Threshold Stopping Research Articles

Calculation of alpha particles detection efficiency for polycarbonate detector using Geant4 toolkit

In the present work, alpha particles detection efficiency of polycarbonate detector (PC) is calculated using Geant4 simulation toolkit. A PC detector with 250 µm thickness and dimension of 2.5 × 2.5 cm2 is considered. Assuming the passage of alpha particles of an 241Am source through brass collimators with different lengths, various alpha energies ranging from 0.2 to 2.5 MeV are modeled. Also, an etching layer of 6 µm related to a given electrochemical etching process as well as a threshold stopping power of 240 keV µm-1 required for forming the tracks are used as the input data. The detection efficiency is determined as the ratio of registered tracks per unit area to the number of alpha particles reaching the PC detector surface. To validate the simulation, the results are compared with the experimental data reported in the literature. It is found that the both results agree well within a maximum variation of 10%.

Spectral theory of diffusion in partially absorbing media

A probabilistic framework for studying single-particle diffusion in partially absorbing media has recently been developed in terms of an encounter-based approach. The latter computes the joint probability density (generalized propagator) for particle position X t and a Brownian functional U t that specifies the amount of time the particle is in contact with a reactive component M . Absorption occurs as soon as U t crosses a randomly distributed threshold (stopping time). Laplace transforming the propagator with respect to U t leads to a classical boundary value problem (BVP) in which the reactive component has a constant rate of absorption z , where z is the corresponding Laplace variable. Hence, a crucial step in the encounter-based approach is finding the inverse Laplace transform. In the case of a reactive boundary ∂ M , this can be achieved by solving a classical Robin BVP in terms of the spectral decomposition of a Dirichlet-to-Neumann (D-to-N) operator on ∂ M . In this paper, we develop the analogous construction in the case of a reactive substrate M . In particular, we show that the Laplace transformed propagator can be computed in terms of the spectral decomposition of a pair of D-to-N operators on ∂ M . However, inverting the Laplace transform with respect to z is considerably more involved. We illustrate the theory by considering the D-to-N operators for some simple geometries.

On the large‐scale production of a new vaccine

Large‐scale production of a new vaccine, such as the COVID‐19 vaccine, is characterized by evolving demand and production yield uncertainties. Further, following its FDA approval for efficacy and safety, a vaccine may not even be manufacturable due to its low production yield and the resulting lack of profitability. To deal with those challenges in practice, a vaccine manufacturer can (stochastically) increase the uncertain yield of a vaccine prior to launching large‐scale production by learning through small‐scale, experimental production runs about manufacturing conditions that are conducive to raising that yield. After starting large‐scale production and receiving revenues from the sale of the vaccine, the manufacturer can continue to stochastically improve vaccine yield by acquiring knowledge from real‐time production data. The two key decisions faced by a vaccine manufacturer concern the optimal timing and capacity of the vaccine's large‐scale production. To determine the structure of vaccine manufacturer's optimal decisions, we formulate and solve a stochastic, multiperiod, sequential‐decision model, while incorporating the dynamic evolution of vaccine yield uncertainty under those two yield improvement strategies. We establish the optimality of a threshold stopping policy for the timing of the large‐scale vaccine production. This policy depends in a fundamental way on the relative stochastic rates of the two yield improvement strategies. We characterize the manufacturer's optimal capacity decision and identify conditions under which optimal capacity and production yield become substitutes. We analyze the implications of our results for rendering a new vaccine large‐scale manufacturable, and bringing it to the market sooner during a pandemic period.

On optimal threshold stopping times for Ito diffusions

The paper deals with an optimal stopping problem for one-dimensional Ito diffusion process and terminal payoff function. We study the following problem: under what conditions the stopping time which is optimal over the class of threshold strategies (specifying by first time when the underlying process exceeds some level) remains optimal over all stopping times. We prove that excessiveness of payoff function is the only necessary and sufficient condition which connects optimality over the class of threshold stopping times and over all stopping times.

Optimality of Threshold Stopping Times for Diffusion Processes

This paper is concerned with the optimal stopping problem for Itô diffusion processes over a class of stopping times. Necessary and sufficient optimality conditions are studied for a parametrically specified class of stopping times. A detailed analysis is given for the case of one-dimensional diffusion processes and threshold stopping times. Necessary and sufficient conditions are put forward for optimality of a threshold stopping time over all stopping times. A number of relations are obtained between the solution of the optimal stopping problem over the class of threshold moments and the solution of the free-boundary problem.

An Empirical Investigation of Bayesian Clinical Trial Design in Metastatic Breast Cancer.

