959 research outputs found
Phase transition and landscape statistics of the number partitioning problem
The phase transition in the number partitioning problem (NPP), i.e., the
transition from a region in the space of control parameters in which almost all
instances have many solutions to a region in which almost all instances have no
solution, is investigated by examining the energy landscape of this classic
optimization problem. This is achieved by coding the information about the
minimum energy paths connecting pairs of minima into a tree structure, termed a
barrier tree, the leaves and internal nodes of which represent, respectively,
the minima and the lowest energy saddles connecting those minima. Here we apply
several measures of shape (balance and symmetry) as well as of branch lengths
(barrier heights) to the barrier trees that result from the landscape of the
NPP, aiming at identifying traces of the easy/hard transition. We find that it
is not possible to tell the easy regime from the hard one by visual inspection
of the trees or by measuring the barrier heights. Only the {\it difficulty}
measure, given by the maximum value of the ratio between the barrier height and
the energy surplus of local minima, succeeded in detecting traces of the phase
transition in the tree. In adddition, we show that the barrier trees associated
with the NPP are very similar to random trees, contrasting dramatically with
trees associated with the spin-glass and random energy models. We also
examine critically a recent conjecture on the equivalence between the NPP and a
truncated random energy model
DNA hybridization catalysts and catalyst circuits
Practically all of life's molecular processes, from chemical synthesis to replication, involve enzymes that carry out their functions through the catalysis of metastable fuels into waste products. Catalytic control of reaction rates will prove to be as useful and ubiquitous in
DNA nanotechnology as it is in biology. Here we present experimental results on the control of the decay rates of a metastable DNA "fuel". We show that the fuel complex can be induced to decay with a rate about 1600 times faster than it would decay spontaneously. The original DNA hybridization catalyst [15] achieved a maximal speed-up of roughly 30. The fuel complex discussed here can therefore serve as the basic ingredient for an improved DNA hybridization catalyst. As an example application for DNA hybridization catalysts, we propose a method for implementing arbitrary digital logic circuits
Divine intervention? A Cochrane review on intercessory prayer gone beyond science and reason
We discuss in this commentary a recent Cochrane review of 10 randomised trials aimed at testing the religious belief that praying to a god can help those who are prayed for. The review concluded that the available studies merit additional research. However, the review presented a scientifically unsound mixture of theological and scientific arguments, and two of the included trials that had a large impact on the findings had problems that were not described in the review. The review fails to live up to the high standards required for Cochrane reviews
Gauge Field Back-reaction on a Black Hole
The order fluctuations of gauge fields in the vicinity of a blackhole
can create a repulsive antigravity region extending out beyond the renormalized
Schwarzschild horizon. If the strength of this repulsive force increases as
higher orders in the back-reaction are included, the formation of a
wormhole-like object could occur.Comment: 17 pages, three figures available on request, in RevTe
Axially symmetric rotating traversable wormholes
This paper generalizes the static and spherically symmetric traversable
wormhole geometry to a rotating axially symmetric one with a time-dependent
angular velocity by means of an exact solution. It was found that the violation
of the weak energy condition, although unavoidable, is considerably less severe
than in the static spherically symmetric case. The radial tidal constraint is
more easily met due to the rotation. Similar improvements are seen in one of
the lateral tidal constraints. The magnitude of the angular velocity may have
little effect on the weak energy condition violation for an axially symmetric
wormhole. For a spherically symmetric one, however, the violation becomes less
severe with increasing angular velocity. The time rate of change of the angular
velocity, on the other hand, was found to have no effect at all. Finally, the
angular velocity must depend only on the radial coordinate, confirming an
earlier result.Comment: 17 pages, AMSTe
Gravitational memory of natural wormholes
A traversable wormhole solution of general scalar-tensor field equations is
presented. We have shown, after a numerical analysis for the behavior of the
scalar field of Brans-Dicke theory, that the solution is completely
singularity--free. Furthermore, the analysis of more general scalar field
dependent coupling constants indicates that the gravitational memory phenomenon
may play an important role in the fate of natural wormholes.Comment: 14 pages revtex, 1 ps figur
Fractal geometry of spin-glass models
Stability and diversity are two key properties that living entities share
with spin glasses, where they are manifested through the breaking of the phase
space into many valleys or local minima connected by saddle points. The
topology of the phase space can be conveniently condensed into a tree
structure, akin to the biological phylogenetic trees, whose tips are the local
minima and internal nodes are the lowest-energy saddles connecting those
minima. For the infinite-range Ising spin glass with p-spin interactions, we
show that the average size-frequency distribution of saddles obeys a power law
, where w=w(s) is the number of minima that can be
connected through saddle s, and D is the fractal dimension of the phase space
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