During April 20-22,2022,colleagues and friends gathered at the Institute of Pure&Applied Mathematics(IPAM),at the University of California at Los Angeles to celebrate Professor Stanley Osher's 8Oth birthday in...During April 20-22,2022,colleagues and friends gathered at the Institute of Pure&Applied Mathematics(IPAM),at the University of California at Los Angeles to celebrate Professor Stanley Osher's 8Oth birthday in a conference focusing on recent developments in"Optimization,Shape analysis,High-dimensional differential equations in science and Engineering,and machine learning Research(OSHER)"This conference hosted in-person talks by mathematicians,scientists,and industrial professionals worldwide.Those who could not attend extended their warm regards and expressed their appreciation for Professor Osher.展开更多
In this paper,we review computational approaches to optimization problems of inhomogeneous rods and plates.We consider both the optimization of eigenvalues and the localization of eigenfunctions.These problems are mot...In this paper,we review computational approaches to optimization problems of inhomogeneous rods and plates.We consider both the optimization of eigenvalues and the localization of eigenfunctions.These problems are motivated by physical problems including the determination of the extremum of the fundamental vibration frequency and the localization of the vibration displacement.We demonstrate how an iterative rearrangement approach and a gradient descent approach with projection can successfully solve these optimization problems under different boundary conditions with different densities given.展开更多
The resurgence of locally acquired malaria cases in the USA and the persistent global challenge of malaria transmission highlight the urgent need for research to prevent this disease. Despite significant eradication e...The resurgence of locally acquired malaria cases in the USA and the persistent global challenge of malaria transmission highlight the urgent need for research to prevent this disease. Despite significant eradication efforts, malaria remains a serious threat, particularly in regions like Africa. This study explores how integrating Gregor’s Type IV theory with Geographic Information Systems (GIS) improves our understanding of disease dynamics, especially Malaria transmission patterns in Uganda. By combining data-driven algorithms, artificial intelligence, and geospatial analysis, the research aims to determine the most reliable predictors of Malaria incident rates and assess the impact of different factors on transmission. Using diverse predictive modeling techniques including Linear Regression, K-Nearest Neighbor, Neural Network, and Random Forest, the study found that;Random Forest model outperformed the others, demonstrating superior predictive accuracy with an R<sup>2</sup> of approximately 0.88 and a Mean Squared Error (MSE) of 0.0534, Antimalarial treatment was identified as the most influential factor, with mosquito net access associated with a significant reduction in incident rates, while higher temperatures correlated with increased rates. Our study concluded that the Random Forest model was effective in predicting malaria incident rates in Uganda and highlighted the significance of climate factors and preventive measures such as mosquito nets and antimalarial drugs. We recommended that districts with malaria hotspots lacking Indoor Residual Spraying (IRS) coverage prioritize its implementation to mitigate incident rates, while those with high malaria rates in 2020 require immediate attention. By advocating for the use of appropriate predictive models, our research emphasized the importance of evidence-based decision-making in malaria control strategies, aiming to reduce transmission rates and save lives.展开更多
Healthcare security and privacy breaches are occurring in the United States (US), and increased substantially during the pandemic. This paper reviews the National Institute of Standards and Technology (NIST) publicati...Healthcare security and privacy breaches are occurring in the United States (US), and increased substantially during the pandemic. This paper reviews the National Institute of Standards and Technology (NIST) publication base as an effective solution. The NIST Special Publication 800-66 Revision 1 was an essential standard in US healthcare, which was withdrawn in February 2024 and superseded by SP 800-66 Revision 2. This review investigates the academic papers concerning the application of the NIST SP 800-66 Revision 1 standard in the US healthcare literature. A systematic review method was used in this study to determine current knowledge gaps of the SP 800-66 Revision 1. Some limitations were employed in the search to enforce validity. A total of eleven articles were found eligible for the study. Consequently, this study suggests the necessity for additional academic papers pertaining to SP 800-66 Revision 2 in the US healthcare literature. In turn, it will enhance awareness of safeguarding electronic protected health information (ePHI), help to mitigate potential future risks, and eventually reduce breaches.展开更多
