Pub Date : 2024-01-01Epub Date: 2024-06-25DOI: 10.3389/fams.2024.1399426
Gilson D Honvoh, Roger S Zoh, Anand Gupta, Mark E Benden, Carmen D Tekwe
Background: Obesity has become an important threat to children's health, with physical and psychological impacts that extend into adulthood. Limited physical activity and sedentary behavior are associated with increased obesity risk. Because children spend approximately 6 h each day in school, researchers increasingly study how obesity is influenced by school-day physical activity and energy expenditure (EE) patterns among school-aged children by using wearable devices that collect data at frequent intervals and generate complex, high-dimensional data. Although clinicians typically define obesity in children as having an age-and sex-adjusted body mass index (BMI) value in the high percentiles, the relationships between school-based physical activity interventions and BMI are analyzed using traditional linear regression models, which are designed to assess the effects of interventions among children with average BMI, limiting insight regarding the effects of interventions among children categorized as overweight or obese.
Methods: We investigate the association between wearable device-based EE measures and age-and sex-adjusted BMI values in data from a cluster-randomized, school-based study. We express and analyze EE levels as both a scalar-valued variable and as a continuous, high-dimensional, functional predictor variable. We investigate the relationship between school-day EE (SDEE) and BMI using four models: a linear mixed-effects model (LMEM), a quantile mixed-effects model (QMEM), a functional mixed-effects model (FMEM), and a functional quantile mixed-effects model (FQMEM). The LMEM and QMEM include SDEE as a summary measure, whereas the FMEM and FQMEM allow for the modeling of SDEE as a high-dimensional covariate. The FMEM and FQMEM allow the influence of the time of day at which physical activity is performed to be assessed, which is not possible using the LMEM or the QMEM. The FMEM assesses how frequently collected SDEE data influences mean BMI, whereas the FQMEM assesses the effects on quantile levels of BMI.
Results: The LMEM and QMEM detected a statistically significant effect of overall mean SDEE on log (BMI) (the natural logarithm of BMI) after adjusting for intervention, age, race, and sex. The FMEM and FQMEM provided evidence for statistically significant associations between SDEE and log (BMI) for only a short time interval. Being a boy or being assigned a stand-biased desk is associated with a lower log (BMI) than being a girl or being assigned a traditional desk. Across our models, age was not a statistically significant covariate, and white students had significantly lower log (BMI) than non-white students in quantile models, but this significant effect was observed for only the 10th and 50th quantile levels of BMI. The functional regression models allow for additional interpretations of the influence of EE patterns on age-and sex-adjusted BMI, whereas the quanti
{"title":"Modeling approaches for assessing device-based measures of energy expenditure in school-based studies of body weight status.","authors":"Gilson D Honvoh, Roger S Zoh, Anand Gupta, Mark E Benden, Carmen D Tekwe","doi":"10.3389/fams.2024.1399426","DOIUrl":"10.3389/fams.2024.1399426","url":null,"abstract":"<p><strong>Background: </strong>Obesity has become an important threat to children's health, with physical and psychological impacts that extend into adulthood. Limited physical activity and sedentary behavior are associated with increased obesity risk. Because children spend approximately 6 h each day in school, researchers increasingly study how obesity is influenced by school-day physical activity and energy expenditure (EE) patterns among school-aged children by using wearable devices that collect data at frequent intervals and generate complex, high-dimensional data. Although clinicians typically define obesity in children as having an age-and sex-adjusted body mass index (BMI) value in the high percentiles, the relationships between school-based physical activity interventions and BMI are analyzed using traditional linear regression models, which are designed to assess the effects of interventions among children with average BMI, limiting insight regarding the effects of interventions among children categorized as overweight or obese.</p><p><strong>Methods: </strong>We investigate the association between wearable device-based EE measures and age-and sex-adjusted BMI values in data from a cluster-randomized, school-based study. We express and analyze EE levels as both a scalar-valued variable and as a continuous, high-dimensional, functional predictor variable. We investigate the relationship between school-day EE (SDEE) and BMI using four models: a linear mixed-effects model (LMEM), a quantile mixed-effects model (QMEM), a functional mixed-effects model (FMEM), and a functional quantile mixed-effects model (FQMEM). The LMEM and QMEM include SDEE as a summary measure, whereas the FMEM and FQMEM allow for the modeling of SDEE as a high-dimensional covariate. The FMEM and FQMEM allow the influence of the time of day at which physical activity is performed to be assessed, which is not possible using the LMEM or the QMEM. The FMEM assesses how frequently collected SDEE data influences mean BMI, whereas the FQMEM assesses the effects on quantile levels of BMI.