22,367 research outputs found
Phase Transitions and Symmetry Breaking in Genetic Algorithms with Crossover
In this paper, we consider the role of the crossover operator in genetic algorithms. Specifically, we study optimisation problems that exhibit many local optima and consider how crossover affects the rate at which the population breaks the symmetry of the problem. As an example of such a problem, we consider the subset sum problem. In so doing, we demonstrate a previously unobserved phenomenon, whereby the genetic algorithm with crossover exhibits a critical mutation rate, at which its performance sharply diverges from that of the genetic algorithm without crossover. At this critical mutation rate, the genetic algorithm with crossover exhibits a rapid increase in population diversity. We calculate the details of this phenomenon on a simple instance of the subset sum problem and show that it is a classic phase transition between ordered and disordered populations. Finally, we show that this critical mutation rate corresponds to the transition between the genetic algorithm accelerating or preventing symmetry breaking and that the critical mutation rate represents an optimum in terms of the balance of exploration and exploitation within the algorithm
Heitler-London model for acceptor-acceptor interactions in doped semiconductors
The interactions between acceptors in semiconductors are often treated in
qualitatively the same manner as those between donors. Acceptor wave functions
are taken to be approximately hydrogenic and the standard hydrogen molecule
Heitler-London model is used to describe acceptor-acceptor interactions. But
due to valence band degeneracy and spin-orbit coupling, acceptor states can be
far more complex than those of hydrogen atoms, which brings into question the
validity of this approximation. To address this issue, we develop an
acceptor-acceptor Heitler-London model using single-acceptor wave functions of
the form proposed by Baldereschi and Lipari, which more accurately capture the
physics of the acceptor states. We calculate the resulting acceptor-pair energy
levels and find, in contrast to the two-level singlet-triplet splitting of the
hydrogen molecule, a rich ten-level energy spectrum. Our results, computed as a
function of inter-acceptor distance and spin-orbit coupling strength, suggest
that acceptor-acceptor interactions can be qualitatively different from
donor-donor interactions, and should therefore be relevant to the control of
two-qubit interactions in acceptor-based qubit implementations, as well as the
magnetic properties of a variety of p-doped semiconductor systems. Further
insight is drawn by fitting numerical results to closed-form energy-level
expressions obtained via an acceptor-acceptor Hubbard model.Comment: 19 pages, 10 figures, text revised, figure quality improved,
additional references adde
Marginal likelihoods in phylogenetics: a review of methods and applications
By providing a framework of accounting for the shared ancestry inherent to
all life, phylogenetics is becoming the statistical foundation of biology. The
importance of model choice continues to grow as phylogenetic models continue to
increase in complexity to better capture micro and macroevolutionary processes.
In a Bayesian framework, the marginal likelihood is how data update our prior
beliefs about models, which gives us an intuitive measure of comparing model
fit that is grounded in probability theory. Given the rapid increase in the
number and complexity of phylogenetic models, methods for approximating
marginal likelihoods are increasingly important. Here we try to provide an
intuitive description of marginal likelihoods and why they are important in
Bayesian model testing. We also categorize and review methods for estimating
marginal likelihoods of phylogenetic models, highlighting several recent
methods that provide well-behaved estimates. Furthermore, we review some
empirical studies that demonstrate how marginal likelihoods can be used to
learn about models of evolution from biological data. We discuss promising
alternatives that can complement marginal likelihoods for Bayesian model
choice, including posterior-predictive methods. Using simulations, we find one
alternative method based on approximate-Bayesian computation (ABC) to be
biased. We conclude by discussing the challenges of Bayesian model choice and
future directions that promise to improve the approximation of marginal
likelihoods and Bayesian phylogenetics as a whole.Comment: 33 pages, 3 figure
Simultaneously Sparse Solutions to Linear Inverse Problems with Multiple System Matrices and a Single Observation Vector
A linear inverse problem is proposed that requires the determination of
multiple unknown signal vectors. Each unknown vector passes through a different
system matrix and the results are added to yield a single observation vector.
Given the matrices and lone observation, the objective is to find a
simultaneously sparse set of unknown vectors that solves the system. We will
refer to this as the multiple-system single-output (MSSO) simultaneous sparsity
problem. This manuscript contrasts the MSSO problem with other simultaneous
sparsity problems and conducts a thorough initial exploration of algorithms
with which to solve it. Seven algorithms are formulated that approximately
solve this NP-Hard problem. Three greedy techniques are developed (matching
pursuit, orthogonal matching pursuit, and least squares matching pursuit) along
with four methods based on a convex relaxation (iteratively reweighted least
squares, two forms of iterative shrinkage, and formulation as a second-order
cone program). The algorithms are evaluated across three experiments: the first
and second involve sparsity profile recovery in noiseless and noisy scenarios,
respectively, while the third deals with magnetic resonance imaging
radio-frequency excitation pulse design.Comment: 36 pages; manuscript unchanged from July 21, 2008, except for updated
references; content appears in September 2008 PhD thesi
P-wave pi pi amplitude from dispersion relations
We solve the dispersion relation for the P-wave pi pi amplitude.We discuss
the role of the left hand cut vs Castillejo-Dalitz-Dyson (CDD), pole
contribution and compare the solution with a generic quark model description.
We review the the generic properties of analytical partial wave scattering and
production amplitudes and discuses their applicability and fits of experimental
data.Comment: 10 pages, 7 figures, typos corrected, reference adde
Hypoxic pre-conditioning increases the infiltration of endothelial cells into scaffolds for dermal regeneration pre-seeded with mesenchymal stem cells.
Many therapies using mesenchymal stem cells (MSC) rely on their ability to produce and release paracrine signals with chemotactic and pro-angiogenic activity. These characteristics, however, are mostly studied under standard in vitro culture conditions. In contrast, various novel cell-based therapies imply pre-seeding MSC into bio-artificial scaffolds. Here we describe human bone marrow-derived MSC seeded in Integra matrices, a common type of scaffold for dermal regeneration (SDR). We show and measured the distribution of MSC within the SDR, where cells clearly establish physical interactions with the scaffold, exhibiting constant metabolic activity for at least 15 days. In the SDR, MSC secrete VEGF and SDF-1α and induce transwell migration of CD34(+) hematopoietic/endothelial progenitor cells, which is inhibited in the presence of a CXCR4/SDF-1α antagonist. MSC in SDR respond to hypoxia by altering levels of angiogenic signals such as Angiogenin, Serpin-1, uPA, and IL-8. Finally, we show that MSC-containing SDR that have been pre-incubated in hypoxia show higher infiltration of endothelial cells after implantation into immune deficient mice. Our data show that MSC are fully functional ex vivo when implanted into SDR. In addition, our results strongly support the notion of hypoxic pre-conditioning MSC-containing SDR, in order to promote angiogenesis in the wounds
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