Finite time and asymptotic behaviour of the maximal excursion of a random walk

We evaluate the limit distribution of the maximal excursion of a random walk in any dimension for homogeneous environments and for self-similar supports under the assumption of spherical symmetry. This distribution is obtained in closed form and is an approximation of the exact distribution comparable to that obtained by real space renormalization methods. Then we focus on the early time behaviour of this quantity. The instantaneous diffusion exponent $\nu_n$ exhibits a systematic overshooting of the long time exponent. Exact results are obtained in one dimension up to third order in $n^{-1/2}$. In two dimensions, on a regular lattice and on the Sierpi\'nski gasket we find numerically that the analytic scaling $\nu_n \simeq \nu+A n^{-\nu}$ holds.Comment: 9 pages, 4 figures, accepted J. Phys.

Einstein-Weyl structures corresponding to diagonal K\"ahler Bianchi IX metrics

We analyse in a systematic way the four dimensionnal Einstein-Weyl spaces equipped with a diagonal K\"ahler Bianchi IX metric. In particular, we show that the subclass of Einstein-Weyl structures with a constant conformal scalar curvature is the one with a conformally scalar flat - but not necessarily scalar flat - metric ; we exhibit its 3-parameter distance and Weyl one-form. This extends previous analysis of Pedersen, Swann and Madsen , limited to the scalar flat, antiself-dual case. We also check that, in agreement with a theorem of Derdzinski, the most general conformally Einstein metric in the family of biaxial K\"ahler Bianchi IX metrics is an extremal metric of Calabi, conformal to Carter's metric, thanks to Chave and Valent's results.Comment: 15 pages, Latex file, minor modifications, to be published in Class. Quant. Gra

Hyperlactatemia and Antiretroviral Therapy: The Swiss HIV Cohort Study

The prevalence, clinical presentation, and risk factors for hyperlactatemia among patients receiving antiretroviral therapy was determined during a 1-month period for patients in the Swiss HIV Cohort Study. Overall, 73 (8.3%) of 880 patients presented an increase in serum lactate of >1.1 times the upper normal limit (UNL). For 9 patients (1%), lactate elevation was moderate or severe (>2.2 times the UNL). Patients who presented with hyperlactatemia were more likely to be receiving stavudine with or without didanosine (odds ratio, 2.7; 95% confidence interval, 1.5-4.8), as compared with patients who received zidovudine-based regimens. The risk increased with increasing time receiving stavudine with or without didanosine. The association between hyperlactatemia and stavudine with or without didanosine was not biased by these medications being more recently available and, therefore, being given preferentially to patients who had prolonged use of nucleoside analog reverse-transcriptase inhibitors. Hyperlactatemia was associated with lipoatrophy, hyperlipidemia, and hyperglycemia. Age, sex, or stage of infection with human immunodeficiency virus were not predictive of hyperlactatemia. Determination of lactate levels may prove useful in the screening for mitochondrial toxicit

Localization of thermal packets and metastable states in Sinai model

We consider the Sinai model describing a particle diffusing in a 1D random force field. As shown by Golosov, this model exhibits a strong localization phenomenon for the thermal packet: the disorder average of the thermal distribution of the relative distance y=x-m(t), with respect to the (disorder-dependent) most probable position m(t), converges in the limit of infinite time towards a distribution P(y). In this paper, we revisit this question of the localization of the thermal packet. We first generalize the result of Golosov by computing explicitly the joint asymptotic distribution of relative position y=x(t)-m(t) and relative energy u=U(x(t))-U(m(t)) for the thermal packet. Next, we compute in the infinite-time limit the localization parameters Y_k, representing the disorder-averaged probabilities that k particles of the thermal packet are at the same place, and the correlation function C(l) representing the disorder-averaged probability that two particles of the thermal packet are at a distance l from each other. We moreover prove that our results for Y_k and C(l) exactly coincide with the thermodynamic limit of the analog quantities computed for independent particles at equilibrium in a finite sample of length L. Finally, we discuss the properties of the finite-time metastable states that are responsible for the localization phenomenon and compare with the general theory of metastable states in glassy systems, in particular as a test of the Edwards conjecture.Comment: 17 page

Options for sampling and stratification for national forest inventories to implement REDD+ under the UNFCCC

<p>Abstract</p> <p>Background</p> <p>Developing countries that are willing to participate in the recently adopted (16^thSession of the Conference of Parties (COP) in Cancun) mitigation mechanism of Reducing emissions from Deforestation and Forest Degradation - and the role of conservation, sustainable management of forests and enhancement of forest carbon stocks (REDD+) - will have to establish a national forest monitoring system in order to assess anthropogenic forest-related greenhouse gas emissions by sources and removals by sinks. Such a system should support the Measurement, Reporting and Verification (MRV) requirement of the United Nations Framework Convention on Climate Change (UNFCCC) as the REDD+ mechanism is results-based. A national forest inventory (NFI) is one potential key component of such an MRV system. Following the Decision adopted during the 15^thSession of the COP in Copenhagen, the most recent Intergovernmental Panel on Climate Change (IPCC) Guidance and Guidelines should be used as a basis for estimating anthropogenic forest-related greenhouse gas emissions by sources and removals by sinks and changes in forest carbon stocks and area.</p> <p>Results</p> <p>First, we present the key indispensable elements of the IPCC Guidance and Guidelines that have been developed to fulfil the UNFCCC reporting requirements. This is done in order to set the framework to develop the MRV requirement in which a NFI for REDD+ implementation could be developed. Second, within this framework, we develop and propose a novel scheme for the stratification of forest land for REDD+. Finally, we present some non-exhaustive optional elements within this framework that a country could consider to successfully operationalise and implement its REDD+ NFI.</p> <p>Conclusion</p> <p>Evidently, both the methodological guidance and political decisions on REDD+ under the UNFCCC will continue to evolve. Even so, and considering that there exists decades of experience in setting up traditional NFIs, developing a NFI that a country may use to directly support REDD+ activities under the UNFCCC represents the development of a new challenge in this field. It is therefore important that both the scientific community and national implementing agencies acquaint themselves with both the context and content of this challenge so that REDD+ mitigation actions may be implemented successfully and with environmental integrity. This paper provides important contributions to the subject through our proposal of the stratification of forest land for REDD+.</p