</p><p><strong>Results: </strong>The LMEM and QMEM detected a statistically significant effect of overall mean SDEE on log (BMI) (the natural logarithm of BMI) after adjusting for intervention, age, race, and sex. The FMEM and FQMEM provided evidence for statistically significant associations between SDEE and log (BMI) for only a short time interval. Being a boy or being assigned a stand-biased desk is associated with a lower log (BMI) than being a girl or being assigned a traditional desk. Across our models, age was not a statistically significant covariate, and white students had significantly lower log (BMI) than non-white students in quantile models, but this significant effect was observed for only the 10th and 50th quantile levels of BMI. The functional regression models allow for additional interpretations of the influence of EE patterns on age-and sex-adjusted BMI, whereas the quanti","PeriodicalId":36662,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":"10 ","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11874168/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143543812","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-01-01Epub Date: 2024-07-11DOI: 10.3389/fams.2024.1403901
Juan Xie, Kyeong Joo Jung, Carter Allen, Yuzhou Chang, Subhadeep Paul, Zihai Li, Qin Ma, Dongjun Chung
Introduction: The advent of high throughput spatial transcriptomics (HST) has allowed for unprecedented characterization of spatially distinct cell communities within a tissue sample. While a wide range of computational tools exist for detecting cell communities in HST data, none allow for the characterization of community connectivity, i.e., the relative similarity of cells within and between found communities-an analysis task that can elucidate cellular dynamics in important settings such as the tumor microenvironment.
Methods: To address this gap, we introduce the analysis of community connectivity (ACC), which facilitates understanding of the relative similarity of cells within and between communities. We develop a Bayesian multi-layer network model called BANYAN for the integration of spatial and gene expression information to achieve ACC.
Results: We demonstrate BANYAN's ability to recover community connectivity structure via a simulation study based on real sagittal mouse brain HST data. Next, we use BANYAN to implement ACC across a wide range of real data scenarios, including 10× Visium data of melanoma brain metastases and invasive ductal carcinoma, and NanoString CosMx data of human-small-cell lung cancer, each of which reveals distinct cliques of interacting cell sub-populations. An R package banyan is available at https://github.com/dongjunchung/banyan.
{"title":"Analysis of community connectivity in spatial transcriptomics data.","authors":"Juan Xie, Kyeong Joo Jung, Carter Allen, Yuzhou Chang, Subhadeep Paul, Zihai Li, Qin Ma, Dongjun Chung","doi":"10.3389/fams.2024.1403901","DOIUrl":"10.3389/fams.2024.1403901","url":null,"abstract":"<p><strong>Introduction: </strong>The advent of high throughput spatial transcriptomics (HST) has allowed for unprecedented characterization of spatially distinct cell communities within a tissue sample. While a wide range of computational tools exist for detecting cell communities in HST data, none allow for the characterization of community connectivity, i.e., the relative similarity of cells within and between found communities-an analysis task that can elucidate cellular dynamics in important settings such as the tumor microenvironment.</p><p><strong>Methods: </strong>To address this gap, we introduce the analysis of community connectivity (ACC), which facilitates understanding of the relative similarity of cells within and between communities. We develop a Bayesian multi-layer network model called BANYAN for the integration of spatial and gene expression information to achieve ACC.</p><p><strong>Results: </strong>We demonstrate BANYAN's ability to recover community connectivity structure via a simulation study based on real sagittal mouse brain HST data. Next, we use BANYAN to implement ACC across a wide range of real data scenarios, including 10× Visium data of melanoma brain metastases and invasive ductal carcinoma, and NanoString CosMx data of human-small-cell lung cancer, each of which reveals distinct cliques of interacting cell sub-populations. An R package banyan is available at https://github.com/dongjunchung/banyan.</p>","PeriodicalId":36662,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":"10 ","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12140621/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144235459","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-19DOI: 10.3389/fams.2023.1282544
Jemal Muhammed Ahmed, Getachew Teshome Tilahun, Shambel Tadesse Degefa
