George P. Yanev

Citrus canker, caused by bacterium Xanthomonas citri subsp. citri (Xcc), affects the citrus industry by making the fruit unmarketable due to unsightly lesions on the fruit. Citrus canker caused by a relatively new A^Wstrain of Xcc was reported on the citrus trees in the residential areas of the Lower Rio Grande Valley (LRGV) of South Texas. Xcc A^W has a limited host range, predominantly affecting limes and a few other citrus species. Previous work has reported prevailing environmental conditions that influence the incidence and spread of the citrus canker caused by the Asiatic A strain. However, no information is available on the environmental factors impacting the incidence of canker caused by A^W strain. In this study, monthly data on temperature, humidity, rainfall, and wind speed were grouped into biologically meaningful categories, and corresponding disease incidence was examined descriptively. Disease incidence was highest under high temperatures, humid conditions, and particularly during periods of rainfall and high wind speeds, which likely facilitated bacterial dispersal. These observed patterns indicate that warm, humid, rainy conditions, and stronger winds are associated with increased citrus canker incidence in the LRGV. This study provides insights into environmental conditions conducive to disease incidence and may serve as a foundation for developing explanatory and predictive models leading to management strategies for protecting citrus production in South Texas.

This paper deals into the long-term behavior of subordinated critical branching processes with migration. We focus on scenarios where emigration is the dominant factor and introduce additional randomness in timing through a subordination mechanism, involving renewal processes. The key findings highlight how the initial population size and the interarrival mean time influence both asymptotic behavior of the non-extinction probability and corresponding Yaglom type limit theorems. We also study an alternating regenerative process, when the population cycles between zero and positive states. This research complements previous studies for processes when immigration prevails over emigration.

This Special Issue is dedicated to the 80th anniversary of Nikolay Yanev, a renowned Bulgarian mathematician and an eminent member of the international branching processes community. We present a brief description of his academic career path and his role as a founder of the Bulgarian school of branching processes and their applications.

The sum of independent, but not necessary identically distributed, exponential random variables follows hypoexponential distribution. We focus on a particular case when all, but one rate parameters of the exponential variables are identical. this is known as exponentially modified Erlang distribution in molecular biology. We prove a characterization of the exponential distribution, which complements previous characterizations via hypoexponential distribution with all rates different from each other.

A class of controlled branching processes with continuous time is introduced and some limiting distributions are obtained in the critical case. An extension of this class as regenerative controlled branching processes with continuous time is proposed and some asymptotic properties are considered.

Arnold and Villasenor (2013) obtain a series of characterizations of the exponential distribution based on random samples of size two. These results were already applied in constructing goodness-of-fit tests. Extending the techniques from Arnold and Villasenor (2013), we prove some of the conjectures for samples of size three. An example with simulated data is discussed.