In epidemiology, the effective reproduction number $R_{e}$ R e is used to characterize the growth... more In epidemiology, the effective reproduction number $R_{e}$ R e is used to characterize the growth rate of an epidemic outbreak. If $R_{e} >1$ R e > 1 , the epidemic worsens, and if $R_{e}< 1$ R e < 1 , then it subsides and eventually dies out. In this paper, we investigate properties of $R_{e}$ R e for a modified SEIR model of COVID-19 in the city of Houston, TX USA, in which the population is divided into low-risk and high-risk subpopulations. The response of $R_{e}$ R e to two types of control measures (testing and distancing) applied to the two different subpopulations is characterized. A nonlinear cost model is used for control measures, to include the effects of diminishing returns. Lowest-cost control combinations for reducing instantaneous $R_{e}$ R e to a given value are computed. We propose three types of heuristic strategies for mitigating COVID-19 that are targeted at reducing $R_{e}$ R e , and we exhibit the tradeoffs between strategy implementation costs and...
Wireless sensor networks (WSNs) are becoming increasingly utilized in applications that require r... more Wireless sensor networks (WSNs) are becoming increasingly utilized in applications that require remote collection of data on environmental conditions. In particular dense WSNs are emerging as an important sensing platforms for the Internet of Things (IoT). WSNs are able to generate huge volumes of raw data, which require network structuring and efficient collaboration between nodes to ensure efficient transmission. In order to reduce the amount of data carried in the network, data aggregation is used in WSNs to define a policy of data fusion and compression. In this paper, we investigate a model for data aggregation in a dense WSN with a single sink. The model divides a circular coverage region centered at the sink into patches which are intersections of sectors of concentric rings, and data in each patch is aggregated at a single node before transmission. Nodes only communicate with other nodes in the same sector. Based on these assumptions, we formulate a linear programming problem to maximize system lifetime by minimizing the maximum proportionate energy consumption over all nodes. Under a wide variety of conditions, the optimal solution employs two transmissions mechanisms: direct transmission, in which nodes send information directly to the sink; and stepwise transmission, in which nodes transmit information to adjacent nodes. An exact formula is given for the proportionate energy consumption rate of the network. Asymptotic forms of this exact solution are also derived, and are verified to agree with the linear programming solution. We investigate three strategies for improving system lifetime: nonuniform energy and information density; iterated compression; and modifications of rings. We conclude that iterated compression has the biggest effect in increasing system lifetime.
Submitted for the TSF15 Meeting of The American Physical Society Quantum Mechanics as the Outcome... more Submitted for the TSF15 Meeting of The American Physical Society Quantum Mechanics as the Outcome of an Accumulative Statistical Process CHRISTOPHER THRON, Texas AM University-Central Texas-For a general quantum theory that is describable by a path integral formalism, we construct a mathematical model of a statistical accumulation-to-threshold process whose outcomes give predictions that are nearly identical to the given quantum theory. The model is neither local nor causal in spacetime, but is both local and causal is in a larger space which includes an additional dimension: the spacetime universe attains its observed configuration by means of a process in which the added dimension is the dynamical variable. The probabilistic nature of the squared wavefunction is a natural consequence of the model, and the model avoids conceptual difficulties encountered by other interpretations of quantum mechanics. We verify the model with simulations, and we discuss possible discrepancies from conventional quantum theory that might be detectable via experiment. Finally, we discuss the physical implications of the model.
Advances in Nature-Inspired Computing and Applications, 2018
The problem of optimally covering a set of point targets in a region with areas of a specific sha... more The problem of optimally covering a set of point targets in a region with areas of a specific shape has several important applications in the fields of communications, remote sensing, and logistics. We consider the case where a target is covered when it falls within a coverage area (so-called “Boolean” coverage), and we specialize to the case of identical circular (or spherical) coverage areas. The problem has been shown to be NP-hard, and most practical algorithms use statistical methods to look for near-optimal solutions. Previous algorithms cannot guarantee 100% target coverage. In this chapter we demonstrate a physics-based algorithm (called the “nebular algorithm”) that guarantees full coverage while seeking to minimize the number of coverage areas employed. This approach can generate solutions with reduced numbers of sensors for systems with thousands of targets within a few hours. The algorithm, its implementation, and simulation results are presented, as well as its potentia...