Malaria is an infectious disease caused by intracellular parasites of the genus Plasmodium. It is a major health problem around the world. In this study, a cell-level mathematical model of malaria parasites with antimalarial drug treatments is formulated and analyzed. The model consists of seven compartments for cell populations. We analyzed the qualitative behavior of the model using various techniques. The stability analysis of the parasite-free equilibrium is obtained, whereas it is locally and globally stable if the basic reproduction number R0<1. The parasite persistence equilibrium point exists, and it is locally asymptotically stable if R0>1. The sensitivity analysis of the basic reproduction number is computed, and the results show that the infection rate of the erythrocyte by merozoites, the average number of merozoites per ruptured infected erythrocyte cells, the natural death rate of merozoites, and the requirement rate of the uninfected erythrocyte are the most influential parameters within-host dynamics of malaria infection. Different numerical simulations are performed to supplement our analytical findings. The effect of primary tissue schizontocides, blood schizontocides, and gametocytocides on infected hepatocytes, infected erythrocytes, and gametocytes have been investigated, respectively. Finally, some counterplots are presented in order to investigate the impact of parameters on the basic reproduction number. The in-host basic reproduction number decreases as the antimalarial treatment administration increases. Therefore, increasing antimalarial treatment administration is the best way to mitigate the in-host malaria infection.
{"title":"A cell-level dynamical model for malaria parasite infection with antimalarial drug treatment","authors":"Jemal Muhammed Ahmed, Getachew Teshome Tilahun, Shambel Tadesse Degefa","doi":"10.3389/fams.2023.1282544","DOIUrl":"https://doi.org/10.3389/fams.2023.1282544","url":null,"abstract":"Malaria is an infectious disease caused by intracellular parasites of the genus Plasmodium. It is a major health problem around the world. In this study, a cell-level mathematical model of malaria parasites with antimalarial drug treatments is formulated and analyzed. The model consists of seven compartments for cell populations. We analyzed the qualitative behavior of the model using various techniques. The stability analysis of the parasite-free equilibrium is obtained, whereas it is locally and globally stable if the basic reproduction number R0<1. The parasite persistence equilibrium point exists, and it is locally asymptotically stable if R0>1. The sensitivity analysis of the basic reproduction number is computed, and the results show that the infection rate of the erythrocyte by merozoites, the average number of merozoites per ruptured infected erythrocyte cells, the natural death rate of merozoites, and the requirement rate of the uninfected erythrocyte are the most influential parameters within-host dynamics of malaria infection. Different numerical simulations are performed to supplement our analytical findings. The effect of primary tissue schizontocides, blood schizontocides, and gametocytocides on infected hepatocytes, infected erythrocytes, and gametocytes have been investigated, respectively. Finally, some counterplots are presented in order to investigate the impact of parameters on the basic reproduction number. The in-host basic reproduction number decreases as the antimalarial treatment administration increases. Therefore, increasing antimalarial treatment administration is the best way to mitigate the in-host malaria infection.","PeriodicalId":36662,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":" 34","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138962081","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-19DOI: 10.3389/fams.2023.1294540
H. Poorhemati, Svetlana V. Komarova
Formation of hydroxyapatite in bone, dentin, and enamel occurs at restricted molecular sites of specific extracellular matrix proteins and is controlled by multiple mineralization inhibitors. However, the role of physicochemical factors, such as the availability of required ions and the saturation status of the aqueous environment in biological mineralization, is not fully understood. The goal of this study was to use mathematical modeling to describe the complex physicochemical environment permissive to the precipitation of biological hydroxyapatite.We simulated the processes occurring in the bone interstitial fluid (ISF) defined as an aqueous environment containing seven chemical components (calcium, phosphate, carbonate, sodium, potassium, magnesium, and chloride) that form 30 chemical species. We simulated reversible equilibrium reactions among these chemical species, and calculated supersaturation for hydroxyapatite and its precipitation rate using kinetic theory.The simulated ISF was of correct ionic strength and predicted the equilibrium component concentrations that were consistent with the experimental findings. Supersaturation of physiological ISF was ~15, which is consistent with prior findings that mineralization inhibitors are required to prevent spontaneous mineral precipitation. Only total calcium, total phosphate and to a lesser degree total carbonate affected ion availability, solution supersaturation and hydroxyapatite precipitation rate. Both calcium and phosphate levels directly affected hydroxyapatite precipitation, and phosphate was affected by pH, which additionally influenced hydroxyapatite precipitation. Integrating mathematical models capturing the physiochemical and biological factors regulating bone mineralization will allow in silico studies of complex clinical scenarios associated with alterations in ISF ion composition, such as rickets, hypophosphatemia, and chronic kidney disease.
