Pharmacokinetic compartment models are the only models that can extract pharmacokinetic parameters from data collected in clinical studies but their estimates lack accuracy, explanations and physiological significance...Pharmacokinetic compartment models are the only models that can extract pharmacokinetic parameters from data collected in clinical studies but their estimates lack accuracy, explanations and physiological significance. The objective of this work was to develop particular solutions to drug concentration and AUC in the form of mathematical series and Heaviside functions for repetitive intermittent infusions in the one- and two-compartment models, as a function of dose number and total time using differential calculus. It was demonstrated that the central and peripheral compartment volumes determined from regression analysis of the aminoglycoside antibiotic Sisomicin concentration in plasma represent the actual physiological body fluid volumes accessible by the drug. The drug peak time and peak concentration in the peripheral compartment were also calculated as a function of dose number. It is also shown that the time of intercompartmental momentary distribution equilibrium can be used to determine the drug’s apparent volume of distribution within any dosing interval in multi-compartment models. These estimates were used to carry out simulations of plasma drug concentration with time in the one-compartment model. In conclusion, the two-compartment open mammillary pharmacokinetic model was fully explained for the aminoglycoside antibiotic sisomicin through the new concept of the apparent volume of distribution.展开更多
A primordial field Self-interaction Principle, analyzed in Hestenes’ Geometric Calculus, leads to Heaviside’s equations of the gravitomagnetic field. When derived from Einstein’s nonlinear field equations Heaviside...A primordial field Self-interaction Principle, analyzed in Hestenes’ Geometric Calculus, leads to Heaviside’s equations of the gravitomagnetic field. When derived from Einstein’s nonlinear field equations Heaviside’s “linearized” equations are known as the “weak field approximation”. When derived from the primordial field equation, there is no mention of field strength;the assumption that the primordial field was predominant at the big bang rather suggests that ultra-strong fields are governed by the equations. This aspect has physical significance, so we explore the assumption by formulating the gauge field version of Heaviside’s theory. We compare with recent linearized gravity formulations and discuss the significance of differences.展开更多
The Heaviside’s(or Benguela)dolphin(Cephalorhynchus heavisidii)is endemic to the west coast of southern Africa.The present study investigated the population genetic structure across a large portion of the species dis...The Heaviside’s(or Benguela)dolphin(Cephalorhynchus heavisidii)is endemic to the west coast of southern Africa.The present study investigated the population genetic structure across a large portion of the species distribution using mitochondrial control region and nuclear(microsatellite)markers.A total of 395 biopsy skin samples were analyzed;they were collected from free-ranging Heaviside’s dolphins in 7 locations along 1650 km of coast between Table Bay,South Africa and Walvis Bay,Namibia.Both genetic markers rejected the hypothesis of 1 homogenous population but revealed contrasting results in the genetic structuring of putative populations.Mitochondrial DNA suggested either 2 populations or a fine-scale division with 6(sub)populations,while microsatellite markers were indicative of 2 widespread populations with measurable gene flow between them.Neutrality tests and mismatch distribution of the mitochondrial sequences indicated a departure from mutation-drift equilibrium due to a population expansion at the 2 extremes of the geographic range,but not towards the middle of the distribution.These results highlight the importance of evaluating multiple genetic markers to gain reliable insights into population processes and structure.展开更多
The variable density topology optimization(TO)method has been applied to various engineering fields because it can effectively and efficiently generate the conceptual design for engineering structures.However,it suffe...The variable density topology optimization(TO)method has been applied to various engineering fields because it can effectively and efficiently generate the conceptual design for engineering structures.However,it suffers from the problem of low continuity resulting from the discreteness of both design variables and explicit Heaviside filter.In this paper,an implicit Heaviside filter with high continuity is introduced to generate black and white designs for TO where the design space is parameterized by suitably graded truncated hierarchical B-splines(THB).In this approach,the fixed analysis mesh of isogeometric analysis is decoupled from the design mesh,whose adaptivity is implemented by truncated hierarchical B-spline subjected to an admissible requirement.Through the intrinsic local support and high continuity of THB basis,an implicit adaptively adjusted Heaviside filter is obtained to remove the checkboard patterns and generate black and white designs.Threefold advantages are attained in the proposed filter:a)The connection between analysis mesh and adaptive design mesh is easily established compared with the traditional adaptive TO method using nodal density;b)the efficiency in updating design variables is remarkably improved than the traditional implicit sensitivity filter based on B-splines under successive global refinement;and c)the generated black and white designs are preliminarily compatible with current commercial computer aided design system.Several numerical examples are used to verify the effectiveness of the proposed implicit Heaviside filter in compliance and compliant mechanism as well as heat conduction TO problems.展开更多
