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This paper presents an inverse reinforcement learning (IRL) framework for Bayesian stopping time problems. By observing the actions of a Bayesian decision maker, we provide a necessary and sufficient condition to identify if these actions are consistent with optimizing a cost function. In a Bayesian (partially observed) setting, the inverse learner can at best identify optimality wrt the observed strategies. Our IRL algorithm identifies optimality and then constructs set-valued estimates of the cost function. To achieve this IRL objective, we use novel ideas from Bayesian revealed preferences stemming from microeconomics. We illustrate the proposed IRL scheme using two important examples of stopping time problems, namely, sequential hypothesis testing and Bayesian search. As a real-world example, we illustrate using a YouTube dataset comprising metadata from 190000 videos how the proposed IRL method predicts user engagement in online multimedia platforms with high accuracy. Finally, for finite datasets, we propose an IRL detection algorithm and give finite sample bounds on its error probabilities. [ABSTRACT FROM AUTHOR]

In this paper, we consider a zero-sum differential game that can be stopped by any of the participants at one of time points known in advance. The cost functional may depend both on the time when the game ends and the position of the system at that time and on the player who initiates the game stopping. When optimizing the expectation of this functional, each player, based on the information the player has about the realized trajectory of the system, makes decisions both about his/her probability of stopping the game and about his/her own control of the conflict-controlled system; however, nondeterministic distribution rules are also allowed. The existence of the game value is shown under the assumption of a saddle point condition in the small game (the Isaacs condition). The construction of a stochastic guide whose model is a continuous-time Markov chain was used to construct approximately optimal strategies for the players. [ABSTRACT FROM AUTHOR]

We start proceeding with the stopping time theory in discrete time with the help of the Mizar system [1], [4]. We prove, that the expression for two stopping times k1 and k2 not always implies a stopping time (k1 + k2) (see Theorem 6 in this paper). If you want to get a stopping time, you have to cut the function e.g. (k1 + k2) ∪ T (see [2, p. 283 Remark 6.14]). Next we introduce the stopping time in continuous time. We are focused on the intervals [0, r] where r ∈ R. We prove, that for I = [0, r] or I = [0,+∞[ the set {A ⋂ I : A ∈ Borel-Sets} is a σ-algebra of I (see Definition 6 in this paper, and more general given in [3, p.12 1.8e]). The interval I can be considered as a timeline from now to some point in the future. This set is necessary to define our next lemma. We prove the existence of the σ-algebra of the τ -past, where τ is a stopping time (see Definition 11 in this paper and [6, p.187, Definition 9.19]). If τ1 and τ2 are stopping times with τ1 is smaller or equal than τ2 we can prove, that the σ-algebra of the τ1-past is a subset of the σ-algebra of the τ2-past (see Theorem 9 in this paper and [6, p.187 Lemma 9.21]). Suppose, that you want to use Lemma 9.21 with some events, that never occur, see as a comparison the paper [5] and the example for ST(1)={+∞} in the Summary. We don't have the element +1 in our above-mentioned time intervals [0, r[ and [0,+1[. This is only possible if we construct a new σ-algebra on R ∪ {−∞,+∞}. This construction is similar to the Borel-Sets and we call this σ-algebra extended Borel sets (see Definition 13 in this paper and [3, p. 21]). It can be proved, that {+∞} is an Element of extended Borel sets (see Theorem 21 in this paper). Now we use the interval [0,+∞] as a basis. We construct a σ-algebra on [0,+∞] similar to the book ([3, p. 12 18e]), see Definition 18 in this paper, and call it extended Borel subsets. We prove for stopping times with this given σ-algebra, that for τ1 and τ2 are stopping times with τ1 is smaller or equal than τ2 we have the σ-algebra of the τ1-past is a subset of the σ-algebra of the τ2-past, see Theorem 25 in this paper. It is obvious, that {+∞} 2 extended Borel subsets. In general, Lemma 9.21 is important for the proof of the Optional Sampling Theorem, see 10.11 Proof of (i) in [6, p. 203]. [ABSTRACT FROM AUTHOR]

