Boyan Dimitrov

Probability distributions in periodic random environment and their applications

Periodic random environments and mechanisms of their effect on imbedded random variables are discussed. The variables under consideration represent either waiting time until some event occurs or the number of events within a given time interval. Their probability distributions have periodic residual lifetime functions and periodic failure rates. The form of the corresponding cumulative distribution functions is derived. Equivalent representations of these random variables as functions of other, suitably chosen independent random variables are established. Other probability properties such as almost lack of memory, invariance with respect to relevation transform, and preservation of service time distribution on nonreliable servers are additional characterizing features of this class of probability distributions. Nonstationary Poisson processes with periodic failure rates appear to be the closest extension of the homogeneous Poisson process to model the number of events imbedded into random environment of p...

On the optimal total processing time using checkpoints

The authors investigate the problem of optimizing the expected blocking time duration by providing a schedule of checkpoints during the required job processing time. They give a general approach for determining the optimal checkpoint schedule and derive some cases when the optimal checkpointing is uniform. The model has applications in unreliable computing systems, multiclient computer service, data transmissions, etc. >

Genotoxic effects of the pesticides Rubigan, Omite and Rovral in root-meristem cells of Crepis capillaris L.

Three pesticides have been studied for their genotoxicity by the use of assays in the plant Crepis capillaris, aimed at measuring chromosomal aberrations, micronuclei and sister chromosome exchange (SCE). The fungicides Rubigan 12 EC (fenarimol) and Rovral 25 Flo (iprodione) and the insecticide Omite 57 E (propargite) are all widely used nowadays. The aim of our study was to evaluate the genotoxic effects of these pesticides at concentrations corresponding to those applied in agricultural practice. In preliminary experiments we found that these concentrations do not influence cell proliferation and do not inhibit the growth of root meristems. In all experiments formulated commercial products were used. From the results we conclude that the three pesticides did not induce chromosomal aberrations as estimated by metaphase and anaphase analyses. They were also not capable to induce SCE. Rubigan did not induce micronucleus formation even at the highest concentration tested, but Omite and Rovral markedly increased micronucleus formation. The MN response depended on the sampling time and the concentration used, which showed a significant dose-response correlation (r=0.978, P<0.01 and r=0.941, P<0.01, respectively). A greater increase in micronucleus frequency was observed after Rovral treatment, where the highest concentration gave a response 8-10-fold above the negative control. Both pesticides induced high frequencies of lagging chromosomes, even after exposure to the lower test concentrations. The presence of lagging chromosomes is an indication of anti-microtubule activity of the pesticides tested. This effect was more strongly expressed after exposure to the two higher concentrations of Omite and Rovral. In this case a complete destruction of the mitotic spindle was observed, resulting in C-mitoses as well as in numerical aberrations-polyploidy and aneuploidy. The present findings suggest that Omite and Rovral at concentrations comparable to those used in practice can be regarded as potential aneugens.

A characterization of probability distributions similar to the exponential

A concept of the lack-of-memory property at a given time point c > 0 is introduced. It is equivalent to the concept of the almost-lack-of-memory (ALM) property of the random variables. A representation theorem is given for the cumulative distribution function of such random variables as well as for corresponding decompositions in terms of independent random variables. It is shown that a periodic failure rate for a random variable is equivalent to the ALM property. In addition some properties of the service time of an unreliable server are observed.

Renewal and nonhomogeneous Poisson processes generated by distributions with periodic failure rate

Two renewal processes, known in reliability maintenance as minimal repair and replacement policy, are considered. Their properties are studied in the case where the generating random sequence has a distribution with periodic failure rate. A characterization theorem establishes necessary and sufficient conditions for a non-stationary Poisson process to have a periodic failure rate. Applications in risk theory are shown.

Regeneration and characterization of plants obtained from anther cultures in Medicago sativa L.

SummaryThe androgenic ability of four Medicago sativa L. genotype (Boynitza 5, Byala, 494, and 3815) was tested. Callus and organogenesis were induced in all lines studied. The percentage of anthers producing calluses and organogenesis showed wide variation (calluses—from 11% up to 77%; organogenesis—4.8% to 15.2%). It has been established that genotype, nutrient medium composition, and stage of pollen development considerably affected both callus production and organogenesis. Androgenesis in M. sativa could be achieved via callus and direct embryogenesis. About 500 morphologically different regenerants were obtained. Wide variability in chromosome number of regenerated plants was observed by cytological studies. Haploid, dihaploid, as well as mixoploid plants were obtained.

Some moment properties and limit theorems of the reversed generalized logistic distribution with applications

In this paper we discuss an extended form of the logistic distribution and refer to it as the reversed generalized logistic distribution. We study some moment properties, and derive exact and explicit formulas for the mean, median, mode, variance, coefficients of skewness and kurtosis, and percentage points of this distribution. In addition, we study its limiting distributions as the shape parameter tends to zero or infinity. We also discuss some possible applications in bioassays through logistic regression approach.

Analysis of MAP/M/2 K queueing model with infinite resequencing buffer

Abstract We consider a MAP/M/2/K queueing model in which messages should leave the system in the order in which they entered into the system. In the case of infinite resequencing buffer, the steady-state probability vector is shown to be of matrix-geometric type. The total sojourn time of an admitted message into the system is shown to be of phase type. Efficient algorithmic procedures for computing various performance measures are given, and some interesting numerical examples are discussed.

THE SERVICE TIME PROPERTIES OF AN UNRELIABLE SERVER CHARACTERIZE THE EXPONENTIAL DISTRIBUTION

Consider the total service time of a job on an unreliable server under preemptiverepeat-different and preemptive-resume service disciplines. With identical initial conditions, for both cases, we notice that the distributions of the total service time under these two disciplines coincide, when the original service time (without interruptions due to server failures) is exponential and independent of the server reliability. We show that this fact under varying server reliability is a characterization of the exponential distribution. Further we show, under the same initial conditions, that the coincidence of the mean values also leads to the same characterization.

Definitions, characterizations and structural properties of probability distributions similar to the exponential

Abstract The concept of almost-lack-of-memory property was introduced in several recent papers of the authors and their principal properties have been studied. The paper is a review of these results scattered in publications, technical reports and manuscripts. Representation theorems are given for the cumulative distribution functions or for the survival functions of the corresponding random variables. Related decompositions in terms of functions of independent random variables are also presented. Physical, analytical and probabilistic properties, which characterize the new classes of probability distributions, are given. For example a periodic failure rate for a random variable and the non-stationary Poisson process with independent increments at a given point are equivalent to an ALM property. Some properties of the service time on an unreliable server are observed. Some other possible generalizations concerning bivariate case, random variables on the real line and the multiplicative ALM properties are also reviewed.