A Mathematical Model of Intermittent Androgen Suppression for Prostate Cancer

For several decades, androgen suppression has been the principal modality for treatment of advanced prostate cancer. Although the androgen deprivation is initially effective, most patients experience a relapse within several years due to the proliferation of so-called androgen-independent tumor cells. Bruchovsky et al. suggested in animal models that intermittent androgen suppression (IAS) can prolong the time to relapse when compared with continuous androgen suppression (CAS). Therefore, IAS has been expected to enhance clinical efficacy in conjunction with reduction in adverse effects and improvement in quality of life of patients during off-treatment periods. This paper presents a mathematical model that describes the growth of a prostate tumor under IAS therapy based on monitoring of the serum prostate-specific antigen (PSA). By treating the cancer tumor as a mixed assembly of androgen-dependent and androgen-independent cells, we investigate the difference between CAS and IAS with respect to factors affecting an androgen-independent relapse. Numerical and bifurcation analyses show how the tumor growth and the relapse time are influenced by the net growth rate of the androgen-independent cells, a protocol of the IAS therapy, and the mutation rate from androgen-dependent cells to androgen-independent ones.

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微波灰化-氢化物发生原子荧光光谱法测定植物油中微量铅

采用微波灰化技术处理样品 ,运用断续流动 氢化物发生原子荧光光谱法测定植物油中的铅 ,探讨了微波灰化条件对铅测定的影响 ;研究了载流和样品酸度、还原剂浓度、基体改进剂以及载流流速对氢化物发生的影响。铅的线性范围为 1 0 0～ 2 0 0 μg·L-1,最低检出限为 0 31μg·L-1,相对标准偏差为 1 84 % ,回收率为 89 2 %～ 97 3%。     

特殊双曲柄机构300fps间歇相机主要问题分析

我们研制的35毫米300fps间歇相机的抓片机构是一个具有可调节环节的特殊双曲柄机构。这个机构是在齿轮双曲柄机构的一个连杆的交接点处增加了一个偏心调节环节(如图1示)。偏心调节环外圈为球面,与抓片爪(连杆BE)孔滑动配合,回转中心在E点,距E点e处是偏心9.5mm齿轮偏心轴轴心C。偏心轴与调节环间用滚动轴承连接,偏心环节与爪组成有三个自由度的连接付。     

Transient simulation of 2–3D stratified and intermittent two-phase flows. Part II: Applications

In this paper a new type of transient multidimensional two-fluid model has been applied to simulate intermittent or slug flow problems. Three different approaches to modelling interfacial friction, including an interfacial tracking scheme, have been investigated. The numerial method is based on an implicit finite difference scheme, solved directly in two steps applying a separate equation for the pressure. 2D predictions of Taylor bubble propagation in horizontal and inclined channels have been compared with experimental data and analytical solutions. The 2D model has also been applied to investigate a number of special phenomena in slug flow, including slug initiation, bubble turning in downflow and the bubble centring process at large liquid flow rates.     

A simplified but intuitive analytical model for intermittent-contact-mode force microscopy based on Hertzian mechanics

The forces acting on the substrate in intermittent-contact-mode (IC mode, tapping mode) atomic force microscopy are not accessible to a direct measurement. For an estimation of these forces, a simple analytical model is developed by considering only the shift of the cantilever resonance frequency caused by Hertzian (contact) forces. Based on the relationship between frequency shift and tip–sample force for large-amplitude frequency-modulation atomic force microscopy, amplitude and phase versus distance curves are calculated for the intermittent contact mode, and the forces on the substrate are calculated. The results show a qualitative agreement with numerical calculations, yielding typical maximal forces of 50–150 nN. When working above the unperturbed resonance, forces are found to be significantly larger than below the resonance.     

Regularity of Intermittent Bursts in BriggsRauscher Oscillating Systems with Phenol

The intermittency or intermittent bursting as the type of dynamic state when two qualitatively different behaviors replace one another randomly during the course of the reaction, although all the control parameters remain constant, is found in the Briggs? Rauscher oscillating system moderated by a very small amount of phenol. Within a range of phenol concentrations, the oscillation amplitude is diminished considerably, and after oscillations cease, they repeat intermittently, giving several bursts of oscillations. For the concentrations used here, the range of phenol concentrations where intermittent bursting oscillations occur in a closed reactor is ca. 1.8×10^?5 to 3.6×10^?5 M . Bursting also occurs in an open reactor and can be sustained indefinitely at 5.53×10^?5 M concentration. The intermittent bursting behavior is robust, and can be achieved at a variety of conditions.     