. We start with the definition of stopping time according to [4], p.283. We prove, that different definitions for stopping time can coincide. We give examples of stopping time using constant-functions or functions defined with the operator max or min (defined in [6], pp.37-38). Finally we give an example with some given filtration. Stopping time is very important for stochastic finance. A stopping time is the moment, where a certain event occurs ([7], p.372) and can be used together with stochastic processes ([4], p.283). Look at the following example: we install a function ST: {1,2,3,4} → {0, 1, 2} ∪ {+∞}, we define:. a. ST(1)=1, ST(2)=1, ST(3)=2, ST(4)=2. b. The set {0,1,2} consists of time points: 0=now, 1=tomorrow, 2=the day after tomorrow. We can prove: c. {w, where w is Element of Ω: ST.w=0}=ø & {w, where w is Element of Ω: ST.w=1}={1,2} & {w, where w is Element of Ω: ST.w=2}={3,4} and ST is a stopping time. We use a function Filt as Filtration of {0,1,2}, Σ where Filt(0)=Ωnow, Filt(1)=Ωfut1 and Filt(2)=Ωfut2. From a.,b. and c. we know that: d. {w, where w is Element of Ω: ST.w=0} in Ωnow and {w, where w is Element of Ω: ST.w=1} in Ωfut1 and {w, where w is Element of Ω: ST.w=2} in Ωfut2. The sets in d. are events, which occur at the time points 0(=now), 1(=tomorrow) or 2(=the day after tomorrow), see also [7], p.371. Suppose we have ST(1)=+∞, then this means that for 1 the corresponding event never occurs. As an interpretation for our installed functions consider the given adapted stochastic process in the article [5]. ST(1)=1 means, that the given element 1 in {1,2,3,4} is stopped in 1 (=tomorrow). That tells us, that we have to look at the value f2(1) which is equal to 80. The same argumentation can be applied for the element 2 in {1,2,3,4}. ST(3)=2 means, that the given element 3 in {1,2,3,4} is stopped in 2 (=the day after tomorrow). That tells us, that we have to look at the value f3(3) which is equal to 100. ST(4)=2 means, that the given element 4 in {1,2,3,4} is stopped in 2 (=the day after tomorrow). That tells us, that we have to look at the value f3(4) which is equal to 120. In the real world, these functions can be used for questions like: when does the share price exceed a certain limit? (see [7], p.372). [ABSTRACT FROM AUTHOR]

Two optimal stopping problems for geometric random walks with the observer's power payoff function, on the finite and infinite horizons, are solved. For these problems, an explicit form of the cut value and also optimal stopping rules are established. It is proved that the optimal stopping rules are nonrandomized thresholds and describe the corresponding free boundary. An explicit form of the free boundary is presented. [ABSTRACT FROM AUTHOR]

In this work, we consider a stochastic differential equation that generalizes the well known Paris’ equation from fracture of materials. The model describes the propagation of cracks on solids, and it includes a deterministic summand and a stochastic component in terms of a Brownian motion. The use of Itô’s stochastic integral gives an equivalent stochastic integral equation that is further generalized here. We note that the probability distribution of the stopping time of the general model satisfies a deterministic diffusion–advection partial differential equation for which the solution is known only in a reduced number of particular cases. Motivated by these analytical results, we develop a fast finite-difference method to approximate the distribution of the stopping time. The method is an explicit exponential-like technique that preserves the main features of a probability distribution, namely, the non-negativity, the boundedness from above by 1 as well as the spatial monotonicity. Moreover, the method is a monotone technique that is also capable of preserving the temporal monotonicity of the approximations. These properties of the proposed methodology are thoroughly established in the present manuscript. A continuity condition of the numerical solutions in terms of the initial conditions and the temporal computational parameter is established also, together with a limiting property of the methodology when the free parameter tends to infinity. For comparison purposes, we are providing an implicit and stable discretization of the mathematical model which has a second order of convergence but for which conditions that guarantee the positivity, the boundedness and the monotonicity of approximations are not available. The numerical simulations obtained with implementations of our techniques show that the explicit method is an efficient scheme that preserves the characteristics of interest (non-negativity, boundedness from above by 1 and monotonicity), and that the numerical approximations are in good agreement with the known exact solutions. [ABSTRACT FROM AUTHOR]

In this paper, we consider a size-dependent renewal risk model with stopping time claim-number process. In this model, we do not make any assumption on the dependence structure of claim sizes and inter-arrival times. We study large deviations of the aggregate amount of claims. For the subexponential heavy-tailed case, we obtain a precise large-deviation formula; our method substantially relies on a martingale for the structure of our models. [ABSTRACT FROM AUTHOR]

When to stop testing is an important aspect in software test management. This paper discusses a new approach to this problem. There are two major improvements in this approach in comparison to the earlier studies. It uses failure size proportional model to estimate the number of failures and the corresponding cost of repair. Instead of reliability it uses a new measure called attained failure size. Failure size is the probability of finding a failure causing input in the input domain. Attained failure size is the failure size at the termination of testing. The advantages of these improvements are also discussed. [ABSTRACT FROM AUTHOR]