{"title":"Mathematical model of physicochemical regulation of precipitation of bone hydroxyapatite","authors":"H. Poorhemati, Svetlana V. Komarova","doi":"10.3389/fams.2023.1294540","DOIUrl":"https://doi.org/10.3389/fams.2023.1294540","url":null,"abstract":"Formation of hydroxyapatite in bone, dentin, and enamel occurs at restricted molecular sites of specific extracellular matrix proteins and is controlled by multiple mineralization inhibitors. However, the role of physicochemical factors, such as the availability of required ions and the saturation status of the aqueous environment in biological mineralization, is not fully understood. The goal of this study was to use mathematical modeling to describe the complex physicochemical environment permissive to the precipitation of biological hydroxyapatite.We simulated the processes occurring in the bone interstitial fluid (ISF) defined as an aqueous environment containing seven chemical components (calcium, phosphate, carbonate, sodium, potassium, magnesium, and chloride) that form 30 chemical species. We simulated reversible equilibrium reactions among these chemical species, and calculated supersaturation for hydroxyapatite and its precipitation rate using kinetic theory.The simulated ISF was of correct ionic strength and predicted the equilibrium component concentrations that were consistent with the experimental findings. Supersaturation of physiological ISF was ~15, which is consistent with prior findings that mineralization inhibitors are required to prevent spontaneous mineral precipitation. Only total calcium, total phosphate and to a lesser degree total carbonate affected ion availability, solution supersaturation and hydroxyapatite precipitation rate. Both calcium and phosphate levels directly affected hydroxyapatite precipitation, and phosphate was affected by pH, which additionally influenced hydroxyapatite precipitation. Integrating mathematical models capturing the physiochemical and biological factors regulating bone mineralization will allow in silico studies of complex clinical scenarios associated with alterations in ISF ion composition, such as rickets, hypophosphatemia, and chronic kidney disease.","PeriodicalId":36662,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":" 28","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138961401","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-18DOI: 10.3389/fams.2023.1261270
A. Appadu, A. Kelil
The time-fractional Korteweg de Vries equation can be viewed as a generalization of the classical KdV equation. The KdV equations can be applied in modeling tsunami propagation, coastal wave dynamics, and oceanic wave interactions. In this study, we construct two standard finite difference methods using finite difference methods with conformable and Caputo approximations to solve a time-fractional Korteweg-de Vries (KdV) equation. These two methods are named as FDMCA and FDMCO. FDMCA utilizes Caputo's derivative and a finite-forward difference approach for discretization, while FDMCO employs conformable discretization. To study the stability, we use the Von Neumann Stability Analysis for some fractional parameter values. We perform error analysis using L1 & L∞ norms and relative errors, and we present results through graphical representations and tables. Our obtained results demonstrate strong agreement between numerical and exact solutions when the fractional operator is close to 1.0 for both methods. Generally, this study enhances our comprehension of the capabilities and constraints of FDMCO and FDMCA when used to solve such types of partial differential equations laying some ground for further research.
