The transform likelihood ratio method for rare event simulation with heavy tails

We present a novel method, called the transform likelihood ratio (TLR) method, for estimation of rare event probabilities with heavy-tailed distributions. Via a simple transformation ( change of variables) technique the TLR method reduces the original rare event probability estimation with heavy tail distributions to an equivalent one with light tail distributions. Once this transformation has been established we estimate the rare event probability via importance sampling, using the classical exponential change of measure or the standard likelihood ratio change of measure. In the latter case the importance sampling distribution is chosen from the same parametric family as the transformed distribution. We estimate the optimal parameter vector of the importance sampling distribution using the cross-entropy method. We prove the polynomial complexity of the TLR method for certain heavy-tailed models and demonstrate numerically its high efficiency for various heavy-tailed models previously thought to be intractable. We also show that the TLR method can be viewed as a universal tool in the sense that not only it provides a unified view for heavy-tailed simulation but also can be efficiently used in simulation with light-tailed distributions. We present extensive simulation results which support the efficiency of the TLR method.

Heavy tails, importance sampling and cross-entropy

We consider the problem of estimating P(Yi + (...) + Y-n > x) by importance sampling when the Yi are i.i.d. and heavy-tailed. The idea is to exploit the cross-entropy method as a toot for choosing good parameters in the importance sampling distribution; in doing so, we use the asymptotic description that given P(Y-1 + (...) + Y-n > x), n - 1 of the Yi have distribution F and one the conditional distribution of Y given Y > x. We show in some specific parametric examples (Pareto and Weibull) how this leads to precise answers which, as demonstrated numerically, are close to being variance minimal within the parametric class under consideration. Related problems for M/G/l and GI/G/l queues are also discussed.

Improved algorithms for rare event simulation with heavy tails

The estimation of P(S-n > u) by simulation, where S, is the sum of independent. identically distributed random varibles Y-1,..., Y-n, is of importance in many applications. We propose two simulation estimators based upon the identity P(S-n > u) = nP(S, > u, M-n = Y-n), where M-n = max(Y-1,..., Y-n). One estimator uses importance sampling (for Y-n only), and the other uses conditional Monte Carlo conditioning upon Y1,..., Yn-1. Properties of the relative error of the estimators are derived and a numerical study given in terms of the M/G/1 queue in which n is replaced by an independent geometric random variable N. The conclusion is that the new estimators compare extremely favorably with previous ones. In particular, the conditional Monte Carlo estimator is the first heavy-tailed example of an estimator with bounded relative error. Further improvements are obtained in the random-N case, by incorporating control variates and stratification techniques into the new estimation procedures.

Inhibition of settlement and metamorphosis of the ascidian Herdmania curvata by non-geniculate coralline algae

The surfaces of non-geniculate coralline algae (NCA) are known to induce the settlement and metamorphosis of disparate marine taxa. In this study we investigate the responsiveness of larvae of Herdmania curvata (Ascidiacea: Stolidobranchia) to three species of NCA (Neo-goniolithon brassica-florida, Hydrolithon onkodes, and Lithothamnium prolifer) that cohabit the slope and crest of Heron Reef, Great Barrier Reef. H. curvata larvae were first exposed to these NCA at or within 2 h of hatching, which is 1 to 2 h prior to attaining competence, and then cultured continuously with the NCA for 12 to 14 h. Rates of settlement and metamorphosis of H, curvata cultured in laboratory chambers in the presence of the different NCA were significantly lower than spontaneous rates in seawater. The limited settlement in treatments containing NCA were confined entirely to the chamber periphery, and settlement never occurred on the surface of the NCA. The inhibitory effect was dose-dependent and was stronger in H. brassica-florida and H. onkodes than in L. prolifer. Larvae that did not settle in treatments with NCA had rounded anterior trunks and, in extreme cases, kinked tails with rounded and dissociated tail muscle cells. In some individuals, we observed the anterior chemosensory papillae being sloughed off the larval body. Morphological analysis of trunk ectodermal and mesenchymal nuclei of larvae cultured in the presence of the NCA revealed that general necrotic cell death was occurring. Importantly, H. curvata larvae that were exposed to NCA could not subsequently be induced to metamorphose in KCl-elevated seawater, whereas larvae not exposed to NCA metamorphosed at high rates in KCl-elevated seawater.

