Glauber and Kawasaki Dynamics for Determinantal Point Processes in Discrete Spaces

We construct the equilibrium Glauber and Kawasaki dynamics on discrete spaces which leave invariant certain determinantal point processes. We will construct Fellerian Markov processes with specified core for the generators. Further, we discuss the ergodicity of the processes

Limit theorems for open quantum random walks

We consider the limit distributions of open quantum random walks on one-dimensional lattice space. We introduce a dual process to the original quantum walk process, which is quite similar to the relation of Schr\"odinger-Heisenberg representation in quantum mechanics. By this, we can compute the distribution of the open quantum random walks concretely for many examples and thereby we can also obtain the limit distributions of them. In particular, it is possible to get rid of the initial state when we consider the evolution of the walk, it appears only in the last step of the computation

Islam and We

Panel: Islam and W

Investigating The Effects of In-vivo Therapeutics Hypoxia Treatment Paradigms In Neurite Outgrowth Patterns

Spinal cord injury, specifically in the cervical C3-C4 region of the cervical spine, contributes to impaired breathing and a diminished quality of life. Therefore it is important to find effective and safe therapeutics to restore breathing function. Indeed, there are a myriad of research being performed in addition to valuable collaboration amongst different institutions. As such, inspired by a previous experiment, we decided to test our hypothesis that an enriching environment consisting of different hypoxic environments - sustained and intermittent hypoxia alongside normoxia - would result in neurite outgrowth. Moreover, we hypothesized that sustained hypoxia would result in the greatest neurite outgrowth, followed by intermittent hypoxia. Lastly, we predicted that normoxia would result in the smallest amount of neurite outgrowth. We tested this hypothesis first in-vivo by placing female, retired breeder rats (n=3) in sustained or intermittent hypoxia or normoxia conditions for a period of 2 hours and 32 minutes. This was followed by dorsal root ganglion (DRG) culturing, plating, and fixing. Notably, because the premise of this experiment is a hybrid of both an in-vivo and in-vitro (specifically an ex-plant) we cannot, with accuracy, state that the growths are of axonal in nature. As such, we will refer them to as neurite. We used NeuronJ to manually trace and measure neurite outgrowth. In addition, we also utilized the Sholl analysis to better understand neurite arborization and their location in relation to the soma. We conclude that, interestingly, normoxia resulted in the greatest neurite outgrowth, followed by intermittent hypoxia and lastly by sustained hypoxia. As such, this experiment augments others experiments that show the promising therapeutic effects of intermittent hypoxia in restoring breathing function whether it is through enhancement of the crossed phrenic pathway or increased serotonergic receptor activation

Quantum Markov chains associated with open quantum random walks

In this paper we construct (nonhomogeneous) quantum Markov chains associated with open quantum random walks. The quantum Markov chain, like the classical Markov chain, is a fundamental tool for the investigation of the basic properties such as reducibility/irreducibility, recurrence/transience, accessibility, ergodicity, etc, of the underlying dynamics. Here we focus on the discussion of the reducibility and irreducibility of open quantum random walks via the corresponding quantum Markov chains. Particularly we show that the concept of reducibility/irreducibility of open quantum random walks in this approach is equivalent to the one previously done by Carbone and Pautrat. We provide with some examples. We will see also that the classical Markov chains can be reconstructed as quantum Markov chains.Comment: 30 page