Mathematical model for comparing proficiency testing results across analytical methods

1991 ◽  
Vol 37 (2) ◽  
pp. 265-269
Author(s):  
James P AuBuchon

Abstract Proficiency testing (PT) programs may fail to establish a range of acceptable performance in a challenge when an insufficient number of participants use a particular method. In this study I analyzed a mathematical approach to establish acceptable performance in alanine aminotransferase (ALT; EC 2.6.1.2) PT challenges. This approach was derived from the mathematical model used in establishing a nationwide ALT standardization system for blood-collection facilities in 1988. A ratio of results was derived between each method in the PT program and an arbitrarily chosen "standard" method. The intent of this approach was to transform a target value for a challenge as determined in the "standard" method to units applicable to methods utilized less often. However, the high degree of variability over time in the ratios for some methods precluded general application of this approach. Therefore, although this simple mathematical method was successful in implementing an ALT standardization system across different methods, a derivation of this approach did not afford comparison of results in PT challenges.

1984 ◽  
Vol 6 (2) ◽  
pp. 117-123 ◽  
Author(s):  
H. Schaeben

The concept of conditional ghost correction is introduced into the vector method of quantitative texture analysis. The mathematical model actually chosen here reduces the texture problem to one of quadratic programming. Thus, a well defined optimization problem has to be solved, the singular system of linear equations governing the correspondence between pole and orientation distribution being reduced to a set of equality constraints of the restated texture problem. This new mathematical approach in terms of the vector method reveals the modeling character of the solution of the texture problem provided by the vector method completely.


1985 ◽  
Vol 249 (1) ◽  
pp. C160-C165 ◽  
Author(s):  
D. Eshel ◽  
Y. Grossman ◽  
Z. Priel

Ciliary beating frequency in tissue culture from frog palate and isolated lung was optically examined using instrumentation that was adjusted to measure a fraction of the surface area of a single ciliary cell. Consecutive 1-s segments of the analogue signal were fast Fourier transformed (FFT) to obtain a power spectrum. At room temperature, these power spectra changed over time from 1 s to the next. Each spectrum contained several dominant frequencies of similar intensities. Cooling the preparation resulted in a single-peak spectrum that was constant over time. A mathematical model is proposed to simulate these findings. The results and the mathematical model support the hypothesis that ciliary beating frequency fluctuates over short periods of time.


2014 ◽  
Vol 915-916 ◽  
pp. 277-280
Author(s):  
Yao Chen Shi ◽  
Zhan Guo Li ◽  
Xiu Guang Yang

The vibration of belt affected the transmission stability of automotive synchronous belt. The mathematical model of longitudinal vibration was established through analyzing the longitudinal vibration of automotive synchronous belt. Developed the vibration dynamic measurement device, aiming at RU style arc teethed synchronous belt transmission process, measured the variety of amplitude over time at the middle of the belt span obtained the rules of amplitude and frequency change along with the rotation speed. It is of certain importance to improving the transmission stability of arc teethed synchronous belt.


2021 ◽  
Vol 2131 (3) ◽  
pp. 032034
Author(s):  
O Lebedev ◽  
I Lipatov

Abstract Determination of the ship’s course width necessary for the ships safe operation is an urgent task due to the increase in the modern ships’ dimensions. The existing methods for assessing the fairway are calculated with a full re-positioning of the propulsion-rudder complex, according to the maximum drift angle. The vessel movement is considered to be steady, that is, the speed, the drift angles do not depend on time. The relevance of this study is associated with the assessment of determining the width of the fairway at any time interval. This is due to the fact that when passing the river sections, the vessels perform maneuvering with the rudder gear shifted for short periods of time and not at the maximum shift angle. Determination of the parameters of the ship’s movement over time when the navigator manipulates the ship’s controls (control of the rudder device, changing the parameters of the main engines) can be determined by the mathematical model of the ship’s movement. This article discusses the issues of creating a model that adequately describe the processes of vessel movement, including in the conditions of vessel movement along a limited ship’s course. The adequacy of the model was verified using the data of field and model experiments. According to the compiled mathematical model, the calculations were made for various projects of dry cargo ships.


