Singular sources in gravity and homotopy in the space of connections

Suppose a Lagrangian is constructed from its fields and their derivatives. When the field configuration is a distribution, it is unambiguously defined as the limit of a sequence of smooth fields. The Lagrangian may or may not be a distribution, depending on whether there is some undefined product of distributions. Supposing that the Lagrangian is a distribution, it is unambiguously defined as the limit of a sequence of Lagrangians. But there still remains the question: Is the distributional Lagrangian uniquely defined by the limiting process for the fields themselves? In this paper a general geometrical construction is advanced to address this question. We describe certain types of singularities, not by distribution valued tensors, but by showing that the action functional for the singular fields is (formally) equivalent to another action built out of \emph{smooth} fields. Thus we manage to make the problem of the lack of a derivative disappear from a system which gives differential equations. Certain ideas from homotopy and homology theory turn out to be of central importance in analyzing the problem and clarifying finer aspects of it. The method is applied to general relativity in first order formalism, which gives some interesting insights into distributional geometries in that theory. Then more general gravitational Lagrangians in first order formalism are considered such as Lovelock terms (for which the action principle admits space-times more singular than other higher curvature theories).Comment: 21 pages, 9 figures, RevTe

A simple method for finite range decomposition of quadratic forms and Gaussian fields

We present a simple method to decompose the Green forms corresponding to a large class of interesting symmetric Dirichlet forms into integrals over symmetric positive semi-definite and finite range (properly supported) forms that are smoother than the original Green form. This result gives rise to multiscale decompositions of the associated Gaussian free fields into sums of independent smoother Gaussian fields with spatially localized correlations. Our method makes use of the finite propagation speed of the wave equation and Chebyshev polynomials. It improves several existing results and also gives simpler proofs.Comment: minor correction for t<

Bargaining over a finite set of alternatives

We analyze bilateral bargaining over a finite set of alternatives. We look for “good” ordinal solutions to such problems and show that Unanimity Compromise and Rational Compromise are the only bargaining rules that satisfy a basic set of properties. We then extend our analysis to admit problems with countably infinite alternatives. We show that, on this class, no bargaining rule choosing finite subsets of alternatives can be neutral. When rephrased in the utility framework of Nash (1950), this implies that there is no ordinal bargaining rule that is finite-valued

Modular Invariance of Finite Size Corrections and a Vortex Critical Phase

We analyze a continuous spin Gaussian model on a toroidal triangular lattice with periods $L_0$ and $L_1$ where the spins carry a representation of the fundamental group of the torus labeled by phases $u_0$ and $u_1$. We find the {\it exact finite size and lattice corrections}, to the partition function $Z$, for arbitrary mass $m$ and phases $u_i$. Summing $Z^{-1/2}$ over phases gives the corresponding result for the Ising model. The limits $m\rightarrow0$ and $u_i\rightarrow0$ do not commute. With $m=0$ the model exhibits a {\it vortex critical phase} when at least one of the $u_i$ is non-zero. In the continuum or scaling limit, for arbitrary $m$, the finite size corrections to $-\ln Z$ are {\it modular invariant} and for the critical phase are given by elliptic theta functions. In the cylinder limit $L_1\rightarrow\infty$ the ``cylinder charge'' $c(u_0,m^2L_0^2)$ is a non-monotonic function of $m$ that ranges from $2(1+6u_0(u_0-1))$ for $m=0$ to zero for $m\rightarrow\infty$.Comment: 12 pages of Plain TeX with two postscript figure insertions called torusfg1.ps and torusfg2.ps which can be obtained upon request from [email protected]

Hot dense capsule implosion cores produced by z-pinch dynamic hohlraum radiation

Hot dense capsule implosions driven by z-pinch x-rays have been measured for the first time. A ~220 eV dynamic hohlraum imploded 1.7-2.1 mm diameter gas-filled CH capsules which absorbed up to ~20 kJ of x-rays. Argon tracer atom spectra were used to measure the Te~ 1keV electron temperature and the ne ~ 1-4 x10^23 cm-3 electron density. Spectra from multiple directions provide core symmetry estimates. Computer simulations agree well with the peak compression values of Te, ne, and symmetry, indicating reasonable understanding of the hohlraum and implosion physics.Comment: submitted to Phys. Rev. Let