{"title":"Some finite difference methods for solving linear fractional KdV equation","authors":"A. Appadu, A. Kelil","doi":"10.3389/fams.2023.1261270","DOIUrl":"https://doi.org/10.3389/fams.2023.1261270","url":null,"abstract":"The time-fractional Korteweg de Vries equation can be viewed as a generalization of the classical KdV equation. The KdV equations can be applied in modeling tsunami propagation, coastal wave dynamics, and oceanic wave interactions. In this study, we construct two standard finite difference methods using finite difference methods with conformable and Caputo approximations to solve a time-fractional Korteweg-de Vries (KdV) equation. These two methods are named as FDMCA and FDMCO. FDMCA utilizes Caputo's derivative and a finite-forward difference approach for discretization, while FDMCO employs conformable discretization. To study the stability, we use the Von Neumann Stability Analysis for some fractional parameter values. We perform error analysis using L1 & L∞ norms and relative errors, and we present results through graphical representations and tables. Our obtained results demonstrate strong agreement between numerical and exact solutions when the fractional operator is close to 1.0 for both methods. Generally, this study enhances our comprehension of the capabilities and constraints of FDMCO and FDMCA when used to solve such types of partial differential equations laying some ground for further research.","PeriodicalId":36662,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":" 20","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138995128","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-12DOI: 10.3389/fams.2023.1260187
Euis Asriani, I. Muchtadi-Alamsyah, Ayu Purwarianti
In the encoding and decoding process of transformer neural networks, a weight matrix-vector multiplication occurs in each multihead attention and feed forward sublayer. Assigning the appropriate weight matrix and algorithm can improve transformer performance, especially for machine translation tasks. In this study, we investigate the use of the real block-circulant matrices and an alternative to the commonly used fast Fourier transform (FFT) algorithm, namely, the discrete cosine transform–discrete sine transform (DCT-DST) algorithm, to be implemented in a transformer. We explore three transformer models that combine the use of real block-circulant matrices with different algorithms. We start from generating two orthogonal matrices, U and Q. The matrix U is spanned by the combination of the reals and imaginary parts of eigenvectors of the real block-circulant matrix, whereas Q is defined such that the matrix multiplication QU can be represented in the shape of a DCT-DST matrix. The final step is defining the Schur form of the real block-circulant matrix. We find that the matrix-vector multiplication using the DCT-DST algorithm can be defined by assigning the Kronecker product between the DCT-DST matrix and an orthogonal matrix in the same order as the dimension of the circulant matrix that spanned the real block circulant. According to the experiment's findings, the dense-real block circulant DCT-DST model with largest matrix dimension was able to reduce the number of model parameters up to 41%. The same model of 128 matrix dimension gained 26.47 of BLEU score, higher compared to the other two models on the same matrix dimensions.
