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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]

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 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]

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]

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]

In this paper, the pure strategy subgame perfect equilibria of a general class of stopping time games are studied. It is shown that there always exists a natural class of Markov Perfect Equilibria, called stopping equilibria. Such equilibria can be computed as a solution of a single agent stopping time problem, rather than of a fixed point problem. A complete characterization of stopping equilibria is presented. Conditions are given under which the outcomes of such equilibria span the set of all possible outcomes from perfect equilibria. Two economic applications of the theory, product innovations and the timing of asset sales, are discussed. [ABSTRACT FROM AUTHOR]

A new distribution called a generalized binomial distribution of order k is defined and some properties are investigated. A class of enumeration schemes for success-runs of a specified length including non-overlapping and overlapping enumeration schemes is rigorously studied. For each nonnegative integer μ less than the specified length of the runs, an enumeration scheme called μ-overlapping way of counting is defined. Let k and ℓ be positive integers satisfying ℓ < k. Based on independent Bernoulli trials, it is shown that the number of (ℓ− 1)-overlapping occurrences of success-run of length k until the n-th overlapping occurrence of success-run of length ℓ follows the generalized binomial distribution of order ( k−ℓ). In particular, the number of non-overlapping occurrences of success-run of length k until the n-th success follows the generalized binomial distribution of order ( k− 1). The distribution remains unchanged essentially even if the underlying sequence is changed from the sequence of independent Bernoulli trials to a dependent sequence such as higher order Markov dependent trials. A practical example of the generalized binomial distribution of order k is also given. [ABSTRACT FROM AUTHOR]

We consider stopping problems in which a decision maker (DM) faces an unknown state of nature and decides sequentially whether to stop and take an irreversible action, or pay a fee and obtain additional information. We discuss the value and quality of information. The former is the maximal discounted expected total payment the DM can generate under a history-dependent fee scheme. We show that among all history-dependent fee schemes, the upfront fee scheme (as opposed, for instance, to pay-for-use) is optimal: it achieves the value of information. The effects on the optimal strategy of obtaining information from a more accurate source and of having a higher discount factor are distinct, as far as expected stopping time and its distribution are concerned. However, these factors have a similar effect in that they both enlarge the set of cases in which the optimal strategy prescribes waiting. [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]

An asymptotic analysis is made to find the penetration depth and the stopping time for a particle impacting a granular bed. Newton's equation is solved with a drag force with two terms, one term proportional to the square of the velocity and one term linear in the depth. The penetration depth is found to increase with the logarithm of the impact velocity, while the stopping time is found to decrease with the inverse of the square root of the logarithm of the impact velocity. [ABSTRACT FROM AUTHOR]

The paper analyzes the implications of extreme events on the proper choice of discounting. Any discounting with constant or declining rates can be linked to random “stopping time” events, which define the internal discount-related horizons of evaluations. Conversely, any stopping time induces a discounting, in particular, with the standard discount rates. The expected duration of the stopping time horizon for discount rates obtained from capital markets does not exceed a few decades and, as such, these rates may significantly underestimate the net benefits of long-term decisions. The alternative undiscounted stopping time criterion allows to induce social discounting focusing on arrival times of potential extreme events rather then horizons of market interests. Induced discount rates are conditional on the degree of social commitment to mitigate risk. In general, extreme events affect these rates, which alter the optimal mitigation efforts that, in turn, change events. The use of undiscounted stopping time criteria requires stochastic optimisation methods. [ABSTRACT FROM AUTHOR]