Chinese medicine has a long history in the United States, dating back to its colonial period and extending up to the present. This essay focuses on the earliest generation of practitioners of traditional Chinese medic...Chinese medicine has a long history in the United States, dating back to its colonial period and extending up to the present. This essay focuses on the earliest generation of practitioners of traditional Chinese medicine in the United States. Although acupuncture is the modality most commonly associated with Chinese medicine in today's medical marketplace, up until the 1970s, Chinese healers in the United States typically specialized in herbalism. Well before mass emigration from China to the United States began, Chinese material medica crossed the oceans, in both directions: Chinese medicinal teas and herbs came west while Appalachian ginseng went east. Beginning in the 1850s, Chinese immigrants came to the United States and transplanted their health practices, sometimes quite literally by propagating medicinal plants in their adopted home. Over time, Chinese doctors learned how to sell their services to non-Chinese patients by presenting herbalism as “nature's remedies.”展开更多
In this work, we focus on the inverse problem of determining the parameters in a partial differential equation from given numerical solutions. For this purpose, we consider a modified Fisher’s equation that includes ...In this work, we focus on the inverse problem of determining the parameters in a partial differential equation from given numerical solutions. For this purpose, we consider a modified Fisher’s equation that includes a relaxation time in relating the flux to the gradient of the density and an added cubic non-linearity. We show that such equations still possess traveling wave solutions by using standard methods for nonlinear dynamical systems in which fixed points in the phase plane are found and their stability characteristics are classified. A heteroclinic orbit in the phase plane connecting a saddle point to a node represents the traveling wave solution. We then design parameter estimation/discovery algorithms for this system including a few based on machine learning methods and compare their performance.展开更多
We consider the so-called Thomson problem which refers to finding the equilibrium distribution of a finite number of mutually repelling point charges on the surface of a sphere, but for the case where the sphere is re...We consider the so-called Thomson problem which refers to finding the equilibrium distribution of a finite number of mutually repelling point charges on the surface of a sphere, but for the case where the sphere is replaced by a spheroid or ellipsoid. To get started, we first consider the problem in two dimensions, with point charges on circles (for which the equilibrium distribution is intuitively obvious) and ellipses. We then generalize the approach to the three-dimensional case of an ellipsoid. The method we use is to begin with a random distribution of charges on the surface and allow each point charge to move tangentially to the surface due to the sum of all Coulomb forces it feels from the other charges. Deriving the proper equations of motion requires using a projection operator to project the total force on each point charge onto the tangent plane of the surface. The position vectors then evolve and find their final equilibrium distribution naturally. For the case of ellipses and ellipsoids or spheroids, we find that multiple distinct equilibria are possible for certain numbers of charges, depending on the starting conditions. We characterize these based on their total potential energies. Some of the equilibria found turn out to represent local minima in the potential energy landscape, while others represent the global minimum. We devise a method based on comparing the moment-of-inertia tensors of the final configurations to distinguish them from one another.展开更多
Alzheimer’s disease(AD)is the sixth leading cause of death in the United States with approximately 5.8 million Americans currently living with AD.Due to the lack of a disease modifying treatment for AD and the aging ...Alzheimer’s disease(AD)is the sixth leading cause of death in the United States with approximately 5.8 million Americans currently living with AD.Due to the lack of a disease modifying treatment for AD and the aging baby boomer generation,this number is projected to grow to 13.8 million by 2050(Gaugler et al.,2019).Amyloid-beta(Aβ)plaque accumulation,one of the major pathological hallmarks of AD,can begin>20 years before clinical symptoms of AD.By the time AD is clinically diagnosed,neuronal loss and neuropathological lesions(Aβplaques and tau tangles)have already.展开更多