{"title":"Real block-circulant matrices and DCT-DST algorithm for transformer neural network","authors":"Euis Asriani, I. Muchtadi-Alamsyah, Ayu Purwarianti","doi":"10.3389/fams.2023.1260187","DOIUrl":"https://doi.org/10.3389/fams.2023.1260187","url":null,"abstract":"In the encoding and decoding process of transformer neural networks, a weight matrix-vector multiplication occurs in each multihead attention and feed forward sublayer. Assigning the appropriate weight matrix and algorithm can improve transformer performance, especially for machine translation tasks. In this study, we investigate the use of the real block-circulant matrices and an alternative to the commonly used fast Fourier transform (FFT) algorithm, namely, the discrete cosine transform–discrete sine transform (DCT-DST) algorithm, to be implemented in a transformer. We explore three transformer models that combine the use of real block-circulant matrices with different algorithms. We start from generating two orthogonal matrices, U and Q. The matrix U is spanned by the combination of the reals and imaginary parts of eigenvectors of the real block-circulant matrix, whereas Q is defined such that the matrix multiplication QU can be represented in the shape of a DCT-DST matrix. The final step is defining the Schur form of the real block-circulant matrix. We find that the matrix-vector multiplication using the DCT-DST algorithm can be defined by assigning the Kronecker product between the DCT-DST matrix and an orthogonal matrix in the same order as the dimension of the circulant matrix that spanned the real block circulant. According to the experiment's findings, the dense-real block circulant DCT-DST model with largest matrix dimension was able to reduce the number of model parameters up to 41%. The same model of 128 matrix dimension gained 26.47 of BLEU score, higher compared to the other two models on the same matrix dimensions.","PeriodicalId":36662,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":"52 14","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139007024","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-11DOI: 10.3389/fams.2023.1144142
Luca Mechelli, Jan Rohleff, Stefan Volkwein
In the present article, optimal control problems for linear parabolic partial differential equations (PDEs) with time-dependent coefficient functions are considered. One of the common approach in literature is to derive the first-order sufficient optimality system and to apply a finite element (FE) discretization. This leads to a specific linear but high-dimensional time variant (LTV) dynamical system. To reduce the size of the LTV system, we apply a tailored reduced order modeling technique based on empirical gramians and derived directly from the first-order optimality system. For testing purpose, we focus on two specific examples: a multiobjective optimization and a closed-loop optimal control problem. Our proposed methodology results to be better performing than a standard proper orthogonal decomposition (POD) approach for the above mentioned examples.
{"title":"Model order reduction for optimality systems through empirical gramians","authors":"Luca Mechelli, Jan Rohleff, Stefan Volkwein","doi":"10.3389/fams.2023.1144142","DOIUrl":"https://doi.org/10.3389/fams.2023.1144142","url":null,"abstract":"In the present article, optimal control problems for linear parabolic partial differential equations (PDEs) with time-dependent coefficient functions are considered. One of the common approach in literature is to derive the first-order sufficient optimality system and to apply a finite element (FE) discretization. This leads to a specific linear but high-dimensional time variant (LTV) dynamical system. To reduce the size of the LTV system, we apply a tailored reduced order modeling technique based on empirical gramians and derived directly from the first-order optimality system. For testing purpose, we focus on two specific examples: a multiobjective optimization and a closed-loop optimal control problem. Our proposed methodology results to be better performing than a standard proper orthogonal decomposition (POD) approach for the above mentioned examples.","PeriodicalId":36662,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":"11 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138979390","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-08DOI: 10.3389/fams.2023.1274846
Masahiro Okada, Hiroshi Ito
Speaker recognition has been performed by considering individual variations in the power spectrograms of speech, which reflect the resonance phenomena in the speaker's vocal tract filter. In recent years, phase-based features have been used for speaker recognition. However, the phase-based features are not in a raw form of the phase but are crafted by humans, suggesting that the role of the raw phase is less interpretable. This study used phase spectrograms, which are calculated by subtracting the phase in the time-frequency domain of the electroglottograph signal from that of speech. The phase spectrograms represent the non-modified phase characteristics of the vocal tract filter.The phase spectrograms were obtained from five Japanese participants. Phase spectrograms corresponding to vowels, called phase spectra, were then extracted and circular-averaged for each vowel. The speakers were determined based on the degree of similarity of the averaged spectra.The accuracy of discriminating speakers using the averaged phase spectra was observed to be high although speakers were discriminated using only phase information without power. In particular, the averaged phase spectra showed different shapes for different speakers, resulting in the similarity between the different speaker spectrum pairs being lower. Therefore, the speakers were distinguished by using phase spectra.This predominance of phase spectra suggested that the phase characteristics of the vocal tract filter reflect the individuality of speakers.