Facial recognition technology has emerged as an attractive solution for many of today’s needs in ... more Facial recognition technology has emerged as an attractive solution for many of today’s needs in identification and identity verification. In recent years, the use of deep learning techniques and convolutional neural networks in particular has led to high-performance systems with near-human recognition capabilities. In general, these models are trained and evaluated on image datasets that do not sufficiently consider the lighting conditions of a real environment. However, in many practical applications the lighting is uncontrolled, which may seriously affect the performance of these systems. In this chapter, we propose a data augmentation method to achieve a model that is robust to variations in brightness. The training dataset is augmented by generating 3D faces from 2D images in the original dataset, followed by a Lambertian reflectance lighting variation that simulates the lighting variations that occur in real environments. The approach is evaluated on the YaleB and ORL datasets...
In this article give a very simple presentation of Bell's inequality by comparing it to a "quantu... more In this article give a very simple presentation of Bell's inequality by comparing it to a "quantum game show", followed by a simple description of Aspect's 1985 experiment involving entangled photons which confirms the inequality. The entire article is non-technical and requires no mathematical background other than high school mathematics and an understanding of basic concepts in probability. The physics involved in Aspect's experiment is also explained.
Like many developing countries, Nigeria, is faced with a number of tradeoffs that pit rapid econo... more Like many developing countries, Nigeria, is faced with a number of tradeoffs that pit rapid economic development against environmental preservation. Sustainable, “green” economic development is slower, more costly, and more difficult than unrestricted, unregulated economic growth. The mathematical model that we develop in this paper suggests that widespread public awareness of environmental issues is insufficient to prevent the tendency towards sacrificing the environment for the sake of growth. Even if people have an understanding of negative impacts and always choose to act in their own self-interest, they may still act collectively in such a way as to bring down the quality of life for the entire society. We conclude that additional actions must be taken besides raising public awareness of the environmental problem.
The problem of covering random points in the plane with disks has applications in operations rese... more The problem of covering random points in the plane with disks has applications in operations research, as well as being of theoretical interest. In this document we show that the computational complexity may be reduced by classifying points and into several classes (uncovered, single-covered, collateral, and indeterminate) and sets into several classes (non-covering, single-covering, collateral, redundant, and indeterminate). Sets that are single-covering are necessary for the cover, while non-covering, collateral, and redundant sets can be excluded. An optimal cover can be found by applying linear programming to just the indeterminate points and sets, which may be much fewer than the original points and sets given. In addition, indeterminate points and sets may be divided into separate ``islands'' that can be solved separately. Hence the actual complexity is determined by the number of points and sets in the largest island. We give several heatmaps to show how the proportion of points and sets of various types depend on two basic scale-invariant parameters related to point and set density. For a few parameters, we compare these results to some theoretical calculations. A detailed code description is given in the Appendix. This paper represents a work in progress. The final section proposes some future directions for research. In particular, the tendency to form islands as a function of system parameters may be quantified.
This paper develops an accurate, efficient filter (called the 'TT filter') for tracking multiple ... more This paper develops an accurate, efficient filter (called the 'TT filter') for tracking multiple targets using a spatially-distributed network of amplitude sensors that estimate distance but not direction. Several innovations are included in the algorithm that increase accuracy and reduce complexity. For initial target acquisition once tracking begins, a constrained Hessian search is used to find the maximum likelihood (ML) target vector, based on the measurement model and a Gaussian approximation of the prior. The Hessian at the ML vector is used to give an initial approximation of the negative log likelihood for the target vector distribution: corrections are applied if the Hessian is not positive definite due to the near-far problem. Further corrections are made by applying a transformation that matches the known nonlinearity introduced by distance-only sensors. A set of integration points is constructed using this information, which are used to estimate the mean and moments of the target vector distribution. Results show that the TT filter gives superior accuracy and lower complexity than previous alternatives such as Kalman-based or particle filters.
