A stochastic fixed point equation for weighted minima and maxima

Given any finite or countable collection of real numbers $T_j,j\in J$, we find all solutions $F$ to the stochastic fixed point equation $$W\stackrel{\mathrm {d}}{=}\inf_{j\in J}T_jW_j,$$ where $W$ and the $W_j,j\in J$, are independent real-valued random variables with distribution $F$ and $\stackrel{\mathrm {d}}{=}$ means equality in distribution. The bulk of the necessary analysis is spent on the case when $|J|\geq 2$ and all $T_j$ are (strictly) positive. Nontrivial solutions are then concentrated on either the positive or negative half line. In the most interesting (and difficult) situation $T$ has a characteristic exponent $\alpha$ given by $\sum_{j\in J}T_j^{\alpha}=1$ and the set of solutions depends on the closed multiplicative subgroup of $\mathbb {R}^{>}=(0,\infty)$ generated by the $T_j$ which is either $\{1\}$, $\mathbb {R}^{>}$ itself or r^{\mathbb {Z}}=\{r^n\dvt n\in \mathbb {Z}\} for some $r>1$. The first case being trivial, the nontrivial fixed points in the second case are either Weibull distributions or their reciprocal reflections to the negative half line (when represented by random variables), while in the third case further periodic solutions arise. Our analysis builds on the observation that the logarithmic survival function of any fixed point is harmonic with respect to $\varLambda =\sum_{j\geq 1}\delta_{T_j}$, i.e. $\varGamma =\varGamma \star \varLambda$, where $\star$ means multiplicative convolution. This will enable us to apply the powerful Choquet--Deny theorem.Comment: Published in at http://dx.doi.org/10.1214/07-AIHP104 the Annales de l'Institut Henri Poincar\'e - Probabilit\'es et Statistiques (http://www.imstat.org/aihp/) by the Institute of Mathematical Statistics (http://www.imstat.org

Efficacy of a competitive exclusion culture against extended-spectrum β-lactamase-producing Escherichia coli strains in broilers using a seeder bird model

Background Administration of a competitive exclusion culture (CE culture) has the potential to induce protective effects in very young chicks against caecal colonisation by EEC (= extended-spectrum β-lactamases [ESBL] and AmpC-type [AmpC] beta-lactamases producing Escherichia coli). The study aimed to verify the protective capacity of a CE culture in broilers using the seeder bird model against EEC exposure of the chicks. Results Introduction of infected seeder birds resulted in rapid and strong caecal colonisation of four different EEC challenge strains tested in untreated contact broilers. Compared to controls the broilers pre-treated with the CE culture showed a considerable decrease in caecal load of different EEC challenge strains from about 3.0–3.5 log10 units (P < 0.05) on day 9 of life to 2.5–3.0 log10 units (P < 0.05) on day 37. A slightly higher protective level of the CE culture in layer birds than in broilers raises the question on reasons for possible differences in the efficacy of CE culture in broiler and layer breeds. Whether the diet’s protein content has an impact on both normal intestinal flora composition and the efficacy of CE cultures against EEC or other pathogens remains open and needs further elucidation. Conclusions Our findings suggest that CE cultures of undefined composition can be valuable to reduce the intestinal colonisation by EEC in newly hatched broilers

A duality relation for entrance and exit laws for Markov processes

AbstractMarkov processes Xt on (X, FX) and Yt on (Y, FY) are said to be dual with respect to the function f(x, y) if Exf(Xt, y) = Eyf(x, Yt for all x ϵ X, y ϵ Y, t ⩾ 0. It is shown that this duality reverses the role of entrance and exit laws for the processes, and that two previously published results of the authors are dual in precisely this sense. The duality relation for the function f(x, y) = 1{x<y} is established for one-dimensional diffusions, and several new results on entrance and exit laws for diffusions, birth-death processes, and discrete time birth-death chains are obtained

MALDI-TOF MS Profiling-Advances in Species Identification of Pests, Parasites, and Vectors