In this paper we design and analyze a class of high order numerical methods to two dimensional Heaviside function integrals. Inspired by our high order numerical methods to two dimensional delta function integrals [19...In this paper we design and analyze a class of high order numerical methods to two dimensional Heaviside function integrals. Inspired by our high order numerical methods to two dimensional delta function integrals [19], the methods comprise approximating the mesh cell restrictions of the Heaviside function integral. In each mesh cell the two dimen- sional Heaviside function integral can be rewritten as a one dimensional ordinary integral with the integrand being a one dimensional Heaviside function integral which is smooth on several subsets of the integral interval. Thus the two dimensional Heaviside function inte- gral is approximated by applying standard one dimensional high order numerical quadra- tures and high order numerical methods to one dimensional Heaviside function integrals. We establish error estimates for the method which show that the method can achieve any desired accuracy by assigning the corresponding accuracy to the sub-algorithms. Numerical examples are presented showing that the in this paper achieve or exceed the expected second to fourth-order methods implemented accuracy.展开更多
Most material distribution-based topology optimization methods work on a relaxed form of the optimization problem and then push the solution toward the binary limits.However,when benchmarking these methods,researchers...Most material distribution-based topology optimization methods work on a relaxed form of the optimization problem and then push the solution toward the binary limits.However,when benchmarking these methods,researchers use known solutions to only a single form of benchmark problem.This paper proposes a comparison platform for systematic benchmarking of topology optimization methods using both binary and relaxed forms.A greyness measure is implemented to evaluate how far a solution is from the desired binary form.The well-known ZhouRozvany(ZR)problem is selected as the benchmarking problem here,making use of available global solutions for both its relaxed and binary forms.The recently developed non-penalization Smooth-edged Material Distribution for Optimizing Topology(SEMDOT),well-established Solid Isotropic Material with Penalization(SIMP),and continuation methods are studied on this platform.Interestingly,in most cases,the grayscale solutions obtained by SEMDOT demonstrate better performance in dealing with the ZR problem than SIMP.The reasons are investigated and attributed to the usage of two different regularization techniques,namely,the Heaviside smooth function in SEMDOT and the power-law penalty in SIMP.More importantly,a simple-to-use benchmarking graph is proposed for evaluating newly developed topology optimization methods.展开更多
文摘Pharmacokinetic compartment models are the only models that can extract pharmacokinetic parameters from data collected in clinical studies but their estimates lack accuracy, explanations and physiological significance. The objective of this work was to develop particular solutions to drug concentration and AUC in the form of mathematical series and Heaviside functions for repetitive intermittent infusions in the one- and two-compartment models, as a function of dose number and total time using differential calculus. It was demonstrated that the central and peripheral compartment volumes determined from regression analysis of the aminoglycoside antibiotic Sisomicin concentration in plasma represent the actual physiological body fluid volumes accessible by the drug. The drug peak time and peak concentration in the peripheral compartment were also calculated as a function of dose number. It is also shown that the time of intercompartmental momentary distribution equilibrium can be used to determine the drug’s apparent volume of distribution within any dosing interval in multi-compartment models. These estimates were used to carry out simulations of plasma drug concentration with time in the one-compartment model. In conclusion, the two-compartment open mammillary pharmacokinetic model was fully explained for the aminoglycoside antibiotic sisomicin through the new concept of the apparent volume of distribution.
文摘A primordial field Self-interaction Principle, analyzed in Hestenes’ Geometric Calculus, leads to Heaviside’s equations of the gravitomagnetic field. When derived from Einstein’s nonlinear field equations Heaviside’s “linearized” equations are known as the “weak field approximation”. When derived from the primordial field equation, there is no mention of field strength;the assumption that the primordial field was predominant at the big bang rather suggests that ultra-strong fields are governed by the equations. This aspect has physical significance, so we explore the assumption by formulating the gauge field version of Heaviside’s theory. We compare with recent linearized gravity formulations and discuss the significance of differences.
