The Cox proportional hazard model is being used extensively in oncology in studying the relationship between survival times and prognostic factors. The main question that needs to be addressed with respect to the appl...The Cox proportional hazard model is being used extensively in oncology in studying the relationship between survival times and prognostic factors. The main question that needs to be addressed with respect to the applicability of the Cox PH model is whether the proportional hazard assumption is met. Failure to justify the subject assumption will lead to misleading results. In addition, identifying the correct functional form of the continuous covariates is an important aspect in the development of a Cox proportional hazard model. The purpose of this study is to develop an extended Cox regression model for breast cancer survival data which takes non-proportional hazards and non-linear effects that exist in prognostic factors into consideration. Non-proportional hazards and non-linear effects are detected using methods based on residuals. An extended Cox model with non-linear effects and time-varying effects is proposed to adjust the Cox proportional hazard model. Age and tumor size were found to have nonlinear effects. Progesterone receptor assay status and age violated the proportional hazard assumption in the Cox model. Quadratic effect of age and progesterone receptor assay status had hazard ratio that changes with time. We have introduced a statistical model to overcome the presence of the proportional hazard assumption violation for the Cox proportional hazard model for breast cancer data. The proposed extended model considers the time varying nature of the hazard ratio and non-linear effects of the covariates. Our improved Cox model gives a better insight on the hazard rates associated with the breast cancer risk factors.展开更多
Background: Novel models for the assessment of non-linear data are being developed for the benefit of making better predictions from the data. Objective: To review traditional and modern models. Results, and Conclusio...Background: Novel models for the assessment of non-linear data are being developed for the benefit of making better predictions from the data. Objective: To review traditional and modern models. Results, and Conclusions: 1) Logit and probit transformations are often successfully used to mimic a linear model. Logistic regression, Cox regression, Poisson regression, and Markow modeling are examples of logit transformation;2) Either the x- or y-axis or both of them can be logarithmically transformed. Also Box Cox transformation equations and ACE (alternating conditional expectations) or AVAS (additive and variance stabilization for regression) packages are simple empirical methods often successful for linearly remodeling of non-linear data;3) Data that are sinusoidal, can, generally, be successfully modeled using polynomial regression or Fourier analysis;4) For exponential patterns like plasma concentration time relationships exponential modeling with or without Laplace transformations is a possibility. Spline and Loess are computationally intensive modern methods, suitable for smoothing data patterns, if the data plot leaves you with no idea of the relationship between the y- and x-values. There are no statistical tests to assess the goodness of fit of these methods, but it is always better than that of traditional models.展开更多
The use of signals of different frequencies determines the geometrical deviation with respect to the optical axes of a given beam. This angle can be determined by Sympletic Map (SM), a powerful and simple mathematical...The use of signals of different frequencies determines the geometrical deviation with respect to the optical axes of a given beam. This angle can be determined by Sympletic Map (SM), a powerful and simple mathematical tool for the characterization and construction of images in Geometrical Optics. The Sympletic Map constitutes a Lie Group, with an algebra associated: the Lie Algebra. In general, the SM can be expressed as an infinite series, where each term corresponds to different contributions produced by the optical devices that constitute the optical system (lenses, apertures, bandwidth cutoff, etc.). The level of correction to be performed on the image to recover the original object is clear and controllable by SM. This formalism can be extended easily to physical optics to describe diffraction and interference phenomena.展开更多
A mathematical model for the fluidized bed biofilm reactor (FBBR) is discussed. An approximate analytical solution of concentration of phenol is obtained using modified Adomian decomposition method (MADM). The main ob...A mathematical model for the fluidized bed biofilm reactor (FBBR) is discussed. An approximate analytical solution of concentration of phenol is obtained using modified Adomian decomposition method (MADM). The main objective is to propose an analytical method of solution, which do not require small parameters and avoid linearization and physically unrealistic assumptions. Theoretical results obtained can be used to predict the biofilm density of a single bioparticle. Satisfactory agreement is obtained in the comparison of approximate analytical solution and numerical simulation.展开更多