A general scale-space algorithm is presented for denoising signals and images with spatially varying dominant scales. The process is formulated as a partial differential equation with spatially varying time. The proposed adaptivity is semilocal and is in conjunction with the classical gradient-based diffusion coefficient, designed to preserve edges. The new algorithm aims at maximizing a local SNR measure of the denoised image. It is based on a generalization of a global stopping time criterion presented recently by the author and his colleagues. Most notably, the method also works well for partially textured images and outperforms any selection of a global stopping time. Given an estimate of the noise variance, the procedure is automatic and can be applied well to most natural images. [ABSTRACT FROM AUTHOR]

In this paper we deal with the optimal bankruptcy problem for agents who can optimally allocate their consumption rate, the amount of capital invested in the risky asset, as well as their leisure time. In our framework, the agents are endowed by an initial debt, and they are required to repay their debt continuously. Declaring bankruptcy, the debt repayment is exempted at the cost of a wealth shrinkage. We implement the duality method to solve the problem analytically and conduct a sensitivity analysis to the bankruptcy cost and benefit parameters. Introducing the flexible leisure/working rate, and therefore the labour income, into the bankruptcy model, we investigate its effect on the optimal strategies. [ABSTRACT FROM AUTHOR]

Background: The Elliot wave principle commonly characterizes the impulsive and corrective wave trends for both financial market trends and electrocardiograms. The impulsive wave trends of electrocardiograms can annotate several wave components of heart-beats including pathological heartbeat waveforms. The stopping time inquires which ordinal element satisfies the assumed mathematical condition within a numerical set. The proposed work constitutes several algorithmic states in reinforcement learning from the stopping time decision, which determines the impulsive wave trends. Each proposed algorithmic state is applicable to any relevant algorithmic state in reinforcement learning with fully numerical explanations. Because commercial electrocardiographs still misinterpret myocardial infarctions from extraordinary electrocardiograms, a novel algorithm needs to be developed to evaluate myocardial infarctions. Moreover, differential diagnosis for right ventricle infarction is required to contraindicate a medication such as nitroglycerin.Methods: The proposed work implements the stopping time theory to impulsive wave trend distribution. The searching process of the stopping time theory is equivalent to the actions toward algorithmic states in reinforcement learning. The state value from each algorithmic state represents the numerically deterministic annotated results from the impulsive wave trend distribution. The shape of the impulsive waveform is evaluated from the interoperable algorithmic states via least-first-power approximation and approximate entropy. The annotated electrocardiograms from the impulsive wave trend distribution utilize a structure of neural networks to approximate the isoelectric baseline amplitude value of the electrocardiograms, and detect the conditions of myocardial infarction. The annotated results from the impulsive wave trend distribution consist of another reinforcement learning environment for the evaluation of impulsive waveform direction.Results: The accuracy to discern myocardial infarction was found to be 99.2754% for the data from the comma-separated value format files, and 99.3579% for those containing representative beats. The clinical dataset included 276 electrocardiograms from the comma-separated value files and 623 representative beats.Conclusions: Our study aims to support clinical interpretation on 12-channel electrocardiograms. The proposed work is suitable for a differential diagnosis under infarction in the right ventricle to avoid contraindicated medication during emergency. An impulsive waveform that is affected by myocardial infarction or the electrical direction of electrocardiography is represented as an inverse waveform. [ABSTRACT FROM AUTHOR]

Abstract: We consider the optimal double stopping time problem for each stopping time S. Following the optimal one stopping time problem, we study the existence of optimal stopping times and give a method to compute them. The key point is the construction of a new reward ϕ such that . [Copyright &y& Elsevier]

We develop a novel time-selection strategy for iterative image restoration techniques: the stopping time is chosen so that the correlation of signal and noise in the filtered image is minimized. The new method is applicable to any images where the noise to be removed is uncorrelated with the signal, under the assumptions that the filter used is suitable for the given type of data, and that neither the additive noise nor the filtering procedure alter the average gray value; no other knowledge (e.g. the noise variance, training data etc.) is needed. We analyse the theoretical properties of the method, then test the performance of our time estimation procedure experimentally, and demonstrate that it yields near-optimal results for a wide range of noise levels and for various filtering methods. [ABSTRACT FROM AUTHOR]

Electronic markets are virtual frameworks where entities not known in advance have the opportunity to interact for the trading of products or services. Usually, a negotiation is necessary for the conclusion of the transaction. The conclusion is either positive (agreement) or negative (conflict). An efficient reasoning mechanism is necessary for players participating in negotiations. In this paper, we focus on the buyer side and propose two decision models based on the optimal stopping theory (OST). OST is proved to be very efficient in cases where an entity tries to find the time to stop a process with the aim of maximizing her utility. The outcome of the proposed decision method indicates whether the buyer stops a negotiation either by accepting the offer or continuing in the negotiation by rejecting it. In our models, we assume zero knowledge on the players' characteristics. Our proposed decision models do not require any complex modeling or any information provided by experts. Experimental results reveal the efficiency of each model and provide a comparison assessment with other research efforts. [ABSTRACT FROM AUTHOR]