The Modified Picard-Chebyshev Method(MPCM)is implemented as an orbit propagation solver for a numerical optimization method that determines minimum time orbit transfer trajectory of a satellite using a series of multi...The Modified Picard-Chebyshev Method(MPCM)is implemented as an orbit propagation solver for a numerical optimization method that determines minimum time orbit transfer trajectory of a satellite using a series of multiple impulses at intermediate waypoints.The waypoints correspond to instantaneous impulses that are determined using a nonlinear constrained optimization routine,SNOPT with numerical force models for both Two-Body and J2 perturbations.It is found that using the MPCM increases run-time performance of the discretized lowthrust optimization method when compared to other sequential numerical solvers,such as Adams-Bashforth-Moulton and Gauss-Jackson 8th order methods.展开更多
The integrity of the basal stem cell layer is critical for epithelial homoeostasis.In this paper,we review the expression of oral mucosal stem cell markers(OM-SCMs)in oral submucous fibrosis(OSF),oral potentially mali...The integrity of the basal stem cell layer is critical for epithelial homoeostasis.In this paper,we review the expression of oral mucosal stem cell markers(OM-SCMs)in oral submucous fibrosis(OSF),oral potentially malignant disorders(OPMDs)and oral squamous cell carcinoma(OSCC)to understand the role of basal cells in potentiating cancer stem cell behaviour in OSF.While the loss of basal cell clonogenicity triggers epithelial atrophy in OSF,the transition of the epithelium from atrophic to hyperplastic and eventually neoplastic involves the reactivation of basal stemness.The vacillating expression patterns of OM-SCMs confirm the role of keratins 5,14,19,CD44,β1-integrin,p63,sex-determining region Y box(SOX2),octamer-binding transcription factor 4(Oct-4),c-MYC,B-cell-specific Moloney murine leukaemia virus integration site 1(Bmi-1)and aldehyde dehydrogenase 1(ALDH1)in OSF,OPMDs and OSCC.The downregulation of OM-SCMs in the atrophic epithelium of OSF and their upregulation during malignant transformation are illustrated with relevant literature in this review.展开更多
Aloe dichotoma (Quiver tree) occurs in the arid regions of Namaqualand and Bushman land in South Africa, and in arid regions of southern Namibia. The Quiver trees are not only threatened by agricultural expansion, ove...Aloe dichotoma (Quiver tree) occurs in the arid regions of Namaqualand and Bushman land in South Africa, and in arid regions of southern Namibia. The Quiver trees are not only threatened by agricultural expansion, overgrazing, and mining;but also by climate changes and droughts. Previous studies show that Quiver trees are very sensitive to environmental changes, and do not respond well to extreme hot and dry conditions. This study investigates the current status of the Quiver tree within its existing environment, and also assesses the projected future changes of the Quiver tree habitat under different climatic scenarios. It provided evidence regarding the importance of the study to understanding the climate change impacts on the Quiver tree and its geographical response to climate changes.展开更多
The well-known Riccati differential equations play a key role in many fields,including problems in protein folding,control and stabilization,stochastic control,and cybersecurity(risk analysis and malware propaga-tion)...The well-known Riccati differential equations play a key role in many fields,including problems in protein folding,control and stabilization,stochastic control,and cybersecurity(risk analysis and malware propaga-tion).Quantum computer algorithms have the potential to implement faster approximate solutions to the Riccati equations compared with strictly classical algorithms.While systems with many qubits are still under development,there is significant interest in developing algorithms for near-term quantum computers to determine their accuracy and limitations.In this paper,we propose a hybrid quantum-classical algorithm,the Matrix Riccati Solver(MRS).This approach uses a transformation of variables to turn a set of nonlinear differential equation into a set of approximate linear differential equations(i.e.,second order non-constant coefficients)which can in turn be solved using a version of the Harrow-Hassidim-Lloyd(HHL)quantum algorithm for the case of Hermitian matrices.We implement this approach using the Qiskit language and compute near-term results using a 4 qubit IBM Q System quantum computer.Comparisons with classical results and areas for future research are discussed.展开更多
