A Numerical Analyst Looks at the "Cutoff Phenomenon" in Card Shuffling and Other Markov Chains

Diaconis and others have shown that certain Markov chains exhibit a "cutoff phenomenon" in which, after an initial period of seemingly little progress, convergence to the steady state occurs suddenly. Since Markov chains are just powers of matrices, how can such effects be explained in the language of applied linear algebra? We attempt to do this, focusing on two examples: random walk on a hypercube, which is essentially the same as the problem of Ehrenfest urns, and the celebrated case of riffle shuffling of a deck of cards. As is typical with transient phenomena in matrix processes, the reason for the cutoff is not readily apparent from an examination of eigenvalues or eigenvectors, but it is reflected strongly in pseudosprectra - provided they are measured in the 1-norm, not the 2-norm. We illustrate and explain the cutoff phenomenon with Matlab computations based in part on a new explicit formula for the entries of the $n \times n$ "riffle shuffle matrix", and note that while the normwise cutoff may occur at one point, such as $\frac{3}{2} \log_{2} n$ for the riffle shuffle, weak convergence may occur at an equally precise earlier point such as $\log_{2} n$

Strategies for the control of Rhipicephalus microplus ticks in a world of conventional acaricide and macrocyclic lactone resistance

Infestations with the cattle tick, Rhipicephalus microplus, constitute the most important ectoparasite problem for cattle production in tropical and subtropical regions worldwide, resulting in major economic losses. The control of R. microplus is mostly based on the use of conventional acaricides and macrocyclic lactones. However, the intensive use of such compounds has resulted in tick populations that exhibit resistance to all major acaricide chemical classes. Consequently, there is a need for the development of alternative approaches, possibly including the use of animal husbandry practices, synergized pesticides, rotation of acaricides, pesticide mixture formulations, manual removal of ticks, selection for host resistance, nutritional management, release of sterile male hybrids, environmental management, plant species that are unfavourable to ticks, pasture management, plant extracts, essential oils and vaccination. Integrated tick management consists of the systematic combination of at least two control technologies aiming to reduce selection pressure in favour of acaricide-resistant individuals, while maintaining adequate levels of animal production. The purpose of this paper is to present a current review on conventional acaricide and macrocyclic lactone resistance for better understanding and control of resistant ticks with particular emphasis on R. microplus on cattle

Identification of a novel ß-adrenergic octopamine receptor-like gene (ßAOR-like) and increased ATP-binding cassette B10 (ABCB10) expression in a Rhipicephalus microplus cell line derived from acaricide-resistant ticks

Background: The cattle tick Rhipicephalus (Boophilus) microplus is an economically important parasite of livestock. Effective control of ticks using acaricides is threatened by the emergence of resistance to many existing compounds. Several continuous R. microplus cell lines have been established and provide an under-utilised resource for studies into acaricide targets and potential genetic mutations associated with resistance. As a first step to genetic studies using these resources, this study aimed to determine the presence or absence of two genes and their transcripts that have been linked with acaricide function in cattle ticks: β-adrenergic octopamine receptor (βAOR, associated with amitraz resistance) and ATP-binding cassette B10 (ABCB10, associated with macrocyclic lactone resistance) in six R. microplus cell lines, five other Rhipicephalus spp. cell lines and three cell lines representing other tick genera (Amblyomma variegatum, Ixodes ricinus and Hyalomma anatolicum). Methods: End-point polymerase chain reaction (PCR) was used for detection of the βAOR gene and transcripts in DNA and RNA extracted from the tick cell lines, followed by capillary sequencing of amplicons. Quantitative real-time PCR (qPCR) was performed to determine the levels of expression of ABCB10. Results: βAOR gene expression was detected in all Rhipicephalus spp. cell lines. We observed a second amplicon of approximately 220 bp for the βAOR gene in the R. microplus cell line BME/CTVM6, derived from acaricide-resistant ticks. Sequencing of this transcript variant identified a 36 bp insertion in the βAOR gene, leading to a 12-amino acid insertion (LLKTLALVTIIS) in the first transmembrane domain of the protein. In addition, nine synonymous SNPs were also discovered in R. appendiculatus, R. evertsi and R. sanguineus cell lines. Some of these SNPs appear to be unique to each species, providing potential tools for differentiating the tick species. The BME/CTVM6 cell line had significantly higher ABCB10 (P = 0.002) expression than the other R. micropluscell lines. Conclusions: The present study has identified a new βAOR gene and demonstrated a higher ABCB10 expression level in the BME/CTVM6 cell line, indicating that tick cell lines provide a useful experimental tool for acaricide resistance studies and further elucidation of tick genetics