Over the past 20years, there has been increasing interest in the use of Bayesian statistical methods for the analysis of clinical trials used to support regulatory decisions. Bayesian methods for the analysis of clinical trials are an attractive option when good prior information is available. Yet, in many cases, prior information is scarce and only tentative or proprietary prior information exists. In these situations, it is necessary to use noninformative type or skeptical-type priors. We undertook a systematic study of Bayesian methods and applied them to 13 randomized clinical trials in metastatic breast cancer submitted to the U.S. Food and Drug Administration for registrational purposes. Across all 13 studies, there were a total of 10,521 patients using 10 experimental agents. Our results demonstrated that Bayesian analyses with noninformative priors provided similar results to more traditional analyses. We also found that early interim looks at the study results can vary widely based upon the type of prior used. Finally, we found that pre-defined threshold stopping rules need to be relatively strong to prevent trials from stopping very early. Our results suggest that, when prior information is limited and a noninformative prior is used, there is little numerical difference between Bayesian methods and more traditional analysis methods. Bayesian methods, however, may provide additional summaries of the data that are more easily interpretable than means and confidence intervals.

Anisotropic diffusion based denoising on concrete images and surface crack segmentation

Purpose Health monitoring of concrete is one of the important tasks in the structural health monitoring. The life of any infrastructure relies on the quality of the concrete. The computer vision-based methods are very useful to identify the structural defects. The identification of minor cracks in the noisy concrete image is complex. The purpose of this paper is to denoise the concrete crack images and also segment the cracks. Design/methodology/approach The novelty of the proposed work lies on the usage of anisotropic diffusion filter in the noisy concrete images. Initially anisotropic diffusion filter is applied to smoothen the concrete images. Adaptive threshold and gray level-based edge stopping constant are used in the diffusion process. The statistical six sigma-based method is utilized to segment the cracks from smoothened concrete images. Findings The proposed method is compared with five state-of-the-art-methods with the performance metrics of mean square error, peak signal to noise ratio and mean structural similarity. The experimental results highlight the advantages of the proposed method. Originality/value The novelty of the proposed work lies on the usage of anisotropic diffusion filter in the noisy concrete images. This research work gives the scope for structural damage evaluation by the automation techniques.

Atomistic Simulation of the Fission-Fragment-Induced Formation of Defects in a Uranium–Molybdenum Alloy

The formation of defects in a uranium–molybdenum alloy induced by xenon and zirconium ion irradiation with energies typical of fission fragments has been simulated within the two-temperature atomistic model and Monte Carlo method. This has allowed estimating the total number of primary radiation defects formed at the “thermal spike” stage and in collision cascades for different temperatures. The calculated threshold stopping powers of ions responsible for the formation of defects at the thermal spike stage are in good agreement with the available theoretical and experimental data.

Optimal Timing of Influenza Vaccine Production Under Yield-Improving and Knowledge Acquisition Strategies

We consider a manufacturer of a new vaccine, such as the COVID-19 vaccine, characterized by evolving demand and production yield uncertainties. At the beginning of the time horizon, a vaccine may not be manufacturable due to its low production yield and the resulting lack of profitability. Prior to launching large-scale production, the manufacturer stochastically increases the uncertain yield of the vaccine by learning through small-scale experimental production runs about manufacturing conditions that are conducive to raising that yield, thus forsaking, in the process, immediate profits but raising future ones. After starting large-scale production and receiving revenues from the sale of the vaccine, the manufacturer can continue to stochastically improve vaccine yield by acquiring knowledge from real-time production data. The two key decisions faced by the vaccine manufacturer who seeks to maximize his total expected profit over the time horizon concern the optimal timing and capacity of the vaccine’s large-scale production. We formulate and solve a stochastic, multi-period, sequential-decision model to determine the structure of the vaccine’s manufacturer’s optimal decisions, while incorporating the dynamic evolution of vaccine yield uncertainty under those two yield improvement strategies. In particular, we establish the optimality of a threshold stopping policy for the timing of the large-scale vaccine production. This policy is found to depend in a fundamental way on the relative stochastic rates of the two yield improvement strategies. We also characterize the manufacturer’s optimal capacity decision and identify conditions under which, for a new vaccine, optimal capacity and production yield become substitutes. We analyze the implications of our results and underlying yield improvement strategies for rendering a new vaccine large-scale manufacturable, and bringing it to the market sooner in the time horizon.