Robust Mixture Modelling Using the t Distribution

Normal mixture models are being increasingly used to model the distributions of a wide variety of random phenomena and to cluster sets of continuous multivariate data. However, for a set of data containing a group or groups of observations with longer than normal tails or atypical observations, the use of normal components may unduly affect the fit of the mixture model. In this paper, we consider a more robust approach by modelling the data by a mixture of t distributions. The use of the ECM algorithm to fit this t mixture model is described and examples of its use are given in the context of clustering multivariate data in the presence of atypical observations in the form of background noise.

Binary games with many players

We examine a problem with n players each facing the same binary choice. One choice is superior to the other. The simple assumption of competition - that an individual's payoff falls with a rise in the number of players making the same choice, guarantees the existence of a unique symmetric equilibrium (involving mixed strategies). As n increases, there are two opposing effects. First, events in the middle of the distribution - where a player finds itself having made the same choice as many others - become more likely, but the payoffs in these events fall. In opposition, events in the tails of the distribution - where a player finds itself having made the same choice as few others - become less likely, but the payoffs in these events remain high. We provide a sufficient condition (strong competition) under which an increase in the number of players leads to a reduction in the equilibrium probability that the superior choice is made.

Induction of metamorphosis with potassium ions requires development of competence and an anterior signalling centre in the ascidian Herdmania momus

Increased Kt concentration in seawater induces metamorphosis in the ascidian Herdmania momus. Larvae cultivated at 24 degrees C exhibit highest rates of metamorphosis when treated with 40 mM KCl-elevated seawater at 21 degrees C. At 24 degrees C, H. momus larvae develop competence to respond to KCl-seawater and initiate metamorphosis approximately 3 h after hatching. Larval trunks and tails separated from the anterior papillae region, but maintained in a common tunic at a distance of greater than 60 mu m, do not undergo metamorphosis when treated with KCl-seawater; normal muscle degradation does not occur in separated tails while ampullae develop from papillae-containing anterior fragments. Normal programmed degradation of myofibrils occurs when posterior fragments are fused to papillae-containing anterior fragments. These data indicate that H. momus settlement and metamorphosis only occurs when larvae have attained competence, and suggest that an anterior signalling centre is stimulated to release a factor that induces metamorphosis.

HI observations of interacting galaxy pair NGC 4038/9

We present the results of new radio interferometer Hi line observations for the merging galaxy pair NGC 4038/9 ('The Antennae'), obtained using the Australia Telescope Compact Array. The results improve substantially with respect to those of van der Hulst and show in detail the two merging galactic discs and the two tidal tails produced by their interaction. The small edge-on spiral dwarf galaxy ESO 572-G045 is also seen near the tip of the southern tail, but distinct from it. It shows no signs of tidal interaction. The northern tidal tail of the Antennae shows no HI connection to the discs and has an extension towards the west. The southern tidal tail is continuous, with a prominent HI concentration at its tip, roughly at the location of the tidal dwarf galaxy observed optically by Mirabel, Dottori & Lutz. Clear velocity structure is seen along the tidal tails and in the galactic discs. Radio continuum images at 20 and 13 cm are also presented, showing the discs in detail.

Energetic costs of tail loss in a montane scincid lizard

Most species of lizards will shed their tails at the point of contact when grasped by a predator. We investigated the energetic consequences of tail loss by measuring lipids in a scincid lizard that stores energy in its tail for reproduction. Most of the lipids were concentrated in the proximal portion of the tail. Thus, partial tail loss may not severely affect energy stores if the distal portion of the tail is shed in predatory encounters. We also found that the width of the tail was a reliable non-invasive index of energy reserves in this species. (C) 2003 Elsevier Science Inc. All rights reserved.