Memory and superposition in a spin glass

Non-equilibrium dynamics in a Ag(Mn) spin glass are investigated by measurements of the temperature dependence of the remanent magnetisation. Using specific cooling protocols before recording the thermo- or isothermal remanent magnetisations on re-heating, it is found that the measured curves effectively disclose non-equilibrium spin glass characteristics such as ageing and memory phenomena as well as an extended validity of the superposition principle for the relaxation. The usefulness of this "simple" dc-method is discussed, as well as its applicability to other disordered magnetic systems.Comment: REVTeX style; 8 pages, 4 figure

Molecular biology of amitraz resistance in cattle ticks of the genus Rhipicephalus

Amitraz is an important product for the control of cattle ticks around the world. In comparison with other products for the control of ticks, it is quite affordable and it has a rapid knock-down effect. It binds with and activates adrenergic neuro-receptors of animals and it inhibits the action of monoamine oxidases (MAO). Resistance to amitraz has been documented in Rhipicephalus microplus, R. decoloratus and R. appendiculatus. Four mechanisms of resistance have been proposed, each of which is supported by evidence but none of which has been definitively confirmed as the cause of resistance in the field. The proposed mechanisms include genetic target site insensitivity in two G protein-coupled receptors, the beta-adrenergic octopamine receptor (BAOR) and the octopamine/tyramine receptor (OCT/Tyr), increased expression or activity of monoamine oxidases and increased expression or activity of the ATP binding cassette transporter

NMR-based metabonomics of bovine blood: an investigation into the effects of long term storage on plasma samples

Freezers in research institutions often contain a plethora of samples left over from studies performed years or even decades ago. Along with samples stored in biobanks, these could prove to be treasure troves for metabonomic research. Although the influence of sample handling and short to medium term storage on conventionally determined blood parameters has been reported, little is known about the effects of long term storage (years to decades) on plasma samples. The aim of this study was to investigate the influence of long term storage on the metabolite profile and to assess the value of archived samples for metabonomic studies. Heparinised plasma samples of 22 Holstein Friesian heifers that had been stored at -20°C for between 2 and 15 years were analysed using proton NMR spectroscopy and statistical analysis techniques. Lactate accounted for principal component one and explained 79.6% of variance between all spectra, but was not correlated with storage time. The highest correlation with storage time (R2 = 0.474) was found for betaine, with other metabolites (acetoacetate, histidines, glycerol, lipids and glucose) also showing moderate correlation (R2 values between 0.217 and 0.437). Our results indicate that samples stored for extended periods of time can potentially be used in metabolomics studies, if precautions are taken during data analysis

Exact ground states of a staggered supersymmetric model for lattice fermions

We study a supersymmetric model for strongly interacting lattice fermions in the presence of a staggering parameter. The staggering is introduced as a tunable parameter in the manifestly supersymmetric Hamiltonian. We obtain analytic expressions for the ground states in the limit of small and large staggering for the model on the class of doubly decorated lattices. On this type of lattice there are two ground states, each with a different density. In one limit we find these ground states to be a simple Wigner crystal and a valence bond solid (VBS) state. In the other limit we find two types of quantum liquids. As a special case, we investigate the quantum liquid state on the one dimensional chain in detail. It is characterized by a massless kink that separates two types of order.Comment: 21 pages, 6 figures, v2: largely rewritten version with more emphasis on physical interpretatio

Contact and Nozzle Wear from 100 Interruptions for a Puffer-Type Air Load Break Switch

One type test requirement for medium voltage load break switches is to interrupt 100 consecutive "mainly active loads". A puffer-type switch with axial-blown arc has been tested according to the 630 A/24 kV ratings. The nozzle and contact wear were measured regularly to investigate design requirements and the impact from nozzle wear on gas flow. The contact wear is only moderate, while the nozzle wear causes a decrease in pressure build-up, which in turn may influence the interruption performance