We develop two new pricing formulae for European options. The purpose of these formulae is to better understand the impact of each term of the model, as well as improve the speed of the calculations. We consider the S...We develop two new pricing formulae for European options. The purpose of these formulae is to better understand the impact of each term of the model, as well as improve the speed of the calculations. We consider the SABR model (with β=1) of stochastic volatility, which we analyze by tools from Malliavin Calculus. We follow the approach of Alòs et al. (2006) who showed that under stochastic volatility framework, the option prices can be written as the sum of the classic Hull-White (1987) term and a correction due to correlation. We derive the Hull-White term, by using the conditional density of the average volatility, and write it as a two-dimensional integral. For the correction part, we use two different approaches. Both approaches rely on the pairing of the exponential formula developed by Jin, Peng, and Schellhorn (2016) with analytical calculations. The first approach, which we call “Dyson series on the return’s idiosyncratic noise” yields a complete series expansion but necessitates the calculation of a 7-dimensional integral. Two of these dimensions come from the use of Yor’s (1992) formula for the joint density of a Brownian motion and the time-integral of geometric Brownian motion. The second approach, which we call “Dyson series on the common noise” necessitates the calculation of only a one-dimensional integral, but the formula is more complex. This research consisted of both analytical derivations and numerical calculations. The latter show that our formulae are in general more exact, yet more time-consuming to calculate, than the first order expansion of Hagan et al. (2002).展开更多
文摘During April 20-22,2022,colleagues and friends gathered at the Institute of Pure&Applied Mathematics(IPAM),at the University of California at Los Angeles to celebrate Professor Stanley Osher's 8Oth birthday in a conference focusing on recent developments in"Optimization,Shape analysis,High-dimensional differential equations in science and Engineering,and machine learning Research(OSHER)"This conference hosted in-person talks by mathematicians,scientists,and industrial professionals worldwide.Those who could not attend extended their warm regards and expressed their appreciation for Professor Osher.
基金supported by the DMS-1853701supported in part by the DMS-2208373.
文摘In this paper,we review computational approaches to optimization problems of inhomogeneous rods and plates.We consider both the optimization of eigenvalues and the localization of eigenfunctions.These problems are motivated by physical problems including the determination of the extremum of the fundamental vibration frequency and the localization of the vibration displacement.We demonstrate how an iterative rearrangement approach and a gradient descent approach with projection can successfully solve these optimization problems under different boundary conditions with different densities given.
文摘The resurgence of locally acquired malaria cases in the USA and the persistent global challenge of malaria transmission highlight the urgent need for research to prevent this disease. Despite significant eradication efforts, malaria remains a serious threat, particularly in regions like Africa. This study explores how integrating Gregor’s Type IV theory with Geographic Information Systems (GIS) improves our understanding of disease dynamics, especially Malaria transmission patterns in Uganda. By combining data-driven algorithms, artificial intelligence, and geospatial analysis, the research aims to determine the most reliable predictors of Malaria incident rates and assess the impact of different factors on transmission. Using diverse predictive modeling techniques including Linear Regression, K-Nearest Neighbor, Neural Network, and Random Forest, the study found that;Random Forest model outperformed the others, demonstrating superior predictive accuracy with an R<sup>2</sup> of approximately 0.88 and a Mean Squared Error (MSE) of 0.0534, Antimalarial treatment was identified as the most influential factor, with mosquito net access associated with a significant reduction in incident rates, while higher temperatures correlated with increased rates. Our study concluded that the Random Forest model was effective in predicting malaria incident rates in Uganda and highlighted the significance of climate factors and preventive measures such as mosquito nets and antimalarial drugs. We recommended that districts with malaria hotspots lacking Indoor Residual Spraying (IRS) coverage prioritize its implementation to mitigate incident rates, while those with high malaria rates in 2020 require immediate attention. By advocating for the use of appropriate predictive models, our research emphasized the importance of evidence-based decision-making in malaria control strategies, aiming to reduce transmission rates and save lives.
