23,771 research outputs found
Dynamic model for failures in biological systems
A dynamic model for failures in biological organisms is proposed and studied
both analytically and numerically. Each cell in the organism becomes dead under
sufficiently strong stress, and is then allowed to be healed with some
probability. It is found that unlike the case of no healing, the organism in
general does not completely break down even in the presence of noise. Revealed
is the characteristic time evolution that the system tends to resist the stress
longer than the system without healing, followed by sudden breakdown with some
fraction of cells surviving. When the noise is weak, the critical stress beyond
which the system breaks down increases rapidly as the healing parameter is
raised from zero, indicative of the importance of healing in biological
systems.Comment: To appear in Europhys. Let
(2,2)-Formalism of General Relativity: An Exact Solution
I discuss the (2,2)-formalism of general relativity based on the
(2,2)-fibration of a generic 4-dimensional spacetime of the Lorentzian
signature. In this formalism general relativity is describable as a Yang-Mills
gauge theory defined on the (1+1)-dimensional base manifold, whose local gauge
symmetry is the group of the diffeomorphisms of the 2-dimensional fibre
manifold. After presenting the Einstein's field equations in this formalism, I
solve them for spherically symmetric case to obtain the Schwarzschild solution.
Then I discuss possible applications of this formalism.Comment: 2 figures included, IOP style file neede
New Hamiltonian formalism and quasi-local conservation equations of general relativity
I describe the Einstein's gravitation of 3+1 dimensional spacetimes using the
(2,2) formalism without assuming isometries. In this formalism, quasi-local
energy, linear momentum, and angular momentum are identified from the four
Einstein's equations of the divergence-type, and are expressed geometrically in
terms of the area of a two-surface and a pair of null vector fields on that
surface. The associated quasi-local balance equations are spelled out, and the
corresponding fluxes are found to assume the canonical form of energy-momentum
flux as in standard field theories. The remaining non-divergence-type
Einstein's equations turn out to be the Hamilton's equations of motion, which
are derivable from the {\it non-vanishing} Hamiltonian by the variational
principle. The Hamilton's equations are the evolution equations along the
out-going null geodesic whose {\it affine} parameter serves as the time
function. In the asymptotic region of asymptotically flat spacetimes, it is
shown that the quasi-local quantities reduce to the Bondi energy, linear
momentum, and angular momentum, and the corresponding fluxes become the Bondi
fluxes. The quasi-local angular momentum turns out to be zero for any
two-surface in the flat Minkowski spacetime. I also present a candidate for
quasi-local {\it rotational} energy which agrees with the Carter's constant in
the asymptotic region of the Kerr spacetime. Finally, a simple relation between
energy-flux and angular momentum-flux of a generic gravitational radiation is
discussed, whose existence reflects the fact that energy-flux always
accompanies angular momentum-flux unless the flux is an s-wave.Comment: 36 pages, 3 figures, RevTex
Dynamic model of fiber bundles
A realistic continuous-time dynamics for fiber bundles is introduced and
studied both analytically and numerically. The equation of motion reproduces
known stationary-state results in the deterministic limit while the system
under non-vanishing stress always breaks down in the presence of noise.
Revealed in particular is the characteristic time evolution that the system
tends to resist the stress for considerable time, followed by sudden complete
rupture. The critical stress beyond which the complete rupture emerges is also
obtained
Statistical Mechanics of Support Vector Networks
Using methods of Statistical Physics, we investigate the generalization
performance of support vector machines (SVMs), which have been recently
introduced as a general alternative to neural networks. For nonlinear
classification rules, the generalization error saturates on a plateau, when the
number of examples is too small to properly estimate the coefficients of the
nonlinear part. When trained on simple rules, we find that SVMs overfit only
weakly. The performance of SVMs is strongly enhanced, when the distribution of
the inputs has a gap in feature space.Comment: REVTeX, 4 pages, 2 figures, accepted by Phys. Rev. Lett (typos
corrected
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