Relaxation dynamics of maximally clustered networks

We study the relaxation dynamics of fully clustered networks (maximal number of triangles) to an unclustered state under two different edge dynamics---the double-edge swap, corresponding to degree-preserving randomization of the configuration model, and single edge replacement, corresponding to full randomization of the Erd\H{o}s--R\'enyi random graph. We derive expressions for the time evolution of the degree distribution, edge multiplicity distribution and clustering coefficient. We show that under both dynamics networks undergo a continuous phase transition in which a giant connected component is formed. We calculate the position of the phase transition analytically using the Erd\H{o}s--R\'enyi phenomenology

Changes in mixing ratio and isotopic composition of CO2 in urban air from the Los Angeles basin, California, between 1972 and 2003

Atmospheric CO2 mixing ratios and C and O isotopic compositions are reported for the Los Angeles basin in southern California, a region renowned for its air pollution. Air samples collected midday on the Caltech campus in Pasadena, California, contained ∼30 ppm more CO2 in 1998–2003 than in 1972–1973 (averaging 397 ppm in 1998–2003 and 366 ppm in 1972–1973) compared to a 47 ppm change in background air CO2, yet the ranges of the carbon and oxygen isotopic compositions remained essentially constant. Because the 1998–2003 data show a significant progression through time, analysis was done on data from 2002 to 2003 complete calendar years (CO2 mixing ratios increased 41 ppm between 1972 and 1973 and 2002–2003). Both 1972–1973 and 2002–2003 data sets display significant correlation between δ 13C and 1/[CO2] with local CO2 source end-member δ 13C values of −30.9 ± 0.5‰ for 1972–1973 and −29.9 ± 0.2‰ for 2002–2003 (1σ errors). Mass balance calculations explain that this apparently coincidental similarity reflects a change in the relative proportion of natural gas and petroleum products burned in the region combined with a change in the origin, and thus isotopic composition, of the petroleum burned. The δ 13C of the average CO2 inventory in Pasadena can be explained by local addition to background air of 38 ± 4 ppm CO2 in 1972–1973 and 29 ± 3 ppm in 2002–2003 from anthropogenic sources, in seeming contradiction to the known increase in CO2 emissions between these two time periods

Canonical General Relativity on a Null Surface with Coordinate and Gauge Fixing

We use the canonical formalism developed together with David Robinson to st= udy the Einstein equations on a null surface. Coordinate and gauge conditions = are introduced to fix the triad and the coordinates on the null surface. Toget= her with the previously found constraints, these form a sufficient number of second class constraints so that the phase space is reduced to one pair of canonically conjugate variables: \Ac_2\and\Sc^2. The formalism is related to both the Bondi-Sachs and the Newman-Penrose methods of studying the gravitational field at null infinity. Asymptotic solutions in the vicinity of null infinity which exclude logarithmic behavior require the connection to fall off like $1/r^3$ after the Minkowski limit. This, of course, gives the previous results of Bondi-Sachs and Newman-Penrose. Introducing terms which fall off more slowly leads to logarithmic behavior which leaves null infinity intact, allows for meaningful gravitational radiation, but the peeling theorem does not extend to $\Psi_1$ in the terminology of Newman-Penrose. The conclusions are in agreement with those of Chrusciel, MacCallum, and Singleton. This work was begun as a preliminary study of a reduced phase space for quantization of general relativity.Comment: magnification set; pagination improved; 20 pages, plain te

Geographic constraints on social network groups

Social groups are fundamental building blocks of human societies. While our social interactions have always been constrained by geography, it has been impossible, due to practical difficulties, to evaluate the nature of this restriction on social group structure. We construct a social network of individuals whose most frequent geographical locations are also known. We also classify the individuals into groups according to a community detection algorithm. We study the variation of geographical span for social groups of varying sizes, and explore the relationship between topological positions and geographic positions of their members. We find that small social groups are geographically very tight, but become much more clumped when the group size exceeds about 30 members. Also, we find no correlation between the topological positions and geographic positions of individuals within network communities. These results suggest that spreading processes face distinct structural and spatial constraints.Comment: 10 pages, 5 figure