Invertebrate pests and parasites of humans, animals, and plants continue to cause serious diseases and remain as a high treat to agricultural productivity and storage. The rapid and accurate species identification of the pests and parasites are needed for understanding epidemiology, monitoring outbreaks, and designing control measures. Matrix-assisted laser desorption ionization time- of-flight mass spectrometry (MALDI-TOF MS) profiling has emerged as a rapid, cost effective, and high throughput technique of microbial species identification in modern diagnostic laboratories. The development of soft ionization techniques and the release of commercial pattern matching software platforms has resulted in the exponential growth of applications in higher organisms including parasitology. The present review discusses the proof-of- principle experiments and various methods of MALDI MS profiling in rapid species identification of both laboratory and field isolates of pests, parasites and vectors

Immundiagnostische Charakterisierung der bovinen Protothekenmastitis

Die Protothekenmastitis des Rindes ist eine therapieresistente, weltweit vorkommende Infektionskrankheit. Das ätiologische Agens, die farblose Alge Prototheca (P.) zopfii, kommt ubiquitär in feuchten Habitaten vor und verursacht fakultativ akute bis chronische Entzündungen des Rindereuters. Es gibt Hinweise auf das Vorkommen eines speziellen, Mastitis-assoziierten Biotyps von P. zopfii, der sogenannten Variante II. Durch die oft zu beobachtende endemische Ausbreitung in Milchviehbeständen sowie durch die nachhaltige Therapieresistenz, welche oft zum wirtschaftlichen Totalverlust der betroffenen Milchkühe führt, stellen Protothekenmastitiden beim Rind ein großes ökonomisches Problem für den betroffenen Betrieb dar. Da bisher nur sehr beschränkte Erkenntnisse zur lokalen und systemischen Immunantwort sowie zur Erregerausscheidung im Verlaufe der Protothekenmastitis des Rindes vorlagen, wurden die verschiedenen klinischen Stadien dieser Infektion serologisch, kulturell sowie durch Bestimmung der Zahl der somatischen Zellen in der Milch charakterisiert. Zu diesem Zwecke wurden drei verschiedene ELISA-Systeme entwickelt, die anschließend auch auf ihren möglichen Einsatz bei der Diagnostik der Protothekenmastitis hin untersucht wurden. Dies geschah in einem hochgradig an Protothekenmastitis erkrankten Milchviehbestand. Darüber hinaus wurden verschiedene Isolate von P. zopfii auxanographisch, biochemisch, serologisch und genetisch untersucht, um eine Differenzierung innerhalb der Algenspezies P. zopfii vornehmen zu können. Anhand der auxanographischen, biochemischen, serologischen und genetischen Untersuchungen war eine eindeutige Differenzierung von drei verschiedenen Bio-, Sero- und Genotypen innerhalb der Algenspezies P. zopfii möglich. Alle untersuchten Mastitisisolate konnten eindeutig der Variante II von P. zopfii zugeordnet werden, womit dieser Variante eine besondere epidemiologische Bedeutung bei der Entstehung der Protothekenmastitis des Rindes zu zukommen scheint. Die Untersuchungen dieser Arbeit zeigen, dass akut infizierte Tiere sowohl die höchsten Antikörperaktivitäten an IgG im Blutserum sowie an IgA und IgG1 im Milchserum als auch die höchsten Gehalte an somatischen Zellen in der Milch aufweisen. Chronisch infizierte Milchkühe weisen zum Teil sehr hohe Antikörperaktivitäten in der Milch auf und unterschieden sich nicht signifikant von akut infizierten Tieren. Demgegenüber weisen diese chronisch infizierten Tiere signifikant höhere IgG-Aktivitäten im Blutserum sowie IgA- und IgG1-Aktivitäten in der Milch auf als nicht infizierte Tiere. Somit ist eine eindeutige Differenzierung zwischen infizierten und nichtinfizierten Kühen möglich. Die ELISAs zum Nachweis von spezifischem IgA und IgG1 im Milchserum erwiesen sich als besonders geeignet, um infizierte Kühe zu identifizieren. Beide serologischen Testsysteme wiesen Sensitivitäten von 96,3 % für IgA sowie 92,6 % für IgG1 und Spezifitäten von 94,4 % (IgA) und 96,3 % (IgG1) auf. Demgegenüber wies der ELISA zum Nachweis von spezifischem IgG im Blutserum bei einer Spezifität von 100 % nur eine Sensitivität von 81,5 % auf. Die sehr gute Reproduzierbarkeit der Tests wurde durch Intra-Assay-Variationen von 6,08 % für den Nachweis von IgA im Milchserum und 7,20 % für IgG1 sowie durch die geringe Inter-Assay-Variation von 6,32 % (IgA) und 9,74 % (IgG1) belegt. Der Einsatz dieser Testsysteme bei der Sanierung eines hochgradig mit P. zopfii infizierten Milchviehbestandes zeigte, dass die serologische Diagnostik dem bisher gebräuchlichen kulturellen Erregernachweis bei der Identifikation intermittierender Erregerausscheider überlegen ist. Es wurde deutlich, dass 70,5% der infizierten Tiere die Erreger über einen Zeitraum von 12 Monaten permanent ausschieden und mindestens weitere 4,9 %, wahrscheinlich jedoch wesentlich mehr, dieser infizierten Tiere intermittierende Erregerausscheider waren. Somit scheint der serologische Erregernachweis für die Diagnostik der Protothekenmastitis des Rindes besser geeignet zu sein als die kulturelle Diagnostik. Dabei wurde die höchste Sensitivität durch die Kombination des Nachweises von spezifischem IgA und IgG1 im Milchserum erzielt.Protothecosis is a severe, often endemic mastitis in cattle caused by colorless algae of the genus Prototheca. Only little and insufficient knowledge about the organism itself, and the host immune response to this infection existed. Therefore, the aim of this thesis was to characterize the local and systemic immune response and the possible elimination or persistence of the pathogen in the host. To gain more information on the specific immune response, different clinical stages of infection were characterized serologically, culturally, and by determination of the number of the somatic cells in milk. Three different ELISA systems were developed, which were also examined for their diagnostic application potential. For the investigations, a dairy herd highly infected with Prototheca zopfii and severe clinical manifestation of protothecal mastitis was used. The ELISA was evaluated using serum and whey from animals with different clinical stages of infection. As antibody isotypes, IgG in serum, and IgA and IgG1 in whey were used. In addition, different isolates of P. zopfii were biochemically, serologically, and genetically examined in order to allow a differentiation of individual isolates within the species P. zopfii. The biochemical, serological and genetic investigations allowed a clear differentiation of the three known Variants of P. zopfii. All examined mastitis isolates could be assigned to variant II of P. zopfii. Therefore, it can be concluded that this variant has a particular epidemiological significance in the etiology of bovine protothecal mastitis. The serological investigations showed high antibody activities during acute and chronic stage of infection. The antibody activity was low in chronically infected, but presently cultural negative animals and also in uninfected animals. A strong correlation was observed between whey IgA and whey IgG1 antibody activity and the count of somatic cells in milk. Whereas, only a weak correlation exists to the number of algae cells excreted with the milk. A sensitivity of 96 % and a specificity of 94 % were calculated for the ELISA based on IgA levels. The ELISA for detection of specific IgG1 in whey shows a sensitivity of 92,6 % and a specificity of 96,3 %. Intra-assay and interassay variations were calculated to be at 6.08 % and 6.32 %, respectively. Based on these data, these ELISAs are suitable for discrimination between infected and uninfected animals, and might therefore be used for the screening of affected herds. When used in the remediation of a high-grade infected dairy herd the serological showed clear advantages in the identification of intermittent shedders. By culturing of Prototheca from milk, it was shown that 70.5% of the infected animals were permanent shedders, whereas 4.9 % were intermittent shedders. Since intermittent shedders could be clearly identified serologically, but might not be recognized by culturing, it can be assumed that serological diagnostics is more suitable for the identification of inapparently infected, intermittent shedders

