Revisiting Offspring Maxima in Branching Processes

We present a progress report for studies on maxima related to offspring in branching processes. We summarize and discuss the findings on the subject that appeared in the last ten years. Some of the results are refined and illustrated with new examples.Comment: To appear in PLISKA Studia Mathematica Bulgaric

Characterizations of exponential distribution via conditional expectations of record values

We prove that the exponential distribution is the only one which satisfies a regression identity. This identity involves conditional expectation of the sample mean of record values given two record values outside of the sample

Limit Theorems for Branching Processes with Random Migration Components

The classical Bienaymé-Galton-Watson (BGW) branching process can be interpreted as mathematical model of population dynamics when the members of an isolated population reproduce themselves independently of each other according to a stochastic law.The work is supported by the Bulgarian National Foundation for Scientific Investigations, grant MM-704/97

Variance estimators in critical branching processes with non-homogeneous immigration

The asymptotic normality of conditional least squares estimators for the offspring variance in critical branching processes with non-homogeneous immigration is established, under moment assumptions on both reproduction and immigration. The proofs use martingale techniques and weak convergence results in Skorokhod spaces.Comment: Accepted for publication in Math Population Studie

Relative frequencies in multitype branching processes

This paper considers the relative frequencies of distinct types of individuals in multitype branching processes. We prove that the frequencies are asymptotically multivariate normal when the initial number of ancestors is large and the time of observation is fixed. The result is valid for any branching process with a finite number of types; the only assumption required is that of independent individual evolutions. The problem under consideration is motivated by applications in the area of cell biology. Specifically, the reported limiting results are of advantage in cell kinetics studies where the relative frequencies but not the absolute cell counts are accessible to measurement. Relevant statistical applications are discussed in the context of asymptotic maximum likelihood inference for multitype branching processes.Comment: Published in at http://dx.doi.org/10.1214/08-AAP539 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Novel biological markers for diagnosis and prognosis of poisoning with organophosphates, with special reference to acylpeptide hydrolase

Finding specific markers for changes in the biological systems after taking drugs or the consequences of exposure to toxic chemicals in the environment are increasingly important. Herein, the available biomarkers for documenting the interaction of organophosphorus compounds (neuroparalytic agents, pesticides, and drug preparations) with the biological systems as inhibition of cholinesterase group enzymes (AChE and BuChE) are reviewed. The advantages in the study of the activity of acylpeptide hydrolase in the blood for prevention and diagnosis of the organism changes after interaction with an organophosphorus compound are highlighted