Sudden, unexpected loading to the trunk has been reported in the literature as a potential cause of low-back disorders. This study’s aim was to investigate the effect of “readiness training” on the response to sudden back loading among untrained healthy individuals. The study included 19 participants and 19 matched controls. All were employees at the National Institute of Occupational Health. The participants received ten 45-min training sessions during a 4-week period. The training focused on reactions to a variety of expected and unexpected sudden trunk loadings, including balance and coordination exercises. Before and after the training, all subjects were tested for reaction to sudden trunk loading (SL). This entailed applying a horizontal force of 58 N to the subject’s upper back. Elapsed time-measured between SL and stopping-decreased significantly in the training group (from 337 to 311 ms) compared with the control group. The improved stopping time was associated with a changed EMG signal, characterized by an increase in the early parts of the response (up to 225 ms) and a subsequent decrease. EMG onset latency was unaffected by training. This study is apparently one of the first to demonstrate that the response to sudden trunk loading can be improved in healthy subjects without an increase in pre-activation and associated trunk stiffness. In perspective, the results indicate a possibility for a training-induced reduction of the risk of low-back injuries, e.g., in nurses exposed to sudden trunk perturbations during patient handling. [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]

Manna and Chaudhuri (Eur. J. Oper. Res. 171(2):557-566, ) presented a production-inventory system for deteriorating items with demand rate being a linearly ramp type function of time and production rate being proportional to the demand rate. The two models without shortages and with shortages were discussed. Both models were studied assuming that the time point at which the demand is stabilized occurs before the production stopping time. In this paper, we complete this model by considering that: (a) for the model with no shortages; the demand rate is stabilized after the production stopping time and (b) for the model with shortages; the demand rate is stabilized after the production stopping time or after the time when the inventory level reaches zero or after the production restarting time. In addition, we extend the work of Manna and Chaudhuri (Eur. J. Oper. Res. 171(2):557-566, ) assuming a general function of time for the variable part of the demand rate. [ABSTRACT FROM AUTHOR]

We study a robust model of the multi-armed bandit (MAB) problem in which the transition probabilities are ambiguous and belong to subsets of the probability simplex. We first show that for each arm there exists a robust counterpart of the Gittins index that is the solution to a robust optimal stopping-time problem and can be computed effectively with an equivalent restart problem. We then characterize the optimal policy of the robust MAB as a project-by-project retirement policy but we show that arms become dependent so the policy based on the robust Gittins index is not optimal. For a project selection problem, we show that the robust Gittins index policy is near optimal but its implementation requires more computational effort than solving a non-robust MAB problem. Hence, we propose a Lagrangian index policy that requires the same computational effort as evaluating the indices of a non-robust MAB and is within 1 % of the optimum in the robust project selection problem. [ABSTRACT FROM AUTHOR]

In this paper we model a decision maker who must exert costly effort to complete a single task by a fixed deadline. Effort costs evolve stochastically in continuous time. The decision maker optimally waits to exert effort until costs are less than a given threshold, the solution to an optimal stopping time problem. We derive the solution to this model for three cases: (1) exponential decision makers, (2) Naïve hyperbolic discounters and (3) sophisticated hyperbolic discounters. Absent deadlines, we show that sophisticated hyperbolic decision makers behave as if they were time consistent but instead have a smaller reward for completing the task, while naïfs never complete the task. In the presence of deadlines, sophisticated decision makers may, counterintuitively, have a threshold which is decreasing as they approach the deadline. An extensive numerical study shows that, unlike exponential or naïfs who always prefer longer deadlines, sophisticated decision makers will often self-impose a binding deadline as a form of commitment, while naïve decision makers will not, and we show how this varies with changes in underlying cost, preference and self-control parameters. [ABSTRACT FROM AUTHOR]

Asymptotic normality of the stopping time of Mukhopadhyay [1976] relating to the point estimation problem is proved. Also moderate sample size behaviour of this stopping time has been studied by Monte-Carlo methods. [ABSTRACT FROM AUTHOR]

We analyze the phenomenon of axion fragmentation when an axion field rolls over many oscillations of a periodic potential. This is particularly relevant for the case of relaxion, in which fragmentation provides the necessary energy dissipation to stop the field evolution. We compare the results of a linear analysis with the ones obtained from a classical lattice simulation, finding an agreement in the stopping time of the zero mode between the two within an O 1 difference. We finally speculate on the generation of bubbles with different VEVs of the axion field, and discuss their cosmological consequences. [ABSTRACT FROM AUTHOR]

