9,549 research outputs found
Generic solutions for some integrable lattice equations
We derive the expressions for -functions and generic solutions of
lattice principal chiral equations, lattice KP hierarchy and hierarchy
including lattice N-wave type equations. -function of free fermions
plays fundamental role in this context. Miwa's coordinates in our case appear
as the lattice parameters.Comment: The text of the talk at NEEDS-93 conference, Gallipoli, Italy,
September-93, LaTeX, 8 pages. Several typos and minor errors are correcte
Confinement effects in a guided-wave interferometer with millimeter-scale arm separation
Guided-wave atom interferometers measure interference effects using atoms
held in a confining potential. In one common implementation, the confinement is
primarily two-dimensional, and the atoms move along the nearly free dimension
under the influence of an off-resonant standing wave laser beam. In this
configuration, residual confinement along the nominally free axis can introduce
a phase gradient to the atoms that limits the arm separation of the
interferometer. We experimentally investigate this effect in detail, and show
that it can be alleviated by having the atoms undergo a more symmetric motion
in the guide. This can be achieved by either using additional laser pulses or
by allowing the atoms to freely oscillate in the potential. Using these
techniques, we demonstrate interferometer measurement times up to 72 ms and arm
separations up to 0.42 mm with a well controlled phase, or times of 0.91 s and
separations of 1.7 mm with an uncontrolled phase.Comment: 14 pages, 6 figure
Module networks revisited: computational assessment and prioritization of model predictions
The solution of high-dimensional inference and prediction problems in
computational biology is almost always a compromise between mathematical theory
and practical constraints such as limited computational resources. As time
progresses, computational power increases but well-established inference
methods often remain locked in their initial suboptimal solution. We revisit
the approach of Segal et al. (2003) to infer regulatory modules and their
condition-specific regulators from gene expression data. In contrast to their
direct optimization-based solution we use a more representative centroid-like
solution extracted from an ensemble of possible statistical models to explain
the data. The ensemble method automatically selects a subset of most
informative genes and builds a quantitatively better model for them. Genes
which cluster together in the majority of models produce functionally more
coherent modules. Regulators which are consistently assigned to a module are
more often supported by literature, but a single model always contains many
regulator assignments not supported by the ensemble. Reliably detecting
condition-specific or combinatorial regulation is particularly hard in a single
optimum but can be achieved using ensemble averaging.Comment: 8 pages REVTeX, 6 figure
Commuting Flows and Conservation Laws for Noncommutative Lax Hierarchies
We discuss commuting flows and conservation laws for Lax hierarchies on
noncommutative spaces in the framework of the Sato theory. On commutative
spaces, the Sato theory has revealed essential aspects of the integrability for
wide class of soliton equations which are derived from the Lax hierarchies in
terms of pseudo-differential operators. Noncommutative extension of the Sato
theory has been already studied by the author and Kouichi Toda, and the
existence of various noncommutative Lax hierarchies are guaranteed. In the
present paper, we present conservation laws for the noncommutative Lax
hierarchies with both space-space and space-time noncommutativities and prove
the existence of infinite number of conserved densities. We also give the
explicit representations of them in terms of Lax operators. Our results include
noncommutative versions of KP, KdV, Boussinesq, coupled KdV, Sawada-Kotera,
modified KdV equations and so on.Comment: 22 pages, LaTeX, v2: typos corrected, references added, version to
appear in JM
Geometric structures on loop and path spaces
Is is known that the loop space associated to a Riemannian manifold admits a
quasi-symplectic structure. This article shows that this structure is not
likely to recover the underlying Riemannian metric by proving a result that is
a strong indication of the "almost" independence of the quasi-symplectic
structure with respect to the metric. Finally conditions to have contact
structures on these spaces are studied.Comment: Final version. To appear in Proceedings of Math. Sci. Indian Academy
of Science
Counting statistics of collective photon transmissions
We theoretically study cooperative effects in the steady-state transmission
of photons through a medium of radiators. Using methods from quantum
transport, we find a cross-over in scaling from to in the current and
even higher powers of in the higher cumulants of the photon counting
statistics as a function of the tunable source occupation. The effect should be
observable for atoms confined within a nano-cell with a pumped optical cavity
as photon source.Comment: extended results, 9 pages, 2 figures, to appear in Annals of Physic
The effect of a finite roll rate on the miss-distance of a bank-to-turn missile
AbstractWe consider a three-dimensional pursuit-evasion situation where a highly maneuverable evader, which we model as a âpedestrianâ ĂĄ la Isaacs, is engaged by a faster-pursuer. The pursuer has limited maneuverability, that is, the pursuer has a minimal turning radius, and in order to change the spatial direction of his velocity vector, he must first re-align his thrust vector in a similar manner to a bank-to-turn missile. The state space of the ensuing differential game is three-dimensional and its complexity is intermediate between Isaac's [1] classical âHomicidal Chauffeurâ and âTwo Carâ differential games. This new DG is solved as a game of kind, and a capture criterion for a faster but less maneuverable pursuer is analytically established in terms of the game parameters
Interventions using behavioural insights to influence children's diet-related outcomes: a systematic review
The global prevalence of children with overweight and obesity continues to rise. Obesity in childhood has dire long-term consequences on health, social and economic outcomes. Promising interventions using behavioural insights to address obesity in childhood have emerged. This systematic review examines the effectiveness and health equity implications of interventions using behavioural insights to improve children's diet-related outcomes. The search strategy included searches on six electronic databases, reference lists of previous systematic reviews and backward searching of all included studies. One-hundred and eight papers describing 137 interventions were included. Interventions using behavioural insights were effective at modifying children's diet-related outcomes in 74% of all included interventions. The most promising approaches involved using incentives, changing defaults and modifying the physical environment. Information provision alone was the least effective approach. Health equity implications were rarely analysed or discussed. There was limited evidence of the sustainability of interventions-both in relation to their overall effectiveness and cost-effectiveness. The limited evidence on health equity, long-term effectiveness and the cost-effectiveness of these interventions limit what can be inferred for policymakers. This review synthesises the use of behavioural insights to improve children's diet-related outcomes, which can be used to inform future interventions
Motif Discovery through Predictive Modeling of Gene Regulation
We present MEDUSA, an integrative method for learning motif models of
transcription factor binding sites by incorporating promoter sequence and gene
expression data. We use a modern large-margin machine learning approach, based
on boosting, to enable feature selection from the high-dimensional search space
of candidate binding sequences while avoiding overfitting. At each iteration of
the algorithm, MEDUSA builds a motif model whose presence in the promoter
region of a gene, coupled with activity of a regulator in an experiment, is
predictive of differential expression. In this way, we learn motifs that are
functional and predictive of regulatory response rather than motifs that are
simply overrepresented in promoter sequences. Moreover, MEDUSA produces a model
of the transcriptional control logic that can predict the expression of any
gene in the organism, given the sequence of the promoter region of the target
gene and the expression state of a set of known or putative transcription
factors and signaling molecules. Each motif model is either a -length
sequence, a dimer, or a PSSM that is built by agglomerative probabilistic
clustering of sequences with similar boosting loss. By applying MEDUSA to a set
of environmental stress response expression data in yeast, we learn motifs
whose ability to predict differential expression of target genes outperforms
motifs from the TRANSFAC dataset and from a previously published candidate set
of PSSMs. We also show that MEDUSA retrieves many experimentally confirmed
binding sites associated with environmental stress response from the
literature.Comment: RECOMB 200
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