基金SANBI to conduct research on Heaviside’s dolphins(001/2011)the work was conducted under permits from the Department of Environmental Affairs(RES2009/06,RES2010/24,RES2011/70 and RES2012/67)Samples from Namibia were exported under permit from the Ministry of Environment and Tourism(78438,120586 and 138004)。
文摘The Heaviside’s(or Benguela)dolphin(Cephalorhynchus heavisidii)is endemic to the west coast of southern Africa.The present study investigated the population genetic structure across a large portion of the species distribution using mitochondrial control region and nuclear(microsatellite)markers.A total of 395 biopsy skin samples were analyzed;they were collected from free-ranging Heaviside’s dolphins in 7 locations along 1650 km of coast between Table Bay,South Africa and Walvis Bay,Namibia.Both genetic markers rejected the hypothesis of 1 homogenous population but revealed contrasting results in the genetic structuring of putative populations.Mitochondrial DNA suggested either 2 populations or a fine-scale division with 6(sub)populations,while microsatellite markers were indicative of 2 widespread populations with measurable gene flow between them.Neutrality tests and mismatch distribution of the mitochondrial sequences indicated a departure from mutation-drift equilibrium due to a population expansion at the 2 extremes of the geographic range,but not towards the middle of the distribution.These results highlight the importance of evaluating multiple genetic markers to gain reliable insights into population processes and structure.
基金This work was supported by the National Key R&D Program of China(Grant No.2020YFB1708300)China Postdoctoral Science Foundation(Grant No.2021M701310).
文摘The variable density topology optimization(TO)method has been applied to various engineering fields because it can effectively and efficiently generate the conceptual design for engineering structures.However,it suffers from the problem of low continuity resulting from the discreteness of both design variables and explicit Heaviside filter.In this paper,an implicit Heaviside filter with high continuity is introduced to generate black and white designs for TO where the design space is parameterized by suitably graded truncated hierarchical B-splines(THB).In this approach,the fixed analysis mesh of isogeometric analysis is decoupled from the design mesh,whose adaptivity is implemented by truncated hierarchical B-spline subjected to an admissible requirement.Through the intrinsic local support and high continuity of THB basis,an implicit adaptively adjusted Heaviside filter is obtained to remove the checkboard patterns and generate black and white designs.Threefold advantages are attained in the proposed filter:a)The connection between analysis mesh and adaptive design mesh is easily established compared with the traditional adaptive TO method using nodal density;b)the efficiency in updating design variables is remarkably improved than the traditional implicit sensitivity filter based on B-splines under successive global refinement;and c)the generated black and white designs are preliminarily compatible with current commercial computer aided design system.Several numerical examples are used to verify the effectiveness of the proposed implicit Heaviside filter in compliance and compliant mechanism as well as heat conduction TO problems.
文摘In this paper we design and analyze a class of high order numerical methods to two dimensional Heaviside function integrals. Inspired by our high order numerical methods to two dimensional delta function integrals [19], the methods comprise approximating the mesh cell restrictions of the Heaviside function integral. In each mesh cell the two dimen- sional Heaviside function integral can be rewritten as a one dimensional ordinary integral with the integrand being a one dimensional Heaviside function integral which is smooth on several subsets of the integral interval. Thus the two dimensional Heaviside function inte- gral is approximated by applying standard one dimensional high order numerical quadra- tures and high order numerical methods to one dimensional Heaviside function integrals. We establish error estimates for the method which show that the method can achieve any desired accuracy by assigning the corresponding accuracy to the sub-algorithms. Numerical examples are presented showing that the in this paper achieve or exceed the expected second to fourth-order methods implemented accuracy.
文摘Most material distribution-based topology optimization methods work on a relaxed form of the optimization problem and then push the solution toward the binary limits.However,when benchmarking these methods,researchers use known solutions to only a single form of benchmark problem.This paper proposes a comparison platform for systematic benchmarking of topology optimization methods using both binary and relaxed forms.A greyness measure is implemented to evaluate how far a solution is from the desired binary form.The well-known ZhouRozvany(ZR)problem is selected as the benchmarking problem here,making use of available global solutions for both its relaxed and binary forms.The recently developed non-penalization Smooth-edged Material Distribution for Optimizing Topology(SEMDOT),well-established Solid Isotropic Material with Penalization(SIMP),and continuation methods are studied on this platform.Interestingly,in most cases,the grayscale solutions obtained by SEMDOT demonstrate better performance in dealing with the ZR problem than SIMP.The reasons are investigated and attributed to the usage of two different regularization techniques,namely,the Heaviside smooth function in SEMDOT and the power-law penalty in SIMP.More importantly,a simple-to-use benchmarking graph is proposed for evaluating newly developed topology optimization methods.
