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In this manuscript the Ebola outbreaks in 2014 and 2018 have been studied. On March 23, 2014, the World Health Organization announced the beginning of the Ebola outbreak in West Africa. The initial...

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.

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.

We report on seven nights of optical observation taken over a two-week period, and the resultant analysis of the intermediate-frequency peaked BL Lac object (IBL), BL Lac itself, at redshift z = 0.069. The microvariable behavior can be confirmed over the course of minutes for each night. A relativistic beaming model was used in our analysis, to infer changes to the line of sight angles for the motion of the different relativistic components. This model has very few free parameters. The light curves we generated show both high and moderate frequency cadence to the variable behavior of BL Lac itself, in addition to the well documented long-term variability.

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.

We report on the optical observations and analysis of the high-energy peaked BL Lac object (HBL), Mrk 501, at redshift z = 0.033. We can confirm microvariable behavior over the course of minutes on several occasions per night. As an alternative to the commonly understood dynamical model of random variations in intensity of the AGN, we develop a relativistic beaming model with a minimum of free parameters, which allows us to infer changes in the line of sight angles for the motion of the different relativistic components. We hope our methods can be used in future studies of beamed emission in other active microvariable sources, similar to the one we explored.

One of the most powerful aspects of our approach to neural networks is not only the development of the Auto-CM neural network but the visualization of its results. In this chapter we look at two visualization approaches—the Minimal Spanning Tree (MST) and the Maximal Regular Graph (MRG). The resultant from Auto-CM is a matrix of weights. This weight matrix naturally fits into a graph theoretic framework since the weights connecting the nodes will be viewed as edges and the weights as the weights on these edges.

We compare Auto-CM with various other methods that extract patterns from data. The way that we measure the results of comparisons uses MST.

Artificial Adaptive Systems include Artificial Neural Networks (ANNs or simply neural networks as they are commonly known). The philosophy of neural networks is to extract from data the underlying model that relates this data as an input/output (domain/range) pair. This is quite different from the way most mathematical modeling processes operate. Most mathematical modeling processes normally impose on the given data a model from which the input to output relationship is obtained. For example, a linear model that is a “best fit” in some sense, that relates the input to the output is such a model. What is imposed on the data by artificial neural networks is an a priori architecture rather than an a priori model. From the architecture, a model is extracted. It is clear, from any process that seeks to relate input to output (domain to range), requires a representation of the relationships among data. The advantage of imposing an architecture rather than a data model, is that it allows for the model to adapt. Fundamentally, a neural network is represented by its architecture. Thus, we look at the architecture first followed by a brief introduction of the two types of approaches for implementing the architecture—supervised and unsupervised neural networks. Recall that Auto-CM, which we discuss in Chap. 3, is an unsupervised ANN while K-CM, discussed in Chap. 6, is a supervised version of Auto-CM. However, in this chapter, we show that, in fact, supervised and unsupervised neural networks can be viewed within one framework in the case of the linear perceptron. The chapter ends with a brief look at some theoretical considerations.

This chapter focuses on Auto-Contractive Maps, which is a particularly useful ANN. Moreover, the relationship between Auto-Contractive Map (Auto-CM), which is the main topic of this monograph, its relationship to other ANNs and some illustrative example applications are presented.

We have looked at how to visualize the relationships among the elements of a dataset in Chap. 4. This chapter is devoted to the use of Auto-CM in the transformation of datasets for the purpose of extracting further relationships among data elements. The first transformation we call the FS-Transform, which looks beyond an all or nothing, binary relationship that is typical of most ANNs. The extraction of these perhaps more subtle relationships can be thought of as gradual relationships, zero denoting no relationship is present and one denoting a full/complete relationship that is absolutely present. It is thus, akin to a fuzzy set. The second transformation is one, which “morph” the delineation between records and variables within records that we call Hyper-Composition.

We look at how to use Auto-CM in the context of datasets that are changing in time. We modify our approach while keeping the original philosophy of Auto-CM.

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. A model for retinal oxygenation estimates ischemia associated with diabetes.The model employs diffusion, saturable consumption, and a nonlinear transport.The model's results reinforces the need for tighter glycemic control.A new extension includes vasodilation as a feedback response to ischemia.

A glance at Bessel functions shows they behave similar to the damped sinusoidal function. In this paper two physical examples (pendulum and spring-mass system with linearly increasing length and mass respectively) have been used as evidence for this observation. It is shown in this paper how Bessel functions can be approximated by the damped sinusoidal function. The numerical method that is introduced works very well in adiabatic condition (slow change) or in small time (independent variable) intervals. The results are also compared with the Lagrange polynomial.

In one dimension, we investigate dynamics using special relativity only, but make no statement regarding any particular insight into the nature of the spacetime continuum. Indeed, we do away completely with any kind of formal tensor algebra or differential topology, but do incorporate scaling into our calculations. The purpose here is primarily pedagogical, as an extension to the standard undergraduate treatment of special relativity, but it is also a calculational tool, to be able to determine the motion of objects in a one-dimensional case even with accelerations and forces, without having to use the full general relativistic treatment. To illustrate this, we directly compare relativistic to Newtonian or non-relativistic motions for particularly instructive selected systems.

High-frequency coaxial waveguide measurements are used to evaluate composition- and frequency-dependent complex permittivities and permeabilities of polycrystalline ferroelectric and ferrimagnetic ceramics. Material dielectric and magnetic property measurements were performed on ferroelectric barium titanate (BaTiO3) and ferrimagnetic yttrium iron garnet (YIG), with the upper measurement frequency bound below gyromagnetic resonance of YIG. These polycrystalline materials were chosen because of their widespread use in voltage- and magnetic field-tunable devices. Wideband frequency material measurements were used to predict dielectric and magnetic properties of various two-phase composite media incorporating BaTiO3 and YIG. Two effective medium theories were used: an asymmetric, modified Maxwell-Garnett type and a symmetric Bruggeman model. The Bruggeman effective medium model is extended to include three-phases. The three-phase Bruggeman predictive model is employed when controlled porosity is introduced into the composite and when two component phases are combined with polytetrafluoroethylene.

