The number of recombination events in a sample history: conflict graph and lower bounds

We consider the following problem: Given a set of binary sequences, determine lower bounds on the minimum number of recombinations required to explain the history of the sample, under the infinite-sites model of mutation. The problem has implications for finding recombination hotspots and for the Ancestral Recombination Graph reconstruction problem. Hudson and Kaplan gave a lower bound based on the four-gamete test. In practice, their bound R/sub m/ often greatly underestimates the minimum number of recombinations. The problem was recently revisited by Myers and Griffiths, who introduced two new lower bounds R/sub h/ and R/sub s/ which are provably better, and also yield good bounds in practice. However, the worst-case complexities of their procedures for computing R/sub h/ and R/sub s/ are exponential and super-exponential, respectively. In this paper, we show that the number of nontrivial connected components, R/sub c/, in the conflict graph for a given set of sequences, computable in time 0(nm/sup 2/), is also a lower bound on the minimum number of recombination events. We show that in many cases, R/sub c/ is a better bound than R/sub h/. The conflict graph was used by Gusfield et al. to obtain a polynomial time algorithm for the galled tree problem, which is a special case of the Ancestral Recombination Graph (ARG) reconstruction problem. Our results also offer some insight into the structural properties of this graph and are of interest for the general Ancestral Recombination Graph reconstruction problem.     

A graph-theoretic method for the basic reproduction number in continuous time epidemiological models

In epidemiological models of infectious diseases the basic reproduction number is used as a threshold parameter to determine the threshold between disease extinction and outbreak. A graph-theoretic form of Gaussian elimination using digraph reduction is derived and an algorithm given for calculating the basic reproduction number in continuous time epidemiological models. Examples illustrate how this method can be applied to compartmental models of infectious diseases modelled by a system of ordinary differential equations. We also show with these examples how lower bounds for can be obtained from the digraphs in the reduction process.     

Sensitivity of vertebral compressive strength to endplate loading distribution

The sensitivity of vertebral body strength to the distribution of axial forces along the endplate has not been comprehensively evaluated. Using quantitative computed tomography-based finite element models of 13 vertebral bodies, an optimization analysis was performed to determine the endplate force distributions that minimized (lower bound) and maximized (upper bound) vertebral strength for a given set of externally applied axial compressive loads. Vertebral strength was also evaluated for three generic boundary conditions: uniform displacement, uniform force, and a nonuniform force distribution in which the interior of the endplate was loaded with a force that was 1.5 times greater than the periphery. Our results showed that the relative difference between the upper and lower bounds on vertebral strength was 14.2 +/- 7.0% (mean +/- SD). While there was a weak trend for the magnitude of the strength bounds to be inversely proportional to bone mineral density (R2 = 0.32, p = 0.02), both upper and lower bound vertebral strength measures were well predicted by the strength response under uniform displacement loading conditions (R2 = 0.91 and R2 = 0.99, respectively). All three generic boundary conditions resulted in vertebral strength values that were statistically indistinguishable from the loading condition that resulted in an upper bound on strength. The results of this study indicate that the uncertainty in strength arising from the unknown condition of the disc is dependent on the condition of the bone (whether it is osteoporotic or normal). Although bone mineral density is not a good predictor of strength sensitivity, vertebral strength under generic boundary conditions, i.e., uniform displacement or force, was strongly correlated with the relative magnitude of the strength bounds. Thus, explicit disc modeling may not be necessary.     

Theory versus data: how to calculate R0?

To predict the potential severity of outbreaks of infectious diseases such as SARS, HIV, TB and smallpox, a summary parameter, the basic reproduction number R(0), is generally calculated from a population-level model. R(0) specifies the average number of secondary infections caused by one infected individual during his/her entire infectious period at the start of an outbreak. R(0) is used to assess the severity of the outbreak, as well as the strength of the medical and/or behavioral interventions necessary for control. Conventionally, it is assumed that if R(0)>1 the outbreak generates an epidemic, and if R(0)<1 the outbreak becomes extinct. Here, we use computational and analytical methods to calculate the average number of secondary infections and to show that it does not necessarily represent an epidemic threshold parameter (as it has been generally assumed). Previously we have constructed a new type of individual-level model (ILM) and linked it with a population-level model. Our ILM generates the same temporal incidence and prevalence patterns as the population-level model; we use our ILM to directly calculate the average number of secondary infections (i.e., R(0)). Surprisingly, we find that this value of R(0) calculated from the ILM is very different from the epidemic threshold calculated from the population-level model. This occurs because many different individual-level processes can generate the same incidence and prevalence patterns. We show that obtaining R(0) from empirical contact tracing data collected by epidemiologists and using this R(0) as a threshold parameter for a population-level model could produce extremely misleading estimates of the infectiousness of the pathogen, the severity of an outbreak, and the strength of the medical and/or behavioral interventions necessary for control.     

