Central limit theorems and diffusion approximations for multiscale Markov chain models

Ordinary differential equations obtained as limits of Markov processes appear in many settings. They may arise by scaling large systems, or by averaging rapidly fluctuating systems, or in systems involving multiple time-scales, by a combination of the two. Motivated by models with multiple time-scales arising in systems biology, we present a general approach to proving a central limit theorem capturing the fluctuations of the original model around the deterministic limit. The central limit theorem provides a method for deriving an appropriate diffusion (Langevin) approximation.Comment: Published in at http://dx.doi.org/10.1214/13-AAP934 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Asymptotic analysis of multiscale approximations to reaction networks

A reaction network is a chemical system involving multiple reactions and chemical species. Stochastic models of such networks treat the system as a continuous time Markov chain on the number of molecules of each species with reactions as possible transitions of the chain. In many cases of biological interest some of the chemical species in the network are present in much greater abundance than others and reaction rate constants can vary over several orders of magnitude. We consider approaches to approximation of such models that take the multiscale nature of the system into account. Our primary example is a model of a cell's viral infection for which we apply a combination of averaging and law of large number arguments to show that the ``slow'' component of the model can be approximated by a deterministic equation and to characterize the asymptotic distribution of the ``fast'' components. The main goal is to illustrate techniques that can be used to reduce the dimensionality of much more complex models.Comment: Published at http://dx.doi.org/10.1214/105051606000000420 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Quantum Chaos, Delocalization, and Entanglement in Disordered Heisenberg Models

We investigate disordered one- and two-dimensional Heisenberg spin lattices across a transition from integrability to quantum chaos from both a statistical many-body and a quantum-information perspective. Special emphasis is devoted to quantitatively exploring the interplay between eigenvector statistics, delocalization, and entanglement in the presence of nontrivial symmetries. The implications of basis dependence of state delocalization indicators (such as the number of principal components) is addressed, and a measure of {\em relative delocalization} is proposed in order to robustly characterize the onset of chaos in the presence of disorder. Both standard multipartite and {\em generalized entanglement} are investigated in a wide parameter regime by using a family of spin- and fermion- purity measures, their dependence on delocalization and on energy spectrum statistics being examined. A distinctive {\em correlation between entanglement, delocalization, and integrability} is uncovered, which may be generic to systems described by the two-body random ensemble and may point to a new diagnostic tool for quantum chaos. Analytical estimates for typical entanglement of random pure states restricted to a proper subspace of the full Hilbert space are also established and compared with random matrix theory predictions.Comment: 17 pages, 10 figures, revised versio

A Dose of Public Health through Grassroots Advocacy: The Development of Tobacco-Control Policy on a College Campus

Maine has the unfortunate distinction of having the highest rate of tobacco use among 18- to 30-year-olds of any state in the nation. Moreover—as Bryant points out—first-time smoking among traditional college-age populations has risen nearly 30 percent in the past decade. Armed with these statistics, it is not difficult to conclude that college campuses in Maine face a serious public health issue. Carried by the momentum of recent tobacco-control policy developments at the state level, the University of Maine at Farmington (UMF) has passed a stringent new tobacco-control policy that places UMF in the forefront of nationwide efforts to curb tobacco use among college-age students, and also to minimize the harmful effects of secondhand smoke. In this article, Bryant traces the grassroots advocacy efforts that led to the recent passage of a new tobacco-control policy at UMF. She concludes with a set of recommendations for policy advocates in other settings

Morphology of passivating organic ligands around a nanocrystal

Semiconductor nanocrystals are a promising class of materials for a variety of novel optoelectronic devices, since many of their properties, such as the electronic gap and conductivity, can be controlled. Much of this control is achieved via the organic ligand shell, through control of the size of the nanocrystal and the distance to other objects. We here simulate ligand-coated CdSe nanocrystals using atomistic molecular dynamics, allowing for the resolution of novel structural details about the ligand shell. We show that the ligands on the surface can lie flat to form a highly anisotropic 'wet hair' layer as opposed to the 'spiky ball' appearance typically considered. We discuss how this can give rise to a dot-to-dot packing distance of one ligand length since the thickness of the ligand shell is reduced to approximately one-half of the ligand length for the system sizes considered here; these distances imply that energy and charge transfer rates between dots and nearby objects will be enhanced due to the thinner than expected ligand shell. Our model predicts a non-linear scaling of ligand shell thickness as the ligands transition from 'spiky' to 'wet hair'. We verify this scaling using TEM on a PbS nanoarray, confirming that this theory gives a qualitatively correct picture of the ligand shell thickness of colloidal quantum dots.Comment: 17 Pages, 9 Figure

Prospects for an evolutionary economic psychology: buying and consumption as a test case

Until a few generations ago, humans made their living by foraging, like other animals. We have therefore inherited genes that allowed our ancestors to thrive as hunters and gatherers. Thriving in a modern economy requires very different behaviours but we cope because the human brain evolved to be flexible with the ability to form cooperative networks with other humans and to maintain the shared body of information, expertise and values which we call "culture". We argue that human economic behaviour is influenced by both the genes and the culture that we "inherit" and that both are a result of a Darwinian evolutionary process. An evolutionary approach is therefore likely to be of value in developing theories of economic behaviour. We then use this approach to analyse in broad terms how people that are born with the brains of foragers living in a small-scale society become consumers in a modern society and where this behaviour is likely to lead our species

Transfer of ultra-low phase noise microwave references over the JANET Aurora fibre network using a femtosecond optical frequency comb

An ultra-low phase noise microwave frequency is transferred over 82 km of installed fibre by propagation of a 30 nm bandwidth optical frequency comb (104 modes). The phase noise induced along the fibre by vibrations and thermal effects is suppressed by implementing a noise cancellation scheme where a portion of the light is sent back to the transmitter through the same fibre. The 6th harmonic of the repetition rate detected before and after the pulse train has travelled a round trip are phase compared and used to generate an error signal that controls a fibre stretcher to compensate for the fibre-induced phase fluctuations. Optical amplifiers are used to compensate for the fibre attenuation and dispersion compensation modules are also employed

P2: DIFFERENTIAL EFFECTS OF ADJACENT-LETTER AND OPEN FLANKING BIGRAMS ON LEXICAL DECISION PERFORMANCE

Some models of word identification hypotheses units responsive to bigrams—letter pairs—that may not be adjacent in a letter-string stimulus. Grainger, Mathot, and Vitu (2014) and Palinski (2016) found, for words, responding was more efficient when flanking bigrams contained target-string letters than when they did not. They also found that responding was more efficient when flanking bigrams contained letters ordered as in the target than switched but whether flanking bigrams were ordered as in the target did not affect performance. Palinski (2016) replicated the results of Grainger et al. (2014) and conducted a second experiment that included four additional conditions in which the flanking bigrams consist of letters separated by one letter in the target (ex. FO FROG RG; RG FROG FO; OF FROG GR; GR FROG OF). Although, for nonadjacent letter bigrams, the pattern of performance over conditions was like that in Grainger et al. (2014) and Palinski (2016) Experiment 1, for adjacent bigrams, the pattern was different. To investigate the stability of these results, we repeated Palinski\u27s second experiment. We replicated her results. The effect of adjacent-letter flanking bigrams may depend on whether nonadjacent-letter flanking bigrams are encountered in the experiment.https://engagedscholarship.csuohio.edu/u_poster_2017/1037/thumbnail.jp