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.

Projectile motion in classical physics can be defined as a two-dimensional motion with constant acceleration in one direction and uniform motion in another direction. In classical mechanics this motion can be achieved if a force is applied in one direction and with some initial velocity in another direction. In relativistic dynamics, the equations of motion in both directions are coupled to each other and surprisingly the object experiences varying accelerations in both directions. We can say the non-relativistic projectile motion is not a projectile motion at all in relativistic physics. In this paper the conditions for the projectile motion in the relativistic regime are discussed. We discuss the two cases of constant force and constant acceleration. Another goal of this paper is that to show a computational example can be discussed in class for students to learn a topic in physics and improve their computational skills.

In this paper we describe a recently developed algorithm called Topological Weighted Centroid (TWC). TWC takes locations of an event of interest and analyzes the possible associated dynamics using the ideas of free energy and entropy. This novel mathematical tool has been applied to a real world example, the epidemic outbreak caused by Escherichia coli that occurred in Germany in 2011, to point out the real source of the outbreak. Other four examples of application to other epidemic spreads are described: Chikungunya fever of 2007 in Italy, Foot and mouth disease of 1967 in England, Cholera of 1854 in London, and the Russian influenza of 1889–1890 in Sweden. Comparisons have been made with other already published algorithms: Rossmo Algorithm, NES, LVM, Mexican Prob. The TWC results are significantly superior in comparison with other algorithms according to four independent indexes: distance from the peak, sensitivity, specificity and searching area. They are consistent with the idea that the spread of infectious disease is not random but follows a progression based on inherent, but as yet undiscovered, mathematical laws. The TWC method could provide an additional powerful tool for the investigation of the early stages of an epidemic and novel simulation methods for understanding the process through which a disease is spread.

The principal of least action is one of the fundamental ideas in physics. The path of the shortest time of a particle in the presence of gravity is an example of this principal. In this paper some methods are introduced to teach the optimal path in introductory physics courses. The optimal path (path of the shortest time) is calculated for a few families of paths. Finally a numerical method according to Snell’s law in a discrete medium is used to find the general optimal path and is compared with the brachistochrone path.

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.

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.

Purpose: To optimize shielding material combinations and thicknesses for megavoltage radiotherapy accelerator vaults for any photon energy using linear programming by minimizing the costs of shielding materials while satisfying the constraints pertaining to regulatory doses and available space. Methods:Radiotherapy accelerator vault construction usually requires an experienced physicist to design the appropriate thicknesses of concrete, steel or lead to satisfy the regulatory limiting doses, available thicknesses for shielding and the budget allocated for the project. We have developed a model and solution using linear programming that minimizes the costs of the shielding materials while satisfying regulatory dose limits and space available for the project. The model considers primary, leakage and scatter x‐ray radiation and neutron contamination using calculation techniques as in NCRP 151. The optimization routine will insert the required tenth value layers (TVLs) of steel or lead depending on the demands and the cost of these materials. The optimization considers neutron contamination as well. We discuss a parameterized version of the model that is never infeasible and which allows the user to weight the space versus cost according user preference. Results: The results of the linear program can be easily checked for correctness using standard calculation techniques. If there is abundant space for the wall thickness, concrete only is the result of the optimization since it has the lowest cost. If the allowed wall thickness is too small for concrete only, the optimization will return combinations of concrete, steel or lead such that all constraints are satisfied and costs are minimized. Existing thicknesses of concrete, for example, are easily incorporated into the model as are special requirements for IMRT. Conclusion: The linear program returns reliable, viable and optimized shielding thicknesses of concrete, steel and lead for primary barriers as well as for leakage and scatterradiation barriers.

Purpose: To compute and to verify experimentally Cherenkov radiation production inside the eye from direct and indirect high energy x‐ray irradiation of the orbit and that it exceeds detectability of Cherenkov radiation in scotopic vision. We show that the Cherenkov yield for direct and indirect irradiation exceeds the detection threshold of 6.4×107 photons/m2s. Methods: In photon and electron beamradiotherapy of intraorbital and periorbital tissues, patients commonly report having light sensations during treatment. The explanation usually offered is that ‘nerve stimulation’ is occurring. The radiotherapy literature reports the effect to be the result of ‘phosphenes’. Although phosphenes may play a role, we propose instead that patients are predominantly seeing Cherenkov radiation resulting from electrons inside the eye having kinetic energy exceeding the Cherenkov radiation threshold of 0.26 MeV. We consider calculations for direct irradiation of the eye from a portal image and indirect irradiation from treatment of peri‐orbital tissues and show that it exceeds threshold detection. Results: We calculate the Cherenkov yield using analytic methods and the measurements were in good agreement with our calculations. The Cherenkov radiation from a distilled water phantom, a square plastic phantom and an anthropomorphic plastic phantom were readily visible with a high quality CCD video camera. A digital camera captures the images from the console monitor. Threshold detection of Cherenkov radiation emanating from the water phantom through the video camera was determined and compared to a measurable source. The calculations for the water phantom match reasonably well with measurements and are roughly 1 lux and 3 lux respectively. Conclusion: We show images of Cherenkov radiation emanating from routine radiotherapytreatments and demonstrate that measurements corresponding to these images match well with calculations. We show that the Cherenkov component generated inside ocular media is sufficient to be detected by the patient.