2,628 research outputs found
The fate of Newton's law in brane-world scenarios
We consider brane-world scenarios embedded into string theory. We find that
the D-brane backreaction induces a large increase in the open string's proper
length. Consequently the stringy nature of elementary particles can be detected
at distances much larger than the fundamental string scale. As an example, we
compute the gravitational potential between two open strings ending on
backreacting D3-branes in four-dimensional compactifications of type II string
theory. We find that the Newtonian potential receives a correction that goes
like 1/r but that is not proportional to the inertial masses of the open
strings, implying a violation of the equivalence principle in the effective
gravitational theory. This stringy correction is screened by thermal effects
when the distance between the strings is greater than the inverse temperature.
This suggests new experimental tests for many phenomenological models in type
II string theory.Comment: 8 pages, 3 figure
Bound states in N=2 Liouville theory with boundary and Deep throat D-branes
We exhibit bound states in the spectrum of non-compact D-branes in N=2
Liouville conformal field theory. We interpret these states in the study of
D-branes in the near-horizon limit of Neveu-Schwarz five-branes spread on a
topologically trivial circle. We match semi-classical di-electric and repulsion
effects with exact conformal field theory results and describe the fate of
D-branes hitting NS5-branes. We also show that the bound states can give rise
to massless vector and hyper multiplets in a low-energy gauge theory on
D-branes deep inside the throat.Comment: 45 pages, 11 figures, references added, JHEP versio
Sparsity vs. Statistical Independence in Adaptive Signal Representations: A Case Study of the Spike Process
Finding a basis/coordinate system that can efficiently represent an input
data stream by viewing them as realizations of a stochastic process is of
tremendous importance in many fields including data compression and
computational neuroscience. Two popular measures of such efficiency of a basis
are sparsity (measured by the expected norm, ) and
statistical independence (measured by the mutual information). Gaining deeper
understanding of their intricate relationship, however, remains elusive.
Therefore, we chose to study a simple synthetic stochastic process called the
spike process, which puts a unit impulse at a random location in an
-dimensional vector for each realization. For this process, we obtained the
following results: 1) The standard basis is the best both in terms of sparsity
and statistical independence if and the search of basis is
restricted within all possible orthonormal bases in ; 2) If we extend our
basis search in all possible invertible linear transformations in , then
the best basis in statistical independence differs from the one in sparsity; 3)
In either of the above, the best basis in statistical independence is not
unique, and there even exist those which make the inputs completely dense; 4)
There is no linear invertible transformation that achieves the true statistical
independence for .Comment: 39 pages, 7 figures, submitted to Annals of the Institute of
Statistical Mathematic
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