In this paper we apply the method of stochastic characteristics to a Lighthill–Whitham–Richards model. The stochastic perturbation can be seen as errors in measurement of the traffic density. For concrete examples we solve the equation perturbed by a standard Brownian motion and the geometric Brownian motion without drift. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the dynamical behavior of a two-group SVIR epidemic model with random effect. Firstly, the two-group SVIR epidemic model with random perturbation of natural death rate is established. The existence and uniqueness of positive solution are proved by using stopping time theory and the Lyapunov analysis method. Secondly, a property of the system solution is obtained by using the law of strong numbers and the continuous local martingale. Finally, a new combination of Lyapunov functions is applied. The solution of the model we obtained is oscillating around a steady state if the basic reproduction number is less than one, which is the disease-free equilibrium of the corresponding deterministic model. A numerical simulation is presented to verify our theoretical results. [ABSTRACT FROM AUTHOR]

This paper concerns a kind of stochastic optimal control problem with recursive utility described by a reflected backward stochastic differential equation (RBSDE, for short) involving diffusion type control which covers regular control problem, singular control problem and impulse control problem. To begin with, the existence and uniqueness of solution for RBSDEs involving diffusion type control is derived. Then, for the related recursive optimal control problem with obstacle constraint, a sufficient condition to obtain the optimal regular control and diffusion type control is provided. Hence, based on the connection between RBSDE and optimal stopping problem, a class of recursive optimal mixed control problem involving diffusion type control is considered to illustrate our theoretical result, and here the explicit optimal control as well as the stopping time are obtained. [ABSTRACT FROM AUTHOR]

In the last two decades, the market of credit derivatives has expanded rapidly, and the importance of pricing problems for credit derivatives has been recognized especially in the last decade. Among these securities, the pricing problems of credit derivatives with an early exercise, such as American put options, have not received enough attention. In view of this need, this paper develops a continuous stochastic model of American put options on defaultable bonds. The method of obtaining a solution is based on a new result of the optimal stopping problem for a diffusion process with a jump. Some characterizations of American put options are provided using partial differential equations. [ABSTRACT FROM AUTHOR]

Stochastic delayed modeling has a significant non-pharmaceutical intervention to control transmission dynamics of infectious diseases and its results are close to the reality of nature. The covid-19 has been controlled globally but there is still a threat and appears in different variants like omicron and SARS-CoV-2 etc. globally. This article, considered pattern a mathematical model based on Susceptible, Infected, and recovered populations with highly nonlinear incidence rates. we studied the dynamics of the coronavirus model; a newly proposed version is a stochastic delayed model that is based on nonlinear stochastic delayed differential equations (SDDEs). Transition probabilities and parametric perturbation methods were used for the construction of the stochastic delayed model. The fundamental properties like positivity, boundedness, existence and uniqueness, and stability results of equilibria of the model with certain conditions of reproduction number are studied regularly. Also, the extinction and persistence of disease are studied with the help of well-known theorems. The numerical methods used to find a visualization of results due to the complexity of stochastic delayed differential equations. Furthermore, for computational analysis, we implemented existing methods in the literature and compared their results with the proposed method like nonstandard finite difference for stochastic delayed model. The proposed method restores all dynamical properties of the model with a free choice of time steps. [ABSTRACT FROM AUTHOR]

Recently, a general version of the Hoffmann-Jørgensen inequality was shown jointly with Rajaratnam [Ann. Probab. 2017], which (a) improved the result even for real-valued variables, but also (b) simultaneously unified and extended several versions in the Banach space literature, including that by Hitczenko–Montgomery-Smith [Ann. Probab. 2001], as well as special cases and variants of results by Johnson–Schechtman [Ann. Probab. 1989] and Klass–Nowicki [Ann. Probab. 2000], in addition to the original versions by Kahane and Hoffmann-Jørgensen. Moreover, our result with Rajaratnam was in a primitive framework: over all semigroups with a bi-invariant metric; this includes Banach spaces as well as compact and abelian Lie groups. In this note we show the result even more generally: over every semigroup G with a strongly left- (or right-)invariant metric. We also prove some applications of this inequality over such G , extending Banach space-valued versions by Hitczenko and Montgomery-Smith [Ann. Probab. 2001] and by Hoffmann-Jørgensen [Studia Math. 1974]. Furthermore, we show several other stochastic inequalities – by Ottaviani–Skorohod, Mogul'skii, and Lévy–Ottaviani – as well as Lévy's equivalence, again over G as above. This setting of generality for G subsumes not only semigroups with bi-invariant metric (thus extending the previously shown results), but it also means that these results now hold over all Lie groups (equipped with a left-invariant Riemannian metric). We also explain why this primitive setting of strongly left/right-invariant metric semigroups G is equivalent to that of left/right-invariant metric monoids G ∘ : each such G embeds in some G ∘ . [ABSTRACT FROM AUTHOR]

