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In this research, the mass stopping powers, projected range, effective atomic numbers, effective electron density, radiation yield and stopping time of light and heavy charged particles such as electron, proton and alpha in the Rene alloys which consist of Rene N4, Rene N5, Rene 41, Rene 65, Rene 80, Rene 88, Rene 95 and Rene 104 were calculated for the first time. The calculations were performed by using the programs, which are called as ESTAR, SRIM and PAGEX codes. Moreover, all the results were compared with each other, and a comprehensive and comparative study of the theoretical results were presented. [ABSTRACT FROM AUTHOR]

We study the infinite horizon discrete time N-player nonzero-sum Dynkin game ( N ≥ 2 ) with stopping times as strategies (or pure strategies). We prove existence of an ε -Nash equilibrium point for the game by presenting a constructive algorithm. One of the main features is that the payoffs of the players depend on the set of players that stop at the termination stage which is the minimal stage in which at least one player stops. The existence result is extended to the case of a nonzero-sum game with finite horizon. Finally, the algorithm is illustrated by two explicit examples in the specific case of finite horizon. [ABSTRACT FROM AUTHOR]

The determination of stopping power and the range of protons present in CH3OH, CH2O, and CO2 was accomplished within the energy range of 0.01–1,000 MeV by employing the Bethe equation and Ziegler equation. The latter two equations utilize quantum mechanics to derive an approximation of the stopping force formula, which applies to highly charged particles. The software MATLAB was utilized in the calculation of the results. A suitable equation for computing the halting power of protons in the range of 0.01–1,000 MeV has been identified. A correlation coefficient of 0.999 was determined, suggesting a high degree of concordance between the derived results and those of the SRIM 2013 and P-STAR programs. Proton stopping power analyses of this nature will aid the scientific community in selecting the optimal formulation of stopping power.

A functional calculus for an order complete vector lattice E was developed by Grobler (Indag Math (NS) 25(2):275–295, 2014) using the Daniell integral. We show that if one represents the universal completion of E as C ∞ (K) , where K is an extremally disconnected compact Hausdorff topological space, then the Daniell functional calculus for continuous functions is exactly the pointwise composition of functions in C ∞ (K) . This representation allows an easy deduction of the various properties of the functional calculus. Afterwards, we study discrete stopping times and stopped processes in C ∞ (K) . We obtain a representation that is analogous to what is expected in probability theory. [ABSTRACT FROM AUTHOR]

Stopping power, range, and time of proton in water, lung, bladder, and intestinal human tissues are calculated using density functional theory and Beth’s relativistic equation in range of proton energy (0.01–1,000 MeV). The experimental data extracted from SRIM-2013 program were used to proton to the same human tissues applied in the MATLAB-2021 program, and the mean ionization potential of water and the studied tissues is calculated using Gaussian 09W program. A good agreement has been found between our calculations for stopping power, range, and time of protons in the studied human body tissues and SRIM-2013 program calculations.

In this study, the energy loss, range, and stopping time were calculated using the Bethe theory for protons in germanium and copper materials over an energy range of 0.01–1,000 MeV. The mathematical equations were programmed and implemented using MATLAB2013 to obtain the results for the relative mass stopping power and range, illustrated in tables and graphs. The computed results from the Bethe and Ziegler equations were compared with the experimental results from Pstar. The results showed a difference between the experimental and theoretical results at the beginning of the range used in the Bethe equation because it is a quantized equation that is not suitable for low energies. Hence, a correction term was proposed for the Bethe equation to correct the results at low energies, which produced negative values. On the other hand, the Ziegler equation showed good agreement along the range used as it is a semi-empirical equation. The range and stopping time of the incident particle increased with increasing incident particle energy in the mentioned materials.

Modern computing and communication technologies can make data collection procedures very efficient, while our ability to analyze and extract information from large data sets is hard-pressed to keep up with our capacity for data collection. If we are interested in learning a classification/prediction rule that was not considered in the original data collection procedure, then there is usually a lack of label information in the original data. Thus, how to start with minimum number of labeled data and aggressively selected most informative samples for being labeled becomes an important issue. The thoughts of active learning, with subjects to be selected sequentially without using label information, is a possible outlet for this situation. In addition, if we can identify variables, from the lengthy variable list of the data set, for constructing an effective classification rule with good interpretation ability will be better. Here, we propose an active learning procedure targeted the maximum area under the receiver operating characteristic curve via a commonly use logistic model, which can sequentially select the effective informative subjects and variables, simultaneously. We discuss the asymptotic properties of the proposed procedure and illustrate it with some synthesized and real data sets. [ABSTRACT FROM AUTHOR]

Based on a deterministic and stochastic process hybrid model, we use white noises to account for patient variabilities in treatment outcomes, use a hyperparameter to represent patient heterogeneity in a cohort, and construct a stochastic model in terms of Ito stochastic differential equations for testing the efficacy of three different treatment protocols in CAR T cell therapy. The stochastic model has three ergodic invariant measures which correspond to three unstable equilibrium solutions of the deterministic system, while the ergodic invariant measures are attractors under some conditions for tumor growth. As the stable dynamics of the stochastic system reflects long-term outcomes of the therapy, the transient dynamics provide chances of cure in short-term. Two stopping times, the time to cure and time to progress, allow us to conduct numerical simulations with three different protocols of CAR T cell treatment through the transient dynamics of the stochastic model. The probability distributions of the time to cure and time to progress present outcome details of different protocols, which are significant for current clinical study of CAR T cell therapy., Competing Interests: Declaration of competing interest There is non-financial interest in this research., (Copyright © 2024 Elsevier Inc. All rights reserved.)

Sequential change-point analysis, which identifies a change of probability distribution in an infinite sequence of random observations, has important applications in many fields. A good method should detect a change point as soon as possible, and keep a low amount of false alarms. As one of the most popular methods, Shiryaev-Roberts (SR) procedure holds many optimalities. However, its implementation requires the pre-change and post-change distributions to be known, which is not achievable in practice. In this paper, we construct a nonparametric version of the SR procedure by embedding different versions of empirical likelihood, assuming two training samples, before and after change, are available for parameter estimations. Simulations are conducted to compare the performance of the proposed method with existing methods. The results show that when the underlying distribution is unknown, and training sample sizes are small, the proposed modified procedure shows advantage by giving a smaller delay of detection., Competing Interests: No potential conflict of interest was reported by the author(s)., (© 2024 Informa UK Limited, trading as Taylor & Francis Group.)