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.

Successive nonparametric estimation of conditional distributions

Spatial characterization of non-Gaussian attributes in earth sciences and engineering commonly requires the estimation of their conditional distribution. The indicator and probability kriging approaches of current nonparametric geostatistics provide approximations for estimating conditional distributions. They do not, however, provide results similar to those in the cumbersome implementation of simultaneous cokriging of indicators. This paper presents a new formulation termed successive cokriging of indicators that avoids the classic simultaneous solution and related computational problems, while obtaining equivalent results to the impractical simultaneous solution of cokriging of indicators. A successive minimization of the estimation variance of probability estimates is performed, as additional data are successively included into the estimation process. In addition, the approach leads to an efficient nonparametric simulation algorithm for non-Gaussian random functions based on residual probabilities.

Patched 1 conditional null allele in mice

The patched gene (Ptc) is a member of the hedgehog signaling pathway which plays a central role in the development of many invertebrate and vertebrate tissues. In addition, Ptc and a number of other pathway members are mutated in some common human cancers. Patched is the receptor for the hedgehog ligand and in the mouse ablation of the Ptc gene leads to developmental defects and an embryonic lethal phenotype. Here we describe a conditional Ptc allele in mice which will have utility for the temporospatial ablation of Ptc function. genesis 36:158-161, 2003. (C) 2003 Wiley-Liss, Inc.

Pseudo memory effects, majorization and entropy in quantum random walks

A quantum random walk on the integers exhibits pseudo memory effects, in that its probability distribution after N steps is determined by reshuffling the first N distributions that arise in a classical random walk with the same initial distribution. In a classical walk, entropy increase can be regarded as a consequence of the majorization ordering of successive distributions. The Lorenz curves of successive distributions for a symmetric quantum walk reveal no majorization ordering in general. Nevertheless, entropy can increase, and computer experiments show that it does so on average. Varying the stages at which the quantum coin system is traced out leads to new quantum walks, including a symmetric walk for which majorization ordering is valid but the spreading rate exceeds that of the usual symmetric quantum walk.

Conditional inactivation of the Men1 gene leads to pancreatic and pituitary tumorigenesis but does not affect normal development of these tissues

Mutations of the MEN1 gene, encoding the tumor suppressor menin, predispose individuals to the cancer syndrome multiple endocrine neoplasia type 1, characterized by the development of tumors of the endocrine pancreas and anterior pituitary and parathyroid glands. We have targeted the murine Men1 gene by using Cre recombinase-loxP technology to develop both total and tissue-specific knockouts of the gene. Conditional homozygous inactivation of the Men1 gene in the pituitary gland and endocrine pancreas bypasses the embryonic lethality associated with a constitutional Men1(-/-) genotype and leads to beta-cell hyperplasia in less than 4 months and insulinomas and prolactinomas starting at 9 months. The pituitary gland and pancreas develop normally in the conditional absence of menin, but loss of this transcriptional cofactor is sufficient to cause beta-cell hyperplasia in some islets; however, such loss is not sufficient to initiate pituitary gland tumorigenesis, suggesting that additional genetic events are necessary for the latter.

Teleonomic entropy: measuring the phase-space of end-directed systems

We introduce a novel way of measuring the entropy of a set of values undergoing changes. Such a measure becomes useful when analyzing the temporal development of an algorithm designed to numerically update a collection of values such as artificial neural network weights undergoing adjustments during learning. We measure the entropy as a function of the phase-space of the values, i.e. their magnitude and velocity of change, using a method based on the abstract measure of entropy introduced by the philosopher Rudolf Carnap. By constructing a time-dynamic two-dimensional Voronoi diagram using Voronoi cell generators with coordinates of value- and value-velocity (change of magnitude), the entropy becomes a function of the cell areas. We term this measure teleonomic entropy since it can be used to describe changes in any end-directed (teleonomic) system. The usefulness of the method is illustrated when comparing the different approaches of two search algorithms, a learning artificial neural network and a population of discovering agents. (C) 2004 Elsevier Inc. All rights reserved.