On analytical approaches to epidemics on networks

One way to describe the spread of an infection on a network is by approximating the network by a random graph. However, the usual way of constructing a random graph does not give any control over the number of triangles in the graph, while these triangles will naturally arise in many networks (e.g. in social networks). In this paper, random graphs with a given degree distribution and a given expected number of triangles are constructed. By using these random graphs we analyze the spread of two types of infection on a network: infections with a fixed infectious period and infections for which an infective individual will infect all of its susceptible neighbors or none. These two types of infection can be used to give upper and lower bounds for R(0), the probability of extinction and other measures of dynamics of infections with more general infectious periods.     

Prevalence of Enhanced Granular Expression of Thrombospondin Type-1 Domain-Containing 7A in the Glomeruli of Japanese Patients with Idiopathic Membranous Nephropathy

Membranous nephropathy (MN) is a leading cause of nephrotic syndrome in adults. Autoantibodies against M-type phospholipase A2 receptor (PLA2R) and thrombospondin type-1 domain-containing 7A (THSD7A), which mainly belong to the IgG4 subclass, were reported as associated antibodies for the development of MN. Although PLA2R is a major target antigen for idiopathic MN, the prevalence of MN patients seropositive for PLA2R in Japan is lower than that in other countries. In this study, we conducted immunohistochemical analysis of the presence of THSD7A and PLA2R in renal specimens of MN patients to estimate the prevalence of THSD7A/PLA2R-related idiopathic MN in Japan. Enhanced granular expression of THSD7A and PLA2R was detected in 9.1% and 52.7%, respectively, of the patients with idiopathic MN. Although none of patients with secondary MN displayed enhanced granular expression of THSD7A, 5.4% of them had enhanced granular expression of PLA2R. In conclusion, the prevalence of enhanced granular expression of THSD7A in the glomeruli of Japanese patients with idiopathic MN was higher than the prevalence of MN patients seropositive for THSD7A in USA and Europe.     

Ultrasound-detected thyroid nodule prevalence and radiation dose from fallout

Settlements near the Semipalatinsk Test Site (SNTS) in northeastern Kazakhstan were exposed to radioactive fallout during 1949-1962. Thyroid disease prevalence among 2994 residents of eight villages was ascertained by ultrasound screening. Malignancy was determined by cytopathology. Individual thyroid doses from external and internal radiation sources were reconstructed from fallout deposition patterns, residential histories and diet, including childhood milk consumption. Point estimates of individual external and internal dose averaged 0.04 Gy (range 0-0.65) and 0.31 Gy (0-9.6), respectively, with a Pearson correlation coefficient of 0.46. Ultrasound-detected thyroid nodule prevalence was 18% and 39% among males and females, respectively. It was significantly and independently associated with both external and internal dose, the main study finding. The estimated relative biological effectiveness of internal compared to external radiation dose was 0.33, with 95% confidence bounds of 0.09-3.11. Prevalence of papillary cancer was 0.9% and was not significantly associated with radiation dose. In terms of excess relative risk per unit dose, our dose-response findings for nodule prevalence are comparable to those from populations exposed to medical X rays and to acute radiation from the Hiroshima and Nagasaki atomic bombings.     

Virulence of parasites in hosts under environmental stress: experiments with anoxia and starvation

Most environments periodically impose severe stress that may cause high mortality and alter population structure, for example, by removing sick and old individuals. We examined how anoxic conditions and starvation of the host affect virulence of two closely related trematode parasites, Rhipidocotyle campanula and R. fennica . These parasites differ by prevalence of infection and by exploitation rate of individual hosts (freshwater clam, Anodonta piscinalis ). Infection by R. campanula is rare (<5% prevalence of infection) and destroys on average 90% of the gonad tissue of the individual host. Infection by R. fennica is more common (20–60% prevalence of infection) and leads to on average 30% gonad destruction. In the end, both infections lead to host infertility. We predicted that R. campanula induces higher host mortality than R. fennica under host stress. In two laboratory experiments, we exposed naturally-infected and uninfected clams to anoxia and to starvation. Anoxia occasionally takes place during winter in eutrophic lakes, while some degree of starvation should occur seasonally. We found that mortality rate of clams was much higher under anoxia than under starvation, and that infection increased mortality rate under both types of host stress. As predicted, R. campanula induced higher host mortality than R. fennica . Host survival was population-specific, suggesting that clams of different origins carried different amount of energy reserves. Severe environmental perturbation may remove R. campanula infected individuals from the host population, but recolonization from the fish host is likely to prevent extinction of the parasite suprapopulation. The observed high host mortality induced by R. campanula may be one ecological explanation for the consistently lower prevalence of infection of R. campanula when compared to R. fennica .     