文摘Healthcare security and privacy breaches are occurring in the United States (US), and increased substantially during the pandemic. This paper reviews the National Institute of Standards and Technology (NIST) publication base as an effective solution. The NIST Special Publication 800-66 Revision 1 was an essential standard in US healthcare, which was withdrawn in February 2024 and superseded by SP 800-66 Revision 2. This review investigates the academic papers concerning the application of the NIST SP 800-66 Revision 1 standard in the US healthcare literature. A systematic review method was used in this study to determine current knowledge gaps of the SP 800-66 Revision 1. Some limitations were employed in the search to enforce validity. A total of eleven articles were found eligible for the study. Consequently, this study suggests the necessity for additional academic papers pertaining to SP 800-66 Revision 2 in the US healthcare literature. In turn, it will enhance awareness of safeguarding electronic protected health information (ePHI), help to mitigate potential future risks, and eventually reduce breaches.
文摘Chinese medicine has a long history in the United States, dating back to its colonial period and extending up to the present. This essay focuses on the earliest generation of practitioners of traditional Chinese medicine in the United States. Although acupuncture is the modality most commonly associated with Chinese medicine in today's medical marketplace, up until the 1970s, Chinese healers in the United States typically specialized in herbalism. Well before mass emigration from China to the United States began, Chinese material medica crossed the oceans, in both directions: Chinese medicinal teas and herbs came west while Appalachian ginseng went east. Beginning in the 1850s, Chinese immigrants came to the United States and transplanted their health practices, sometimes quite literally by propagating medicinal plants in their adopted home. Over time, Chinese doctors learned how to sell their services to non-Chinese patients by presenting herbalism as “nature's remedies.”
文摘In this work, we focus on the inverse problem of determining the parameters in a partial differential equation from given numerical solutions. For this purpose, we consider a modified Fisher’s equation that includes a relaxation time in relating the flux to the gradient of the density and an added cubic non-linearity. We show that such equations still possess traveling wave solutions by using standard methods for nonlinear dynamical systems in which fixed points in the phase plane are found and their stability characteristics are classified. A heteroclinic orbit in the phase plane connecting a saddle point to a node represents the traveling wave solution. We then design parameter estimation/discovery algorithms for this system including a few based on machine learning methods and compare their performance.
文摘We consider the so-called Thomson problem which refers to finding the equilibrium distribution of a finite number of mutually repelling point charges on the surface of a sphere, but for the case where the sphere is replaced by a spheroid or ellipsoid. To get started, we first consider the problem in two dimensions, with point charges on circles (for which the equilibrium distribution is intuitively obvious) and ellipses. We then generalize the approach to the three-dimensional case of an ellipsoid. The method we use is to begin with a random distribution of charges on the surface and allow each point charge to move tangentially to the surface due to the sum of all Coulomb forces it feels from the other charges. Deriving the proper equations of motion requires using a projection operator to project the total force on each point charge onto the tangent plane of the surface. The position vectors then evolve and find their final equilibrium distribution naturally. For the case of ellipses and ellipsoids or spheroids, we find that multiple distinct equilibria are possible for certain numbers of charges, depending on the starting conditions. We characterize these based on their total potential energies. Some of the equilibria found turn out to represent local minima in the potential energy landscape, while others represent the global minimum. We devise a method based on comparing the moment-of-inertia tensors of the final configurations to distinguish them from one another.
基金supported by grants from the National Institute of Health,NIA R21AG055949 and R01AG062840。
文摘Alzheimer’s disease(AD)is the sixth leading cause of death in the United States with approximately 5.8 million Americans currently living with AD.Due to the lack of a disease modifying treatment for AD and the aging baby boomer generation,this number is projected to grow to 13.8 million by 2050(Gaugler et al.,2019).Amyloid-beta(Aβ)plaque accumulation,one of the major pathological hallmarks of AD,can begin>20 years before clinical symptoms of AD.By the time AD is clinically diagnosed,neuronal loss and neuropathological lesions(Aβplaques and tau tangles)have already.
文摘The Modified Picard-Chebyshev Method(MPCM)is implemented as an orbit propagation solver for a numerical optimization method that determines minimum time orbit transfer trajectory of a satellite using a series of multiple impulses at intermediate waypoints.The waypoints correspond to instantaneous impulses that are determined using a nonlinear constrained optimization routine,SNOPT with numerical force models for both Two-Body and J2 perturbations.It is found that using the MPCM increases run-time performance of the discretized lowthrust optimization method when compared to other sequential numerical solvers,such as Adams-Bashforth-Moulton and Gauss-Jackson 8th order methods.