As an image-making tool for scientists studying the transient, instantaneous photography has long been seen as opening up a visual realm previously inaccessible to the inferior testimony of the human eye. But when photographic pioneer Henry Fox Talbot took the first photograph of a moving object by the light of an electric spark in 1851, he was guided by existing visual practices designed to create instantaneous vision in the eye itself. Exploring the background behind the peculiar subject of his experiment – a mechanically spinning disc – reveals a hidden prehistory of spark-illuminated photography: physicists’ pre-photographic techniques for stopping time. [Copyright &y& Elsevier]

We consider denoising applications using nonlinear diffusion filters of BV type. Using the multiple timescales method, an equation is derived that approximates the time evolution of the image noise. Analysis of the corresponding variational inequality leads to an estimate of the timescale over which the noise decays to its local mean, given in terms of the filter parameters. We present a number of computed examples that demonstrate the validity of our stopping time estimate. [ABSTRACT FROM AUTHOR]

Fixed-horizon planning considers a weighted graph and asks to construct a path that maximizes the sum of weights for a given time horizon T. However, in many scenarios, the time horizon is not fixed, but the stopping time is chosen according to some distribution such that the expected stopping time is T. If the stopping-time distribution is not known, then to ensure robustness, the distribution is chosen by an adversary as the worst-case scenario. A stationary plan for every vertex always chooses the same outgoing edge. For fixed horizon or fixed stopping-time distribution, stationary plans are not sufficient for optimality. Quite surprisingly we show that when an adversary chooses the stopping-time distribution with expected stopping-time T , then stationary plans are sufficient. While computing optimal stationary plans for fixed horizon is NP-complete, we show that computing optimal stationary plans under adversarial stopping-time distribution can be achieved in polynomial time. [ABSTRACT FROM AUTHOR]

Studies the tension between the claim that Article V of the U.S. Constitution articulates the exclusive procedure by which the Constitution may be amended and the historical commitment of the U.S. to the ideal that the people are sovereign. Background on Article V; Political positions on the resolution of Representative Thomas Corwin of Ohio to amend the U.S. Constitution; Efficacy of the Corwin amendment.

Data often come in the form of a longitudinal series, say N(⋅), whose observation has been "stopped" either by a terminal event U (e.g., death) or censoring event C (e.g., lost to follow-up). When N(⋅) is not deterministic, it is generally not possible to use standard survival analysis tools (e.g., the Kaplan-Meier estimator) to consistently estimate functionals of the distribution of N(U) because of "induced" informative censoring. Various seemingly unrelated estimators recently have been proposed to handle this difficulty within the context of specific problems, ranging from the analysis of quality-adjusted survival data to recurrent event data to lifetime medical cost data. In this article I consider a general framework containing each of these specific examples as a special case, propose a class of estimators for the mean of the stopped longitudinal process, and establish the asymptotic properties of this class of estimators. Connections between the aforementioned estimators are established, and questions related to asymptotic relative efficiency of the various estimators are addressed. Based on these results, I propose some new estimators with finite-sample optimality properties. Finally, I investigate the utility of the proposed estimators in two simulated examples, and discuss potential extensions of this work. [ABSTRACT FROM AUTHOR]

Results are obtained on the limiting distribution and corresponding moment convergence for the (normalized) stopping time of an SPRT, as the boundaries of the continuation region become infinite. These asymptotic results suggest a certain approximation for the variance of the stopping time, which is compared with some Monte Carlo results of Cox and Roseberry (1966) and an approximation due to Ghosh (1969), in the case of testing a normal mean with known variance. The approximation appears to be good provided that the mean of the loglikelihood ratio is not too close to zero. [ABSTRACT FROM AUTHOR]

In visible light communication (VLC), the precise latency evaluation of wireless access networks and the efficient forwarding strategy of core networks are the crux for end-to-end reliability provisioning. Leveraging martingale theory, an elegant latency-bounded reliability analysis framework is studied for the VLC network. Considering the characteristic that VLC links are easy to block, the martingale of the service process is constructed. Based on the time shift features, the martingale process related to latency is proposed for the VLC system, which models the influence of entanglement between aggregate arrivals and random service on latency. A stopping time event about latency is defined. Renting the stopping time theory, a tight upper bound of the unreliability with regard to latency is derived. In the core network, a dynamic forward backhaul framework is proposed, which uses the relay selection algorithm based on back-pressure theory to improve data transmission quality. The theoretical latency-bounded reliability matches the simulation results well, which verifies the effectiveness of the proposed analysis framework, and the proposed relay selection algorithm can also improve network performance under data-intensive transmission. [ABSTRACT FROM AUTHOR]