New constraints for canonical general relativity

Ashtekar's canonical theory of classical complex Euclidean GR (no Lorentzian reality conditions) is found to be invariant under the full algebra of infinitesimal 4-diffeomorphisms, but non-invariant under some finite proper 4-diffeos when the densitized dreibein, \tilE^a_i, is degenerate. The breakdown of 4-diffeo invariance appears to be due to the inability of the Ashtekar Hamiltonian to generate births and deaths of \tilE flux loops (leaving open the possibility that a new `causality condition' forbidding the birth of flux loops might justify the non-invariance of the theory). A fully 4-diffeo invariant canonical theory in Ashtekar's variables, derived from Plebanski's action, is found to have constraints that are stronger than Ashtekar's for rank\tilE < 2. The corresponding Hamiltonian generates births and deaths of \tilE flux loops. It is argued that this implies a finite amplitude for births and deaths of loops in the physical states of quantum GR in the loop representation, thus modifying this (partly defined) theory substantially. Some of the new constraints are second class, leading to difficulties in quantization in the connection representation. This problem might be overcome in a very nice way by transforming to the classical loop variables, or the `Faraday line' variables of Newman and Rovelli, and then solving the offending constraints. Note that, though motivated by quantum considerations, the present paper is classical in substance.Comment: Version to appear in Nuclear Physics B. Discussion of 4-diffeo invariance, Dirac brackets improved. Proof of theorem connecting self-dual 2-forms and orthonormal tetrads replaced. Latex 57 pages, 7 uuencoded postscript figures. Uses macro psfig.tex available from this archive (and appended to this posting for your convenience). After latexing use dvips - not - dvi2ps to get postscript file

Shift invariant preduals of &#8467;₁(&#8484;)

The Banach space &#8467;&lt;sub&gt;1&lt;/sub&gt;(&#8484;) admits many non-isomorphic preduals, for example, C(K) for any compact countable space K, along with many more exotic Banach spaces. In this paper, we impose an extra condition: the predual must make the bilateral shift on &#8467;&lt;sub&gt;1&lt;/sub&gt;(&#8484;) weak&lt;sup&gt;*&lt;/sup&gt;-continuous. This is equivalent to making the natural convolution multiplication on &#8467;&lt;sub&gt;1&lt;/sub&gt;(&#8484;) separately weak*-continuous and so turning &#8467;&lt;sub&gt;1&lt;/sub&gt;(&#8484;) into a dual Banach algebra. We call such preduals &lt;i&gt;shift-invariant&lt;/i&gt;. It is known that the only shift-invariant predual arising from the standard duality between C&lt;sub&gt;0&lt;/sub&gt;(K) (for countable locally compact K) and &#8467;&lt;sub&gt;1&lt;/sub&gt;(&#8484;) is c&lt;sub&gt;0&lt;/sub&gt;(&#8484;). We provide an explicit construction of an uncountable family of distinct preduals which do make the bilateral shift weak&lt;sup&gt;*&lt;/sup&gt;-continuous. Using Szlenk index arguments, we show that merely as Banach spaces, these are all isomorphic to c&lt;sub&gt;0&lt;/sub&gt;. We then build some theory to study such preduals, showing that they arise from certain semigroup compactifications of &#8484;. This allows us to produce a large number of other examples, including non-isometric preduals, and preduals which are not Banach space isomorphic to c&lt;sub&gt;0&lt;/sub&gt;

Effective and Asymptotic Critical Exponents of Weakly Diluted Quenched Ising Model: 3d Approach Versus ϵ1/2\epsilon^{1/2}-Expansion