Muscle Volume Increases Following 16 Weeks of Resistive Exercise Training with the Advanced Resistive Exercise Device (ARED) and Free Weights

Space flight-induced muscle atrophy, particularly in the postural and locomotorymuscles, may impair task performance during long-duration space missions and planetary exploration. High intensity free weight (FW) resistive exercise training has been shown to prevent atrophy during bed rest, a space flight analog. NASA developed the Advanced Resistive Exercise Device (ARED) to simulate the characteristics of FW exercise (i.e. constant mass, inertial force) and to be used as a countermeasure during International Space Station (ISS) missions. PURPOSE: To compare the efficacy of ARED and FW training to induce hypertrophy in specific muscle groups in ambulatory subjects prior to deploying ARED on the ISS. METHODS: Twenty untrained subjects were assigned to either the ARED (8 males, 3 females) or FW (6 males, 3 females) group and participated in a periodizedtraining protocol consisting of squat (SQ), heel raise (HR), and deadlift(DL) exercises 3 d wk-1 for 16 wks. SQ, HR, and DL muscle strength (1RM) was measured before, after 8 wks, and after 16 wks of training to prescribe exercise and measure strength changes. Muscle volume of the vastigroup (V), hamstring group (H), hip adductor group (ADD), medial gastrocnemius(MG), lateral gastrocnemius(LG), and deep posterior muscles including soleus(DP) was measured using MRI pre-and post-training. Consecutive cross-sectional images (8 mm slices with a 2 mm gap) were analyzed and summed. Anatomical references insured that the same muscle sections were analyzed pre-and post-training. Two-way repeated measures ANOVAs (p<0.05) were used to test for differences in muscle strength and volume between training devices. RESULTS: SQ, HR, and DL 1RM increased in both FW (SQ: 49+/-6%, HR: 12+/-2%, DL: 23+/-4%) and ARED (SQ: 31+/-4%, HR: 18+/-2%, DL: 23+/-3%) groups. Both groups increased muscle volume in the V (FW: 13+/-2%, ARED: 10+/-2%), H (FW: 3+/-1%, ARED: 3+/-1 %), ADD (FW: 15=/-2%, ARED: 10+/-1%), LG (FW: 7+/-2%, ARED: 4+/-1%), MG (FW: 7+/-2%, ARED: 5+/-2%), and DP (FW: 2+/-1%; ARED: 2+/-1%) after training. There were no between group differences in muscle strength or volume. CONCLUSIONS: The increase in muscle volume and strength following ARED training is not different than FW training. With the training effects similar to FW and a 600 lb load capacity, ARED likely will protect against muscle atrophy in microgravity

Switching to second-line antiretroviral therapy in resource-limited settings: comparison of programmes with and without viral load monitoring.

In high-income countries, viral load is routinely measured to detect failure of antiretroviral therapy (ART) and guide switching to second-line ART. Viral load monitoring is not generally available in resource-limited settings. We examined switching from nonnucleoside reverse transcriptase inhibitor (NNRTI)-based first-line regimens to protease inhibitor-based regimens in Africa, South America and Asia

A New Non-Perturbative Approach to Quantum Theory in Curved Spacetime Using the Wigner Function

A new non-perturbative approach to quantum theory in curved spacetime and to quantum gravity, based on a generalisation of the Wigner equation, is proposed. Our definition for a Wigner equation differs from what have otherwise been proposed, and does not imply any approximations. It is a completely exact equation, fully equivalent to the Heisenberg equations of motion. The approach makes different approximation schemes possible, e.g. it is possible to perform a systematic calculation of the quantum effects order by order. An iterative scheme for this is also proposed. The method is illustrated with some simple examples and applications. A calculation of the trace of the renormalised energy-momentum tensor is done, and the conformal anomaly is thereby related to non-conservation of a current in d=2 dimensions and a relationship between a vector and an axial-vector current in d=4 dimensions. The corresponding ``hydrodynamic equations'' governing the evolution of macroscopic quantities are derived by taking appropriate moments. The emphasis is put on the spin-1/2 case, but it is shown how to extend to arbitrary spins. Gravity is treated first in the Palatini formalism, which is not very tractable, and then more successfully in the Ashtekar formalism, where the constraints lead to infinite order differential equations for the Wigner functions.Comment: LaTeX2e (uses amssymb), 36 page