Reversibility Checking for Markov Chains

In this paper, we present reversibility preserving operations on Markov chain transition matrices. Simple row and column operations allow us to create new reversible transition matrices and yield an easy method for checking a Markov chain for reversibility

A novel application of queueing theory on the Caulerpenyne secreted by invasive Caulerpa taxifolia (Vahl) C.Agardh (Ulvophyceae, Caulerpales): a preliminary study

Aquarium originated marine green alga Caulerpa taxifolia was introduced into the Mediterranean Sea accidentally in 1984. This invasion has been negatively affecting the sub-littoral ecosystem of the Mediterranean. One of the important reasons for its success in the Mediterranean is its secondary toxic metabolite called caulerpenyne (CPN). Furthermore, CPN has anti-proliferative and apoptotic activities, therefore, CPN can be considered as a potential native source in cancer therapy. For that reason, modeling this metabolite might be of importance. Increase and decrease of the CPN level before reaching the critical level can be expressed by means of a queueing system in which the number of ‘customers' increases and decreases. In fact, production of CPN shows fluctuations for many environmental reasons, which allow us to apply queueing theory. In the present study, the expected time to reach the maximum caulerpenyne level was analyzed and evaluated using queueing theory

The secretary problem for a random walk

The secretary problem for a random walk is described. A particle has equal probabilities of moving j steps up or j steps down. The optimal strategy of picking the maximum height in n steps without the opportunity of recall is found. The best strategy is shown to be exactly the same as the naive strategy of choosing the first element of the sequence. The theory is extended to symmetric continuous distributions.secretary problem random walk optimal stopping

On the choice of support of Re-descendingψ-Functions in linear models with asymmetric error distributions

Primary 62F35, secondary 62G05, 62J05, Linear models, asymmetric errors, robust estimation, re-descending influence functions,

A method for obtaining Laplace transforms of order statistics of Erlang random variables

We present a path-counting method for deriving Laplace transforms of order statistics of independent but not necessarily identically distributed Erlang random variables, based on a probabilistic interpretation of the Laplace transform. The method is applicable also to generalized Erlang variates having different parameters for the exponential stages. The idea is to provide an intuitive understanding of the Laplace transform, based on the Markovian properties of the stages of the Erlang random variable. Thus the derivation technique is applicable to many other Markovian stochastic models. Motivational examples for queues and reliability are mentioned. Computational considerations are discussed.

A novel application of queueing theory on the Caulerpenyne secreted by invasive Caulerpa taxifolia (Vahl) C.Agardh (Ulvophyceae, Caulerpales): a preliminary study

Aquarium originated marine green alga Caulerpa taxifolia was introduced into the Mediterranean Sea accidentally in 1984. This invasion has been negatively affecting the sub-littoral ecosystem of the Mediterranean. One of the important reasons for its success in the Mediterranean is its secondary toxic metabolite called caulerpenyne (CPN). Furthermore, CPN has anti-proliferative and apoptotic activities, therefore, CPN can be considered as a potential native source in cancer therapy. For that reason, modeling this metabolite might be of importance. Increase and decrease of the CPN level before, reaching the critical level can be expressed by means of a queueing system in which the number of 'customers' increases and decreases. In fact, production of CPN shows fluctuations for many environmental reasons, which allow us to apply queueing theory. In the present study, the expected time to reach the maximum cauler-penyne level was analyzed and evaluated using queueing theory