Universality in kinetic models of circadian rhythms in [Formula: see text].

Biological evolution has endowed the plant Arabidopsis thaliana with genetically regulated circadian rhythms. A number of authors have published kinetic models for these oscillating chemical reactions based on a network of interacting genes. To investigate the hypothesis that the Arabidopsis circadian dynamical system is poised near a Hopf bifurcation like some other biological oscillators, we varied the kinetic parameters in the models and searched for bifurcations. Finding that each model does exhibit a supercritical Hopf bifurcation, we performed a weakly nonlinear analysis near the bifurcation points to derive the Stuart-Landau amplitude equation. To illustrate a common dynamical structure, we scaled the numerical solutions to the models with the asymptotic solutions to the Stuart-Landau equation to collapse the circadian oscillations onto two universal curves-one for amplitude, and one for frequency. However, some models are close to bifurcation while others are far, some models are post-bifurcation while others are pre-bifurcation, and kinetic parameters that lead to a bifurcation in some models do not lead to a bifurcation in others. Future kinetic modeling can make use of our analysis to ensure models are consistent with each other and with the dynamics of the Arabidopsis circadian rhythm.

Analysis of COVID-19 pandemic in USA, using Topological Weighted Centroid.

The first case of COVID-19 in USA was reported on January 20, 2020. The number of COVID-19 confirmed cases and death has increased since the first reported case and the outbreak has appeared in all states. This paper analyzes disease outbreak using Topological Weighted Centroid (TWC), which is a data driven intelligent geographical dynamical system that models disease spread in space and time. In this analysis the COVID-19 cases in USA on March 26, 2020 as provided by Johns Hopkins University is used. The COVID-19 outbreak is mapped by the TWC method. We were able to predict and capture some features of the pandemic spread using the early data. Although we have used the geographical distance from the latitude and longitude coordinates, our results indicate that one of the main paths of diseases spread are arguably airline routes. In this analysis, we used a large set of data. A modified version of TWC, is named TWC-Windowing to elaborate the effect of data from all places.

Theoretical estimation of retinal oxygenation in chronic diabetic retinopathy.

This paper uses computer modeling to estimate the progressive decline in oxygenation that occurs in the human diabetic retina after years of slowly progressive ischemic insult. An established model combines diffusion, saturable consumption, and blood capillary sources to determine the oxygen distribution across the retina. Incorporating long-term degradation of blood supply from the retinal capillaries into the model yields insight into the effects of progressive ischemia associated with prolonged hyperglycemia, suggesting time-scales over which therapeutic mitigation could have beneficial effect. A new extension of the model for oxygen distribution introduces a feedback mechanism for vasodilation and its potential to prolong healthy retinal function.

Visual sensations during megavoltage radiotherapy to the orbit attributable to Cherenkov radiation.

During megavoltage photon and electron beam radiotherapy treatment involving the eye, patients commonly report visual sensations; "nerve stimulation" is the conventional explanation. We propose that the phenomenon can be attributed to Cherenkov radiation inside the eye. The threshold electron energy for Cherenkov radiation in water is 260 keV. The human retina is able to perceive approximately 5-14 visible photons in 0.001 s. A single 500 keV electron traversing 1 mm of water will induce nearly 15 Cherenkov visible range photons. We propose that a portal image involving the eye will produce sufficient Cherenkov radiation to be detected by the retina.

An optimization model and solution for radiation shielding design of radiotherapy treatment vaults.

In radiation shielding design, one is usually faced with a set of conflicting goals that are navigated by an experienced physicist. If one has abundant space, the task is simplified because concrete is relatively inexpensive and will provide adequate shielding for high energy photons and neutrons, when applicable. However, if space is constrained (which is usually the case), the design becomes more difficult since one will likely have to employ combinations of steel, lead, and concrete, or other new materials--each with different properties and costs. Very experienced shielding designers can draw upon previous plans, but they do not know if their design is optimal in any sense. We have constructed a linear program that minimizes the cost of the shielding materials and minimizes the dose at the protection point or the shielding thickness subject to space constraints and to Federal or State regulations regarding the allowable exposure to individuals adjacent to the radiotherapy vault. In spite of what appears to be a simple model, the solution may require iterations of the optimization to arrive at the optimal solution.

Biophotonic and other physical methods for characterizing oral mucosa.

This article discusses biophotonic and other physical methods for characterizing oral mucosa.