1,955 research outputs found
Violation of Energy Bounds in Designer Gravity
We continue our study of the stability of designer gravity theories, where
one considers anti-de Sitter gravity coupled to certain tachyonic scalars with
boundary conditions defined by a smooth function W. It has recently been argued
there is a lower bound on the conserved energy in terms of the global minimum
of W, if the scalar potential arises from a superpotential P and the scalar
reaches an extremum of P at infinity. We show, however, there are
superpotentials for which these bounds do not hold.Comment: 16 pages, 4 figures, v2: discussion of vacuum decay included, typos
corrected, reference adde
Exploitation, secondary extinction and the altered trophic structure of Jamaican coral reefs
Coral reef communities of the Greater Antilles in the Caribbean have a long history of anthropogenic disturbance, driven by the exploitation for food of both vertebrate and invertebrate species. Exploitation, coupled with region wide declines of coral environments has resulted in local and regional vertebrate extinctions. The impact of those extinctions on reef communities, however, remains largely unexplored. Here we show, using a highly resolved model coral reef-seagrass food web, that at least 40 of 188 expected vertebrate species are absent from Jamaican coral reefs. Twenty one of the absent species are of high trophic level and are exploited by humans. The remainder of the absent species are unexploited, and comprises a significantly high proportion of specialized reef foragers. Many of those species are also more trophically specialized than their closest trophic competitors. We conclude that the absence of unexploited species from Jamaica is caused by the overexploitation of high trophic level species, and consequent trophic cascades and secondary extinction among their prey in an increasingly degraded reef environment. The result is a reef community depauperate of both exploited high trophic level predators, and unexploited, specialized lower trophic level reef foragers
Gravitational wave signatures from kink proliferation on cosmic (super-) strings
Junctions on cosmic string loops give rise to the proliferation of sharp
kinks. We study the effect of this proliferation on the gravitational wave (GW)
signals emitted from string networks with junctions, assuming a scaling
solution. We calculate the rate of occurrence and the distribution in amplitude
of the GW bursts emitted at cusps and kinks in the frequency bands of LIGO and
LISA as a function of the string tension, the number of sharp kinks on loops
with junctions and the fraction of loops in the cosmological network which have
junctions. Combining our results with current observational constraints, we
find that pulsar data rule out a significant number of kinks on loops for
strings with tensions G\mu > 10^{-12}. By contrast, for smaller tensions
current observations allow for a large number of kinks on loops. If this is the
case, the incoherent superposition of small bursts emitted at kink-kink
encounters leads to an enhanced GW background that hides the strong individual
bursts from kinks and cusps.Comment: 32 pages, 13 figure
Immunizing Conic Quadratic Optimization Problems Against Implementation Errors
We show that the robust counterpart of a convex quadratic constraint with ellipsoidal implementation error is equivalent to a system of conic quadratic constraints. To prove this result we first derive a sharper result for the S-lemma in case the two matrices involved can be simultaneously diagonalized. This extension of the S-lemma may also be useful for other purposes. We extend the result to the case in which the uncertainty region is the intersection of two convex quadratic inequalities. The robust counterpart for this case is also equivalent to a system of conic quadratic constraints. Results for convex conic quadratic constraints with implementation error are also given. We conclude with showing how the theory developed can be applied in robust linear optimization with jointly uncertain parameters and implementation errors, in sequential robust quadratic programming, in Taguchiâs robust approach, and in the adjustable robust counterpart.Conic Quadratic Program;hidden convexity;implementation error;robust optimization;simultaneous diagonalizability;S-lemma
Particle Production near an AdS Crunch
We numerically study the dual field theory evolution of five-dimensional
asymptotically anti-de Sitter solutions of supergravity that develop
cosmological singularities. The dual theory is an unstable deformation of the N
= 4 gauge theory on R S3, and the big crunch singularity in the bulk
occurs when a boundary scalar field runs to infinity. Consistent quantum
evolution requires one imposes boundary conditions at infinity. Modeling these
by a steep regularization of the scalar potential, we find that when an
initially nearly homogeneous wavepacket rolls down the potential, most of the
potential energy of the initial configuration is converted into gradient energy
during the first oscillation of the field. This indicates there is no
transition from a big crunch to a big bang in the bulk for dual boundary
conditions of this kind.Comment: 20 pages, 6 figure
Stability in Designer Gravity
We study the stability of designer gravity theories, in which one considers
gravity coupled to a tachyonic scalar with anti-de Sitter boundary conditions
defined by a smooth function W. We construct Hamiltonian generators of the
asymptotic symmetries using the covariant phase space method of Wald et al.and
find they differ from the spinor charges except when W=0. The positivity of the
spinor charge is used to establish a lower bound on the conserved energy of any
solution that satisfies boundary conditions for which has a global minimum.
A large class of designer gravity theories therefore have a stable ground
state, which the AdS/CFT correspondence indicates should be the lowest energy
soliton. We make progress towards proving this, by showing that minimum energy
solutions are static. The generalization of our results to designer gravity
theories in higher dimensions involving several tachyonic scalars is discussed.Comment: 29 page
Holographic Description of AdS Cosmologies
To gain insight in the quantum nature of the big bang, we study the dual
field theory description of asymptotically anti-de Sitter solutions of
supergravity that have cosmological singularities. The dual theories do not
appear to have a stable ground state. One regularization of the theory causes
the cosmological singularities in the bulk to turn into giant black holes with
scalar hair. We interpret these hairy black holes in the dual field theory and
use them to compute a finite temperature effective potential. In our study of
the field theory evolution, we find no evidence for a "bounce" from a big
crunch to a big bang. Instead, it appears that the big bang is a rare
fluctuation from a generic equilibrium quantum gravity state.Comment: 34 pages, 8 figures, v2: minor changes, references adde
Hidden Convexity in Partially Separable Optimization
The paper identifies classes of nonconvex optimization problems whose convex relaxations have optimal solutions which at the same time are global optimal solutions of the original nonconvex problems. Such a hidden convexity property was so far limited to quadratically constrained quadratic problems with one or two constraints. We extend it here to problems with some partial separable structure. Among other things, the new hidden convexity results open up the possibility to solve multi-stage robust optimization problems using certain nonlinear decision rules.convex relaxation of nonconvex problems;hidden convexity;partially separable functions;robust optimization
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