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Nonlinear ill-posed problem in low-dose dental cone-beam computed tomography 低剂量牙锥束计算机断层扫描的非线性不适定问题
4区 数学
IMA Journal of Applied Mathematics Pub Date : 2023-06-23 DOI: 10.1093/imamat/hxad016
Hyoung Suk Park, Chang Min Hyun, Jin Keun Seo
{"title":"Nonlinear ill-posed problem in low-dose dental cone-beam computed tomography","authors":"Hyoung Suk Park, Chang Min Hyun, Jin Keun Seo","doi":"10.1093/imamat/hxad016","DOIUrl":"https://doi.org/10.1093/imamat/hxad016","url":null,"abstract":"Abstract This paper describes the mathematical structure of the ill-posed nonlinear inverse problem of low-dose dental cone-beam computed tomography (CBCT) and explains the advantages of a deep learning-based approach to the reconstruction of computed tomography images over conventional regularization methods. This paper explains the underlying reasons why dental CBCT is more ill-posed than standard computed tomography. Despite this severe ill-posedness, the demand for dental CBCT systems is rapidly growing because of their cost competitiveness and low radiation dose. We then describe the limitations of existing methods in the accurate restoration of the morphological structures of teeth using dental CBCT data severely damaged by metal implants. We further discuss the usefulness of panoramic images generated from CBCT data for accurate tooth segmentation. We also discuss the possibility of utilizing radiation-free intra-oral scan data as prior information in CBCT image reconstruction to compensate for the damage to data caused by metal implants.","PeriodicalId":56297,"journal":{"name":"IMA Journal of Applied Mathematics","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135999983","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Stability of fixed points in an approximate solution of the spring-mass running model 弹簧-质量运行模型近似解中不动点的稳定性
4区 数学
IMA Journal of Applied Mathematics Pub Date : 2023-04-12 DOI: 10.1093/imamat/hxad014
Zofia Wróblewska, Piotr Kowalczyk, Łukasz Płociniczak
{"title":"Stability of fixed points in an approximate solution of the spring-mass running model","authors":"Zofia Wróblewska, Piotr Kowalczyk, Łukasz Płociniczak","doi":"10.1093/imamat/hxad014","DOIUrl":"https://doi.org/10.1093/imamat/hxad014","url":null,"abstract":"Abstract We consider a classical spring-mass model of human running which is built upon an inverted elastic pendulum. Based on previous results concerning asymptotic solutions for large spring constant (or small angle of attack), we introduce an analytical approximation of a reduced mapping. Although approximate solutions already exist in the literature, our results have some benefits over them. They give us an advantage of being able to explicitly control the error of the approximation in terms of the small parameter, which has a physical meaning—the inverse of the square-root of the spring constant. Our approximation also shows how the solutions are asymptotically related to the magnitude of attack angle $alpha $. The model itself consists of two sets of differential equations—one set describes the motion of the centre of mass of a runner in contact with the ground (support phase), and the second set describes the phase of no contact with the ground (flight phase). By appropriately concatenating asymptotic solutions for the two phases we are able to reduce the dynamics to a one-dimensional apex to apex return map. We find sufficient conditions for this map to have a unique stable fixed point. By numerical continuation of fixed points with respect to energy, we find a transcritical bifurcation in our model system.","PeriodicalId":56297,"journal":{"name":"IMA Journal of Applied Mathematics","volume":"278 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134951306","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On a hierarchy of effective models for the biomechanics of human compact bone tissue 人体致密骨组织生物力学有效模型的层次结构
IF 1.2 4区 数学
IMA Journal of Applied Mathematics Pub Date : 2023-04-04 DOI: 10.1093/imamat/hxad011
Grigor Nika
{"title":"On a hierarchy of effective models for the biomechanics of human compact bone tissue","authors":"Grigor Nika","doi":"10.1093/imamat/hxad011","DOIUrl":"https://doi.org/10.1093/imamat/hxad011","url":null,"abstract":"\u0000 We derive a hierarchy of effective models that can be used to model the biomechanics of human compact bone taking into account scale-size effects observed experimentally. The classification of the effective models depends on the hierarchy of four characteristic lengths: The size of the heterogeneities, two intrinsic lengths of the constituents, and the overall characteristic length of the domain. Depending on the different scale interactions between the size of the heterogeneities, the two intrinsic lengths of the constituents, and the characteristic length of the domain we obtain either an effective Cauchy continuum or an effective Cosserat continuum. The passage to the limit relies on suitable use of the periodic unfolding operator. Moreover, we perform numerical simulations to validate our results.","PeriodicalId":56297,"journal":{"name":"IMA Journal of Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46772191","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Dynamics of an age-structured HIV model with general nonlinear infection rate 具有一般非线性感染率的年龄结构HIV模型的动力学
IF 1.2 4区 数学
IMA Journal of Applied Mathematics Pub Date : 2023-04-04 DOI: 10.1093/imamat/hxad010
Yuan Yuan, Xianlong Fu