文摘The integrity of the basal stem cell layer is critical for epithelial homoeostasis.In this paper,we review the expression of oral mucosal stem cell markers(OM-SCMs)in oral submucous fibrosis(OSF),oral potentially malignant disorders(OPMDs)and oral squamous cell carcinoma(OSCC)to understand the role of basal cells in potentiating cancer stem cell behaviour in OSF.While the loss of basal cell clonogenicity triggers epithelial atrophy in OSF,the transition of the epithelium from atrophic to hyperplastic and eventually neoplastic involves the reactivation of basal stemness.The vacillating expression patterns of OM-SCMs confirm the role of keratins 5,14,19,CD44,β1-integrin,p63,sex-determining region Y box(SOX2),octamer-binding transcription factor 4(Oct-4),c-MYC,B-cell-specific Moloney murine leukaemia virus integration site 1(Bmi-1)and aldehyde dehydrogenase 1(ALDH1)in OSF,OPMDs and OSCC.The downregulation of OM-SCMs in the atrophic epithelium of OSF and their upregulation during malignant transformation are illustrated with relevant literature in this review.
文摘Aloe dichotoma (Quiver tree) occurs in the arid regions of Namaqualand and Bushman land in South Africa, and in arid regions of southern Namibia. The Quiver trees are not only threatened by agricultural expansion, overgrazing, and mining;but also by climate changes and droughts. Previous studies show that Quiver trees are very sensitive to environmental changes, and do not respond well to extreme hot and dry conditions. This study investigates the current status of the Quiver tree within its existing environment, and also assesses the projected future changes of the Quiver tree habitat under different climatic scenarios. It provided evidence regarding the importance of the study to understanding the climate change impacts on the Quiver tree and its geographical response to climate changes.
文摘The well-known Riccati differential equations play a key role in many fields,including problems in protein folding,control and stabilization,stochastic control,and cybersecurity(risk analysis and malware propaga-tion).Quantum computer algorithms have the potential to implement faster approximate solutions to the Riccati equations compared with strictly classical algorithms.While systems with many qubits are still under development,there is significant interest in developing algorithms for near-term quantum computers to determine their accuracy and limitations.In this paper,we propose a hybrid quantum-classical algorithm,the Matrix Riccati Solver(MRS).This approach uses a transformation of variables to turn a set of nonlinear differential equation into a set of approximate linear differential equations(i.e.,second order non-constant coefficients)which can in turn be solved using a version of the Harrow-Hassidim-Lloyd(HHL)quantum algorithm for the case of Hermitian matrices.We implement this approach using the Qiskit language and compute near-term results using a 4 qubit IBM Q System quantum computer.Comparisons with classical results and areas for future research are discussed.
文摘We develop two new pricing formulae for European options. The purpose of these formulae is to better understand the impact of each term of the model, as well as improve the speed of the calculations. We consider the SABR model (with β=1) of stochastic volatility, which we analyze by tools from Malliavin Calculus. We follow the approach of Alòs et al. (2006) who showed that under stochastic volatility framework, the option prices can be written as the sum of the classic Hull-White (1987) term and a correction due to correlation. We derive the Hull-White term, by using the conditional density of the average volatility, and write it as a two-dimensional integral. For the correction part, we use two different approaches. Both approaches rely on the pairing of the exponential formula developed by Jin, Peng, and Schellhorn (2016) with analytical calculations. The first approach, which we call “Dyson series on the return’s idiosyncratic noise” yields a complete series expansion but necessitates the calculation of a 7-dimensional integral. Two of these dimensions come from the use of Yor’s (1992) formula for the joint density of a Brownian motion and the time-integral of geometric Brownian motion. The second approach, which we call “Dyson series on the common noise” necessitates the calculation of only a one-dimensional integral, but the formula is more complex. This research consisted of both analytical derivations and numerical calculations. The latter show that our formulae are in general more exact, yet more time-consuming to calculate, than the first order expansion of Hagan et al. (2002).
