A q-deformed nonlinear map

A scheme of q-deformation of nonlinear maps is introduced. As a specific example, a q-deformation procedure related to the Tsallis q-exponential function is applied to the logistic map. Compared to the canonical logistic map, the resulting family of q-logistic maps is shown to have a wider spectrum of interesting behaviours, including the co-existence of attractors -- a phenomenon rare in one dimensional maps.Comment: 17 pages, 19 figure

Simple theory of extremely overdoped HTS

We demonstrate the existence of a simple physical picture of superconductivity for extremely overdoped CuO2 planes. It possesses all characteristic features of HTS, such as a high superconducting transition temperature, the $d_{x^2 - y^2}$ symmetry of order parameter, and the coexistence of a single electron Fermi surface and a pseudogap in the normal state. Values of pseudogap are calculated for different doping levels. An orbital paramagnetism of preformed pairs is predicted.Comment: 7 pages, 1 figur

Boundary crossing Random Walks, clinical trials and multinomial sequential estimation

A sufficient condition for the uniqueness of multinomial sequential unbiased estimators is provided generalizing a classical result for binomial samples. Unbiased estimators are applied to infer the parameters of multidimensional or multinomial Random Walks which are observed until they reach a boundary. An application to clinical trials is presented

The statistical laws of popularity: Universal properties of the box office dynamics of motion pictures

Are there general principles governing the process by which certain products or ideas become popular relative to other (often qualitatively similar) competitors? To investigate this question in detail, we have focused on the popularity of movies as measured by their box-office income. We observe that the log-normal distribution describes well the tail (corresponding to the most successful movies) of the empirical distributions for the total income, the income on the opening week, as well as, the weekly income per theater. This observation suggests that popularity may be the outcome of a linear multiplicative stochastic process. In addition, the distributions of the total income and the opening income show a bimodal form, with the majority of movies either performing very well or very poorly in theaters. We also observe that the gross income per theater for a movie at any point during its lifetime is, on average, inversely proportional to the period that has elapsed after its release. We argue that (i) the log-normal nature of the tail, (ii) the bimodal form of the overall gross income distribution, and (iii) the decay of gross income per theater with time as a power law, constitute the fundamental set of {\em stylized facts} (i.e., empirical "laws") that can be used to explain other observations about movie popularity. We show that, in conjunction with an assumption of a fixed lower cut-off for income per theater below which a movie is withdrawn from a cinema, these laws can be used to derive a Weibull distribution for the survival probability of movies which agrees with empirical data. The connection to extreme-value distributions suggests that popularity can be viewed as a process where a product becomes popular by avoiding failure (i.e., being pulled out from circulation) for many successive time periods. We suggest that these results may apply to popularity in general.Comment: 14 pages, 11 figure

Nonlinear Pseudo-Supersymmetry in the Framework of N-fold Supersymmetry

We recall the importance of recognizing the different mathematical nature of various concepts relating to PT-symmetric quantum theories. After clarifying the relation between supersymmetry and pseudo-supersymmetry, we prove generically that nonlinear pseudo-supersymmetry, recently proposed by Sinha and Roy, is just a special case of N-fold supersymmetry. In particular, we show that all the models constructed by these authors have type A 2-fold supersymmetry. Furthermore, we prove that an arbitrary one-body quantum Hamiltonian which admits two (local) solutions in closed form belongs to type A 2-fold supersymmetry, irrespective of whether or not it is Hermitian, PT-symmetric, pseudo-Hermitian, and so on.Comment: 10 pages, no figures; typos correcte

Dynamic behavior of a magnetic bearing supported jet engine rotor with auxiliary bearings

This paper presents a study of the dynamic behavior of a rotor system supported by auxiliary bearings. The steady-state behavior of a simulation model based upon a production jet engine is explored over a wide range of operating conditions for varying rotor imbalance, support stiffness, and damping. Interesting dynamical phenomena, such as chaos, subharmonic responses, and double-valued responses, are presented and discussed

Total OH reactivity measurements using a new fast Gas Chromatographic Photo-Ionization Detector (GC-PID)

The primary and most important oxidant in the atmosphere is the hydroxyl radical (OH). Currently OH sinks, particularly gas phase reactions, are poorly constrained. One way to characterize the overall sink of OH is to measure directly the ambient loss rate of OH, the total OH reactivity. To date, direct measurements of total OH reactivity have been either performed using a Laser-Induced Fluorescence (LIF) system ("pump-and-probe" or "flow reactor") or the Comparative Reactivity Method (CRM) with a Proton-Transfer-Reaction Mass Spectrometer (PTR-MS). Both techniques require large, complex and expensive detection systems. This study presents a feasibility assessment for CRM total OH reactivity measurements using a new detector, a Gas Chromatographic Photoionization Detector (GC-PID). Such a system is smaller, more portable, less power consuming and less expensive than other total OH reactivity measurement techniques. <br><br> Total OH reactivity is measured by the CRM using a competitive reaction between a reagent (here pyrrole) with OH alone and in the presence of atmospheric reactive molecules. The new CRM method for total OH reactivity has been tested with parallel measurements of the GC-PID and the previously validated PTR-MS as detector for the reagent pyrrole during laboratory experiments, plant chamber and boreal field studies. Excellent agreement of both detectors was found when the GC-PID was operated under optimum conditions. Time resolution (60–70 s), sensitivity (LOD 3–6 s<sup>−1</sup>) and overall uncertainty (25% in optimum conditions) for total OH reactivity were similar to PTR-MS based total OH reactivity measurements. One drawback of the GC-PID system was the steady loss of sensitivity and accuracy during intensive measurements lasting several weeks, and a possible toluene interference. Generally, the GC-PID system has been shown to produce closely comparable results to the PTR-MS and thus in suitable environments (e.g. forests) it presents a viably economical alternative for groups interested in total OH reactivity observations

Sediment Sorting and Rounding in a Basaltic Glacio-Fluvio-Aeolian Environment: hrisjkull Glacier, Iceland

Sediments and sedimentary rocks preserve a rich history of environment and climate. Identifying these signals requires an understanding of the physical and chemical processes that have affected sedimentary deposits [1]. Such processes include sorting and rounding during transport and chemical alteration through weathering and diagenesis. Although these processes have long been studied in quartz-dominated sedimentary systems [2], a lack of studies of basaltic sedimentary systems limits our interpretations of the environment and climate where mafic source rocks dominate, such as on Mars [3,4]. As part of the SAND-E: Semi-Autonomous Navigation for Detrital Environments project [5], which uses robotic operations to examine physical and chemical changes to sediments in basaltic glacio-fluvialaeolian environments, this research studies changes in sorting and rounding of fluvial-aeolian sediments along a glacier-proximal-to-glacier-distal transect in the outwash-plain of the risjkull glacier in SW Iceland (Fig. 1

An update on the human and animal enteric pathogen Clostridium perfringens

Clostridium perfringens, a rapid-growing pathogen known to secrete an arsenal of >20 virulent toxins, has been associated with intestinal diseases in both animals and humans throughout the past century. Recent advances in genomic analysis and experimental systems make it timely to re-visit this clinically and veterinary important pathogen. This Review will summarise our understanding of the genomics and virulence-linked factors, including antimicrobial potentials and secreted toxins of this gut pathogen, and then its up-to-date clinical epidemiology and biological role in the pathogenesis of several important human and animal-associated intestinal diseases, including pre-term necrotising enterocolitis. Finally, we highlight some of the important unresolved questions in relation to C. perfringens-mediated infections, and implications for future research directions