This paper presents a generalized software reliability modeling framework that predominantly encompasses randomness of field environment, fault reduction factor (FRF), and change point to study their simultaneous effect on software bug removal process. To address and capture unpredicted randomness of the field environment in testing phase it is assumed that the environment before and after a change point may not be the same and therefore there is a need to consider distinct environment factors before and after the change point in the modeling of bug removal action. Based on the general approach, three new change point-based software reliability growth models (SRGMs) are proposed incorporating time-dependent exponentiated Weibull (EW) FRF and distinct random environment distributions. To elaborate, in SRGM-I and SRGM-II, a steady environment is supposed before the change point whereas one-parameter exponential environment is assumed after the change point in SRGM-I and a two-parameter Gamma environment is considered after the change point in SRGM-II while in SRGM-III, exponential environment before change point and Gamma environment after change point are taken into consideration. In addition, a few established FRF-based models are deduced from the proposed general approach. Estimation of parameters of proposed SRGMs is carried out in two phases using three real test data sets and their validation is evaluated through several performance measures including coefficient of determination, mean square error, bias, variation, root mean square prediction error and Akaike information criteria. Fitting of the models to the datasets is also examined in related goodness of fit curves. Further, numerical illustration is worked out to conduct a cost-reliability assessment and suggest optimum release time. [ABSTRACT FROM AUTHOR]

In this paper, we are interested in the optimal investment and reinsurance strategies of an insurer who wishes to maximize the expected power utility of its terminal wealth on finite time horizon. We are also interested in the problem of maximizing the growth rate of expected power utility per unit time on the infinite time horizon. The risk process of the insurer is described by an approximation of the classical Cramér–Lundberg process. The insurer invests in a market consisting of a bank account and multiple risky assets. The mean returns of the risky assets depend linearly on economic factors that are formulated as the solutions of linear stochastic differential equations. With this setting, Hamilton–Jacobi–Bellman equations that are derived via a dynamic programming approach have explicit solution obtained by solving a matrix Riccati equation. Hence, the optimal investment and reinsurance strategies can be constructed explicitly. Finally, we present some numerical results related to properties of our optimal strategy and the ruin probability using the optimal strategy. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of scheduling independent jobs with release dates on identical parallel machines with a single server. The goal consists in minimizing the maximum lateness. This is a realistic extension of the traditional parallel machine scheduling problem with a single server, in which all jobs are assumed to be available at the beginning of the schedule. This problem, referred to as P , S 1 | r j | L max , has various applications in practice. To date, research on it has focused on complexity analysis. To solve small-sized instances of the problem, we present two mixed-integer-programming formulations, along with a valid inequality. Due to the N P -hard nature of the problem, we propose a constructive heuristic and two metaheuristics, namely a General Variable Neighborhood Search (GVNS) and a Greedy Randomized Adaptive Search Procedures, both using a Variable Neighborhood Descent as an intensification operator. In the experiments, the proposed algorithms are compared using a set of new instances generated randomly with up to 500 jobs, in line with the related literature. It turns out that GVNS outperforms by far the other approaches. [ABSTRACT FROM AUTHOR]