Intermittent demand: Linking forecasting to inventory obsolescence

The standard method to forecast intermittent demand is that by Croston. This method is available in ERP-type solutions such as SAP and specialised forecasting software packages (e.g. Forecast Pro), and often applied in practice. It uses exponential smoothing to separately update the estimated demand size and demand interval whenever a positive demand occurs, and their ratio provides the forecast of demand per period. The Croston method has two important disadvantages. First and foremost, not updating after (many) periods with zero demand renders the method unsuitable for dealing with obsolescence issues. Second, the method is positively biased and this is true for all points in time (i.e. considering the forecasts made at an arbitrary time period) and issue points only (i.e. considering the forecasts following a positive demand occurrence only). The second issue has been addressed in the literature by the proposal of an estimator (Syntetos-Boylan Approximation, SBA) that is approximately unbiased. In this paper, we propose a new method that overcomes both these shortcomings while not adding complexity. Different from the Croston method, the new method is unbiased (for all points in time) and it updates the demand probability instead of the demand interval, doing so in every period. The comparative merits of the new estimator are assessed by means of an extensive simulation experiment. The results indicate its superior performance and enable insights to be gained into the linkage between demand forecasting and obsolescence.     

On the bias of Croston’s forecasting method

Croston’s forecasting method (CR) has been shown to be appropriate in dealing with intermittent demand items. The method, however, suffers from a positive bias as discussed by Syntetos and Boylan [Syntetos, A.A., Boylan, J.E., 2005a. The accuracy of intermittent demand estimates. International Journal of Forecasting 21, 303–314] who proposed a modification (SB). Unfortunately, the modification ignores the damping effect on the bias of the probability that a demand occurs. This leads to overcompensation and a negative bias, which can in fact be larger than the positive bias of the original method. Syntetos [Syntetos, A.A., 2001. Forecasting for Intermittent Demand, Unpublished Ph.D thesis, Buckinghamshire Chilterns University College, Brunel University] proposed another modification (SY) that takes the damping effect into account, thereby reducing the bias. However, he eventually disregarded it from the empirical analysis, because of the analytical results that SY never dominates SB as well as CR when both bias and variance are considered. Levén and Segerstedt [Levén, E., Segerstedt, A., 2004. Inventory control with a modified Croston procedure and Erlang distribution. International Journal of Production Economics 90, 361–367] also proposed a modified Croston method (LS) and claimed it to be unbiased. We compare all four methods in a numerical study. Our results strengthen the finding from Boylan and Syntetos [Boylan, J.E., Syntetos A.A., 2007. The accuracy of a modified Croston procedure. International Journal of Production Economics 107, 511–517] that LS suffers from a much more severe bias that the other methods. They also confirm SB as the best method when the Mean Square Error is considered. However, SY has a much smaller average absolute bias of 1% compared to 5% for the SB method. From an inventory control point of view, this is an important advantage of the SY method, since biases distort calculations of the expected lead time demand as well as safety stock calculations. An additional advantage of the SY method is its robust performance over the range of parameter values that we considered. Based on these results, we suggest that the SY method should receive more consideration as an alternative to CR and SB.     

Novel electron holes of Gaussian type due to second order,non-perturbative electron trapping and the general loss of identifiability of hole structures in experiments

A second order non-perturbative trapping scenario is employed to show the existence of a new Gaussian type of solitary electron holes. Use is thereby made of Schamel's pseudo-potential method, the only method that can guarantee the completeness of an equilibrium solution of the Vlasov-Poisson system in addition to its existence. The new potential is of the form $e^{-X{(x)}^2}$ where $X(x)=sinh(x)$ and is hence reminiscent of the Gaussian potential appearing in its “second generation”. The simultaneous presence of both trapping generations hence establishes a one-parametric continuum spectrum of solitary electron holes all of them being, through appropriate fitting, potential candidates for identifying structures in experimental observations and numerical simulations. Taking into account the possibility of many more trapping scenarios moreover, a unique identification of structures, the desired goal expressed in the current literature when interpreting structure formation, is therefore not achievable. Origin of this intrinsic ambiguity is the loss of mathematical stringency in the kinetic regime through chaos triggered by the ergodic particle trajectories in the resonant region of phase space in the single particle – coherent wave interaction process.