We analyze an epidemiological model to evaluate the effectiveness of multiple means of control in... more We analyze an epidemiological model to evaluate the effectiveness of multiple means of control in malariaendemic areas. The mathematical model consists of a system of several ordinary differential equations, and is based on a multicompartment representation of the system. The model takes into account the mutliple resting-questing stages undergone by adult female mosquitos during the period in which they function as disease vectors. We compute the basic reproduction number R 0 , and show that that if R 0 < 1, the disease free equilibrium (DFE) is globally asymptotically stable (GAS) on the non-negative orthant. If R 0 > 1, the system admits a unique endemic equilibrium (EE) that is GAS. We perform a sensitivity analysis of the dependence of R 0 and the EE on parameters related to control measures, such as killing effectiveness and bite prevention. Finally, we discuss the implications for a comprehensive, cost-effective strategy for malaria control.
Journal of Artificial Societies and Social Simulation, 2016
This paper presents a semi-quantitative mathematical model of the changes over time in the statis... more This paper presents a semi-quantitative mathematical model of the changes over time in the statistical distribution of well-being of individuals in a society. The model predicts that when individuals overvalue the more socially conspicuous aspects of well-being in their lifestyle choices, then the average well-being of the overall population may experience continuous decline. In addition to tradeoff cost and overvaluation, we identify statistical variation in individuals' well-being and turnover within the population as key factors driving negative trends. We investigate the influence of the effects of heterogeneity in the population, as well as economic and/or technological progress.
Disruptive Technologies in Sensors and Sensor Systems, 2017
We present a proof-of-concept investigation into the use of sensor networks for tracking of WiFi ... more We present a proof-of-concept investigation into the use of sensor networks for tracking of WiFi users in outdoor urban environments. Sensors are fixed, and are capable of measuring signal power from users' WiFi devices. We derive a maximum likelihood estimate for user location based on instantaneous sensor power measurements. The algorithm takes into account the effects of power control, and is self-calibrating in that the signal power model used by the location algorithm is adjusted and improved as part of the operation of the network. Simulation results to verify the system's performance are presented. The simulation scenario is based on a 1.5 km 2 area of lower Manhattan, The self-calibration mechanism was verified for initial rms (root mean square) errors of up to 12 dB in the channel power estimates: rms errors were reduced by over 60% in 300 track-hours, in systems with limited power control. Under typical operating conditions with (without) power control, location rms errors are about 8.5 (5) meters with 90% accuracy within 9 (13) meters, for both pedestrian and vehicular users. The distance error distributions for smaller distances (<30 m) are well-approximated by an exponential distribution, while the distributions for large distance errors have fat tails. The issue of optimal sensor placement in the sensor network is also addressed. We specify a linear programming algorithm for determining sensor placement for networks with reduced number of sensors. In our test case, the algorithm produces a network with 18.5% fewer sensors with comparable accuracy estimation performance. Finally, we discuss future research directions for improving the accuracy and capabilities of sensor network systems in urban environments.
Large applications of sensor networks, such as environmental risk monitoring, require the deploym... more Large applications of sensor networks, such as environmental risk monitoring, require the deployment of hundreds or even thousands of nodes. This study proposes and implements a novel stochastic physics-based optimisation algorithm that is both efficient (guarantees full target coverage with a reduced number of sensors) and scalable (meaning that it can be executed for very large-scale problems in a reasonable computation time). The algorithm employs 'virtual sensors' which move, merge, recombine, and 'explode' during the course of the algorithm, where the process of merging and recombining virtual sensors reduces the number of actual sensors while maintaining full coverage. The parameters which control sensor merging and explosion are varied during the algorithm to perform the same function as an annealing schedule in simulated annealing. Simulation results illustrate the rapidity and the effectiveness of the proposed method.
2015 IEEE International Symposium on Signal Processing and Information Technology (ISSPIT), 2015
The problem of optimal beamforming for two-way relay (TWR) systems with perfect channel state inf... more The problem of optimal beamforming for two-way relay (TWR) systems with perfect channel state information (CSI) that use analog network coding (ANC) is reduced to a pair of algebraic equations in two variables that can be solved very inexpensively using the conjugate gradient algorithm. The solution has greatly reduced complexity compared to previous optimal solutions via semidefinite programming (SDP). Together with a previously-designed linearized algorithm for beamforming in the robust (imperfect CSI) case, it provides a high-performance, low-complexity robust beamforming solution for 2-way relays.
