595 research outputs found
The 2+1 Kepler Problem and Its Quantization
We study a system of two pointlike particles coupled to three dimensional
Einstein gravity. The reduced phase space can be considered as a deformed
version of the phase space of two special-relativistic point particles in the
centre of mass frame. When the system is quantized, we find some possibly
general effects of quantum gravity, such as a minimal distances and a foaminess
of the spacetime at the order of the Planck length. We also obtain a
quantization of geometry, which restricts the possible asymptotic geometries of
the universe.Comment: 59 pages, LaTeX2e, 9 eps figure
Hamiltonian solutions of the 3-body problem in (2+1)-gravity
We present a full study of the 3-body problem in gravity in flat
(2+1)-dimensional space-time, and in the nonrelativistic limit of small
velocities. We provide an explicit form of the ADM Hamiltonian in a regular
coordinate system and we set up all the ingredients for canonical quantization.
We emphasize the role of a U(2) symmetry under which the Hamiltonian is
invariant and which should generalize to a U(N-1) symmetry for N bodies. This
symmetry seems to stem from a braid group structure in the operations of
looping of particles around each other, and guarantees the single-valuedness of
the Hamiltonian. Its role for the construction of single-valued energy
eigenfunctions is also discussed.Comment: 25 pages, no figure. v2: some calculation details removed to make the
paper more concise (see v1 for the longer version), minor correction in a
formula in the section on quantization, references added; results and
conclusions unchange
Mechanical Instabilities of Biological Tubes
We study theoretically the shapes of biological tubes affected by various
pathologies. When epithelial cells grow at an uncontrolled rate, the negative
tension produced by their division provokes a buckling instability. Several
shapes are investigated : varicose, enlarged, sinusoidal or sausage-like, all
of which are found in pathologies of tracheal, renal tubes or arteries. The
final shape depends crucially on the mechanical parameters of the tissues :
Young modulus, wall-to-lumen ratio, homeostatic pressure. We argue that since
tissues must be in quasistatic mechanical equilibrium, abnormal shapes convey
information as to what causes the pathology. We calculate a phase diagram of
tubular instabilities which could be a helpful guide for investigating the
underlying genetic regulation
Hamiltonian structure and quantization of 2+1 dimensional gravity coupled to particles
It is shown that the reduced particle dynamics of 2+1 dimensional gravity in
the maximally slicing gauge has hamiltonian form. This is proved directly for
the two body problem and for the three body problem by using the Garnier
equations for isomonodromic transformations. For a number of particles greater
than three the existence of the hamiltonian is shown to be a consequence of a
conjecture by Polyakov which connects the auxiliary parameters of the fuchsian
differential equation which solves the SU(1,1) Riemann-Hilbert problem, to the
Liouville action of the conformal factor which describes the space-metric. We
give the exact diffeomorphism which transforms the expression of the spinning
cone geometry in the Deser, Jackiw, 't Hooft gauge to the maximally slicing
gauge. It is explicitly shown that the boundary term in the action, written in
hamiltonian form gives the hamiltonian for the reduced particle dynamics. The
quantum mechanical translation of the two particle hamiltonian gives rise to
the logarithm of the Laplace-Beltrami operator on a cone whose angular deficit
is given by the total energy of the system irrespective of the masses of the
particles thus proving at the quantum level a conjecture by 't Hooft on the two
particle dynamics. The quantum mechanical Green's function for the two body
problem is given.Comment: 34 pages LaTe
Discrete structures in gravity
Discrete approaches to gravity, both classical and quantum, are reviewed
briefly, with emphasis on the method using piecewise-linear spaces. Models of
3-dimensional quantum gravity involving 6j-symbols are then described, and
progress in generalising these models to four dimensions is discussed, as is
the relationship of these models in both three and four dimensions to
topological theories. Finally, the repercussions of the generalisations are
explored for the original formulation of discrete gravity using edge-length
variables.Comment: 30 pages, 4 figure
How valid are assessments of conception probability in ovulatory cycle research? Evaluations, recommendations, and theoretical implications
Over the past two decades, a large literature examining psychological changes across women's ovulatory cycles has accumulated, emphasizing comparisons between fertile and non-fertile phases of the cycle. While some studies have verified ovulation using luteinizing hormone (LH) tests, counting methods â assessments of conception probability based on counting forward from actual or retrospectively recalled onset of last menses, or backward from actual or anticipated onset of next menses â are more common. The validity of these methods remains largely unexplored. Based on published data on the distributions of the lengths of follicular and luteal phases, we created a sample of 58,000+ simulated cycles. We used the sample to assess the validity of counting methods. Aside from methods that count backward from a confirmed onset of next menses, validities are modest, generally ranging from about .40â.55. We offer power estimates and make recommendations for future work. We also discuss implications for interpreting past research
Estimation of cold plasma outflow during geomagnetic storms
Low-energy ions of ionospheric origin constitute a significant contributor to the magnetospheric plasma population. Measuring cold ions is difficult though. Observations have to be done at sufficiently high altitudes and typically in regions of space where spacecraft attain a positive charge due to solar illumination. Cold ions are therefore shielded from the satellite particle detectors. Furthermore, spacecraft can only cover key regions of ion outflow during segments of their orbit, so additional complications arise if continuous longtime observations, such as during a geomagnetic storm, are needed. In this paper we suggest a new approach, based on a combination of synoptic observations and a novel technique to estimate the flux and total outflow during the various phases of geomagnetic storms. Our results indicate large variations in both outflow rates and transport throughout the storm. Prior to the storm main phase, outflow rates are moderate, and the cold ions are mainly emanating from moderately sized polar cap regions. Throughout the main phase of the storm, outflow rates increase and the polar cap source regions expand. Furthermore, faster transport, resulting from enhanced convection, leads to a much larger supply of cold ions to the near-Earth region during geomagnetic storms. ©2015. The Authors
Infinite factorization of multiple non-parametric views
Combined analysis of multiple data sources has increasing application interest, in particular for distinguishing shared and source-specific aspects. We extend this rationale of classical canonical correlation analysis into a flexible, generative and non-parametric clustering
setting, by introducing a novel non-parametric hierarchical
mixture model. The lower level of the model describes each source with a flexible non-parametric mixture, and the top level combines these to describe commonalities of the sources. The lower-level clusters arise from hierarchical Dirichlet Processes, inducing an infinite-dimensional contingency table between the views. The commonalities between the sources are modeled by an infinite block
model of the contingency table, interpretable as non-negative factorization of infinite matrices, or as a prior for infinite contingency tables. With Gaussian mixture components plugged in for continuous measurements, the model is applied to two views of genes, mRNA expression and abundance of the produced proteins, to expose groups of genes that are co-regulated in either or both of the views.
Cluster analysis of co-expression is a standard simple way of screening for co-regulation, and the two-view analysis extends the approach to distinguishing between pre- and post-translational regulation
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