Motivated by problems in behavioural finance, we provide two explicit constructions of a randomized stopping time which embeds a given centred distribution μ on integers into a simple symmetric random walk in a uniformly integrable manner. Our first construction has a simple Markovian structure: at each step, we stop if an independent coin with a state-dependent bias returns tails. Our second construction is a discrete analogue of the celebrated Azéma–Yor solution and requires independent coin tosses only when excursions away from maximum breach predefined levels. Further, this construction maximizes the distribution of the stopped running maximum among all uniformly integrable embeddings of μ. [ABSTRACT FROM AUTHOR]

In this paper, we investigate an application of the statistical concept of causality, based on Granger's definition of causality, on raw increasing processes as well as on optional and predictable measures. A raw increasing process is optional (predictable) if the bounded (left-continuous) process X, associated with the measure μ A (X) , is self-caused. Also, the measure μ A (X) is optional (predictable) if an associated process X is self-caused with some additional assumptions. Some of the obtained results, in terms of self-causality, can be directly applied to defining conditions for an optional stopping time to become predictable. [ABSTRACT FROM AUTHOR]

We consider the stochastic Navier–Stokes equations in three dimensions and prove that the law of analytically weak solutions is not unique. In particular, we focus on three examples of a stochastic perturbation: an additive, a linear multiplicative and a nonlinear noise of cylindrical type, all driven by a Wiener process. In these settings, we develop a stochastic counterpart of the convex integration method introduced recently by Buckmaster and Vicol. This permits us to construct probabilistically strong and analytically weak solutions defined up to a suitable stopping time. In addition, these solutions fail to satisfy the corresponding energy inequality at a prescribed time with a prescribed probability. Then we introduce a general probabilistic construction used to extend the convex integration solutions beyond the stopping time and in particular to the whole time interval [0,∞). Finally, we show that their law is distinct from the law of solutions obtained by Galerkin approximation. In particular, non uniqueness in law holds on an arbitrary time interval[0,T], T > 0. [ABSTRACT FROM AUTHOR]

We study a class of non-linear Backward stochastic differential equations (BSDE) with a superlinear driver process f adapted to a filtration F and over a random time interval [[0, S]] where S is a stopping time of F. The terminal condition ξ is allowed to take the value +∞, i.e., singular. We call a stopping time S solvable with respect to a given BSDE and filtration if the BSDE has a minimal supersolution with terminal value ∞ at terminal time S. Our goal is to show existence of solutions to the BSDE for a range of singular terminal values under the assumption that S is solvable. We will do so by proving that the minimal supersolution to the BSDE is a solution, i.e., it is continuous at time S and attains the terminal value with probability 1. We consider three types of terminal values: 1) Markovian: i.e., ξ is of the form ξ = g(ΞS) where Ξ is a continuous Markovian diffusion process, S is a hitting time of Ξ and g is a deterministic function 2) terminal conditions of the form ξ1 = ∞· 1(τ≥) and 3) ξ2 = ∞· 1(τ≥) where τ is another stopping time. For general ξ we prove that minimal supersolution has a limit at time S provided that F is left continuous at time S. Finally, we discuss the implications of our results about Markovian terminal conditions to the solution of non-linear elliptic PDE with singular boundary conditions. [ABSTRACT FROM AUTHOR]

In this paper we study the stochastic area swept by a regular time-homogeneous diffusion till a stopping time. This unifies some recent literature in this area. Through stochastic time-change we establish a link between the stochastic area and the stopping time of another associated time-homogeneous diffusion. Then we characterize the Laplace transform and integer moments of the stochastic area in terms of the eigenfunctions of the associated diffusion. We show applications of the results to a new structural model of default (Yildirim [28] ) and the Omega risk model of bankruptcy in risk analysis (Gerber, Shiu and Yang [11] ). [ABSTRACT FROM AUTHOR]

Experimental observations of vacuum radiation and vacuum frictional torque are challenging due to their vanishingly small effects in practical systems. For example, a nanosphere rotating at 1 GHz in free space slows down due to friction from vacuum fluctuations with a stopping time around the age of the Universe. Here, we show that a spinning yttrium iron garnet (YIG) nanosphere near aluminum or YIG slabs generates vacuum radiation with radiation power eight orders of magnitude larger than other metallic or dielectric spinning nanospheres. We achieve this giant enhancement by exploiting the large near-field magnetic local density of states in YIG systems, which occurs in the low-frequency GHz regime comparable to the rotation frequency. Furthermore, we propose a realistic experimental setup for observing the effects of this large vacuum radiation and frictional torque under experimentally accessible conditions. [ABSTRACT FROM AUTHOR]