The first part of this paper is presents a method for producing the composite which shows ferromagnetic, highly-elastic and electrically-conducting properties. This composite consists of ferromagnetic particles of the...The first part of this paper is presents a method for producing the composite which shows ferromagnetic, highly-elastic and electrically-conducting properties. This composite consists of ferromagnetic particles of the size 0.15-0.25 mm made of the chemically pure iron. The mentioned particles were dispersed in the elastic porous silicone the matrix with pores of the size 0.15-0.25 mm. Colloidal graphite particles of the size not exceeding 0.5 μm were added to the matrix to increase electrical conductivity. The production method consist in mixing particles of iron, graphite and sodium chloride with non-polymerized silicone and rinsing salt particles by water after the matrix polymerization. In its second part the paper provides a description of the measurement system for longitudinal magnetostriction and the Hall voltage. The magnetic field with the induction of ± 8 T produced by the Bitter type magnet was applied to the composite samples. The supplying voltage was applied to these samples and the Hall voltage was measured at the electrodes glued to them. The longitudinal magnetostriction was measured by means of the capacitor with a variable capacity placed at the upper surface of these samples. The linear magnetostriction exceeding ± 6 % and the Hall voltage reaching ± 5.5 nV were detected by the conducted measurements. Both the longitudinal magnetostriction and the Hall voltage show nonlinear changes and hysteresis lopes during the magnetic field application and the supplying current flow. The coupling of these changes and other regularities observed in the investigated composites and especially their non-linearity and hysteresis, are discussed in the final part of the paper.展开更多
Effects of water to binder ratio (m(W)/m(B)), types and addition content of mineral admixtures ont he autogenous relative humidity (ARH) change of concrete resulting from self-desiccation were studies. The parameters ...Effects of water to binder ratio (m(W)/m(B)), types and addition content of mineral admixtures ont he autogenous relative humidity (ARH) change of concrete resulting from self-desiccation were studies. The parameters of coefficient of mineral self-desiccation-effect ka nd efficient water to binder ratio r(e) were proposed, and experimental results were fitted non-linearly and analyzed using these proposed parameters. The experimental results indicate that ARH reduction of concrete at different ages increases with the decrease of m(W)/m(B). The ARH changes laws of concrete with m(W)/m(B) lower than 0.4 can be expressed with a non-linear equation. The extent of the effect of types and addition content of mineral admixures on ARH reduction of concrete resulting from self-desiccation can be reflected by the non-linear equation with the parameter of efficient water to binder ratio r(e) effectively.展开更多
Promotion is an essential element in the marketing mix. It is used by businesses to inform, influence and persuade customers to adopt the products and services they offer. Without promotion, business would be stagnant...Promotion is an essential element in the marketing mix. It is used by businesses to inform, influence and persuade customers to adopt the products and services they offer. Without promotion, business would be stagnant and lack substantial growth because the brands would have low visibility in the market. Moreover, today’s vast and assorted markets comprise of customers with different needs and varied behavior. So it is rarely possible for companies to satisfy all customers by treating them alike. Thus there arises a need to divide the market into segments having customers with similar traits/characteristics. After identifying appropriate market segments, firms can design differentiated promotional campaigns for each segment. At the same time there can be a mass market promotional campaign that reaches different segments with a fixed spectrum. Also since promotional effort resources are limited, one must use them judiciously. In this paper, we formulate mathematical programming problem under repeat purchase scenario, which optimally allocates mass promotional effort resources and differentiated promotional effort resources across the segments dynamically in order to maximize the overall sales obtained from multiple products of a product line under budgetary and minimum sales aspiration level constraint on each product under consideration in each segment. The planning horizon is divided into multi periods, the adoption pattern of each product in each segment is observed in every subinterval and accordingly promotional effort allocations are determined for the next period till we reach the end of planning period. The optimization model has been further extended to incorporate minimum aspiration level constraints on total sales for each product under consideration from all the segments taken together. The non linear programming problem so formulated is solved using differential evolution approach. A numerical example has been discussed to illustrate applicability of the model.展开更多