Mine flooding accidents have occurred frequently in recent years, and the predicting of mine water inflow is one of the most crucial flood warning indicators. Further, the mine water inflow is characterized by non-linearity and instability, making it difficult to predict. Accordingly, we propose a time series prediction model based on the fusion of the Transformer algorithm, which relies on self-attention, and the LSTM algorithm, which captures long-term dependencies. In this paper, Baotailong mine water inflow in Heilongjiang Province is used as sample data, and the sample data is divided into different ratios of the training set and test set in order to obtain optimal prediction results. In this study, we demonstrate that the LSTM-Transformer model exhibits the highest training accuracy when the ratio is 7:3. To improve the efficiency of search, the combination of random search and Bayesian optimization is used to determine the network model parameters and regularization parameters. Finally, in order to verify the accuracy of the LSTM-Transformer model, the LSTM-Transformer model is compared with LSTM, CNN, Transformer and CNN–LSTM models. The results prove that LSTM-Transformer has the highest prediction accuracy, and all the indicators of its model are well improved. [ABSTRACT FROM AUTHOR]

This article examines the operational functionality of intelligent transport systems to enhance smart cities by reducing traffic congestion. Given the increasing populations of smart cities, there is a growing demand for public transit systems to address the issue of traffic congestion. Therefore, the suggested system is developed using a few parametric design models, which combine point-to-point protocol and mode control optimization. The multi-objective parametric design for a smart transportation system is conducted using min–max functions to minimize the waiting time period for end users. Furthermore, customers are given the option to utilize a line following mechanism that offers suitable connectivity, along with independent identification and revitalize functions. The predicted model effectively eliminates the delay produced by transportation devices when positioning units are involved, ensuring that individual messages are delivered without any interruptions. In order to evaluate the results of the proposed system model, four different scenarios were examined. A comparison analysis revealed that the suggested method achieves a suitable directional flow for 96% of smart transport units. Additionally, it reduces delays and waiting periods by 2% and 6% respectively, while increasing energy consumption by 29%. [ABSTRACT FROM AUTHOR]

Rodlike ZSM-5 zeolite microspheres (R-Z5) were synthesized via a seed induced hydrothermal method with S-1 seeds in the presence of β-cyclodextrin (CD). The synthesized ZSM-5 zeolites were characterized with XRD, SEM, N2 adsorption and desorption, NH3-TPD, the catalytic performance of R-Z5 catalysts was studied for the methanol to propylene (MTP) reaction. The effects of the ratio of CD/SiO2 on the morphologies and textural properties of the products were discussed in detail. A possible formation process of R-Z5 was proposed. The results showed that CD played a key role in the preparation of R-Z5, which could be ascribed to the amphipathy of CD for the formation of rodlike ZSM-5 crystals. Compared with the conventional seed induced method, R-Z5 zeolites possessed the larger BET surface area and mesopore volumes and the more moderate acidic sites. Moreover, the synthesized R-Z5 catalysts exhibited excellent conversion activity (64 h) and propylene selectivity (41.35%) in the primary catalytic performance of MTP reaction. [ABSTRACT FROM AUTHOR]

We reconsider the problem of simultaneous estimation of the mean and variance of a normal distribution along the lines of Mukhopadhyay (1981), and derive the rate of convergence of the appropriately normalized stopping time to normality. The Berry-Esseen type results for randomly stopped U-statistics have been utilized repeatedly in this context. [ABSTRACT FROM AUTHOR]

This paper studies the issue of coordinating equipment maintenance operations with capital investment strategy in the presence of random equipment failures. The traditional approach, developed by Kamien and Schwartz (KS) in their celebrated paper published in 1971, is to formulate the problem as a deterministic optimal control problem with the probability of machine failure as the state variable. With this approach, the optimal policy is deterministic. As a major departure from the KS approach, we explicitly model the underlying stochastic process of machine failures. Our analysis of the stochastic dynamic programming model offers new insights into the problem. Under a long planning horizon with a limited replacement opportunity, each individual machine serves as a revenue generator and contributes a significant amount to the profit of the system. In contrast, when the replacement budget is quite generous over a relatively short planning horizon, adding one extra machine only helps as a backup for unexpected failures of the machines purchased before it. An interesting result derived from this comparison is that a deterministic policy turns out to be optimal for the former, while a state-contingent policy must be applied to the latter. In other words, the deterministic KS approach does not work in general when a chain of machine replacement is considered. We further characterize the effects of the discount rate, productivity deterioration, learning, decision delay, and technology advancement on the optimal policy. [ABSTRACT FROM AUTHOR]