{"title":"Phase characteristics of vocal tract filter can distinguish speakers","authors":"Masahiro Okada, Hiroshi Ito","doi":"10.3389/fams.2023.1274846","DOIUrl":"https://doi.org/10.3389/fams.2023.1274846","url":null,"abstract":"Speaker recognition has been performed by considering individual variations in the power spectrograms of speech, which reflect the resonance phenomena in the speaker's vocal tract filter. In recent years, phase-based features have been used for speaker recognition. However, the phase-based features are not in a raw form of the phase but are crafted by humans, suggesting that the role of the raw phase is less interpretable. This study used phase spectrograms, which are calculated by subtracting the phase in the time-frequency domain of the electroglottograph signal from that of speech. The phase spectrograms represent the non-modified phase characteristics of the vocal tract filter.The phase spectrograms were obtained from five Japanese participants. Phase spectrograms corresponding to vowels, called phase spectra, were then extracted and circular-averaged for each vowel. The speakers were determined based on the degree of similarity of the averaged spectra.The accuracy of discriminating speakers using the averaged phase spectra was observed to be high although speakers were discriminated using only phase information without power. In particular, the averaged phase spectra showed different shapes for different speakers, resulting in the similarity between the different speaker spectrum pairs being lower. Therefore, the speakers were distinguished by using phase spectra.This predominance of phase spectra suggested that the phase characteristics of the vocal tract filter reflect the individuality of speakers.","PeriodicalId":36662,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":"30 38","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138588856","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-07DOI: 10.3389/fams.2023.1292443
Isaac Mwangi Wangari, Samson Olaniyi, R. Lebelo, K. Okosun
The unexpected emergence of novel coronavirus identified as SAR-CoV-2 virus (severe acute respiratory syndrome corona virus 2) disrupted the world order to an extent that the human activities that are core to survival came almost to a halt. The COVID-19 pandemic created an insurmountable global health crisis that led to a united front among all nations to research on effective pharmaceutical measures that could stop COVID-19 proliferation. Consequently, different types of vaccines were discovered (single-dose and double-dose vaccines). However, the speed at which these vaccines were developed and approved to be administered created other challenges (vaccine skepticism and hesitancy).This paper therefore tracks the transmission dynamics of COVID-19 using a non-linear deterministic system that accounts for the unwillingness of both susceptible and partially vaccinated individuals to receive either single-dose or double-dose vaccines (vaccine hesitancy). Further the model is extended to incorporate three time-dependent non-pharmaceutical and pharmaceutical intervention controls, namely preventive control, control associated with screening-management of both truly asymptomatic and symptomatic infectious individuals and control associated with vaccination of susceptible individuals with a single dose vaccine. The Pontryagin's Maximum Principle is applied to establish the optimality conditions associated with the optimal controls.If COVID-19 vaccines administered are imperfect and transient then there exist a parameter space where backward bifurcation occurs. Time profile projections depict that in a setting where vaccine hesitancy is present, administering single dose vaccines leads to a significant reduction of COVID-19 prevalence than when double dose vaccines are administered. Comparison of the impact of vaccine hesitancy against either single dose or double dose on COVID-19 prevalence reveals that vaccine hesitancy against single dose is more detrimental than vaccine hesitancy against a double dose vaccine. Optimal analysis results reveal that non-pharmaceutical time-dependent control significantly flattens the COVID-19 epidemic curve when compared with pharmaceutical controls. Cost-effectiveness assessment suggest that non-pharmaceutical control is the most cost-effective COVID-19 mitigation strategy that should be implemented in a setting where resources are limited.Policy makers and medical practitioners should assess the level of COVID-19 vaccine hesitancy inorder to decide on the type of vaccine (single-dose or double-dose) to administer to the population.