The Bernoulli sieve revisited

We consider an occupancy scheme in which "balls" are identified with $n$ points sampled from the standard exponential distribution, while the role of "boxes" is played by the spacings induced by an independent random walk with positive and nonlattice steps. We discuss the asymptotic behavior of five quantities: the index $K_n^*$ of the last occupied box, the number $K_n$ of occupied boxes, the number $K_{n,0}$ of empty boxes whose index is at most $K_n^*$, the index $W_n$ of the first empty box and the number of balls $Z_n$ in the last occupied box. It is shown that the limiting distribution of properly scaled and centered $K_n^*$ coincides with that of the number of renewals not exceeding $\log n$. A similar result is shown for $K_n$ and $W_n$ under a side condition that prevents occurrence of very small boxes. The condition also ensures that $K_{n,0}$ converges in distribution. Limiting results for $Z_n$ are established under an assumption of regular variation.Comment: Published in at http://dx.doi.org/10.1214/08-AAP592 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

In vitro susceptibility of Staphylococcus aureus strains isolated from cows with subclinical mastitis to different antimicrobial agents

Sensitivity to commercial teat dips (nonoxinol-9 iodine complex and chlorhexidine digluconate) of 56 Staphylococcus (S.) aureus strains isolated from quarter milk samples of various German dairy herds treated with different teat dipping schemes was investigated in this study. The minimum inhibitory concentration was determined using a broth macrodilution method according to the German Veterinary Association guidelines. The main objective of the current study was to induce in vitro resistance induction of S. aureus to chemical disinfectants. Ten different strains were repeatedly passed ten times in growth media with sub-lethal concentrations of disinfectants. Nine strains showed a significant reduction in susceptibility to the nonoxinol-9 iodine complex but only one strain developed resistance to chlorhexidine digluconate. Stability of the acquired resistance was observed in all S. aureus strains adapted to the nonoxinol-9 iodine complex and chlorhexidine digluconate. In contrast, simultaneous resistance to different antibiotics was not observed in any of the ten investigated S. aureus strains. However, the isolates exhibited a high degree of resistance to penicillin G. Based on these results, resistance of S. aureus to chemical disinfectants may be more likely to develop if the chemicals are used at concentrations lower than that required for an optimal biocidal effect

Drug Susceptibility Profiling of Prototheca Species Isolated from Cases of Human Protothecosis

Prototheca are unicellular, achlorophyllous, yeast-like microalgae that occur in a wide range of natural habitats. At least five species have been implicated as the causative agents of opportunistic infections of men. Human protothecosis typically manifests as cutaneous, articular, or systemic disease. Treatment is largely empirical with poorly predictable and often unsuccessful outcomes. This is largely due to the frequently observed resistance of Prototheca species to conventional antimicrobial agents. This work is the first to perform drug susceptibility profiling exclusively on isolates from human cases of protothecosis. A total of 23 such isolates were tested against amphotericin B and 9 azoles, including efinaconazole and luliconazole, whose activities against Prototheca have never been studied before. Efinaconazole was the most active, with median minimum inhibitory concentration (MIC) and minimum algicidal concentration (MAC) values of 0.031 mg/L and 0.063 mg/L, respectively. Fluconazole and luliconazole had the lowest activity, with median MIC and MAC values of 128 mg/L. To conclude, amphotericin B and most of the azoles showed in vitro activity, with an algicidal rather than algistatic effect, against Prototheca. Still, the activity of individual drugs differed significantly between the species and even between strains of the same species. These differences can be attributed to a species-specific potential for acquiring drug resistance, which, in turn, might be linked to the treatment history of the patient from whom the strain was recovered. The results of this study underscore the potential clinical utility of efinaconazole as a promising therapeutic agent for the treatment of human protothecosis

Impact of air humidity on the tenacity of different agents in bioaerosols

Despite the variety of pathogens that are transmitted via the airborne route, few data are available on factors that influence the tenacity of airborne pathogens. In order to better understand and thus control airborne infections, knowledge of these factors is important. In this study, three agents, S. aureus, G. stearothermophilus spores and the MS2 bacteriophage, were aerosolized at relative humidities (RH) varying between 30% and 70%. Air samples were then analyzed to determine the concentration of the agents. S. aureus was found to have significantly lower survival rate in the aerosol at RH above 60%. It showed the lowest recovery rates of the three agents, ranging from 0.13% at approximately 70% RH to 4.39% at 30% RH. G. stearothermophilus spores showed the highest tenacity with recovery rates ranging from 41.85% to 61.73% with little effect of RH. For the MS2 bacteriophage, a significantly lower tenacity in the aerosol was observed with a recovery rate of 4.24% for intermediate RH of approximately 50%. The results of this study confirm the significant influence of the RH on the tenacity of airborne microorganisms depending on the specific agent. These data show that the behavior of microorganism in bioaerosols is varies under different environmental conditions