The decision on polishing operation stopping time when employing a robot-assisted polishing machine is a critical issue for the full automation of the polishing process. In this paper, a machining learning approach based on artificial neural networks was developed using multiple sensor monitoring data to realize an intelligent system capable to determine the state of the polishing process in terms of target surface roughness achievement. During the experimental tests, surface roughness measurements were performed on each polished workpiece and the acquired sensor signals were analyzed and processed by applying two kinds of feature extraction procedures: statistical features extraction and principal component analysis. By feeding diverse types of feature pattern vectors to artificial neural networks, a highly accurate classification of the polishing process state was obtained using the principal component feature pattern vectors. [ABSTRACT FROM AUTHOR]

We investigate how people make choices when they are unsure about the value of the options they face and have to decide whether to choose now or wait and acquire more information first. In an experiment, we find that participants deviate from optimal information acquisition in a systematic manner. They acquire too much information (when they should only collect little) or not enough (when they should collect a lot). We show that this pattern can be explained as naturally emerging from Fechner cognitive errors. Over time participants tend to learn to approximate the optimal strategy when information is relatively costly. [ABSTRACT FROM AUTHOR]

Rapid urbanization has led to increasingly prominent urban heat island phenomena and social inequality. It is urgent to quantify the threshold area of urban parks from multiple perspectives to maximize the cooling effect and improve the equity of park cooling services. Using 33 urban parks in Harbin City as research objects, four indices, i.e., park cooling intensity (PCI), park cooling distance (PCD), park cooling area (PCA), and park cooling efficiency (PCE), were used to explore the park cooling effect and the threshold value of efficiency (TVoE) of the size. The OD (origin–destination) matrix model was constructed to assess the spatial accessibility from the community to the cooling range. The Gini coefficient was used to assess the equity of cooling range accessibility. The relative contribution of each influencing factor to the cooling indicator was quantified through regression modeling. The results showed that the average PCI was 3.27 ℃, the average PCD was 277 m, the average PCA was 115.35 ha, and the average PCE was 5.74. Gray space area was the dominant factor for PCI, PCD, and PCA (relative contributions of 100%, 31%, and 19%, respectively). Park area was the dominant factor for PCE (relative contribution of 28%). The TVoE of park sizes based on PCA and PCE were calculated as 82.37 ha and 2.56 ha, respectively. 39.2% and 94.01% of communities can reach cooling ranges within 15 min in walk mode and transit mode, respectively. Approximately 18% of neighborhood residents are experiencing severe inequities in cooling range accessibility. This study can guide park design that maximizes cooling effects, as well as inform city planners on more equitable allocation of urban park resources. [ABSTRACT FROM AUTHOR]

In epidemic modeling, interpretation of compartment quantities, such as s, i, and r in relevant equations, is not always straightforward. Ambiguities regarding whether these quantities represent numbers or fractions of individuals in each compartment rise questions about significance of the involved parameters. In this paper, we address these challenges by considering a density-dependent epidemic modelling by a birth-death process approach inspired by Kurtz from 1970s'. In contrast to existing literature, which employs population size scaling under constant population condition, we scale with respect to the area. Namely, under the assumption of spatial homogeneity of the population, we consider the quantities of susceptible, infective and recovered per unit area. This spatial scaling allows diffusion approximation for birth-death type epidemic models with varying population size. By adopting this approach, we anticipate to contribute to a clear and transparent description of compartment quantities and parameters in epidemic modeling. [ABSTRACT FROM AUTHOR]