{"title":"Transmission of COVID-19 in the presence of single-dose and double-dose vaccines with hesitancy: mathematical modeling and optimal control analysis","authors":"Isaac Mwangi Wangari, Samson Olaniyi, R. Lebelo, K. Okosun","doi":"10.3389/fams.2023.1292443","DOIUrl":"https://doi.org/10.3389/fams.2023.1292443","url":null,"abstract":"The unexpected emergence of novel coronavirus identified as SAR-CoV-2 virus (severe acute respiratory syndrome corona virus 2) disrupted the world order to an extent that the human activities that are core to survival came almost to a halt. The COVID-19 pandemic created an insurmountable global health crisis that led to a united front among all nations to research on effective pharmaceutical measures that could stop COVID-19 proliferation. Consequently, different types of vaccines were discovered (single-dose and double-dose vaccines). However, the speed at which these vaccines were developed and approved to be administered created other challenges (vaccine skepticism and hesitancy).This paper therefore tracks the transmission dynamics of COVID-19 using a non-linear deterministic system that accounts for the unwillingness of both susceptible and partially vaccinated individuals to receive either single-dose or double-dose vaccines (vaccine hesitancy). Further the model is extended to incorporate three time-dependent non-pharmaceutical and pharmaceutical intervention controls, namely preventive control, control associated with screening-management of both truly asymptomatic and symptomatic infectious individuals and control associated with vaccination of susceptible individuals with a single dose vaccine. The Pontryagin's Maximum Principle is applied to establish the optimality conditions associated with the optimal controls.If COVID-19 vaccines administered are imperfect and transient then there exist a parameter space where backward bifurcation occurs. Time profile projections depict that in a setting where vaccine hesitancy is present, administering single dose vaccines leads to a significant reduction of COVID-19 prevalence than when double dose vaccines are administered. Comparison of the impact of vaccine hesitancy against either single dose or double dose on COVID-19 prevalence reveals that vaccine hesitancy against single dose is more detrimental than vaccine hesitancy against a double dose vaccine. Optimal analysis results reveal that non-pharmaceutical time-dependent control significantly flattens the COVID-19 epidemic curve when compared with pharmaceutical controls. Cost-effectiveness assessment suggest that non-pharmaceutical control is the most cost-effective COVID-19 mitigation strategy that should be implemented in a setting where resources are limited.Policy makers and medical practitioners should assess the level of COVID-19 vaccine hesitancy inorder to decide on the type of vaccine (single-dose or double-dose) to administer to the population.","PeriodicalId":36662,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":"16 7","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138591655","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-07DOI: 10.3389/fams.2023.1274787
Yuhe Wang, Eugene Pinsky
Triangular distributions are widely used in many applications with limited sample data, business simulations, and project management. As with other distributions, a standard way to measure deviations is to compute the standard deviation. However, the standard deviation is sensitive to outliers. In this paper, we consider and compare other deviation metrics, namely the mean absolute deviation from the mean, the median, and the quantile-based deviation. We show the simple geometric interpretations for these deviation measures and how to construct them using a compass and a straightedge. The explicit formula of mean absolute deviation from the median for triangular distribution is derived in this paper for the first time. It has a simple geometric interpretation. It is the least volatile and is always better than the standard or mean absolute deviation from the mean. Although greater than the quantile deviation, it is easier to compute with limited sample data. We present a new procedure to estimate the parameters of this distribution in terms of this deviation. This procedure is computationally simple and may be superior to other methods when dealing with limited sample data, as is often the case with triangle distributions.
{"title":"Geometry of deviation measures for triangular distributions","authors":"Yuhe Wang, Eugene Pinsky","doi":"10.3389/fams.2023.1274787","DOIUrl":"https://doi.org/10.3389/fams.2023.1274787","url":null,"abstract":"Triangular distributions are widely used in many applications with limited sample data, business simulations, and project management. As with other distributions, a standard way to measure deviations is to compute the standard deviation. However, the standard deviation is sensitive to outliers. In this paper, we consider and compare other deviation metrics, namely the mean absolute deviation from the mean, the median, and the quantile-based deviation. We show the simple geometric interpretations for these deviation measures and how to construct them using a compass and a straightedge. The explicit formula of mean absolute deviation from the median for triangular distribution is derived in this paper for the first time. It has a simple geometric interpretation. It is the least volatile and is always better than the standard or mean absolute deviation from the mean. Although greater than the quantile deviation, it is easier to compute with limited sample data. We present a new procedure to estimate the parameters of this distribution in terms of this deviation. This procedure is computationally simple and may be superior to other methods when dealing with limited sample data, as is often the case with triangle distributions.","PeriodicalId":36662,"journal":{"name":"Frontiers in Applied Mathematics and Statistics","volume":"23 5","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138594160","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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