scholarly journals Poincaré-Type Inequalities for Compact Degenerate Pure Jump Markov Processes

Mathematics ◽  
2019 ◽  
Vol 7 (6) ◽  
pp. 518 ◽  
Author(s):  
Pierre Hodara ◽  
Ioannis Papageorgiou
Keyword(s):  
Membrane Potential ◽  
Point Process ◽  
Markov Processes ◽  
Relevant Information ◽  
Neural System ◽  
Brain Neurons ◽  
Actual Position ◽  
The Past ◽  
Poincaré Type Inequalities ◽  
Jump Markov Processes

We aim to prove Poincaré inequalities for a class of pure jump Markov processes inspired by the model introduced by Galves and Löcherbach to describe the behavior of interacting brain neurons. In particular, we consider neurons with degenerate jumps, i.e., which lose their memory when they spike, while the probability of a spike depends on the actual position and thus the past of the whole neural system. The process studied by Galves and Löcherbach is a point process counting the spike events of the system and is therefore non-Markovian. In this work, we consider a process describing the membrane potential of each neuron that contains the relevant information of the past. This allows us to work in a Markovian framework.

Fluorescent potentiometric dyes for membrane-potential imaging

1994 ◽  
Vol 52 ◽  
pp. 166-167
Author(s):  
Leslie M. Loew
Keyword(s):  
Membrane Potential ◽  
Single Cells ◽  
Quantitative Imaging ◽  
Optical Recording ◽  
Biological Processes ◽  
Major Focus ◽  
The Past ◽  
Excitable Systems ◽  
Major Application ◽  
The Impact

A major application of potentiometric dyes has been the multisite optical recording of electrical activity in excitable systems. After being championed by L.B. Cohen and his colleagues for the past 20 years, the impact of this technology is rapidly being felt and is spreading to an increasing number of neuroscience laboratories. A second class of experiments involves using dyes to image membrane potential distributions in single cells by digital imaging microscopy - a major focus of this lab. These studies usually do not require the temporal resolution of multisite optical recording, being primarily focussed on slow cell biological processes, and therefore can achieve much higher spatial resolution. We have developed 2 methods for quantitative imaging of membrane potential. One method uses dual wavelength imaging of membrane-staining dyes and the other uses quantitative 3D imaging of a fluorescent lipophilic cation; the dyes used in each case were synthesized for this purpose in this laboratory.

Pharmaceutical Considerations of Nitroglycerin

1983 ◽  
Vol 17 (4) ◽  
pp. 255-263 ◽  
Author(s):  
Avraham Yacobi ◽  
Anton H. Amann ◽  
David M. Baaske
Keyword(s):  
Quality Control ◽  
Clinical Pharmacy ◽  
Analytical Techniques ◽  
Relevant Information ◽  
Dosage Forms ◽  
Delivery Systems ◽  
The Past ◽  
Rapid Changes ◽  
Pharmaceutical Uses

During the past few years, there have been rapid changes in the pharmaceutical uses of nitroglycerin. New dosage forms and new delivery systems have become available, which have resulted in potential confusion to all concerned with the proper use of these systems. The goal of this review is to prevent confusion and to bring all the relevant information together. The various analytical techniques available for quality control of the dosage forms and for the study of the pharmacokinetics are reviewed, with the intent of enabling the reader to identify pertinent references rapidly. The interaction of nitroglycerin with packaging and plastic delivery devices is also reviewed so that the reader can make informed choices. Finally, the clinical pharmacy and pharmacokinetics are reviewed so as to bring the reader up to date in that area. After reading this article, the areas of nitroglycerin research that still need to be explored should be apparent.

Solutions of ordinary differential equations as limits of pure jump markov processes

1970 ◽  
Vol 7 (1) ◽  
pp. 49-58 ◽  
Author(s):  
Thomas G. Kurtz
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Population Growth ◽  
Ordinary Differential Equations ◽  
Markov Processes ◽  
Radioactive Decay ◽  
Dynamic Processes ◽  
Deterministic Models ◽  
Image Position ◽  
Jump Markov Processes

In a great variety of fields, e.g., biology, epidemic theory, physics, and chemistry, ordinary differential equations are used to give continuous deterministic models for dynamic processes which are actually discrete and random in their development. Perhaps the simplest example is the differential equation used to describe a number of processes including radioactive decay and population growth.

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