Free-choice Nets with Home Clusters are Lucent

A marked Petri net is lucent if there are no two different reachable markings enabling the same set of transitions, i.e., states are fully characterized by the transitions they enable. Characterizing the class of systems that are lucent is a foundational and also challenging question. However, little research has been done on the topic. In this paper, it is shown that all free-choice nets having a home cluster are lucent. These nets have a so-called home marking such that it is always possible to reach this marking again. Such a home marking can serve as a regeneration point or as an end-point. The result is highly relevant because in many applications, we want the system to be lucent and many “well-behaved” process models fall into the class identified in this paper. Unlike previous work, we do not require the marked Petri net to be live and stronglyconnected. Most of the analysis techniques for free-choice nets are tailored towards well-formed nets. The approach presented in this paper provides a novel perspective enabling new analysis techniques for free-choice nets that do not need to be well-formed. Therefore, we can also model systems and processes that are terminating and/or have an initialization phase.

Mammals fail to regenerate organs when wound contraction drives scar formation

To understand why mammals generally do not regenerate injured organs, we considered the exceptional case of spontaneous skin regeneration in the early lamb fetus. Whereas during the early fetal stage skin wounds heal by regeneration, in the late fetal stage, and after birth, skin wounds close instead by scar formation. We review independent evidence that this switch in wound healing response coincides with the onset of wound contraction, which is also enabled during late fetal gestation. The crucial role of wound contraction in determining the wound healing outcome in adults has been demonstrated in three mammalian models of severe injury (excised guinea pig skin, transected rat sciatic nerve, excised rabbit conjunctival stroma) where grafting the injury with DRT, a contraction-blocking scaffold of highly-specific structure, altered significantly the wound healing outcome. While spontaneous healing resulted in scar formation in these animal models, DRT grafting significantly reduced the extent of wound contraction, prevented scar synthesis, and resulted in partial regeneration. These findings, as well as independent data from species that heal spontaneously via regeneration, point to a striking hypothesis: The process of regeneration lies dormant in mammals until appropriately activated by injury. In spontaneous wound healing of the late fetus and in adult mammals, wound contraction impedes such endogenous regeneration mechanisms. However, engineered treatments, such as DRT, that block wound contraction can cancel its effects and favor wound healing by regeneration instead of scar formation.

On the limit behavior of certain quantities in a subcritical storage model

The limit behavior of the content of a subcriticai storage model defined on a semi-Markov process is examined. This is achieved by creating a renewal equation using a regeneration point (i0,0) of the process. By showing that the expected return time to (i0, 0) is finite, the conditions needed for the basic renewal theorem are established. The joint asymptotic distribution of the content of the storage at time t and the accumulated amount of the unmet (lost) demands during (0,t) is then established by showing the asymptotic independence of these two.

On the limit behavior of certain quantities in a subcritical storage model

The limit behavior of the content of a subcriticai storage model defined on a semi-Markov process is examined. This is achieved by creating a renewal equation using a regeneration point (i 0,0) of the process. By showing that the expected return time to (i 0, 0) is finite, the conditions needed for the basic renewal theorem are established. The joint asymptotic distribution of the content of the storage at time t and the accumulated amount of the unmet (lost) demands during (0,t) is then established by showing the asymptotic independence of these two.

Correlation functions in the G/M/1 system

The G/G/1 queueing system is studied by means of the regeneration point method, exploiting the concept of busy cycles. Recurrence relations are set-up for the distribution of the queue length at the arrival epochs. The same method is used to obtain the correlation structure of arrivals and departures for the G/M/1 queue.

Correlation functions in the G/M/1 system

The G/G/1 queueing system is studied by means of the regeneration point method, exploiting the concept of busy cycles. Recurrence relations are set-up for the distribution of the queue length at the arrival epochs. The same method is used to obtain the correlation structure of arrivals and departures for the G/M/1 queue.

A stochastic theory of particle transport

A probability balance equation is formulated for the number of particles present in a cascade resulting from multiple births at each collision. Janossy’s regeneration point method is used and it leads to an integro differential equation for the generating function from which statistical information can readily be extracted. The technique is applied to the interpretation of radiation damage cascades in a homogeneous, amorphous medium in which two particles are ‘born’ per collision. The history of a single chain is followed and equations for the mean and variance are obtained as well as for individual probabilities. It is further shown how the backward and forward forms of the Boltzmann equation are related via the Green function of the system. Additional study shows that the variance also obeys a forward type of equation although its solution is not obtained as conveniently as that of the corresponding backward equation. Several analogies are made with other branches of particle physics; in particular, cosmic rays and neutron transport.