Cut-off for lamplighter chains on tori: dimension interpolation and phase transition

Given a finite, connected graph \SG, the lamplighter chain on \SG is the lazy random walk $X^\diamond$ on the associated lamplighter graph \SG^\diamond=\Z_2 \wr \SG. The mixing time of the lamplighter chain on the torus $\Z_n^d$ is known to have a cutoff at a time asymptotic to the cover time of $\Z_n^d$ if $d=2$, and to half the cover time if $d \ge 3$. We show that the mixing time of the lamplighter chain on \ttorus=\Z_n^2 \times \Z_{a \log n} has a cutoff at $\psi(a)$ times the cover time of \ttorus as $n \to \infty$, where $\psi$ is an explicit weakly decreasing map from $(0,\infty)$ onto $[1/2,1)$. In particular, as $a > 0$ varies, the threshold continuously interpolates between the known thresholds for $\Z_n^2$ and $\Z_n^3$. Perhaps surprisingly, we find a phase transition (non-smoothness of $\psi$) at the point $a_*=\pi r_3 (1+\sqrt{2})$, where high dimensional behavior ($\psi(a)=1/2$ for all $a \ge a_*$) commences. Here $r_3$ is the effective resistance from $0$ to $\infty$ in $\Z^3$

Generalizations of the genomic rank distance to indels

MOTIVATION: The rank distance model represents genome rearrangements in multi-chromosomal genomes as matrix operations, which allows the reconstruction of parsimonious histories of evolution by rearrangements. We seek to generalize this model by allowing for genomes with different gene content, to accommodate a broader range of biological contexts. We approach this generalization by using a matrix representation of genomes. This leads to simple distance formulas and sorting algorithms for genomes with different gene contents, but without duplications. RESULTS: We generalize the rank distance to genomes with different gene content in two different ways. The first approach adds insertions, deletions and the substitution of a single extremity to the basic operations. We show how to efficiently compute this distance. To avoid genomes with incomplete markers, our alternative distance, the rank-indel distance, only uses insertions and deletions of entire chromosomes. We construct phylogenetic trees with our distances and the DCJ-Indel distance for simulated data and real prokaryotic genomes, and compare them against reference trees. For simulated data, our distances outperform the DCJ-Indel distance using the Quartet metric as baseline. This suggests that rank distances are more robust for comparing distantly related species. For real prokaryotic genomes, all rearrangement-based distances yield phylogenetic trees that are topologically distant from the reference (65% similarity with Quartet metric), but are able to cluster related species within their respective clades and distinguish the Shigella strains as the farthest relative of the Escherichia coli strains, a feature not seen in the reference tree. AVAILABILITY AND IMPLEMENTATION: Code and instructions are available at https://github.com/meidanis-lab/rank-indel. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online

Quantum enhanced positioning and clock synchronization

A wide variety of positioning and ranging procedures are based on repeatedly sending electromagnetic pulses through space and measuring their time of arrival. This paper shows that quantum entanglement and squeezing can be employed to overcome the classical power/bandwidth limits on these procedures, enhancing their accuracy. Frequency entangled pulses could be used to construct quantum positioning systems (QPS), to perform clock synchronization, or to do ranging (quantum radar): all of these techniques exhibit a similar enhancement compared with analogous protocols that use classical light. Quantum entanglement and squeezing have been exploited in the context of interferometry, frequency measurements, lithography, and algorithms. Here, the problem of positioning a party (say Alice) with respect to a fixed array of reference points will be analyzed.Comment: 4 pages, 2 figures. Accepted for publication by Natur

Social and dental status along the life course and oral health impacts in adolescents: a population-based birth cohort

<p>Abstract</p> <p>Background</p> <p>Harmful social conditions in early life might predispose individuals to dental status which in turn may impact on adolescents' quality of life.</p> <p>Aims</p> <p>To estimate the prevalence of oral health impacts among 12 yr-old Brazilian adolescents (<it>n </it>= 359) and its association with life course socioeconomic variables, dental status and dental services utilization in a population-based birth cohort in Southern Brazil.</p> <p>Methods</p> <p>Exploratory variables were collected at birth, at 6 and 12 yr of age. The Oral Impacts on Daily Performances index (OIDP) was collected in adolescence and it was analyzed as a ranked outcome (OIDP from 0 to 9). Unadjusted and adjusted multivariable Poisson regression with robust variance was performed guided by a theoretical determination model.</p> <p>Results</p> <p>The response rate was of 94.4% (<it>n </it>= 339). The prevalence of OIDP = 1 was 30.1% (CI95%25.2;35.0) and OIDP ≥ 2 was 28.0% (CI95%23.2;32.8). The most common daily activity affected was eating (44.8%), follow by cleaning the mouth and smiling (15.6%, and 15.0%, respectively). In the final model mother schooling and mother employment status in early cohort participant's life were associated with OIDP in adolescence. As higher untreated dental caries at age 6 and 12 years, and the presence of dental pain, gingival bleeding and incisal crowing in adolescence as higher the OIDP score. On the other hand, dental fluorosis was associated with low OIDP score.</p> <p>Conclusion</p> <p>Our findings highlight the importance of adolescent's early life social environmental as mother schooling and mother employment status and the early and later dental status on the adolescent's quality of life regardless family income and use of dental services.</p

Observation of Electron-Hole Puddles in Graphene Using a Scanning Single Electron Transistor