{"title":"Dynamics of an age-structured HIV model with general nonlinear infection rate","authors":"Yuan Yuan, Xianlong Fu","doi":"10.1093/imamat/hxad010","DOIUrl":"https://doi.org/10.1093/imamat/hxad010","url":null,"abstract":"\u0000 In this paper, the asymptotical behavior of an age-structured HIV infection model with general nonlinear infection function and logistic proliferation term is studied. Based on the existence of the equilibria and theory of operator semigroups, linearized stability/instability of the disease-free and endemic equilibria are investigated through the distribution of eigenvalues of the linear operator. Then persistence of the solution semi-flow of the considered system is studied by showing the existence of a global attractor and the obtained result shows that the solution semi-flow is persistent as long as the basic reproduction number $R_0>1$. Moreover, Hopf bifurcations problem around the endemic equilibrium is also considered for the situation with a specific infection function. Since the system has two different delays, four cases are discussed to investigate the influence of the time delays on the dynamics of system around the endemic equilibrium including stability and Hopf bifurcations. At last, some numerical examples with concrete parameters are provided to illustrate the obtained results.","PeriodicalId":56297,"journal":{"name":"IMA Journal of Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41729063","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Identifying a response parameter in a model of brain tumor evolution under therapy 确定治疗下脑肿瘤进化模型中的反应参数
IF 1.2 4区 数学
IMA Journal of Applied Mathematics Pub Date : 2023-04-04 DOI: 10.1093/imamat/hxad013
{"title":"Identifying a response parameter in a model of brain tumor evolution under therapy","authors":"","doi":"10.1093/imamat/hxad013","DOIUrl":"https://doi.org/10.1093/imamat/hxad013","url":null,"abstract":"\u0000 A nonlinear conjugate gradient method is derived for the inverse problem of identifying a treatment parameter in a nonlinear model of reaction-diffusion type corresponding to the evolution of brain tumors under therapy. The treatment parameter is reconstructed from additional information about the tumour taken at a fixed instance of time. Well-posedness of the direct problems used in the iterative method is outlined as well as uniqueness of a solution to the inverse problem. Moreover, the parameter identification is recast as the minimization of a Tikhonov type functional and the existence of a minimizer to this functional is shown. Finite difference discretization of the space and time derivatives are employed for the numerical implementation. Numerical simulations on full 3-dimensional brain data is included showing that information about a spacewise dependent treatment parameter can be recovered in a stable way.","PeriodicalId":56297,"journal":{"name":"IMA Journal of Applied Mathematics","volume":"1 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"61109929","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Global threshold dynamics of a spatial chemotactic mosquito-borne disease model 空间趋化性蚊媒疾病模型的全局阈值动力学
IF 1.2 4区 数学
IMA Journal of Applied Mathematics Pub Date : 2023-04-04 DOI: 10.1093/imamat/hxad009
Kai Wang, Hao Wang, Hongyong Zhao
{"title":"Global threshold dynamics of a spatial chemotactic mosquito-borne disease model","authors":"Kai Wang, Hao Wang, Hongyong Zhao","doi":"10.1093/imamat/hxad009","DOIUrl":"https://doi.org/10.1093/imamat/hxad009","url":null,"abstract":"\u0000 It is natural that mosquitoes move toward high human population density and environmental heterogeneity plays a pivotal role on disease transmission, and thus we formulate and analyze a mosquito-borne disease model with chemotaxis and spatial heterogeneity. The global existence and boundedness of solutions are proven to guarantee the solvability of the model and is challenging due to the model complexity. Under appropriate conditions, we demonstrate the disease-free equilibrium is globally asymptotically stable provided that the basic reproduction number $mathcal {R}_0$ is less than one, and the system is uniformly persistent and admits at least one endemic equilibrium if $mathcal {R}_0$ is greater than one. Furthermore, we numerically explore the impacts of chemotactic effect, spatial heterogeneity and dispersal rates of infected individuals to provide a clear picture on disease severity. In particular, the mosquito chemotaxis causes disease mild in some regions but severe in others, which suggests developing targeted strategies to control mosquitoes in specific locations and achieves a deep understanding on the chemotaxis.","PeriodicalId":56297,"journal":{"name":"IMA Journal of Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46031581","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Scattering in a partially open waveguide: the forward problem 部分开放波导中的散射：前向问题
IF 1.2 4区 数学
IMA Journal of Applied Mathematics Pub Date : 2023-02-02 DOI: 10.1093/imamat/hxad004
L. Bourgeois, S. Fliss, Jean-François Fritsch, C. Hazard, A. Recoquillay
{"title":"Scattering in a partially open waveguide: the forward problem","authors":"L. Bourgeois, S. Fliss, Jean-François Fritsch, C. Hazard, A. Recoquillay","doi":"10.1093/imamat/hxad004","DOIUrl":"https://doi.org/10.1093/imamat/hxad004","url":null,"abstract":"\u0000 This paper is dedicated to an acoustic scattering problem in a two-dimensional partially open waveguide, in the sense that the left part of the waveguide is closed, that is with a bounded cross-section, while the right part is bounded in the transverse direction by some Perfectly Matched Layers that mimic the situation of an open waveguide, that is with an unbounded cross-section. We prove well-posedness of such scattering problem in the Fredholm sense (uniqueness implies existence) and exhibit the asymptotic behaviour of the solution in the longitudinal direction with the help of the Kondratiev approach. Having in mind the numerical computation of the solution, we also propose some transparent boundary conditions in such longitudinal direction, based on Dirichlet-to-Neumann operators. After proving that such artificial conditions actually enable us to approximate the exact solution, some numerical experiments illustrate the quality of such approximation.","PeriodicalId":56297,"journal":{"name":"IMA Journal of Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48882379","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Correction to: A degenerating convection–diffusion system modelling froth flotation with drainage 修正:一个退化的对流-扩散系统，模拟了带排水的泡沫浮选