In the past decades, the necessity for detailed earthquake microzonation studies was recognized worldwide. Therefore, different approaches were established and applied. Unfortunately, the majority of these approaches ...In the past decades, the necessity for detailed earthquake microzonation studies was recognized worldwide. Therefore, different approaches were established and applied. Unfortunately, the majority of these approaches are not based on pre-existing field data but require extensive seismic measurements and investigations. Furthermore, these approaches incorporate non-linearity inadequately and cannot take groundwater level changes into account. For this purpose, notably numerical models are most suitable. These models require a good knowledge of the local geological conditions （especially of the uppermost unconsolidated units）, information about the geotechnical parameters of these units, and a hydrogeological model of the investigated area. Most of this information can be obtained from geotechnical investigations and surveys that have already been carried out in most densely populated areas. In a case study for Bucharest City, non-linear analyses were performed using software that is based on the visco-hypoplastic constitutive law. The results indicate that groundwater level changes have an important influence on duration and amplitude of ground response and thus should be considered for seismic microzonation studies. This approach ean be used to display site effects and to identify different microzones taking different earthquake magnitudes and groundwater levels into account.展开更多
文摘The Cox proportional hazard model is being used extensively in oncology in studying the relationship between survival times and prognostic factors. The main question that needs to be addressed with respect to the applicability of the Cox PH model is whether the proportional hazard assumption is met. Failure to justify the subject assumption will lead to misleading results. In addition, identifying the correct functional form of the continuous covariates is an important aspect in the development of a Cox proportional hazard model. The purpose of this study is to develop an extended Cox regression model for breast cancer survival data which takes non-proportional hazards and non-linear effects that exist in prognostic factors into consideration. Non-proportional hazards and non-linear effects are detected using methods based on residuals. An extended Cox model with non-linear effects and time-varying effects is proposed to adjust the Cox proportional hazard model. Age and tumor size were found to have nonlinear effects. Progesterone receptor assay status and age violated the proportional hazard assumption in the Cox model. Quadratic effect of age and progesterone receptor assay status had hazard ratio that changes with time. We have introduced a statistical model to overcome the presence of the proportional hazard assumption violation for the Cox proportional hazard model for breast cancer data. The proposed extended model considers the time varying nature of the hazard ratio and non-linear effects of the covariates. Our improved Cox model gives a better insight on the hazard rates associated with the breast cancer risk factors.
文摘Background: Novel models for the assessment of non-linear data are being developed for the benefit of making better predictions from the data. Objective: To review traditional and modern models. Results, and Conclusions: 1) Logit and probit transformations are often successfully used to mimic a linear model. Logistic regression, Cox regression, Poisson regression, and Markow modeling are examples of logit transformation;2) Either the x- or y-axis or both of them can be logarithmically transformed. Also Box Cox transformation equations and ACE (alternating conditional expectations) or AVAS (additive and variance stabilization for regression) packages are simple empirical methods often successful for linearly remodeling of non-linear data;3) Data that are sinusoidal, can, generally, be successfully modeled using polynomial regression or Fourier analysis;4) For exponential patterns like plasma concentration time relationships exponential modeling with or without Laplace transformations is a possibility. Spline and Loess are computationally intensive modern methods, suitable for smoothing data patterns, if the data plot leaves you with no idea of the relationship between the y- and x-values. There are no statistical tests to assess the goodness of fit of these methods, but it is always better than that of traditional models.
文摘The use of signals of different frequencies determines the geometrical deviation with respect to the optical axes of a given beam. This angle can be determined by Sympletic Map (SM), a powerful and simple mathematical tool for the characterization and construction of images in Geometrical Optics. The Sympletic Map constitutes a Lie Group, with an algebra associated: the Lie Algebra. In general, the SM can be expressed as an infinite series, where each term corresponds to different contributions produced by the optical devices that constitute the optical system (lenses, apertures, bandwidth cutoff, etc.). The level of correction to be performed on the image to recover the original object is clear and controllable by SM. This formalism can be extended easily to physical optics to describe diffraction and interference phenomena.
文摘A mathematical model for the fluidized bed biofilm reactor (FBBR) is discussed. An approximate analytical solution of concentration of phenol is obtained using modified Adomian decomposition method (MADM). The main objective is to propose an analytical method of solution, which do not require small parameters and avoid linearization and physically unrealistic assumptions. Theoretical results obtained can be used to predict the biofilm density of a single bioparticle. Satisfactory agreement is obtained in the comparison of approximate analytical solution and numerical simulation.