Buy-and-hold mean-variance portfolios with a random exit strategy

We show how buy-and-hold investors can move from horizon uncertainty to profit opportunity. The analysis is conducted under a risk-averse framework rather than the standard Markowitz formulation in the case of i.i.d. asset processes. We make this practical achievement by considering a threshold stopping rule as the strategy to determine when to exit the market. The resulting investment horizon is random and can be correlated with the market. Under this setting, we first provide an analytical approximation to optimal weights, and then identify a class of reference variables associated with the stopping rule that leads to ex-ante improvements in portfolio allocation, vis-a-vis the fixed exit time alternative. The latter conclusion is based on a generalization of the Sharpe ratio, adjusted for horizon uncertainty. The obtained investment suggestion is simple and can be implemented empirically.

Atomistic simulation of defect formation and structure transitions in U-Mo alloys in swift heavy ion irradiation

In irradiation of swift heavy ions, the defects formation frequently takes place in crystals. High energy transfer into the electronic subsystem and relaxations processes lead to the formation of structural defects and cause specific effects, such as the track formation. There is a large interest to understanding of the mechanisms of defects/tracks formation due to the heating of the electron subsystem. In this work, the atomistic simulation of defects formation and structure transitions in U-Mo alloys in irradiation of swift heavy ions has been carried out. We use the two-temperature atomistic model with explicit account of electron pressure and electron thermal conductivity. This two-temperature model describes ionic subsystem by means of molecular dynamics while the electron subsystem is considered in the continuum approach. The various mechanisms of structure changes in irradiation are examined. In particular, the simulation results indicate that the defects formation may be produced without melting and subsequent crystallization. Threshold stopping power of swift ions for the defects formation in irradiation in the various conditions are calculated.

Atomistic simulation of defects formation and structure transitions in U-Mo alloys at swift heavy ion irradiation

At irradiation of swift heavy ions, the track formation frequently takes place in nuclear materials. There is a large interest to understanding of the mechanisms of defects/track formation at this phenomenon. In this work, the atomistic simulation of defects formation and melting in U-Mo alloys at irradiation of swift heavy ions has been carried out. We use the two-temperature atomistic model with explicit account of electron pressure and electron thermal conductivity. This two-temperature model describes ionic subsystem by means of molecular dynamics while the electron subsystem is considered in the continuum approach. The various mechanisms of structure changes at irradiation are examined. In particular, the simulation results indicate that the defects formation may be produced without melting and subsequent crystallization. Threshold stopping power of swift ions for the defects formation at irradiation in the various conditions are calculated.

Cumulative approaches to track formation under swift heavy ion (SHI) irradiation: Phenomenological correlation with formation energies of Frenkel pairs

An extensive survey for the formation energies of Frenkel pairs, as representative candidates for radiation-induced point defects, is presented and discussed in relation to the cumulative mechanisms (CM) of track formation in dielectric materials under swift heavy ion (SHI) irradiation. These mechanisms rely on the generation and accumulation of point defects during irradiation followed by collapse of the lattice once a threshold defect concentration is reached. The physical basis of those approaches has been discussed by Fecht as a defect-assisted transition to an amorphous phase. Although a first quantitative analysis of the CM model was previously performed for LiNbO3 crystals, we have, here, adopted a broader phenomenological approach. It explores the correlation between track formation thresholds and the energies for Frenkel pair formation for a broad range of materials. It is concluded that the threshold stopping powers can be roughly scaled with the energies required to generate a critical Frenkel pair concentration in the order of a few percent of the total atomic content. Finally, a comparison with the predictions of the thermal spike model is discussed within the analytical Szenes approximation.

Characterizing the Structure of the Optimal Stopping Policies Arising in Operations

This paper studies a stochastic model of optimal stopping processes that arise frequently in operational problems (e.g., when a manager needs to determine an optimal epoch to stop a process). For such problems, we propose an effective method that characterizes the structure of the optimal stopping policy for the class of discrete-time optimal stopping problems. Using the method, we also provide a set of metatheorems that characterize when a threshold or control-band type stopping policy is optimal. We show that our proposed method can characterize the structure of the optimal policy for some stopping problems for which conventional methods fail to do so. Our method also simplifies the analysis of some existing results. In addition, the metatheorems help identify sufficient conditions that yield simple optimal policies when such policies are not generally optimal. We show the aforementioned benefits of our method by applying it to several optimal stopping problems frequently encountered, for example, in operations, marketing, finance and economics literature. We remark that structural results make an optimal-stopping policy easier to follow, describe, compute and hence implement. They also help understand how a stopping policy should respond to changes in the operational environment. In addition, structural results are critical for the development of efficient algorithms to solve optimal stopping problems numerically.