Machine learning (ML) newly enables tests for higher inter-species diversity in visible phenotype (disparity) among males versus females, predictions made from Darwinian sexual selection versus Wallacean natural selection, respectively. Here, we use ML to quantify variation across a sample of > 16,000 dorsal and ventral photographs of the sexually dimorphic birdwing butterflies (Lepidoptera: Papilionidae). Validation of image embedding distances, learnt by a triplet-trained, deep convolutional neural network, shows ML can be used for automated reconstruction of phenotypic evolution achieving measures of phylogenetic congruence to genetic species trees within a range sampled among genetic trees themselves. Quantification of sexual disparity difference (male versus female embedding distance), shows sexually and phylogenetically variable inter-species disparity. Ornithoptera exemplify high embedded male image disparity, diversification of selective optima in fitted multi-peak OU models and accelerated divergence, with cases of extreme divergence in allopatry and sympatry. However, genus Troides shows inverted patterns, including comparatively static male embedded phenotype, and higher female than male disparity – though within an inferred selective regime common to these females. Birdwing shapes and colour patterns that are most phenotypically distinctive in ML similarity are generally those of males. However, either sex can contribute majoritively to observed phenotypic diversity among species. Machine learning on over 16 thousand photos of birdwing butterflies detected both examples of higher male than female variation, and vice versa, testing predictions of natural versus sexual selection debated by Darwin and Wallace. [ABSTRACT FROM AUTHOR]

The clogging phenomenon finds extensive application in both industrial processes and daily life events. While this broad spectrum of application motivated extensive research to identify the general factors underlying the clogging mechanism, it results in a fragmented and system-specific understanding of the entire clogging process. Therefore, it is essential to establish a holistic understanding of all contributing factors of clogging based on the microscopic physical mechanisms. In this paper, we experimentally investigate clogging of granular materials in a two-dimensional hopper flow and present a self-consistent physical mechanism of clogging based on precursory chain structures. These chain structures follow a specific modified restricted random walk, and clogging occurs when they are mechanically stable enough to withstand the flow fluctuations. We introduce a single-particle model that can explain the arch-forming probability. Our results provide insight into the microscopic mechanism behind clogging and a broader understanding of the dynamics of dense granular flow. The study of the general factors underlying clogging are fragmented and application-driven due to its broad spectrum of applications. The authors propose a holistic understanding of the clogging process by investigating the clogging of a granular hopper flow using high-speed imaging, finding a signature formation of precursory chain structures. [ABSTRACT FROM AUTHOR]

Scientific information on the spatial variability of soil properties is critical for sustainable production and designing appropriate measures for efficient soil–crop management. The growing urban areas in fertile landscapes are a major concern experiencing a huge anthropogenic onslaught and lack of information on spatial variability of soil properties. Therefore, the present study was carried out to delineate the spatial distribution of some selected soil properties from Balh Valley and its catchment area (Suketi basin) in lower Himachal Himalaya, India. A total of 468 geo-referenced surface soil samples were collected and analyzed for soil pH, EC, OC; primary nutrients (N, P, K); secondary nutrients (Ca and Mg); and DTPA-extractable micronutrients (Zn, Fe, Mn and Cu)following standard procedures. The results showed a significant variation in soil pH (acidic to alkaline), EC (0.08–0.70 dS/m), OC (3–26 g/kg), major nutrients N (41.96–208.03 mg/kg), P (5.80–18.75 mg/kg), and K (53.57–163.64 mg/kg). Among micronutrients, Zn was found below the critical limit toward the extreme fringes of the basin. The data were analyzed with descriptive statistics and geostatistical approach. The spatial maps were prepared with ordinary kriging (OK) technique after semivariogram modeling and cross-validation approach. The five principal components (PCs) chosen depicted a moderate correlation between the calculated soil attributes. The two management zones (MZs) were derived by performing the fuzzy c-means clustering analysis based on fuzzy performance index (FPI) and normalized classification entropy (NCE) analysis. The spatial maps represent the distribution of soil properties in the valley and its catchment area. The information generated provides baseline data for site-specific fertilizer recommendations for precision agriculture and minimize downstream adverse environmental impact in the Himalayan ecosystem. [ABSTRACT FROM AUTHOR]