Author(s):  
Robert P. Culp

<p class="MsoNormal" style="text-align: justify; line-height: normal; margin: 0in 0.5in 0pt;"><span style="font-size: 10pt;"><span style="font-family: Times New Roman;">The purpose of this paper is to develop a purely mathematical approach to determining consumer demand. The model developed allows the researcher to derive demand in an oligopoly market from observed firm output and market prices using only assumptions about each firm, modest restrictions on consumer behavior, and limitations on market structure. The advantage of this revealed demand approach is that it does not require the specification of the consumer&rsquo;s utility function or any firm&rsquo;s production function. In addition, this mathematical approach allows for the estimation of own price and cross price elasticities of demand without statistical regression. </span></span></p><p class="MsoNormal" style="text-align: justify; line-height: normal; margin: 0in 0.5in 0pt;"><span style="font-size: 10pt;"><span style="font-family: Times New Roman;">&nbsp;</span></span></p><p class="MsoNormal" style="text-align: justify; line-height: normal; margin: 0in 0.5in 0pt;"><span style="font-size: 10pt;"><span style="font-family: Times New Roman;">The mathematical model developed is applied to the automobile industry assuming a market characterized by Cournot-Nash behavior and divided into five homogenous vehicle segments. A global optimization program is used to mathematically determine the range of values the coefficients of demand must take in each segment to satisfy market equilibrium. These coefficients can be used to estimate own and cross price elasticities of demand and construct demand equations. </span></span></p><p class="MsoNormal" style="text-align: justify; line-height: normal; margin: 0in 0.5in 0pt;"><span style="font-size: 10pt;"><span style="font-family: Times New Roman;">&nbsp;</span></span></p><p class="MsoNormal" style="text-align: justify; line-height: normal; margin: 0in 0.5in 0pt;"><span style="font-size: 10pt;"><span style="font-family: Times New Roman;">The elasticity estimates generated by the mathematical model of the automobile industry are compared to other estimates of elasticity found by statistical estimation. It is shown that the mathematical model generates results that are consistent with the statistical methods of the automobile market used by other researchers.<span style="mso-spacerun: yes;">&nbsp; </span></span></span></p>


Blood ◽  
2015 ◽  
Vol 126 (23) ◽  
pp. 130-130 ◽  
Author(s):  
David M. Kurtz ◽  
Florian Scherer ◽  
Aaron M. Newman ◽  
Alexander F. Lovejoy ◽  
Daniel M. Klass ◽  
...  

Abstract Background: The prognosis for diffuse large B-cell lymphoma (DLBCL) patients who fail initial therapy remains poor. Current prognostic methods to identify patients destined for failure employ baseline molecular profiles or imaging data at fixed milestones, thus sub-optimally capturing functional response dynamics. Noninvasive detection of tumor-specific DNA sequences in the plasma, or circulating tumor DNA (ctDNA), provides a window of opportunity to observe these changes early during therapy. We sought to relate early ctDNA kinetics during therapy to tumor volume, therapeutic responses, and ultimate clinical outcomes. Methods: Using CAPP-Seq, a next-generation sequencing platform for detection of ctDNA (Newman Nature Medicine 2014), we prospectively profiled patients with DLBCL receiving combination immunochemotherapy at Stanford University. Tumor samples were used to define tumor specific somatic alterations, which were then monitored in plasma. We examined two methods of assessing ctDNA change over time: a simple heuristic model (assessing the change in ctDNA concentration from cycle 1 to cycle 2), and a biologically based mathematical model of ctDNA dynamics to predict tumor volume and patient outcomes. Results: We sequenced tumor and plasma samples (n=135) from ten patients receiving Rituximab-containing regimens. Plasma samples were collected prior to, during, and immediately after chemotherapy, with a median of 7 samples per patient during the first therapy cycle. Across patients, ctDNA concentrations varied over a 6-log range (Figure 1). The change in ctDNA concentration between cycle 1 and cycle 2 generally tracked with FDG PET/CT response - patients achieving a PR or CR had an average decrease of 2.9±0.8 logs in ctDNA concentration, compared to an increase of 0.3±0.8 logs for those with SD or PD (p<0.001). However, this metric failed to capture some patients who ultimately relapsed after radiographic remission. We therefore developed a multi-compartmental ordinary-differential equation (ODE) model of tumor dynamics capturing tumor volume, ctDNA, and the effect of chemotherapy. We performed nonlinear regression to fit data to this model using serial ctDNA measurements from individual patients, thereby creating continuous, patient-specific models of both ctDNA and tumor volume (Figure 1a-b). This mathematical model significantly fit ctDNA measurements and predicted tumor volumes across patients and samples (Figure 1c). Using ctDNA measurements from the first 2 cycles of therapy, this model accurately predicted clinical outcomes for all ten patients, including relapse after radiographic remission. An additional cohort of patients will be presented at this meeting. Conclusions: Given its high specificity and large dynamic range, ctDNA provides an opportunity to monitor the dynamics of therapeutic response in patients with DLBCL. Methods capturing these dynamics correlate with radiographic response. Given the complexity of tumor dynamics, heuristic models of ctDNA may less faithfully capture ultimate clinical outcomes. Personalized mathematical models of ctDNA can potentially reflect tumor dynamics and predict clinical outcomes for individual patients. Figure 1. Personalized tumor modeling from ctDNA tumor dynamics. a) An example of a model of ctDNA fit to observed data for a single patient (DLBCL010). b) The corresponding tumor volume prediction over time for patient DLBCL010. c) Summary of the mathematical model across ten patients, demonstrating the fit between measured data and the model. Figure 1. Personalized tumor modeling from ctDNA tumor dynamics. a) An example of a model of ctDNA fit to observed data for a single patient (DLBCL010). b) The corresponding tumor volume prediction over time for patient DLBCL010. c) Summary of the mathematical model across ten patients, demonstrating the fit between measured data and the model. Disclosures Newman: Roche: Consultancy. Klass:Roche: Employment. Gambhir:CellSight: Consultancy. Diehn:Roche: Consultancy. Alizadeh:Genentech: Consultancy; Roche: Consultancy; Celgene: Consultancy.