This paper considers a pair (F , τ) , where F is a filtration representing the "public" flow of information that is available to all agents over time, and τ is a random time that might not be an F -stopping time. This setting covers the case of a credit risk framework, where τ models the default time of a firm or client, and the setting of life insurance, where τ is the death time of an agent. It is clear that random times cannot be observed before their occurrence. Thus, the larger filtration, G , which incorporates F and makes τ observable, results from the progressive enlargement of F with τ. For this informational setting, governed by G , we analyze the optimal stopping problem in three main directions. The first direction consists of characterizing the existence of the solution to this problem in terms of F -observable processes. The second direction lies in deriving the mathematical structures of the value process of this control problem, while the third direction singles out the associated optimal stopping problem under F. These three aspects allow us to deeply quantify how τ impacts the optimal stopping problem and are also vital for studying reflected backward stochastic differential equations that arise naturally from pricing and hedging of vulnerable claims. [ABSTRACT FROM AUTHOR]

We present an implicit method for solving the diffusion equation for the evolution of the dust fraction in the terminal velocity approximation using dust-as-mixture smoothed particle hydrodynamics. The numerical scheme involves casting the dust diffusion equation into implicit form, rearranging into its resolvent cubic equation and solving analytically. This method is relevant for small grains that are tightly coupled to the gas, such as sub-micron dust grains in the interstellar medium or millimetre-sized dust grains in protoplanetary discs. The method avoids problems with the variable used to evolve the dust fraction becoming negative when evolved explicitly and is fast and accurate, avoiding the need for dust stopping time limiters and significantly reducing computational expense. Whilst this method is an improvement over using the explicit terminal velocity approximation method, as with any dust-as-mixture method it still fails to give accurate solutions in the limit of large (weakly coupled) grains. [ABSTRACT FROM AUTHOR]

Timing the selling of crude oil futures to control risk is a worth studying question given the swift fall of their prices. This paper proposes an optimal stopping model to find the optimal selling time at the beginning of the downtrend. The model depends on the crude oil futures prices drawdown and the boundary to identify the occurrence of downtrend in real-time. The numerical simulation and empirical analyses help verify the effectiveness of the proposed optimal stopping time model, especially, in 2007, when the model can effectively avoid losses. The conclusions of the paper provide a new perspective for investors to control risk. [ABSTRACT FROM AUTHOR]

The Train Operation Plan (TOP) of urban rail transit (URT) is a comprehensive plan for the operation of trains, the use of facilities and equipment, and the organization of other operational tasks. The TOP should not only be formulated in terms of time-varying passenger flow periods, but it should also be arranged to consider the substitutability of trains between multiple routes combined with the passenger choice. Based on the principle of "operating by the flow" and the requirement for precise allocation of transport capacity for multiple routes, this article constructs a multiobjective nonlinear integer programming model by taking the minimized generalized travel cost of passengers, total running mileage of trains, fluctuation of trains for each route (as optimization targets), and the combination of requirements of both headways and fully loaded rates as constraints. A multiobjective genetic-based algorithm is designed to simultaneously optimize the TOP and the two-way train stopping time in each period. Finally, the proposed model and algorithm are validated with the real data from the Guangzhou Metro Line 2. The results show that the Pareto optimal TOP and dynamic train stopping time are significantly improved compared to the original values. [ABSTRACT FROM AUTHOR]

Most results regarding Skorokhod embedding problems SEP so far rely on the assumption that the corresponding stopped process is uniformly integrable, which is equivalent to the convex ordering condition U μ ≤ U ν when the underlying process is a local martingale. In this paper, we study the existence, construction of Root's solutions to SEP, in the absence of this convex ordering condition. We replace the uniform integrability condition by the minimality condition (Monroe, 1972), as the criterion of "good" solutions. A sufficient and necessary condition (in terms of local time) for minimality is given. We also discuss the optimality of such minimal solutions. These results extend the generality of the results given by Cox and Wang (2013) and Gassiat et al. (2015). At last, we extend all the results above to multi-marginal embedding problems based on the work of Cox et al. (2018). [ABSTRACT FROM AUTHOR]