The electronic density of states of graphene is equivalent to that of relativistic electrons. In the absence of disorder or external doping the Fermi energy lies at the Dirac point where the density of states vanishes. Although transport measurements at high carrier densities indicate rather high mobilities, many questions pertaining to disorder remain unanswered. In particular, it has been argued theoretically, that when the average carrier density is zero, the inescapable presence of disorder will lead to electron and hole puddles with equal probability. In this work, we use a scanning single electron transistor to image the carrier density landscape of graphene in the vicinity of the neutrality point. Our results clearly show the electron-hole puddles expected theoretically. In addition, our measurement technique enables to determine locally the density of states in graphene. In contrast to previously studied massive two dimensional electron systems, the kinetic contribution to the density of states accounts quantitatively for the measured signal. Our results suggests that exchange and correlation effects are either weak or have canceling contributions.Comment: 13 pages, 5 figure

Environmental Costs of Government-Sponsored Agrarian Settlements in Brazilian Amazonia

Brazil has presided over the most comprehensive agrarian reform frontier colonization program on Earth, in which ~1.2 million settlers have been translocated by successive governments since the 1970's, mostly into forested hinterlands of Brazilian Amazonia. These settlements encompass 5.3% of this ~5 million km2 region, but have contributed with 13.5% of all land conversion into agropastoral land uses. The Brazilian Federal Agrarian Agency (INCRA) has repeatedly claimed that deforestation in these areas largely predates the sanctioned arrival of new settlers. Here, we quantify rates of natural vegetation conversion across 1911 agrarian settlements allocated to 568 Amazonian counties and compare fire incidence and deforestation rates before and after the official occupation of settlements by migrant farmers. The timing and spatial distribution of deforestation and fires in our analysis provides irrefutable chronological and spatially explicit evidence of agropastoral conversion both inside and immediately outside agrarian settlements over the last decade. Deforestation rates are strongly related to local human population density and road access to regional markets. Agrarian settlements consistently accelerated rates of deforestation and fires, compared to neighboring areas outside settlements, but within the same counties. Relocated smallholders allocated to forest areas undoubtedly operate as pivotal agents of deforestation, and most of the forest clearance occurs in the aftermath of government-induced migration

Social deprivation and exposure to health promotion. A study of the distribution of health promotion resources to schools in England

This article has been made available through the Brunel Open Access Publishing Fund and is available from the specified link - Copyright @ 2010 Chivu and ReidpathBACKGROUND: Area deprivation is a known determinant of health. It is also known that area deprivation is associated with lower impact health promotion. It is less well known, however, whether deprived areas are less responsive to health promotion, or whether they are less exposed. Using data from a national, school-based campaign to promote vaccination against the human papilloma virus (HPV), the relationship between area deprivation and exposure was examined. METHODS: Taking advantage of a health promotion campaign to provide information to schools about HPV vaccination, a cross sectional study was conducted to examine the relationship between area level, social deprivation, and take-up of (i.e., exposure to) available health promotion material. The sample was 4,750 schools across England, including government maintained and independent schools. The relationship between area deprivation and exposure was examined using bi- and multivariate logistic regression. RESULTS: It was found that schools in the least deprived quintile had 1.32 times the odds of requesting health promotion materials than schools in the most deprived areas (p = .01). This effect was independent of the school size, the type of school, and the geographic region. Conclusion The relationship between area deprivation and the impact of health promotion may be due, at least in part, to differential levels of exposure. The study was limited in scope, pointing to the need for more research, but also points to potentially important policy implications

Quantum Correlations in NMR systems

In conventional NMR experiments, the Zeeman energy gaps of the nuclear spin ensembles are much lower than their thermal energies, and accordingly exhibit tiny polarizations. Generally such low-purity quantum states are devoid of quantum entanglement. However, there exist certain nonclassical correlations which can be observed even in such systems. In this chapter, we discuss three such quantum correlations, namely, quantum contextuality, Leggett-Garg temporal correlations, and quantum discord. In each case, we provide a brief theoretical background and then describe some results from NMR experiments.Comment: 21 pages, 7 figure

The relativistic Sagnac Effect: two derivations

The phase shift due to the Sagnac Effect, for relativistic matter and electromagnetic beams, counter-propagating in a rotating interferometer, is deduced using two different approaches. From one hand, we show that the relativistic law of velocity addition leads to the well known Sagnac time difference, which is the same independently of the physical nature of the interfering beams, evidencing in this way the universality of the effect. Another derivation is based on a formal analogy with the phase shift induced by the magnetic potential for charged particles travelling in a region where a constant vector potential is present: this is the so called Aharonov-Bohm effect. Both derivations are carried out in a fully relativistic context, using a suitable 1+3 splitting that allows us to recognize and define the space where electromagnetic and matter waves propagate: this is an extended 3-space, which we call "relative space". It is recognized as the only space having an actual physical meaning from an operational point of view, and it is identified as the 'physical space of the rotating platform': the geometry of this space turns out to be non Euclidean, according to Einstein's early intuition.Comment: 49 pages, LaTeX, 3 EPS figures. Revised (final) version, minor corrections; to appear in "Relativity in Rotating Frames", ed. G. Rizzi and M.L. Ruggiero, Kluwer Academic Publishers, Dordrecht, (2003). See also http://digilander.libero.it/solciclo