Damped finite-time-singularity driven by noise

We consider the combined influence of linear damping and noise on a dynamical finite-time-singularity model for a single degree of freedom. We find that the noise effectively resolves the finite-time-singularity and replaces it by a first-passage-time or absorbing state distribution with a peak at the singularity and a long time tail. The damping introduces a characteristic cross-over time. In the early time regime the probability distribution and first-passage-time distribution show a power law behavior with scaling exponent depending on the ratio of the non linear coupling strength to the noise strength. In the late time regime the behavior is controlled by the damping. The study might be of relevance in the context of hydrodynamics on a nanometer scale, in material physics, and in biophysics.Comment: 9 pages, 4 eps-figures, revtex4 fil

A terminal assessment of stages theory : introducing a dynamic states approach to entrepreneurship

Stages of Growth models were the most frequent theoretical approach to understanding entrepreneurial business growth from 1962 to 2006; they built on the growth imperative and developmental models of that time. An analysis of the universe of such models (N=104) published in the management literature shows no consensus on basic constructs of the approach, nor is there any empirical confirmations of stages theory. However, by changing two propositions of the stages models, a new dynamic states approach is derived. The dynamic states approach has far greater explanatory power than its precursor, and is compatible with leading edge research in entrepreneurship

Impaired Light Adaptation of ON-Sustained Ganglion Cells in Early Diabetes Is Attributable to Diminished Response to Dopamine D4 Receptor Activation

PURPOSE. Retinal neuronal signaling is disrupted early in diabetes, before the onset of the vascular pathologies associated with diabetic retinopathy. There is also growing evidence that retinal dopamine, a neuromodulator that mediates light adaptation, is reduced in early diabetes. Previously, we have shown that after 6 weeks of diabetes, light adaptation is impaired in ON-sustained (ON-s) ganglion cells in the mouse retina. The purpose of this study was to determine whether changes in the response to dopamine receptor activation contribute to this dysfunction. METHODS. Single-cell retinal patch-clamp recordings from the mouse retina were used to determine how activating dopamine type D4 receptors (D4Rs) changes the light-evoked and spontaneous excitatory inputs to ON-s ganglion cells, in both control and 6-week diabetic (STZ-injected) animals. Fluorescence in situ hybridization was also used to assess whether D4R expression was affected by diabetes. RESULTS. D4R activation decreased light-evoked and spontaneous inputs to ON-s ganglion cells in control and diabetic retinas. However, D4R activation caused a smaller reduction in light-evoked excitatory inputs to ON-s ganglion cells in diabetic retinas compared to controls. This impaired D4R signaling is not attributable to a decline in D4R expression, as there was no change in D4R mRNA density in the diabetic retinas. CONCLUSIONS. These results suggest that the cellular response to dopamine signaling is disrupted in early diabetes and may be amenable to chronic dopamine supplementation therapy. © 2022 Association for Research in Vision and Ophthalmology Inc.. All rights reserved.Open access journalThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]