Let X be a progressively measurable, almost surely right-continuous stochastic process such that X τ ∈ L 1 and E [ X τ ] = E [ X 0 ] for each finite stopping time τ . In 2006, Cherny showed that X is then a uniformly integrable martingale provided that X is additionally nonnegative. Cherny then posed the question whether this implication also holds even if X is not necessarily nonnegative. We provide an example that illustrates that this implication is wrong, in general. If, however, an additional integrability assumption is made on the limit inferior of | X | then the implication holds. Finally, we argue that this integrability assumption holds if the stopping times are allowed to be randomized in a suitable sense. [ABSTRACT FROM AUTHOR]

The streaming instability, a promising mechanism to drive planetesimal formation in dusty protoplanetary discs, relies on aerodynamic drag naturally induced by the background radial pressure gradient. This gradient should vary in discs, but its effect on the streaming instability has not been sufficiently explored. For this purpose, we use numerical simulations of an unstratified disc to study the non-linear saturation of the streaming instability with mono-disperse dust particles and survey a wide range of gradients for two distinct combinations of the particle stopping time and the dust-to-gas mass ratio. As the gradient increases, we find most kinematic and morphological properties increase but not always in linear proportion. The density distributions of tightly coupled particles are insensitive to the gradient whereas marginally coupled particles tend to concentrate by more than an order of magnitude as the gradient decreases. Moreover, dust–gas vortices for tightly coupled particles shrink as the gradient decreases, and we note higher resolutions are required to trigger the instability in this case. In addition, we find various properties at saturation that depend on the gradient may be observable and may help reconstruct models of observed discs dominated by streaming turbulence. In general, increased dust diffusion from stronger gradients can lower the concentration of dust filaments and can explain the higher solid abundances needed to trigger strong particle clumping and the reduced planetesimal formation efficiency previously found in vertically stratified simulations. [ABSTRACT FROM AUTHOR]

We study the asymptotic duration of optimal stopping problems involving a sequence of independent random variables that are drawn from a known continuous distribution. These variables are observed as a sequence, where no recall of previous observations is permitted, and the objective is to form an optimal strategy to maximise the expected reward. In our previous work, we presented a methodology, borrowing techniques from applied mathematics, for obtaining asymptotic expressions for the expectation duration of the optimal stopping time where one stop is permitted. In this study, we generalise further to the case where more than one stop is permitted, with an updated objective function of maximising the expected sum of the variables chosen. We formulate a complete generalisation for an exponential family as well as the uniform distribution by utilising an inductive approach in the formulation of the stopping rule. Explicit examples are shown for common probability functions as well as simulations to verify the asymptotic calculations. [ABSTRACT FROM AUTHOR]

The aim of this work is to investigate the influence of nonlinear multiplicative noise on the Cauchy problem of the nonlinear fractional Schrödinger equation in the non-radial case. Local well-posedness follows from estimates related to the stochastic convolution and deterministic non-radial Strichartz estimates. Furthermore, the blow-up criterion is presented. Then, with the help of Itô's lemma and stopping time arguments, the global solution is constructed almost surely. The main innovation is that the non-radial global solution is given under fractional-order derivatives and a nonlinear noise term. [ABSTRACT FROM AUTHOR]

This study aims to identify key factors and sensitive intervals affect the school road traffic characteristics. We collect traffic data from the parking area and the school road (400-700 meters). The simulation is calibrated to ensure the error of outputs are within 1.5%. A sensitivity analysis method is proposed, it makes the multifactor comparable. The sensitivity factors of vehicle delay, queue length, and average speed are 1.44, 2.03, and 0.28 in school road, and the bottleneck road are 3.07, 4.44, and 0.65. The traffic indicators change more concentrated in bottleneck road but greater in school road. 6 scenarios are created to analyze school road traffic characteristics. Traffic flow (TF), number of parking spaces (NPS), and stopping time (ST) are selected as variables. Scenarios 1-3 are univariate, and scenarios 4-6 are bivariate. TF is the key factor with a sensitivity interval of [1300,1700]. [ABSTRACT FROM AUTHOR]

This paper derives upper and lower bounds of the price in the optimal stopping problem for a an adapted random sequence in the case of finite horizon. As is demonstrated below, the bounds can be found by solving the maximax and maximin setups of optimal stopping problems. For these setups, we obtain conditions under which 1) a recurrent relation is satisfied for the upper (lower) truncated sequence of optimal stopping prices; 2) an optimality criterion is constructed for the stopping times; 3) the structure and invariance of the optimal stopping times are established. Some examples with explicit solutions of the maximax and maximin setups of optimal stopping problems are given. [ABSTRACT FROM AUTHOR]