We present a field-theoretical treatment of the critical behavior of three-dimensional weakly diluted quenched Ising model. To this end we analyse in a replica limit n=0 5-loop renormalization group functions of the $\phi^4$-theory with O(n)-symmetric and cubic interactions (H.Kleinert and V.Schulte-Frohlinde, Phys.Lett. B342, 284 (1995)). The minimal subtraction scheme allows to develop either the $\epsilon^{1/2}$-expansion series or to proceed in the 3d approach, performing expansions in terms of renormalized couplings. Doing so, we compare both perturbation approaches and discuss their convergence and possible Borel summability. To study the crossover effect we calculate the effective critical exponents providing a local measure for the degree of singularity of different physical quantities in the critical region. We report resummed numerical values for the effective and asymptotic critical exponents. Obtained within the 3d approach results agree pretty well with recent Monte Carlo simulations. $\epsilon^{1/2}$-expansion does not allow reliable estimates for d=3.Comment: 35 pages, Latex, 9 eps-figures included. The reference list is refreshed and typos are corrected in the 2nd versio

Experiences regarding nutrition and exercise among women during early postpartum: A qualitative grounded theory study

Background: Excess gestational weight gain has long- and short-term implications for women and children, and postpartum weight retention is associated with an increased risk of long-term obesity. Despite the existence of dietary and exercise guidelines, many women struggle to return to pre-pregnancy weight. Experiences of women in tackling postpartum weight loss are poorly understood. We undertook this study to explore experiences related to nutrition, exercise and weight in the postpartum in women in Ontario, Canada. Methods: This was a nested qualitative study within The Be Healthy in Pregnancy Study, a randomized controlled trial. Women randomized to the control group were invited to participate. Semi-structured focus groups were conducted at 4-6 months postpartum. Focus groups were audio recorded, transcribed verbatim, coded and analyzed thematically using a constructivist grounded theory approach. Results: Women experienced a complex relationship with their body image, due to unrealistic expectations related to their postpartum body. Participants identified barriers and enablers to healthy habits during pregnancy and postpartum. Gestational weight gain guidelines were regarded as unhelpful and unrealistic. A lack of guidance and information about weight management, healthy eating, and exercise in the postpartum period was highlighted. Conclusion: Strategies for weight management that target the unique characteristics of the postpartum period have been neglected in research and in patient counselling. Postpartum women may begin preparing for their next pregnancy and support during this period could improve their health for subsequent pregnancies

Evaluating behavioral responses of nesting lesser snow geese to unmanned aircraft surveys

Unmanned aircraft systems (UAS) are relatively new technologies gaining popularity among wildlife biologists. As with any new tool in wildlife science, operating protocols must be developed through rigorous protocol testing. Few studies have been conducted that quantify the impacts UAS may have on unhabituated individuals in the wild using standard aerial survey protocols. We evaluated impacts of unmanned surveys by measuring UAS-induced behavioral responses during the nesting phase of lesser snow geese (Anser caerulescens caerulescens) in Wapusk National Park, Manitoba, Canada. We conducted surveys with a fixed-wing Trimble UX5 and monitored behavioral changes via discreet surveillance cameras at 25 nests. Days with UAS surveys resulted in decreased resting and increased nest maintenance, low scanning, high scanning, head-cocking and off-nest behaviors when compared to days without UAS surveys. In the group of birds flown over, head-cocking for overhead vigilance was rarely seen prior to launch or after landing (mean estimates 0.03% and 0.02%, respectively) but increased to 0.56% of the time when the aircraft was flying overhead suggesting that birds were able to detect the aircraft during flight. Neither UAS survey altitude nor launch distance alone in this study was strong predictors of nesting behaviors, although our flight altitudes (≥75 m above ground level) were much higher than previously published behavioral studies. Synthesis and applications: The diversity of UAS models makes generalizations on behavioral impacts difficult, and we caution that researchers should design UAS studies with knowledge that some minimal disturbance is likely to occur. We recommend flight designs take potential behavioral impacts into account by increasing survey altitude where data quality requirements permit. Such flight designs should consider a priori knowledge of focal species’ behavioral characteristics. Research is needed to determine whether any such disturbance is a result of visual or auditory stimuli