4,926 research outputs found
Neighbours of Einstein's Equations: Connections and Curvatures
Once the action for Einstein's equations is rewritten as a functional of an
SO(3,C) connection and a conformal factor of the metric, it admits a family of
``neighbours'' having the same number of degrees of freedom and a precisely
defined metric tensor. This paper analyzes the relation between the Riemann
tensor of that metric and the curvature tensor of the SO(3) connection. The
relation is in general very complicated. The Einstein case is distinguished by
the fact that two natural SO(3) metrics on the GL(3) fibers coincide. In the
general case the theory is bimetric on the fibers.Comment: 16 pages, LaTe
Degenerate Metric Phase Boundaries
The structure of boundaries between degenerate and nondegenerate solutions of
Ashtekar's canonical reformulation of Einstein's equations is studied. Several
examples are given of such "phase boundaries" in which the metric is degenerate
on one side of a null hypersurface and non-degenerate on the other side. These
include portions of flat space, Schwarzschild, and plane wave solutions joined
to degenerate regions. In the last case, the wave collides with a planar phase
boundary and continues on with the same curvature but degenerate triad, while
the phase boundary continues in the opposite direction. We conjecture that
degenerate phase boundaries are always null.Comment: 16 pages, 2 figures; erratum included in separate file: errors in
section 4, degenerate phase boundary is null without imposing field equation
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Performance bounds for particle filters using the optimal proposal
Particle filters may suffer from degeneracy of the particle weights. For the simplest "bootstrap" filter, it is known that avoiding degeneracy in large systems requires that the ensemble size must increase exponentially with the variance of the observation log-likelihood. The present article shows first that a similar result applies to particle filters using sequential importance sampling and the optimal proposal distribution and, second, that the optimal proposal yields minimal degeneracy when compared to any other proposal distribution that depends only on the previous state and the most recent observations. Thus, the optimal proposal provides performance bounds for filters using sequential importance sampling and any such proposal. An example with independent and identically distributed degrees of freedom illustrates both the need for exponentially large ensemble size with the optimal proposal as the system dimension increases and the potentially dramatic advantages of the optimal proposal relative to simpler proposals. Those advantages depend crucially on the magnitude of the system noise
Degenerate Sectors of the Ashtekar Gravity
This work completes the task of solving locally the Einstein-Ashtekar
equations for degenerate data. The two remaining degenerate sectors of the
classical 3+1 dimensional theory are considered. First, with all densitized
triad vectors linearly dependent and second, with only two independent ones. It
is shown how to solve the Einstein-Ashtekar equations completely by suitable
gauge fixing and choice of coordinates. Remarkably, the Hamiltonian weakly
Poisson commutes with the conditions defining the sectors. The summary of
degenerate solutions is given in the Appendix.Comment: 19 pages, late
Probability-based comparison of quantum states
We address the following state comparison problem: is it possible to design
an experiment enabling us to unambiguously decide (based on the observed
outcome statistics) on the sameness or difference of two unknown state
preparations without revealing complete information about the states? We find
that the claim "the same" can never be concluded without any doubts unless the
information is complete. Moreover, we prove that a universal comparison (that
perfectly distinguishes all states) also requires complete information about
the states. Nevertheless, for some measurements, the probability distribution
of outcomes still allows one to make an unambiguous conclusion regarding the
difference between the states even in the case of incomplete information. We
analyze an efficiency of such a comparison of qudit states when it is based on
the SWAP-measurement. For qubit states, we consider in detail the performance
of special families of two-valued measurements enabling us to successfully
compare at most half of the pairs of states. Finally, we introduce almost
universal comparison measurements which can distinguish almost all
non-identical states (up to a set of measure zero). The explicit form of such
measurements with two and more outcomes is found in any dimension.Comment: 12 pages, 6 figures, 1 table, some results are extende
A trick for passing degenerate points in Ashtekar formulation
We examine one of the advantages of Ashtekar's formulation of general
relativity: a tractability of degenerate points from the point of view of
following the dynamics of classical spacetime. Assuming that all dynamical
variables are finite, we conclude that an essential trick for such a continuous
evolution is in complexifying variables. In order to restrict the complex
region locally, we propose some `reality recovering' conditions on spacetime.
Using a degenerate solution derived by pull-back technique, and integrating the
dynamical equations numerically, we show that this idea works in an actual
dynamical problem. We also discuss some features of these applications.Comment: 9 pages by RevTeX or 16 pages by LaTeX, 3 eps figures and epsf-style
file are include
Causal structure and degenerate phase boundaries
Timelike and null hypersurfaces in the degenerate space-times in the Ashtekar
theory are defined in the light of the degenerate causal structure proposed by
Matschull. Using the new definition of null hypersufaces, the conjecture that
the "phase boundary" separating the degenerate space-time region from the
non-degenerate one in Ashtekar's gravity is always null is proved under certain
circumstances.Comment: 13 pages, Revte
Demographic Effects on the Swedish Pension System
The present study describes the effect that different demographic developments will have on the Swedish pension system. Projections of expenditures for old age pensions, survivor pensions, and disability pensions were made for the period 1985-2050 on the basis of future developments of the population and its structure (age, sex, and marital status). Six demographic scenarios were formulated: Benchmark, High Fertility, Low Mortality, West European, National 1, and National 2 scenarios. Together they cover a wide range of demographic developments, not to say all probable developments.
A model of the current Swedish pension system is combined with all six demographic scenarios. Projections of expenditures as well as of contributions and benefits in the pension system are made. The pension system will be put under severe strain whatever the demographic development. In all scenarios, expenditures will continue to increase until 2030, in the beginning as a result of the maturing of the system, but after the turn of the century mainly as a result of demographic changes. Expenditures will increase by about 75% in the "most favorable" scenarios (Benchmark/High Fertility, Western European) and by 100% to 130% in the "least favorable" scenarios (Low Mortality, National 1 and 2). After 2030, expenditures decrease in all scenarios except in National 2 where they remain constant. The contribution rates will have to be increased from about 20% in 1985 to between 36% (National 1) and 49.9% (Low Mortality) of the wage sum in 2030.
The impact on contributions and benefits of three selected policy measures are studied: a raising of the retirement age by two years, an extension of the number of years on which benefits are based and an increase in labor force. All three measures will ease the pressure on the system but only to some extent. The main conclusion is that there is a need for a fundamental change in the Swedish pension system
The reality conditions for the new canonical variables of General Relativity
We examine the constraints and the reality conditions that have to be imposed
in the canonical theory of 4--d gravity formulated in terms of Ashtekar
variables. We find that the polynomial reality conditions are consistent with
the constraints, and make the theory equivalent to Einstein's, as long as the
inverse metric is not degenerate; when it is degenerate, reality conditions
cannot be consistently imposed in general, and the theory describes complex
general relativity.Comment: 11
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