In epidemiology, the effective reproduction number $R_{e}$ R e is used to characterize the growth... more In epidemiology, the effective reproduction number $R_{e}$ R e is used to characterize the growth rate of an epidemic outbreak. If $R_{e} >1$ R e > 1 , the epidemic worsens, and if $R_{e}< 1$ R e < 1 , then it subsides and eventually dies out. In this paper, we investigate properties of $R_{e}$ R e for a modified SEIR model of COVID-19 in the city of Houston, TX USA, in which the population is divided into low-risk and high-risk subpopulations. The response of $R_{e}$ R e to two types of control measures (testing and distancing) applied to the two different subpopulations is characterized. A nonlinear cost model is used for control measures, to include the effects of diminishing returns. Lowest-cost control combinations for reducing instantaneous $R_{e}$ R e to a given value are computed. We propose three types of heuristic strategies for mitigating COVID-19 that are targeted at reducing $R_{e}$ R e , and we exhibit the tradeoffs between strategy implementation costs and...
Wireless sensor networks (WSNs) are becoming increasingly utilized in applications that require r... more Wireless sensor networks (WSNs) are becoming increasingly utilized in applications that require remote collection of data on environmental conditions. In particular dense WSNs are emerging as an important sensing platforms for the Internet of Things (IoT). WSNs are able to generate huge volumes of raw data, which require network structuring and efficient collaboration between nodes to ensure efficient transmission. In order to reduce the amount of data carried in the network, data aggregation is used in WSNs to define a policy of data fusion and compression. In this paper, we investigate a model for data aggregation in a dense WSN with a single sink. The model divides a circular coverage region centered at the sink into patches which are intersections of sectors of concentric rings, and data in each patch is aggregated at a single node before transmission. Nodes only communicate with other nodes in the same sector. Based on these assumptions, we formulate a linear programming problem to maximize system lifetime by minimizing the maximum proportionate energy consumption over all nodes. Under a wide variety of conditions, the optimal solution employs two transmissions mechanisms: direct transmission, in which nodes send information directly to the sink; and stepwise transmission, in which nodes transmit information to adjacent nodes. An exact formula is given for the proportionate energy consumption rate of the network. Asymptotic forms of this exact solution are also derived, and are verified to agree with the linear programming solution. We investigate three strategies for improving system lifetime: nonuniform energy and information density; iterated compression; and modifications of rings. We conclude that iterated compression has the biggest effect in increasing system lifetime.
Submitted for the TSF15 Meeting of The American Physical Society Quantum Mechanics as the Outcome... more Submitted for the TSF15 Meeting of The American Physical Society Quantum Mechanics as the Outcome of an Accumulative Statistical Process CHRISTOPHER THRON, Texas AM University-Central Texas-For a general quantum theory that is describable by a path integral formalism, we construct a mathematical model of a statistical accumulation-to-threshold process whose outcomes give predictions that are nearly identical to the given quantum theory. The model is neither local nor causal in spacetime, but is both local and causal is in a larger space which includes an additional dimension: the spacetime universe attains its observed configuration by means of a process in which the added dimension is the dynamical variable. The probabilistic nature of the squared wavefunction is a natural consequence of the model, and the model avoids conceptual difficulties encountered by other interpretations of quantum mechanics. We verify the model with simulations, and we discuss possible discrepancies from conventional quantum theory that might be detectable via experiment. Finally, we discuss the physical implications of the model.
Advances in Nature-Inspired Computing and Applications, 2018
The problem of optimally covering a set of point targets in a region with areas of a specific sha... more The problem of optimally covering a set of point targets in a region with areas of a specific shape has several important applications in the fields of communications, remote sensing, and logistics. We consider the case where a target is covered when it falls within a coverage area (so-called “Boolean” coverage), and we specialize to the case of identical circular (or spherical) coverage areas. The problem has been shown to be NP-hard, and most practical algorithms use statistical methods to look for near-optimal solutions. Previous algorithms cannot guarantee 100% target coverage. In this chapter we demonstrate a physics-based algorithm (called the “nebular algorithm”) that guarantees full coverage while seeking to minimize the number of coverage areas employed. This approach can generate solutions with reduced numbers of sensors for systems with thousands of targets within a few hours. The algorithm, its implementation, and simulation results are presented, as well as its potentia...