The express/local mode of municipal rail transit provides passengers with multiple alternatives to achieve more efficient and superior travel, in contrast to the conventional all-stop operation mode. However, the various route choices (including direct express trains, direct local trains, or transfers) covering different passenger groups pose a significant challenge to passenger flow assignment. To understand route choice behavior, it is crucial to measure the passenger heterogeneity (variability in individual and trip attributes) in order to propose targeted solutions for operation schemes and service planning. This paper proposes a hybrid model by integrating structural equation modeling and the mixed logit model under express/local mode to estimate the impact of passenger heterogeneity on route choice. An empirical study with revealed preference and stated preference surveys carried out in Shanghai revealed how individual and trip attributes quantitatively impact the sensitivity of factors in route choice. The results show that age and trip purpose are more significant factors. Compared to the control group, the probability of express trains is reduced by 10.22% for the elderly and by 11.36% for non-commuters. Our findings can provide support for more reasonable operation schemes and more targeted services. [ABSTRACT FROM AUTHOR]

We consider the problem faced by a central bank which bails out distressed financial institutions that pose systemic risk to the banking sector. In a structural default model with mutual obligations, the central agent seeks to inject a minimum amount of cash in order to limit defaults to a given proportion of entities. We prove that the value of the central agent's control problem converges as the number of defaultable institutions goes to infinity, and that it satisfies a drift controlled version of the supercooled Stefan problem. We compute optimal strategies in feedback form by solving numerically a regularized version of the corresponding mean field control problem using a policy gradient method. Our simulations show that the central agent's optimal strategy is to subsidise banks whose equity values lie in a non-trivial time-dependent region. [ABSTRACT FROM AUTHOR]

Previous literature shows that prevalent risk measures such as value at risk or expected shortfall are ineffective to curb excessive risk-taking by a tail-risk-seeking trader with S-shaped utility function in the context of portfolio optimisation. However, these conclusions hold only when the constraints are static in the sense that the risk measure is just applied to the terminal portfolio value. In this paper, we consider a portfolio optimisation problem featuring S-shaped utility and a dynamic risk constraint which is imposed throughout the entire trading horizon. Provided that the risk control policy is sufficiently strict relative to the Sharpe ratio of the asset, the trader's portfolio strategies and the resulting maximal expected utility can be effectively constrained by a dynamic risk measure. Finally, we argue that dynamic risk constraints might still be ineffective if the trader has access to a derivatives market. [ABSTRACT FROM AUTHOR]

Most of the existing literature on optimal trade execution in limit order book models assumes that resilience is positive. But negative resilience also has a natural interpretation, as it models self-exciting behaviour of the price impact, where trading activities of the large investor stimulate other market participants to trade in the same direction. In the paper we discuss several new qualitative effects on optimal trade execution that arise when we allow resilience to take negative values. We do this in a framework where both market depth and resilience are stochastic processes. [ABSTRACT FROM AUTHOR]

This paper deals with minimization of the variances of the total discounted costs for constrained Continuous-Time Markov Decision Processes (CTMDPs). The costs consist of cumulative costs incurred between jumps and instant costs incurred at jump epochs. We interpret discounting as an exponentially distributed stopping time. According to existing theory, for the expected total discounted costs optimal policies exist in the forms of randomized stationary and switching stationary policies. While the former is typically unique, the latter forms a finite set whose number of elements grows exponentially with the number of constraints. This paper investigates the problem when the process stops immediately after the first jump. For costs up to the first jump we provide an index for selection of actions by switching stationary policies and show that the indexed switching policy achieves a smaller variance than the randomized stationary policy. For problems without instant costs, the indexed switching policy achieves the minimum variance of costs up to the first jump among all the equivalent switching policies. [ABSTRACT FROM AUTHOR]

We consider the optimal stopping problem with a possible compensated refusal of reward. We discuss functionals of exponential Brownian motion. The optimal stopping time is defined on the set of all finite stopping times. The functionals under consideration correspond to payments for standard American options. [ABSTRACT FROM AUTHOR]