ATCA HI observations of the peculiar galaxy IC 2554

ATCA H I and radio continuum observations of the peculiar southern galaxy IC 2554 and its surroundings reveal typical signatures of an interacting galaxy group. We detected a large H I cloud between IC 2554 and the elliptical galaxy NGC 3136B. The gas dynamics in IC 2554 itself, which is sometimes described as a colliding pair, are surprisingly regular, whereas NGC 3136B was not detected. The H I cloud, which emerges from IC 2554 as a large arc-shaped plume, has a size of similar to30 kpc, larger than that of IC 2554. The total H I mass of the IC 2554 system is similar to2 x 10(9) M., one-third of which resides in the H I cloud. It is possible that tidal interaction between IC 2554 and NGC 3136B caused this spectacular H I cloud, but the possibility of IC 2554 being a merger remnant is also discussed. We also detected H I gas in the nearby galaxies ESO 092-G009 and RKK 1959 and an associated H I cloud, ATCA J1006-6710. Together they have an H I mass of similar to4.6 x 10(8) M-.. Another new H I source, ATCA J1007-6659, with an H I mass of only similar to2.2 x 10(7) M. was detected roughly between IC 2554 and ESO 092-G009 and corresponds to a face-on low surface brightness dwarf galaxy. Star formation is evident only in the galaxy IC 2554 with a rate of similar to4 M. yr(-1).

Carboxy terminus of glucose transporter 3 contains an apical membrane targeting domain

We previously demonstrated that distinct facilitative glucose transporter isoforms display differential sorting in polarized epithelial cells. In Madin-Darby canine kidney (MDCK) cells, glucose transporter 1 and 2 (GLUT1 and GLUT2) are localized to the basolateral cell surface whereas GLUTs 3 and 5 are targeted to the apical membrane. To explore the molecular mechanisms underlying this asymmetric distribution, we analyzed the targeting of chimeric glucose transporter proteins in MDCK cells. Replacement of the carboxy-terminal cytosolic tail of GLUT1, GLUT2, or GLUT4 with that from GLUT3 resulted in apical targeting. Conversely, a GLUT3 chimera containing the cytosolic carboxy terminus of GLUT2 was sorted to the basolateral membrane. These findings are not attributable to the presence of a basolateral signal in the tails of GLUTs 1, 2, and 4 because the basolateral targeting of GLUT1 was retained in a GLUT1 chimera containing the carboxy terminus of GLUT5. In addition, we were unable to demonstrate the presence of an autonomous basolateral sorting signal in the GLUT1 tail using the low-density lipoprotein receptor as a reporter. By examining the targeting of a series of more defined GLUT1/3 chimeras, we found evidence of an apical targeting signal involving residues 473 - 484 (DRSGKDGVMEMN) in the carboxy tail. We conclude that the targeting of GLUT3 to the apical cell surface in MDCK cells is regulated by a unique cytosolic sorting motif.

Predator-specific changes in the morphology and swimming performance of larval Rana lessonae

1. We investigated the morphological responses of larval Rana lessonae to the presence of two predators with substantially different prey-detection and capture techniques; larval dragonflies (Aeshna cyanea) and the Pumpkinseed Sunfish (Lepomis gibossus). 2. We also examined the functional implications of any predator-induced morphological variation on their swimming ability by assessing performance during the initial stages of a startle response. 3. We found the morphological responses of larval R. lessonae were dependent on the specific predator present. Tadpoles raised in the presence of dragonfly larvae preying upon conspecific tadpoles developed total tail heights 5.4% deeper and tail muscles 4.7% shallower than tadpoles raised in a non-predator environment, while tadpoles raised with sunfish possessed tails 2% shallower and tail muscles 2.5% higher than non-predator-exposed tadpoles. 4. Predator-induced morphological variation also significantly influenced swimming performance. Tadpoles raised with sunfish possessed swimming speeds 9.5 and 14.6% higher than non- and dragonfly predator groups, respectively. 5. Thus, the expression of these alternative predator-morphs leads to a functional trade-off in performance between the different environments.