A quantitative model of cellular elasticity based on tensegrity

A tensegrity structure composed of six struts interconnected with 24 elastic cables is used as a quantitative model of the steady-state elastic response of cells, with the struts and cables representing microtubules and actin filaments, respectively. The model is stretched uniaxially and the Young's modulus (E0) is obtained from the initial slope of the stress versus strain curve of an equivalent continuum. It is found that E0 is directly proportional to the pre-existing tension in the cables (or compression in the struts) and inversely proportional to the cable (or strut) length square. This relationship is used to predict the upper and lower bounds of E0 of cells, assuming that the cable tension equals the yield force of actin (approximately 400 pN) for the upper bound, and that the strut compression equals the critical buckling force of microtubules for the lower bound. The cable (or strut) length is determined from the assumption that model dimensions match the diameter of probes used in standard mechanical tests on cells. Predicted values are compared to reported data for the Young's modulus of various cells. If the probe diameter is greater than or equal to 3 microns, these data are closer to the lower bound than to the upper bound. This, in turn, suggests that microtubules of the CSK carry initial compression that exceeds their critical buckling force (order of 10(0)-10(1) pN), but is much smaller than the yield force of actin. If the probe diameter is less than or equal to 2 microns, experimental data fall outside the region defined by the upper and lower bounds.     

Modelling transmission of vector-borne pathogens shows complex dynamics when vector feeding sites are limited

The relationship between species richness and the prevalence of vector-borne disease has been widely studied with a range of outcomes. Increasing the number of host species for a pathogen may decrease infection prevalence (dilution effect), increase it (amplification), or have no effect. We derive a general model, and a specific implementation, which show that when the number of vector feeding sites on each host is limiting, the effects on pathogen dynamics of host population size are more complex than previously thought. The model examines vector-borne disease in the presence of different host species that are either competent or incompetent (i.e. that cannot transmit the pathogen to vectors) as reservoirs for the pathogen. With a single host species present, the basic reproduction ratio R(0) is a non-monotonic function of the population size of host individuals (H), i.e. a value [Formula: see text] exists that maximises R(0). Surprisingly, if [Formula: see text] a reduction in host population size may actually increase R(0). Extending this model to a two-host species system, incompetent individuals from the second host species can alter the value of [Formula: see text] which may reverse the effect on pathogen prevalence of host population reduction. We argue that when vector-feeding sites on hosts are limiting, the net effect of increasing host diversity might not be correctly predicted using simple frequency-dependent epidemiological models.     

HYPER: A hierarchical algorithm for automatic determination of protein dihedral-angle constraints and stereospecific CβH2 resonance assignments from NMR data

A new computer program, HYPER, has been developed for automated analysis of protein dihedral angle values and CH₂ stereospecific assignments from NMR data. HYPER uses a hierarchical grid-search algorithm to determine allowed values of , , and ₁ dihedral angles and CH₂ stereospecific assignments based on a set of NMR-derived distance and/or scalar-coupling constraints. Dihedral-angle constraints are valuable for restricting conformational space and improving convergence in three-dimensional structure calculations. HYPER computes the set of , , and ₁dihedral angles and CH₂ stereospecific assignments that are consistent with up to nine intraresidue and sequential distance bounds, two pairs of relative distance bounds, thirteen homo- and heteronuclear scalar coupling bounds, and two pairs of relative scalar coupling constant bounds. The program is designed to be very flexible, and provides for simple user modification of Karplus equations and standard polypeptide geometries, allowing it to accommodate recent and future improved calibrations of Karplus curves. The C code has been optimized to execute rapidly (0.3–1.5 CPU-sec residue^–1 using a 5° grid) on Silicon Graphics R8000, R10000 and Intel Pentium CPUs, making it useful for interactive evaluation of inconsistent experimental constraints. The HYPER program has been tested for internal consistency and reliability using both simulated and real protein NMR data sets.     