Radiation damage in cubic-stabilized zirconia

Cubic yttria-stabilized zirconia (YSZ) can be used for nuclear applications as an inert matrix for actinide immobilization or transmutation . Indeed, the large amount of native oxygen vacancies leads to a high radiation tolerance of this material owing to defect recombination occurring in the atomic displacement cascades induced by fast neutron irradiation or ion implantations , as showed by molecular dynamics (MD) simulations. Amorphization cannot be obtained in YSZ either by nuclear-collision or electronic-excitation damage, just like in urania. A kind of polygonization structure with slightly disoriented crystalline domains is obtained in both cases. In the first steps of damage, specific isolated point defects (like F + -type color centers) and point-defect clusters are produced by nuclear collisions with charged particles or neutrons. Further increase of damage leads to dislocation-loop formation then to collapse of the dislocation network into a polygonization structure. For swift heavy ion irradiations , a similar polygonization structure is obtained above a threshold stopping power value of about 20–30 keV nm −1 .

Threshold stopping rules for diffusion processes and Stefan’s problem

Threshold stopping rules for diffusion processes and Stefan’s problem

Making tracks: electronic excitation roles in forming swift heavy ion tracks

Swift heavy ions cause material modification along their tracks, changes primarily due to theirvery dense electronic excitation. The available data for threshold stopping powers indicatetwo main classes of materials. Group I, with threshold stopping powers above about10 keV nm−1, includes some metals, crystalline semiconductors and a few insulators. Group II,with lower thresholds, comprises many insulators, amorphous materials and highTc oxide superconductors. We show that the systematic differences in behaviourresult from different coupling of the dense excited electrons, holes and excitonsto atomic (ionic) motions, and the consequent lattice relaxation. The couplingstrength of excitons and charge carriers with the lattice is crucial. For group II, themechanism appears to be the self-trapped exciton model of Itoh and Stoneham (1998Nucl. Instrum. Methods Phys. Res. B 146 362): the local structural changes occurroughly when the exciton concentration exceeds the number of lattice sites. Inmaterials of group I, excitons are not self-trapped and structural change requiresexcitation of a substantial fraction of bonding electrons, which induces spontaneouslattice expansion within a few hundred femtoseconds, as recently observed bylaser-induced time-resolved x-ray diffraction of semiconductors. Our analysis addresses anumber of experimental results, such as track morphology, the efficiency of trackregistration and the ratios of the threshold stopping power of various materials.

On the multi-attribute stopping problem with general value functions

We examine a sequential selection problem in which a single option must be selected. Each option's value is a function of its attributes, whose precise values can be ascertained at a given cost. We prove the optimality of a threshold stopping rule for a general class of objective functions.

Electronic sputtering of thin SiO 2 films by MeV heavy ions

The rate of removal of material from SiO 2 as a result of heavy ion irradiation, with energies in which energy loss via excitation and ionization of the solid predominates, depends strongly on the stopping power and angle of incidence of the incoming ions. There appears to be a threshold stopping power for SiO 2 of 500 eV/(10 15 at/cm 2) (or 3.5 keV/nm). This electronic sputter yield has been found to reach values as large as 10 4 atoms/incoming ion for 66 MeV Ag ions at an angle of incidence of 7° with the plane of the surface. Strikingly, the electronic sputter yield is very small for thin SiO 2 layers of a thickness ⩽1 nm when grown on c-Si, but it is appreciable for such layers deposited on the insulator silicon nitride. The data are discussed in the light of existing models for electronic sputtering invoking also models for potential sputtering of SiO 2 by low-energy, highly charged ions.

Simple ratio prophet inequalities for a mortal with multiple choices

Let X i ≥ 0 be independent, i = 1,…, n, with known distributions and let X n *= max(X 1,…,X n ). The classical ‘ratio prophet inequality’ compares the return to a prophet, which is EX n *, to that of a mortal, who observes the X i s sequentially, and must resort to a stopping rule t. The mortal's return is V(X 1,…,X n ) = max EX t , where the maximum is over all stopping rules. The classical inequality states that EX n * < 2V(X 1,…,X n ). In the present paper the mortal is given k ≥ 1 chances to choose. If he uses stopping rules t 1,…,t k his return is E(max(X t 1,…,X t k )). Let t(b) be the ‘simple threshold stopping rule’ defined to be the smallest i for which X i ≥ b, or n if there is no such i. We show that there always exists a proper choice of k thresholds, such that EX n * ≤ ((k+1)/k)Emax(X t 1,…,X t k )), where t i is of the form t(b i ) with some added randomization. Actually the thresholds can be taken to be thej/(k+1) percentile points of the distribution of X n *, j = 1,…,k, and hence only knowledge of the distribution of X n * is needed.