Facial recognition technology has emerged as an attractive solution for many of today’s needs in ... more Facial recognition technology has emerged as an attractive solution for many of today’s needs in identification and identity verification. In recent years, the use of deep learning techniques and convolutional neural networks in particular has led to high-performance systems with near-human recognition capabilities. In general, these models are trained and evaluated on image datasets that do not sufficiently consider the lighting conditions of a real environment. However, in many practical applications the lighting is uncontrolled, which may seriously affect the performance of these systems. In this chapter, we propose a data augmentation method to achieve a model that is robust to variations in brightness. The training dataset is augmented by generating 3D faces from 2D images in the original dataset, followed by a Lambertian reflectance lighting variation that simulates the lighting variations that occur in real environments. The approach is evaluated on the YaleB and ORL datasets...
In this article give a very simple presentation of Bell's inequality by comparing it to a "quantu... more In this article give a very simple presentation of Bell's inequality by comparing it to a "quantum game show", followed by a simple description of Aspect's 1985 experiment involving entangled photons which confirms the inequality. The entire article is non-technical and requires no mathematical background other than high school mathematics and an understanding of basic concepts in probability. The physics involved in Aspect's experiment is also explained.
Like many developing countries, Nigeria, is faced with a number of tradeoffs that pit rapid econo... more Like many developing countries, Nigeria, is faced with a number of tradeoffs that pit rapid economic development against environmental preservation. Sustainable, “green” economic development is slower, more costly, and more difficult than unrestricted, unregulated economic growth. The mathematical model that we develop in this paper suggests that widespread public awareness of environmental issues is insufficient to prevent the tendency towards sacrificing the environment for the sake of growth. Even if people have an understanding of negative impacts and always choose to act in their own self-interest, they may still act collectively in such a way as to bring down the quality of life for the entire society. We conclude that additional actions must be taken besides raising public awareness of the environmental problem.
The problem of covering random points in the plane with disks has applications in operations rese... more The problem of covering random points in the plane with disks has applications in operations research, as well as being of theoretical interest. In this document we show that the computational complexity may be reduced by classifying points and into several classes (uncovered, single-covered, collateral, and indeterminate) and sets into several classes (non-covering, single-covering, collateral, redundant, and indeterminate). Sets that are single-covering are necessary for the cover, while non-covering, collateral, and redundant sets can be excluded. An optimal cover can be found by applying linear programming to just the indeterminate points and sets, which may be much fewer than the original points and sets given. In addition, indeterminate points and sets may be divided into separate ``islands'' that can be solved separately. Hence the actual complexity is determined by the number of points and sets in the largest island. We give several heatmaps to show how the proportion of points and sets of various types depend on two basic scale-invariant parameters related to point and set density. For a few parameters, we compare these results to some theoretical calculations. A detailed code description is given in the Appendix. This paper represents a work in progress. The final section proposes some future directions for research. In particular, the tendency to form islands as a function of system parameters may be quantified.
This paper develops an accurate, efficient filter (called the 'TT filter') for tracking multiple ... more This paper develops an accurate, efficient filter (called the 'TT filter') for tracking multiple targets using a spatially-distributed network of amplitude sensors that estimate distance but not direction. Several innovations are included in the algorithm that increase accuracy and reduce complexity. For initial target acquisition once tracking begins, a constrained Hessian search is used to find the maximum likelihood (ML) target vector, based on the measurement model and a Gaussian approximation of the prior. The Hessian at the ML vector is used to give an initial approximation of the negative log likelihood for the target vector distribution: corrections are applied if the Hessian is not positive definite due to the near-far problem. Further corrections are made by applying a transformation that matches the known nonlinearity introduced by distance-only sensors. A set of integration points is constructed using this information, which are used to estimate the mean and moments of the target vector distribution. Results show that the TT filter gives superior accuracy and lower complexity than previous alternatives such as Kalman-based or particle filters.