Concerted changes in tropical forest structure and dynamics: evidence from 50 South American long-term plots

Several widespread changes in the ecology of old-growth tropical forests have recently been documented for the late twentieth century, in particular an increase in stem turnover (pan-tropical), and an increase in above-ground biomass (neotropical). Whether these changes are synchronous and whether changes in growth are also occurring is not known. We analysed stand-level changes within 50 long-term. monitoring plots from across South America spanning 1971-2002. We show that: (i) basal area (BA: sum of the cross-sectional areas of all trees in a plot) increased significantly over time (by 0.10 +/- 0.04 m(2) ha(-1) yr(-1), mean +/- 95% CI); as did both (ii) stand-level BA growth rates (sum of the increments of BA of surviving trees and BA of new trees that recruited into a plot); and (iii) stand-level BA mortality rates (sum of the cross-sectional areas of all trees that died in a plot). Similar patterns were observed on a per-stem basis: (i) stem density (number of stems per hectare; 1 hectare is 10(4) m(2)) increased significantly over time (0.94 +/- 0.63 stems ha(-1) yr(-1)); as did both (ii) stem recruitment rates; and (iii) stem mortality rates. In relative terms, the pools of BA and stem density increased by 0.38 +/- 0.15% and 0.18 +/- 0.12% yr(-1), respectively. The fluxes into and out of these pools-stand-level BA growth, stand-level BA mortality, stem recruitment and stem mortality rates-increased, in relative terms, by an order of magnitude more. The gain terms (BA growth, stem recruitment) consistently exceeded the loss terms (BA loss, stem mortality) throughout the period, suggesting that whatever process is driving these changes was already acting before the plot network was established. Large long-term increases in stand-level BA growth and simultaneous increases in stand BA and stem density imply a continent-wide increase in resource availability which is increasing net primary productivity and altering forest dynamics. Continent-wide changes in incoming solar radiation, and increases in atmospheric concentrations of CO2 and air temperatures may have increased resource supply over recent decades, thus causing accelerated growth and increased dynamism across the world's largest tract of tropical forest

Pliocene Te Aute limestones, New Zealand: Expanding concepts for cool-water shelf carbonates

Acceptance of a spectrum of warm- through cold-water shallow-marine carbonate facies has become of fundamental importance for correctly interpreting the origin and significance of all ancient platform limestones. Among other attributes, properties that have become a hallmark for characterising many Cenozoic non-tropical occurrences include: (1) the presence of common bryozoan and epifaunal bivalve skeletons; (2) a calcite-dominated mineralogy; (3) relatively thin deposits exhibiting low rates of sediment accumulation; (4) an overall destructive early diagenetic regime; and (5) that major porosity destruction and lithification occur mainly in response to chemical compaction of calcitic skeletons during moderate to deep burial. The Pliocene Te Aute limestones are non-tropical skeletal carbonates formed at paleolatitudes near 40-42°S under the influence of commonly strong tidal flows along the margins of an actively deforming and differentially uplifting forearc basin seaway, immediately inboard of the convergent Pacific-Australian plate boundary off eastern North Island, New Zealand. This dynamic depositional and tectonic setting strongly influenced both the style and subsequent diagenetic evolution of the limestones. Some of the Te Aute limestones exhibit the above kinds of "normal" non-tropical characteristics, but others do not. For example, many are barnacle and/or bivalve dominated, and several include attributes that at least superficially resemble properties of certain tropical carbonates. In this regard, a number of the limestones are infaunal bivalve rich and dominated by an aragonite over a calcite primary mineralogy, with consequently relatively high diagenetic potential. Individual limestone units are also often rather thick (e.g., up to 50-300 m), with accumulation rates from 0.2 to 0.5 m/ka, and locally as high as 1 m/ka. Moreover, there can be a remarkable array of diagenetic features in the limestones, involving grain alteration and/or cementation to widely varying extents within any, or some combination of, the marine phreatic, burial, and meteoric diagenetic environments, including locally widespread development of meteoric cement sourced from aragonite dissolution. The message is that non-tropical shelf carbonates include a more diverse array of geological settings, of skeletal and mineralogical facies, and of diagenetic features than current sedimentary models mainly advocate. While several attributes positively distinguish tropical from non-tropical limestones, continued detailed documentation of the wide spectrum of shallow-marine carbonate deposits formed outside tropical regions remains an important challenge in carbonate sedimentology