Author(s):  
A. I. Malyshev

This paper reports the estimation of the predictability of seismicity and large earthquakes in Kamchatka as inferred from data in the Kamchatka regional catalog for 1962–2014. The mathematical model uses a second-order nonlinear differential equation, while the optimization algorithm and the estimates of predictability are the author’s own. The estimates show a high predictability of seismicity; the extrema of prediction nonlinearity typical of large earthquakes usually occur simultaneously with similar extrema of seismicity as a whole. Overall, 220 large (K ≥ 13.3) Kamchatka earthquakes were analyzed to find that foreshock predictability was available for 200 earthquakes (~30000 determinations) and aftershock predictability for 215 earthquakes (~300000 determinations). The predictability related to large earthquakes began to be seen and was rapidly increasing at intermediate (7.5–30 km) radii of hypocenter samples. The prediction distances over time were some tens and hundreds of days for foreshock predictability and some hundreds and thousands of days for aftershock predictability. These results demonstrate very good promise for the approximation extrapolation approach to the prediction of both large earthquakes themselves and of subsequent aftershock decay of seismic activity.


10.29007/shrz ◽  
2020 ◽  
Author(s):  
Csaba Imre Hencz ◽  
Tamás Hartványi

In this research, we intend to present a novel mathematical approach to logistics which allows (financial) value to be associated with information as a central corporate resource. The inherent logistics processes (transport, production, sales) uncertainty requires continuous inventory monitoring and maintenance of safety stock levels. Literature and practice show that logistics responds to poor quality or incomplete information by increasing inventory.In our research, we are looking for a minimum of safety stock levels based on the processing of information available in space and time and I intend to give a formal description of the mathematical model and present an example of its application.


Author(s):  
A. I. Malyshev

This paper reports the estimation of the predictability of seismicity and large earthquakes in Kamchatka as inferred from data in the Kamchatka regional catalog for 1962–2014. The mathematical model uses a second-order nonlinear differential equation, while the optimization algorithm and the estimates of predictability are the author’s own. The estimates show a high predictability of seismicity; the extrema of prediction nonlinearity typical of large earthquakes usually occur simultaneously with similar extrema of seismicity as a whole. Overall, 220 large (K ≥ 13.3) Kamchatka earthquakes were analyzed to find that foreshock predictability was available for 200 earthquakes (~30000 determinations) and aftershock predictability for 215 earthquakes (~300000 determinations). The predictability related to large earthquakes began to be seen and was rapidly increasing at intermediate (7.5–30 km) radii of hypocenter samples. The prediction distances over time were some tens and hundreds of days for foreshock predictability and some hundreds and thousands of days for aftershock predictability. These results demonstrate very good promise for the approximation extrapolation approach to the prediction of both large earthquakes themselves and of subsequent aftershock decay of seismic activity.


Author(s):  
Oleh Velychko ◽  
Oleh Hrabovskyi

Modern measuring instruments (MIs) are designed to obtain complete and reliable measuring information. To perform this important function, MIs must be of appropriate quality and must be reliably assessed. Using mathematical models simulate the operation of technical systems in order to decide on the optimization of its characteristics. As a result of the analysis of the model, the specific features of the studied processes and certain quantitative regularities are established. This allows to predict the processes in the system over time and determine their quantitative characteristics. The article presents the results of mathematical modeling of system-oriented measuring instruments as a system and its software as a subsystem using the apparatus of general systems theory. Such models with its graphical interpretation allow obtaining the necessary and useful information about the properties of the MIs as a technical system. The performed modeling makes it possible to describe the functioning of the MIs and to obtain a certain assessment of quality indicators.


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