文摘The first part of this paper is presents a method for producing the composite which shows ferromagnetic, highly-elastic and electrically-conducting properties. This composite consists of ferromagnetic particles of the size 0.15-0.25 mm made of the chemically pure iron. The mentioned particles were dispersed in the elastic porous silicone the matrix with pores of the size 0.15-0.25 mm. Colloidal graphite particles of the size not exceeding 0.5 μm were added to the matrix to increase electrical conductivity. The production method consist in mixing particles of iron, graphite and sodium chloride with non-polymerized silicone and rinsing salt particles by water after the matrix polymerization. In its second part the paper provides a description of the measurement system for longitudinal magnetostriction and the Hall voltage. The magnetic field with the induction of ± 8 T produced by the Bitter type magnet was applied to the composite samples. The supplying voltage was applied to these samples and the Hall voltage was measured at the electrodes glued to them. The longitudinal magnetostriction was measured by means of the capacitor with a variable capacity placed at the upper surface of these samples. The linear magnetostriction exceeding ± 6 % and the Hall voltage reaching ± 5.5 nV were detected by the conducted measurements. Both the longitudinal magnetostriction and the Hall voltage show nonlinear changes and hysteresis lopes during the magnetic field application and the supplying current flow. The coupling of these changes and other regularities observed in the investigated composites and especially their non-linearity and hysteresis, are discussed in the final part of the paper.
文摘Effects of water to binder ratio (m(W)/m(B)), types and addition content of mineral admixtures ont he autogenous relative humidity (ARH) change of concrete resulting from self-desiccation were studies. The parameters of coefficient of mineral self-desiccation-effect ka nd efficient water to binder ratio r(e) were proposed, and experimental results were fitted non-linearly and analyzed using these proposed parameters. The experimental results indicate that ARH reduction of concrete at different ages increases with the decrease of m(W)/m(B). The ARH changes laws of concrete with m(W)/m(B) lower than 0.4 can be expressed with a non-linear equation. The extent of the effect of types and addition content of mineral admixures on ARH reduction of concrete resulting from self-desiccation can be reflected by the non-linear equation with the parameter of efficient water to binder ratio r(e) effectively.
文摘Promotion is an essential element in the marketing mix. It is used by businesses to inform, influence and persuade customers to adopt the products and services they offer. Without promotion, business would be stagnant and lack substantial growth because the brands would have low visibility in the market. Moreover, today’s vast and assorted markets comprise of customers with different needs and varied behavior. So it is rarely possible for companies to satisfy all customers by treating them alike. Thus there arises a need to divide the market into segments having customers with similar traits/characteristics. After identifying appropriate market segments, firms can design differentiated promotional campaigns for each segment. At the same time there can be a mass market promotional campaign that reaches different segments with a fixed spectrum. Also since promotional effort resources are limited, one must use them judiciously. In this paper, we formulate mathematical programming problem under repeat purchase scenario, which optimally allocates mass promotional effort resources and differentiated promotional effort resources across the segments dynamically in order to maximize the overall sales obtained from multiple products of a product line under budgetary and minimum sales aspiration level constraint on each product under consideration in each segment. The planning horizon is divided into multi periods, the adoption pattern of each product in each segment is observed in every subinterval and accordingly promotional effort allocations are determined for the next period till we reach the end of planning period. The optimization model has been further extended to incorporate minimum aspiration level constraints on total sales for each product under consideration from all the segments taken together. The non linear programming problem so formulated is solved using differential evolution approach. A numerical example has been discussed to illustrate applicability of the model.
基金supported by the German Research Foundation(DFG), the State of Baden-Württemberg, and the University(TH) of Karlsruhe
文摘In the past decades, the necessity for detailed earthquake microzonation studies was recognized worldwide. Therefore, different approaches were established and applied. Unfortunately, the majority of these approaches are not based on pre-existing field data but require extensive seismic measurements and investigations. Furthermore, these approaches incorporate non-linearity inadequately and cannot take groundwater level changes into account. For this purpose, notably numerical models are most suitable. These models require a good knowledge of the local geological conditions （especially of the uppermost unconsolidated units）, information about the geotechnical parameters of these units, and a hydrogeological model of the investigated area. Most of this information can be obtained from geotechnical investigations and surveys that have already been carried out in most densely populated areas. In a case study for Bucharest City, non-linear analyses were performed using software that is based on the visco-hypoplastic constitutive law. The results indicate that groundwater level changes have an important influence on duration and amplitude of ground response and thus should be considered for seismic microzonation studies. This approach ean be used to display site effects and to identify different microzones taking different earthquake magnitudes and groundwater levels into account.
