249 research outputs found
Gradual sub-lattice reduction and a new complexity for factoring polynomials
We present a lattice algorithm specifically designed for some classical
applications of lattice reduction. The applications are for lattice bases with
a generalized knapsack-type structure, where the target vectors are boundably
short. For such applications, the complexity of the algorithm improves
traditional lattice reduction by replacing some dependence on the bit-length of
the input vectors by some dependence on the bound for the output vectors. If
the bit-length of the target vectors is unrelated to the bit-length of the
input, then our algorithm is only linear in the bit-length of the input
entries, which is an improvement over the quadratic complexity floating-point
LLL algorithms. To illustrate the usefulness of this algorithm we show that a
direct application to factoring univariate polynomials over the integers leads
to the first complexity bound improvement since 1984. A second application is
algebraic number reconstruction, where a new complexity bound is obtained as
well
An Exact Algorithm for Side-Chain Placement in Protein Design
Computational protein design aims at constructing novel or improved functions
on the structure of a given protein backbone and has important applications in
the pharmaceutical and biotechnical industry. The underlying combinatorial
side-chain placement problem consists of choosing a side-chain placement for
each residue position such that the resulting overall energy is minimum. The
choice of the side-chain then also determines the amino acid for this position.
Many algorithms for this NP-hard problem have been proposed in the context of
homology modeling, which, however, reach their limits when faced with large
protein design instances.
In this paper, we propose a new exact method for the side-chain placement
problem that works well even for large instance sizes as they appear in protein
design. Our main contribution is a dedicated branch-and-bound algorithm that
combines tight upper and lower bounds resulting from a novel Lagrangian
relaxation approach for side-chain placement. Our experimental results show
that our method outperforms alternative state-of-the art exact approaches and
makes it possible to optimally solve large protein design instances routinely
On the consistency of de Sitter vacua
In this paper the consistency of the de Sitter invariant -vacua,
which have been introduced as simple tools to study the effects of
transplanckian physics, is investigated. In particular possible non
renormalization problems are discussed, as well as non standard properties of
Greens functions. We also discuss the non thermal properties of the -vacua and the necessity of to change. The conclusion is that non of
these problems necessarily exclude an application of the -vacua to
inflation.Comment: 12 pages, v2: minor clarifications and corrections to reference
Squeezed States in the de Sitter Vacuum
We discuss the treatment of squeezed states as excitations in the Euclidean
vacuum of de Sitter space. A comparison with the treatment of these states as
candidate no-particle states, or alpha-vacua, shows important differences
already in the free theory. At the interacting level alpha-vacua are
inconsistent, but squeezed state excitations seem perfectly acceptable. Indeed,
matrix elements can be renormalized in the excited states using precisely the
standard local counterterms of the Euclidean vacuum. Implications for
inflationary scenarios in cosmology are discussed.Comment: 15 pages, no figures. One new citation in version 3; no other change
Quantum Search with Two-atom Collisions in Cavity QED
We propose a scheme to implement two-qubit Grover's quantum search algorithm
using Cavity Quantum Electrodynamics. Circular Rydberg atoms are used as
quantum bits (qubits). They interact with the electromagnetic field of a
non-resonant cavity . The quantum gate dynamics is provided by a
cavity-assisted collision, robust against decoherence processes. We present the
detailed procedure and analyze the experimental feasibility.Comment: 4 pages, 2 figure
On Thermalization in de Sitter Space
We discuss thermalization in de Sitter space and argue, from two different
points of view, that the typical time needed for thermalization is of order
, where is the radius of the de Sitter space in question.
This time scale gives plenty of room for non-thermal deviations to survive
during long periods of inflation. We also speculate in more general terms on
the meaning of the time scale for finite quantum systems inside isolated boxes,
and comment on the relation to the Poincar\'{e} recurrence time.Comment: 14 pages, 2 figures, latex, references added. Improved discussion in
section 3 adde
Modification to the power spectrum in the brane world inflation driven by the bulk inflaton
We compute the cosmological perturbations generated in the brane world
inflation driven by the bulk inflaton. Different from the model that the
inflation is a brane effect, we exhibit the modification of the power spectrum
of scalar perturbations due to the existence of the fifth dimension. With the
change of the initial vacuum, we investigate the dependence of the correction
of the power spectrum on the choice of the vacuum.Comment: replaced with the revised version, accepted for publication in PR
Primeval Corrections to the CMB Anisotropies
We show that deviations of the quantum state of the inflaton from the thermal
vacuum of inflation may leave an imprint in the CMB anisotropies. The quantum
dynamics of the inflaton in such a state produces corrections to the
inflationary fluctuations, which may be observable. Because these effects
originate from IR physics below the Planck scale, they will dominate over any
trans-Planckian imprints in any theory which obeys decoupling. Inflation sweeps
away these initial deviations and forces its quantum state closer to the
thermal vacuum. We view this as the quantum version of the cosmic no-hair
theorem. Such imprints in the CMB may be a useful, independent test of the
duration of inflation, or of significant features in the inflaton potential
about 60 e-folds before inflation ended, instead of an unlikely discovery of
the signatures of quantum gravity. The absence of any such substructure would
suggest that inflation lasted uninterrupted much longer than
e-folds.Comment: 17 pages, latex, no figures; v3: added references and comments, final
version to appear in Phys. Rev.
A comment on multiple vacua, particle production and the time dependent AdS/CFT correspondence
We give an explicit formulation of the time dependent AdS/CFT correspondence
when there are multiple vacua present in Lorentzian signature. By computing
sample two point functions we show how different amplitudes are related by
cosmological particle production. We illustrate our methods in two example
spacetimes: (a) a ``bubble of nothing'' in AdS space, and (b) an asymptotically
locally AdS spacetime with a bubble of nothing on the boundary. In both cases
the alpha vacua of de Sitter space make an interesting appearance.Comment: 9 page
The long-time dynamics of two hydrodynamically-coupled swimming cells
Swimming micro-organisms such as bacteria or spermatozoa are typically found
in dense suspensions, and exhibit collective modes of locomotion qualitatively
different from that displayed by isolated cells. In the dilute limit where
fluid-mediated interactions can be treated rigorously, the long-time
hydrodynamics of a collection of cells result from interactions with many other
cells, and as such typically eludes an analytical approach. Here we consider
the only case where such problem can be treated rigorously analytically, namely
when the cells have spatially confined trajectories, such as the spermatozoa of
some marine invertebrates. We consider two spherical cells swimming, when
isolated, with arbitrary circular trajectories, and derive the long-time
kinematics of their relative locomotion. We show that in the dilute limit where
the cells are much further away than their size, and the size of their circular
motion, a separation of time scale occurs between a fast (intrinsic) swimming
time, and a slow time where hydrodynamic interactions lead to change in the
relative position and orientation of the swimmers. We perform a multiple-scale
analysis and derive the effective dynamical system - of dimension two -
describing the long-time behavior of the pair of cells. We show that the system
displays one type of equilibrium, and two types of rotational equilibrium, all
of which are found to be unstable. A detailed mathematical analysis of the
dynamical systems further allows us to show that only two cell-cell behaviors
are possible in the limit of , either the cells are attracted to
each other (possibly monotonically), or they are repelled (possibly
monotonically as well), which we confirm with numerical computations
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