Evolution of pathogens towards low R0 in heterogeneous populations

Maximization of the basic reproduction ratio or R(0) is widely believed to drive the emergence of novel pathogens. The presence of exploitable heterogeneities in a population, such as high variance in the number of potentially infectious contacts, increases R(0) and thus pathogens that can exploit heterogeneities in the contact structure have an advantage over those that do not. However, exploitation of heterogeneities results in a more rapid depletion of the potentially susceptible neighbourhood for an infected host. Here a simple model of pathogen evolution in a heterogeneous environment is developed and placed in the context of HIV transmission. In this model, it is shown that pathogens may evolve towards lower R(0), even if this results in pathogen extinction. For sufficiently high transmissibility, two locally stable strategies exist for an evolving pathogen, one that exploits heterogeneities and results in higher R(0), and one that does not, and results in lower R(0). While the low R(0) strategy is never evolutionarily stable, invading strains with higher R(0) will also converge to the low R(0) strategy if not sufficiently different from the resident strain. Heterogenous transmission is increasingly recognized as fundamental to epidemiological dynamics and the evolution of pathogens; here, it is shown that the ability to exploit heterogeneity is a strategy that can itself evolve.     

Population size estimation with interval censored counts and external information: Prevalence of multiple sclerosis in Rome

We discuss Bayesian log-linear models for incomplete contingency tables with both missing and interval censored cells, with the aim of obtaining reliable population size estimates. We also discuss use of external information on the censoring probability, which may substantially reduce uncertainty. We show in simulation that information on lower bounds and external information can each improve the mean squared error of population size estimates, even when the external information is not completely accurate. We conclude with an original example on estimation of prevalence of multiple sclerosis in the metropolitan area of Rome, where five out of six lists have interval censored counts. External information comes from mortality rates of multiple sclerosis patients.     

Computational experience with a parallel algorithm for tetrangle inequality bound smoothing

Determining molecular structure from interatomic distances is an important and challenging problem. Given a molecule with n atoms, lower and upper bounds on interatomic distances can usually be obtained only for a small subset of the atom pairs, using NMR. Given the bounds so obtained on the distances between some of the atom pairs, it is often useful to compute tighter bounds on all the pairwise distances. This process is referred to as bound smoothing. The initial lower and upper bounds for the pairwise distances not measured are usually assumed to be 0 and ∞. One method for bound smoothing is to use the limits imposed by the triangle inequality. The distance bounds so obtained can often be tightened further by applying the tetrangle inequality—the limits imposed on the six pairwise distances among a set of four atoms (instead of three for the triangle inequalities). The tetrangle inequality is expressed by the Cayley—Menger determinants. For every quadruple of atoms, each pass of the tetrangle inequality bound smoothing procedure finds upper and lower limits on each of the six distances in the quadruple. Applying the tetrangle inequalities to each of the ( ₄ ⁿ ) quadruples requires O(n ⁴) time. Here, we propose a parallel algorithm for bound smoothing employing the tetrangle inequality. Each pass of our algorithm requires O(n ³ log n) time on a CREW PRAM (Concurrent Read Exclusive Write Parallel Random Access Machine) with processors. An implementation of this parallel algorithm on the Intel Paragon XP/S and its performance are also discussed.     

Life‐history costs associated with resistance to lambda‐cyhalothrin in the predatory ladybird beetle Eriopis connexa

• 1 The present study assessed the fitness of a lambda‐cyhalothrin‐resistant population of Eriopis connexa (Germar) with respect to development, reproduction, survival under prey scarcity and prey consumption.
• 2 Nontreated resistant females (R0) and females recovered after the topical application of 0.05, 0.10 and 0.25 mg active ingredient/mL of lambda‐cyhalothrin (R0.05, R0.10 and R0.25) produced, on average, 50% less eggs than susceptible females (S0), irrespective of the applied dose. All of the other traits evaluated remained similar. With respect to developmental characteristics, the larval viability and weight of adult male R0.25 progeny were statistically lower compared with the R0 and S0 progenies. Prey scarcity between days 3 and 13 of adulthood did not affect R0 and R0.25 survival, although egg production was significantly lower for R0 females, followed by R0.25 females, compared with S0 females.
• 3 The mean consumption of cotton aphids Aphis gossypii Glover over 5 consecutive days was significantly higher for S0, followed by R0 and R0.25, up to day 3 of observation. However, after day 4, prey consumption was similar among the three populations.
• 4 The results obtained in the present study show that resistant females have a lower reproductive output than susceptible females and that this is not related to the knockdown effect; however, the costs of recovering from knockdown interfere with the survival of offspring and also slightly with prey consumption. Thus, we conclude that the lambda‐cyhalothrin‐resistant E. connexa population exhibits an egg production disadvantage relative to the susceptible population and that this is increased when the population is subjected to prey scarcity.