Inherent size constraints on prokaryote gene networks due to "accelerating" growth

Networks exhibiting accelerating growth have total link numbers growing faster than linearly with network size and either reach a limit or exhibit graduated transitions from nonstationary-to-stationary statistics and from random to scale-free to regular statistics as the network size grows. However, if for any reason the network cannot tolerate such gross structural changes then accelerating networks are constrained to have sizes below some critical value. This is of interest as the regulatory gene networks of single-celled prokaryotes are characterized by an accelerating quadratic growth and are size constrained to be less than about 10,000 genes encoded in DNA sequence of less than about 10 megabases. This paper presents a probabilistic accelerating network model for prokaryotic gene regulation which closely matches observed statistics by employing two classes of network nodes (regulatory and non-regulatory) and directed links whose inbound heads are exponentially distributed over all nodes and whose outbound tails are preferentially attached to regulatory nodes and described by a scale-free distribution. This model explains the observed quadratic growth in regulator number with gene number and predicts an upper prokaryote size limit closely approximating the observed value. (c) 2005 Elsevier GmbH. All rights reserved.

Receptor binding studies disclose a novel class of high-affinity inhibitors of the Escherichia coli FimH adhesin

Mannose-binding type 1 pili are important virulence factors for the establishment of Escherichia coli urinary tract infections (UTIs). These infections are initiated by adhesion of uropathogenic E. coli to uroplakin receptors in the uroepithelium via the FimH adhesin located at the tips of type 1 pili. Blocking of bacterial adhesion is able to prevent infection. Here, we provide for the first time binding data of the molecular events underlying type 1 fimbrial adherence, by crystallographic analyses of the FimH receptor binding domains from a uropathogenic and a K-12 strain, and affinity measurements with mannose, common mono- and disaccharides, and a series of alkyl and aryl mannosides. Our results illustrate that the lectin domain of the FimH adhesin is a stable and functional entity and that an exogenous butyl alpha- D-mannoside, bound in the crystal structures, exhibits a significantly better affinity for FimH (K-d = 0.15 muM) than mannose (K-d = 2.3 muM). Exploration of the binding affinities of alpha-D-mannosides with longer alkyl tails revealed affinities up to 5 nM. Aryl mannosides and fructose can also bind with high affinities to the FimH lectin domain, with a 100-fold improvement and 15-fold reduction in affinity, respectively, compared with mannose. Taken together, these relative FimH affinities correlate exceptionally well with the relative concentrations of the same glycans needed for the inhibition of adherence of type 1 piliated E. coli. We foresee that our findings will spark new ideas and initiatives for the development of UTI vaccines and anti-adhesive drugs to prevent anticipated and recurrent UTIs.

Using extreme value theory to measure value-at-risk for daily electricity spot prices

The recent deregulation in electricity markets worldwide has heightened the importance of risk management in energy markets. Assessing Value-at-Risk (VaR) in electricity markets is arguably more difficult than in traditional financial markets because the distinctive features of the former result in a highly unusual distribution of returns-electricity returns are highly volatile, display seasonalities in both their mean and volatility, exhibit leverage effects and clustering in volatility, and feature extreme levels of skewness and kurtosis. With electricity applications in mind, this paper proposes a model that accommodates autoregression and weekly seasonals in both the conditional mean and conditional volatility of returns, as well as leverage effects via an EGARCH specification. In addition, extreme value theory (EVT) is adopted to explicitly model the tails of the return distribution. Compared to a number of other parametric models and simple historical simulation based approaches, the proposed EVT-based model performs well in forecasting out-of-sample VaR. In addition, statistical tests show that the proposed model provides appropriate interval coverage in both unconditional and, more importantly, conditional contexts. Overall, the results are encouraging in suggesting that the proposed EVT-based model is a useful technique in forecasting VaR in electricity markets. (c) 2005 International Institute of Forecasters. Published by Elsevier B.V. All rights reserved.