Quantum Mechanics of a Point Particle in 2+1 Dimensional Gravity

We study the phase space structure and the quantization of a pointlike particle in 2+1 dimensional gravity. By adding boundary terms to the first order Einstein Hilbert action, and removing all redundant gauge degrees of freedom, we arrive at a reduced action for a gravitating particle in 2+1 dimensions, which is invariant under Lorentz transformations and a group of generalized translations. The momentum space of the particle turns out to be the group manifold SL(2). Its position coordinates have non-vanishing Poisson brackets, resulting in a non-commutative quantum spacetime. We use the representation theory of SL(2) to investigate its structure. We find a discretization of time, and some semi-discrete structure of space. An uncertainty relation forbids a fully localized particle. The quantum dynamics is described by a discretized Klein Gordon equation.Comment: 58 pages, 3 eps figures, presentation of the classical theory improve

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

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

(2+1)-dimensional Einstein-Kepler problem in the centre-of-mass frame

We formulate and analyze the Hamiltonian dynamics of a pair of massive spinless point particles in (2+1)-dimensional Einstein gravity by anchoring the system to a conical infinity, isometric to the infinity generated by a single massive but possibly spinning particle. The reduced phase space \Gamma_{red} has dimension four and topology R^3 x S^1. \Gamma_{red} is analogous to the phase space of a Newtonian two-body system in the centre-of-mass frame, and we find on \Gamma_{red} a canonical chart that makes this analogue explicit and reduces to the Newtonian chart in the appropriate limit. Prospects for quantization are commented on.Comment: 38 pages, REVTeX v3.1 with amsfonts and epsf, 12 eps figures. (v2: Presentational improvement, references added, typos corrected.

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

The two‐way relationship between ionospheric outflow and the ring current

It is now well established that the ionosphere, because it acts as a significant source of plasma, plays a critical role in ring current dynamics. However, because the ring current deposits energy into the ionosphere, the inverse may also be true: the ring current can play a critical role in the dynamics of ionospheric outflow. This study uses a set of coupled, first‐principles‐based numerical models to test the dependence of ionospheric outflow on ring current‐driven region 2 field‐aligned currents (FACs). A moderate magnetospheric storm event is modeled with the Space Weather Modeling Framework using a global MHD code (Block Adaptive Tree Solar wind Roe‐type Upwind Scheme, BATS‐R‐US), a polar wind model (Polar Wind Outflow Model), and a bounce‐averaged kinetic ring current model (ring current atmosphere interaction model with self‐consistent magnetic field, RAM‐SCB). Initially, each code is two‐way coupled to all others except for RAM‐SCB, which receives inputs from the other models but is not allowed to feed back pressure into the MHD model. The simulation is repeated with pressure coupling activated, which drives strong pressure gradients and region 2 FACs in BATS‐R‐US. It is found that the region 2 FACs increase heavy ion outflow by up to 6 times over the noncoupled results. The additional outflow further energizes the ring current, establishing an ionosphere‐magnetosphere mass feedback loop. This study further demonstrates that ionospheric outflow is not merely a plasma source for the magnetosphere but an integral part in the nonlinear ionosphere‐magnetosphere‐ring current system.Key PointsRegion 2 field‐aligned currents drive additional ionospheric O+ outflowThis additional outflow feeds the ring current, creating a feedback systemIonospheric outflow is a tightly coupled piece of the M‐I systemPeer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/112284/1/jgra51836.pd

Gravity in 2+1 dimensions as a Riemann-Hilbert problem

In this paper we consider 2+1-dimensional gravity coupled to N point-particles. We introduce a gauge in which the $z$- and $\bar{z}$-components of the dreibein field become holomorphic and anti-holomorphic respectively. As a result we can restrict ourselves to the complex plane. Next we show that solving the dreibein-field: $e^a_z(z)$ is equivalent to solving the Riemann-Hilbert problem for the group $SO(2,1)$. We give the explicit solution for 2 particles in terms of hypergeometric functions. In the N-particle case we give a representation in terms of conformal field theory. The dreibeins are expressed as correlators of 2 free fermion fields and twistoperators at the position of the particles.Comment: 32 pages Latex, 4 figures (uuencoded

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 – 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 – 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 .40–.55. We offer power estimates and make recommendations for future work. We also discuss implications for interpreting past research

Patient Selection for Bronchoscopic Lung Volume Reduction

Purpose: Bronchoscopic lung volume reduction (BLVR) is a valuable treatment option for carefully selected patients with severe COPD. There is limited knowledge about the characteristics and outcomes of patients referred to a specialized center for BLVR. The study objectives were to investigate the selection rate for BLVR treatment in patients referred for this treatment and to investigate the differences between patients that were selected for BLVR and patients that were not. Patients and Methods: We performed a retrospective analysis of patients with severe COPD who were referred to our hospital to assess eligibility for BLVR treatment. Our parameters included demographics, comorbidity, chest computed tomography characteristics, reasons for rejection from BLVR treatment and patient survival. Results: In total, 1500 patients were included (mean age 62 years, 50% female and forced expiratory volume in 1 s 33% of predicted). Out of this group, 282 (19%) patients were selected for BLVR treatment. The absence of a suitable target lobe for treatment, an unsuitable disease phenotype and insufficient lung hyperinflation were the most important factors for not being selected. Patients that were selected for any BLVR option lived significantly longer than the group of patients that were not selected for BLVR (median 3060 versus 2079 days, P<0.001). Conclusion: We found that only a small proportion of patients that are referred for BLVR treatment is eligible for a BLVR treatment, indicating a need for both better referral tools and for the development of new therapies for this group of patients. Furthermore, our data suggest that selection for BLVR is associated with a significant survival benefit

Efficient Attack Graph Analysis through Approximate Inference

Attack graphs provide compact representations of the attack paths that an attacker can follow to compromise network resources by analysing network vulnerabilities and topology. These representations are a powerful tool for security risk assessment. Bayesian inference on attack graphs enables the estimation of the risk of compromise to the system's components given their vulnerabilities and interconnections, and accounts for multi-step attacks spreading through the system. Whilst static analysis considers the risk posture at rest, dynamic analysis also accounts for evidence of compromise, e.g. from SIEM software or forensic investigation. However, in this context, exact Bayesian inference techniques do not scale well. In this paper we show how Loopy Belief Propagation - an approximate inference technique - can be applied to attack graphs, and that it scales linearly in the number of nodes for both static and dynamic analysis, making such analyses viable for larger networks. We experiment with different topologies and network clustering on synthetic Bayesian attack graphs with thousands of nodes to show that the algorithm's accuracy is acceptable and converge to a stable solution. We compare sequential and parallel versions of Loopy Belief Propagation with exact inference techniques for both static and dynamic analysis, showing the advantages of approximate inference techniques to scale to larger attack graphs.Comment: 30 pages, 14 figure