Conditional production of superpositions of coherent states with inefficient photon detection

It is shown that a linear superposition of two macroscopically distinguishable optical coherent states can be generated using a single photon source and simple all-optical operations. Weak squeezing on a single photon, beam mixing with an auxiliary coherent state, and photon detecting with imperfect threshold detectors are enough to generate a coherent state superposition in a free propagating optical field with a large coherent amplitude (alpha>2) and high fidelity (F>0.99). In contrast to all previous schemes to generate such a state, our scheme does not need photon number resolving measurements nor Kerr-type nonlinear interactions. Furthermore, it is robust to detection inefficiency and exhibits some resilience to photon production inefficiency.

Future long-horizon performance measurement conditional on past survival

This paper examines the measurement of long-horizon abnormal performance when stock selection is conditional on an extended period of past survival. Filtering on survival results in a sample driven towards more-established, frequently traded stocks and this has implications for the choice of benchmark used in performance measurement (especially in the presence of the well-documented size effect). A simulation study is conducted to document the properties of commonly employed performance measures conditional on past survival. The results suggest that the popular index benchmarks used in long-horizon event studies are severely biased and yield test statistics that are badly misspecified. In contrast, a matched-stock benchmark based on size and industry performs consistently well. Also, an eligible-stock index designed to mitigate the influence of the size effect proves effective.

A tutorial on the cross-entropy method

The cross-entropy (CE) method is a new generic approach to combinatorial and multi-extremal optimization and rare event simulation. The purpose of this tutorial is to give a gentle introduction to the CE method. We present the CE methodology, the basic algorithm and its modifications, and discuss applications in combinatorial optimization and machine learning. combinatorial optimization

The cross-entropy method for network reliability estimation

Consider a network of unreliable links, modelling for example a communication network. Estimating the reliability of the network-expressed as the probability that certain nodes in the network are connected-is a computationally difficult task. In this paper we study how the Cross-Entropy method can be used to obtain more efficient network reliability estimation procedures. Three techniques of estimation are considered: Crude Monte Carlo and the more sophisticated Permutation Monte Carlo and Merge Process. We show that the Cross-Entropy method yields a speed-up over all three techniques.

Application of the cross-entropy method to the buffer allocation problem in a simulation-based environment

The buffer allocation problem (BAP) is a well-known difficult problem in the design of production lines. We present a stochastic algorithm for solving the BAP, based on the cross-entropy method, a new paradigm for stochastic optimization. The algorithm involves the following iterative steps: (a) the generation of buffer allocations according to a certain random mechanism, followed by (b) the modification of this mechanism on the basis of cross-entropy minimization. Through various numerical experiments we demonstrate the efficiency of the proposed algorithm and show that the method can quickly generate (near-)optimal buffer allocations for fairly large production lines.

Conditional performance evaluation and the relevance of money flows for Australian international equity funds

This paper assesses the importance of fund flows in the performance evaluation of Australian international equity funds. Two concepts of fund flows are considered in the context of a conditional asset pricing model. The first measure is net fund flow relative to fund size and the second is net fund flow relative to sector flows. We find that incorporating a fund flow measure relative to the sector flow results in a reduction of measured perverse market timing. The results indicate that, at the individual fund level, cash flows are relevant in assessing management outcomes.

Matching conditional moments in PDF modelling of nonpremixed combustion

The rate of generation of fluctuations with respect to the scalar values conditioned on the mixture fraction, which significantly affects turbulent nonpremixed combustion processes, is examined. Simulation of the rate in a major mixing model is investigated and the derived equations can assist in selecting the model parameters so that the level of conditional fluctuations is better reproduced by the models. A more general formulation of the multiple mapping conditioning (MMC) model that distinguishes the reference and conditioning variables is suggested. This formulation can be viewed as a methodology of enforcing certain desired conditional properties onto conventional mixing models. Examples of constructing consistent MMC models with dissipation and velocity conditioning as well as of combining MMC with large eddy simulations (LES) are also provided. (c) 2005 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

Conditional risk, return and contagion in the banking sector in Asia

This paper investigates risk and return in the banking sector in three Asian markets of Taiwan, China and Hong Kong. The study focuses on the risk-return relation in a conditional factor GARCH-M framework that controls for time-series effects. The factor approach is adopted to incorporate intra-industry contagion and an analysis of spillovers between large banks and small banks. Finally, the study provides evidence on these relations before and after the Asian financial crisis of 1997. The results are generally consistent across the markets and with expectations.