from the possibility of employing a superposition of
states, of following many distinct computation paths and of producing a final
output that depends on the interference of all of them. This ``quantum
parallelism'' outstrips by far any parallelism that can be thought of in
classical computation and is responsible for the ``exponential'' speed-up of
computation.
This is a non-technical (or at least not too technical) introduction to the
field of quantum computation. It does not cover very recent topics, such as
error-correction.Comment: 27 pages, LaTeX, 8 PostScript figures embedded. A bug in one of the
postscript files has been fixed. Reprints available from the author. The
files are also available from
http://eve.physics.ox.ac.uk/Articles/QC.Articles.htm
Dobiński relations and ordering of boson operators
We introduce a generalization of the Dobiński relation, through which we define a family of Bell-type numbers and polynomials. Such generalized Dobiński relations are coherent state matrix elements of expressions involving boson ladder operators. This may be used in order to obtain normally ordered forms of polynomials in creation and annihilation operators, both if the latter satisfy canonical and deformed commutation relations
Cumulants and the moment algebra: tools for analysing weak measurements
Recently it has been shown that cumulants significantly simplify the analysis
of multipartite weak measurements. Here we consider the mathematical structure
that underlies this, and find that it can be formulated in terms of what we
call the moment algebra. Apart from resulting in simpler proofs, the
flexibility of this structure allows generalizations of the original results to
a number of weak measurement scenarios, including one where the weakly
interacting pointers reach thermal equilibrium with the probed system.Comment: Journal reference added, minor correction
Network robustness and fragility: Percolation on random graphs
Recent work on the internet, social networks, and the power grid has
addressed the resilience of these networks to either random or targeted
deletion of network nodes. Such deletions include, for example, the failure of
internet routers or power transmission lines. Percolation models on random
graphs provide a simple representation of this process, but have typically been
limited to graphs with Poisson degree distribution at their vertices. Such
graphs are quite unlike real world networks, which often possess power-law or
other highly skewed degree distributions. In this paper we study percolation on
graphs with completely general degree distribution, giving exact solutions for
a variety of cases, including site percolation, bond percolation, and models in
which occupation probabilities depend on vertex degree. We discuss the
application of our theory to the understanding of network resilience.Comment: 4 pages, 2 figure
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