4区 数学
IMA Journal of Applied Mathematics Pub Date : 2023-02-01 DOI: 10.1093/imamat/hxad001
{"title":"Correction to: A degenerating convection–diffusion system modelling froth flotation with drainage","authors":"","doi":"10.1093/imamat/hxad001","DOIUrl":"https://doi.org/10.1093/imamat/hxad001","url":null,"abstract":"","PeriodicalId":56297,"journal":{"name":"IMA Journal of Applied Mathematics","volume":"115 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136297796","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On global in time self-similar solutions of Smoluchowski equation with multiplicative kernel 带乘核的Smoluchowski方程的全局时间自相似解
IF 1.2 4区 数学
IMA Journal of Applied Mathematics Pub Date : 2022-12-23 DOI: 10.1093/imamat/hxad012
G. Breschi, M. Fontelos
{"title":"On global in time self-similar solutions of Smoluchowski equation with multiplicative kernel","authors":"G. Breschi, M. Fontelos","doi":"10.1093/imamat/hxad012","DOIUrl":"https://doi.org/10.1093/imamat/hxad012","url":null,"abstract":"\u0000 We study the similarity solutions (SS) of Smoluchowski coagulation equation with multiplicative kernel $K(x,y)=(xy)^{s}$ for $s<frac {1}{2}$. When $s<0$ , the SS consists of three regions with distinct asymptotic behaviours. The appropriate matching yields a global description of the solution consisting of a Gamma distribution tail, an intermediate region described by a lognormal distribution and a region of very fast decay of the solutions to zero near the origin. When $sin left ( 0,frac {1}{2}right ) $, the SS is unbounded at the origin. It also presents three regions: a Gamma distribution tail, an intermediate region of power-like (or Pareto distribution) decay and the region close to the origin where a singularity occurs. Finally, full numerical simulations of Smoluchowski equation serve to verify our theoretical results and show the convergence of solutions to the selfsimilar regime.","PeriodicalId":56297,"journal":{"name":"IMA Journal of Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2022-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44728371","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Numerical methods and hypoexponential approximations for gamma distributed delay differential equations. 分布延迟微分方程的数值方法和次指数逼近。
IF 1.2 4区 数学
IMA Journal of Applied Mathematics Pub Date : 2022-12-13 eCollection Date: 2022-12-01 DOI: 10.1093/imamat/hxac027
Tyler Cassidy, Peter Gillich, Antony R Humphries, Christiaan H van Dorp
{"title":"Numerical methods and hypoexponential approximations for gamma distributed delay differential equations.","authors":"Tyler Cassidy, Peter Gillich, Antony R Humphries, Christiaan H van Dorp","doi":"10.1093/imamat/hxac027","DOIUrl":"10.1093/imamat/hxac027","url":null,"abstract":"<p><p>Gamma distributed delay differential equations (DDEs) arise naturally in many modelling applications. However, appropriate numerical methods for generic gamma distributed DDEs have not previously been implemented. Modellers have therefore resorted to approximating the gamma distribution with an Erlang distribution and using the linear chain technique to derive an equivalent system of ordinary differential equations (ODEs). In this work, we address the lack of appropriate numerical tools for gamma distributed DDEs in two ways. First, we develop a functional continuous Runge-Kutta (FCRK) method to numerically integrate the gamma distributed DDE without resorting to Erlang approximation. We prove the fourth-order convergence of the FCRK method and perform numerical tests to demonstrate the accuracy of the new numerical method. Nevertheless, FCRK methods for infinite delay DDEs are not widely available in existing scientific software packages. As an alternative approach to solving gamma distributed DDEs, we also derive a hypoexponential approximation of the gamma distributed DDE. This hypoexponential approach is a more accurate approximation of the true gamma distributed DDE than the common Erlang approximation but, like the Erlang approximation, can be formulated as a system of ODEs and solved numerically using standard ODE software. Using our FCRK method to provide reference solutions, we show that the common Erlang approximation may produce solutions that are qualitatively different from the underlying gamma distributed DDE. However, the proposed hypoexponential approximations do not have this limitation. Finally, we apply our hypoexponential approximations to perform statistical inference on synthetic epidemiological data to illustrate the utility of the hypoexponential approximation.</p>","PeriodicalId":56297,"journal":{"name":"IMA Journal of Applied Mathematics","volume":"87 6","pages":"1043-1089"},"PeriodicalIF":1.2,"publicationDate":"2022-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9850366/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"10667425","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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