We analyze an epidemiological model to evaluate the effectiveness of multiple means of control in... more We analyze an epidemiological model to evaluate the effectiveness of multiple means of control in malariaendemic areas. The mathematical model consists of a system of several ordinary differential equations, and is based on a multicompartment representation of the system. The model takes into account the mutliple resting-questing stages undergone by adult female mosquitos during the period in which they function as disease vectors. We compute the basic reproduction number R 0 , and show that that if R 0 < 1, the disease free equilibrium (DFE) is globally asymptotically stable (GAS) on the non-negative orthant. If R 0 > 1, the system admits a unique endemic equilibrium (EE) that is GAS. We perform a sensitivity analysis of the dependence of R 0 and the EE on parameters related to control measures, such as killing effectiveness and bite prevention. Finally, we discuss the implications for a comprehensive, cost-effective strategy for malaria control.
Journal of Artificial Societies and Social Simulation, 2016
This paper presents a semi-quantitative mathematical model of the changes over time in the statis... more This paper presents a semi-quantitative mathematical model of the changes over time in the statistical distribution of well-being of individuals in a society. The model predicts that when individuals overvalue the more socially conspicuous aspects of well-being in their lifestyle choices, then the average well-being of the overall population may experience continuous decline. In addition to tradeoff cost and overvaluation, we identify statistical variation in individuals' well-being and turnover within the population as key factors driving negative trends. We investigate the influence of the effects of heterogeneity in the population, as well as economic and/or technological progress.
Disruptive Technologies in Sensors and Sensor Systems, 2017
We present a proof-of-concept investigation into the use of sensor networks for tracking of WiFi ... more We present a proof-of-concept investigation into the use of sensor networks for tracking of WiFi users in outdoor urban environments. Sensors are fixed, and are capable of measuring signal power from users' WiFi devices. We derive a maximum likelihood estimate for user location based on instantaneous sensor power measurements. The algorithm takes into account the effects of power control, and is self-calibrating in that the signal power model used by the location algorithm is adjusted and improved as part of the operation of the network. Simulation results to verify the system's performance are presented. The simulation scenario is based on a 1.5 km 2 area of lower Manhattan, The self-calibration mechanism was verified for initial rms (root mean square) errors of up to 12 dB in the channel power estimates: rms errors were reduced by over 60% in 300 track-hours, in systems with limited power control. Under typical operating conditions with (without) power control, location rms errors are about 8.5 (5) meters with 90% accuracy within 9 (13) meters, for both pedestrian and vehicular users. The distance error distributions for smaller distances (<30 m) are well-approximated by an exponential distribution, while the distributions for large distance errors have fat tails. The issue of optimal sensor placement in the sensor network is also addressed. We specify a linear programming algorithm for determining sensor placement for networks with reduced number of sensors. In our test case, the algorithm produces a network with 18.5% fewer sensors with comparable accuracy estimation performance. Finally, we discuss future research directions for improving the accuracy and capabilities of sensor network systems in urban environments.
Large applications of sensor networks, such as environmental risk monitoring, require the deploym... more Large applications of sensor networks, such as environmental risk monitoring, require the deployment of hundreds or even thousands of nodes. This study proposes and implements a novel stochastic physics-based optimisation algorithm that is both efficient (guarantees full target coverage with a reduced number of sensors) and scalable (meaning that it can be executed for very large-scale problems in a reasonable computation time). The algorithm employs 'virtual sensors' which move, merge, recombine, and 'explode' during the course of the algorithm, where the process of merging and recombining virtual sensors reduces the number of actual sensors while maintaining full coverage. The parameters which control sensor merging and explosion are varied during the algorithm to perform the same function as an annealing schedule in simulated annealing. Simulation results illustrate the rapidity and the effectiveness of the proposed method.
2015 IEEE International Symposium on Signal Processing and Information Technology (ISSPIT), 2015
The problem of optimal beamforming for two-way relay (TWR) systems with perfect channel state inf... more The problem of optimal beamforming for two-way relay (TWR) systems with perfect channel state information (CSI) that use analog network coding (ANC) is reduced to a pair of algebraic equations in two variables that can be solved very inexpensively using the conjugate gradient algorithm. The solution has greatly reduced complexity compared to previous optimal solutions via semidefinite programming (SDP). Together with a previously-designed linearized algorithm for beamforming in the robust (imperfect CSI) case, it provides a high-performance, low-complexity robust beamforming solution for 2-way relays.
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Papers by Chris Thron