     

Three stage AIDS incubation period: a worst case scenario using addict-needle interaction assumptions

In this paper we develop and analyse a model for the spread of HIV/AIDS amongst a population of injecting drug users. We start off with a brief literature survey and review; this is followed by the derivation of a model which allows addicts to progress through three distinct stages of variable infectivity prior to the onset of full blown AIDS and where the class of infectious needles is split into three according to the different levels of infectivity in addicts. Given the structure of this model we are required to make assumptions regarding the interaction of addicts and needles of different infectivity levels. We deliberately choose these assumptions so that our model serves as an upper bound for the prevalence of HIV under the assumption of a three stage AIDS incubation period. We then perform an equilibrium and stability analysis on this model. We find that there is a critical threshold parameter R(0) which determines the behaviour of the model. If R(0)< or =1, then irrespective of the initial conditions of the system HIV will die out in all addicts and all needles. If R(0)>1, then there is a unique endemic equilibrium which is locally stable if, as is realistic, the time scale on which addicts inject is much shorter than that of the other epidemiological and demographic processes. Simulations indicate that if R(0)>1, then provided that disease is initially present in at least one addict or needle it will tend to the endemic equilibrium. In addition we derive conditions which guarantee this. We also find that under calibration the long term prevalence of disease in our variable infectivity model is always greater than in an equivalent constant infectivity model. These results are confirmed and explored further by simulation. We conclude with a short discussion.     

Core recruitment effects in SIS models with constant total populations

We consider a set of SIS models for a heterosexually transmitted disease in which there is recruitment between core and non-core subpopulations as a function of prevalence of the disease. Behavior diverges from the traditional R0 threshold behavior and yields an extra pair of endemic equilibria in one case and a limit cycle in the other. Total at-risk population is constant.     

Improved protocol for isolation of Campylobacter spp. from retail broiler meat and use of pulsed field gel electrophoresis for the typing of isolates

To improve the detection of Campylobacter spp. in retail broiler meat, a reference method (R subsamples) based on the enrichment of 25 g of meat in Bolton broth at 42 °C under microaerobiosis was compared with an alternative method (A subsamples) consisting in the rinsing of meat samples for 30 s in buffered peptone water with antimicrobials with incubation at 42 °C under aerobiosis. One piece of meat (breasts, tenderloins and thighs) was rinse in experiment 1 (A1) and two pieces in experiment 2 (A2). Campylobacter spp. were isolated on agar plates and identified by PCR. Retail samples in Alabama had less prevalence (P ≤ 0.05) than samples in the state of Washington. The percentage of positive was higher (P ≤ 0.05) in A than in R subsamples and rinsing two pieces of meat yielded the highest percentage of positive subsamples. R subsamples showed variations in the prevalence by product. However, A subsamples had similar prevalence of positives among products compare to the result from reference method. More Campylobacter coli isolates were collected in A2 subsamples. Pulse field gel electrophoresis (PFGE) was used as subtyping method to study the genome similarity among the isolates from all methods. A larger diversity of isolates were detected by PFGE in A2 subsamples. Denaturing gradient gel electrophoresis analysis suggested that the initial bacterial populations of the meat samples impact the final bacterial profile after enrichment. Rinsing broiler meats was less time consuming, required less sample preparation and was more sensitive than the reference method for the isolation of naturally occurring Campylobacter spp. This new method could help with epidemiological and intervention studies to control Campylobacter spp.     

The calculation of probabilities in rejecting bioequivalence

Methods are given for deriving the lower and upper bounds of the probabilities for rejecting bioequivalence. Except when two formulations are nearly equal, the lower and upper bounds become very close and thus give an exact probability. The methods can be used in two- or higher-way crossover or parallel groups designs. One can also determine the sample size from the equations. The results are compared with the probabilities obtained by simulation.     

Exact methods for the robotic cell problem

This paper investigates an exact method for the Robotic Cell Problem. We present a branch-and-bound algorithm which is the first exact procedure specifically designed with regard to this complex flow shop scheduling variant. Also, we propose a new mathematical programming model as well as new lower bounds. Furthermore, we describe an effective genetic algorithm that includes, as a mutation operator, a local search procedure. We report the results of a computational study that provides evidence that medium-sized instances, with up to 176 operations, can be optimally solved. Also, we found that the new proposed lower bounds outperform lower bounds from the literature. Finally, we show, that the genetic algorithm delivers good solutions while requiring short CPU times.