Visible-light-based transmission application plays an important role in various types of sensor services for the Internet of Things (IoTs). However, in big data scenarios, current visible-light-based systems cannot achieve concurrent high-speed communication, low-speed communication, and positioning. Therefore, in this article, we propose a smart visible-light-based fusion applications system, named Fasys, to solve the above problem for the big data traffic with heterogeneity. Specifically, for low-speed data services, we propose a novel linear block coding and bit interleaving mechanism, which enhances the LED positioning accuracy and recovers the lost data bits in the interframe gap (IFG). For high-speed data services with traffic possessing burstiness, an elegant statistical reliability analysis framework in regard to latency is proposed based on martingale theory. The backlog martingale process is constructed. Leveraging stopping time theory, a tight upper bound of unreliability is obtained. An arrival abstraction and traffic allocation scheme is designed, which contributes to decouple the reliability requirement as the maximum supportable arrival load. Finally, we implement our Fasys system, and extensive experimental results show that our system can achieve consistent high-precision positioning and low-BER data communication for low-speed data services. And the proposed martingale-based traffic allocation scheme can achieve the provisioning of reliability in regard to the latency for high-speed data services. [ABSTRACT FROM AUTHOR]

In this article, we study fractional stochastic Burgers equations perturbed by fractional noise. Existence and uniqueness of a mild solution is given by a fixed point argument. Then, we explore Hölder regularity of the mild solution in C'([0, T*]; LP (Ω; Ḣγ) for some stopping time T*. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the early stopping strategy for the iterative regularization technique, which is based on gradient descent of convex loss functions in reproducing kernel Hilbert spaces without an explicit regularization term. This work shows that projecting the last iterate of the stopping time produces an estimator that can improve the generalization ability. Using the upper bound of the generalization errors, we establish a close link between the iterative regularization and Tikhonov regularization scheme and explain theoretically why the two schemes have similar regularization paths in the existing numerical simulations. We introduce a data-dependent way based on cross-validation to select the stopping time. We prove that the a-posteriori selection way can retain the comparable generalization errors to those obtained by our stopping rules with a-prior parameters. [ABSTRACT FROM AUTHOR]

The paper considers the problem of optimal control in models with disorder and provides the computational scheme of its solution. The proposed method is based on replacing the disorder with its estimate by the stopping time. The calculations take place on the binary tree with nodes divided into two classes. The division of tree nodes into two classes is carried out using a decision rule associated either with testing two hypothesis, or with the optimal stopping of a Markov process developing on a binary tree. The estimate of the disorder is the moment at which the walk on the tree is placed in a node of the first class for the first time. The example of the optimal control problem is related to the problem of quantile hedging of a payoff. [ABSTRACT FROM AUTHOR]

Background: The hepatopulmonary syndrome (HPS) is a pulmonary complication of liver disease found in 10 to 32% of patients with cirrhosis and is characterized by intrapulmonary vascular dilatations and abnormal oxygenation. Liver transplantation is the only effective therapy for this disease. Patients with HPS have significant exercise limitations, impacting their quality of life and associated with poor liver transplant outcomes. Many patients with HPS exhibit orthodeoxia-an improvement in oxygenation in the supine compared to the upright position. We hypothesize that exercise capacity will be superior in the supine compared to the upright position in such patients.Methods: We propose a randomized controlled crossover trial in patients with moderate HPS (PaO2 < 80 mmHg) and orthodeoxia (supine to upright PaO2 decrease > 4 mmHg) comparing the effect of supine vs upright position on exercise. Patients with pulmonary hypertension, FEV1/FVC ratio < 0.65, significant coronary artery disease, disorders preventing or contraindicating use of a cycle ergometer, and/or moderate or severe ascites will be excluded. Participants will be randomized to cycle ergometry in either the supine or upright position. After a short washout period (a minimum of 1 day to a maximum of 4 weeks), participants will crossover and perform an exercise in the alternate position. Exercise will be performed at a constant work rate of 70-85% of the predicted peak work rate until the "stopping time" is reached, defined by exhaustion, profound desaturation, or safety concerns (drop in systolic blood pressure or life-threatening arrhythmia). The primary outcome will be the difference in the stopping time between exercise positions, compared with a repeated measures analysis of variance method with a mixed effects model approach. The model will be adjusted for period effects. P < 0.05 will be considered statistically significant.Discussion: HPS patients have hypoxemia leading to significant exercise limitations. If our study is positive, a supine exercise regimen could become a routine prescription for patients with HPS and orthodeoxia, enabling them to exercise more effectively. Future studies could explore the corresponding effects of a supine exercise training regimen on physiologic variables such as long-term exercise capacity, quality of life, dyspnea, and liver transplantation outcomes.Trial Registration: ClinicalTrials.gov Protocol Registration and Results System (PRS) NCT04004104 . Registered on 1 July 2019. [ABSTRACT FROM AUTHOR]