On Asymptotics of Optimal Stopping Times

We consider optimal stopping problems, in which a sequence of independent random variables is drawn from a known continuous density. The objective of such problems is to find a procedure which maximizes the expected reward. In this analysis, we obtained asymptotic expressions for the expectation and variance of the optimal stopping time as the number of drawn variables became large. In the case of distributions with infinite upper bound, the asymptotic behaviour of these statistics depends solely on the algebraic power of the probability distribution decay rate in the upper limit. In the case of densities with finite upper bound, the asymptotic behaviour of these statistics depends on the algebraic form of the distribution near the finite upper bound. Explicit calculations are provided for several common probability density functions.

Self Tuning PID Control of Antilock Braking System using Electronic Wedge Brake

This paper describes the design of an antilock braking system (ABS) control for a passenger vehicle that employs an electronic wedge brake (EWB). The system is based on a two-degree-of-freedom (2-DOF) vehicle dynamic traction model, with the EWB acting as the brake actuator. The developed control structure, known as the Self-Tuning PID controller, is made up of a proportional-integral-derivative (PID) controller that serves as the main feedback loop control and a fuzzy supervisory system that serves as a tuner for the PID controller gains. This control structure is generated through two structures, namely FPID and SFPID, where the difference between these two structures is based on the fuzzy input used. An ABS-based PID controller and a fuzzy fractional PID controller developed in previous works were used as the benchmark, as well as the testing method, to evaluate the effectiveness of the controller structure. According to the results of the tests, the performance of the SFPID controller is better than that of other PID and FPID controllers, being 10% and 1% faster in terms of stopping time, 8% and 1% shorter in terms of stopping distance, 9% and 1% faster in terms of settling time, and 40% and 5% more efficient in reaching the target slip, respectively.

Synergistic effects of iron and hexagonal-Boron Nitride additions in copper-based composites for braking application

This paper explores the addition of h-BN and iron to Cu-based brake pads on the performance benefits. It also investigates the effect of graded layering by synthesizing three and four-layer brake pads by powder compaction and sintering route. The top one or two layers are made of Cu-based composite containing Fe, h-BN, and W, while the middle layer is pure Cu and, bottom steel plate. Two different compositions were explored for the composites by varying Fe content. From the two composite compositions, brake pads with single-layer composite or two-layer composite were synthesized. Characterization of brake pad specimens was carried out using density measurements, optical microscopy, scanning electron microscopy, energy dispersive spectroscopy. The brake pads were subjected to simulated braking tests at braking energy/cycle of 60, 96, and 136 K Joules. Wear rate, coefficient of friction, stopping distance, stopping time, and hardness were measured and compared among other brake pads. The brake pad containing single-layer Fe rich Cu composite showed the best performance in the simulated braking tests. EDS analysis of wear debris shows the formation of iron (boride, nitride, oxide) complex which is indicative of a surface with superior dry lubricating properties. This surface is a result of synergetic interaction between h-BN and Fe particles. The iron particles which are scattered in the Cu matrix composite act as low friction regions on the brake pad surface that interrupt the high friction regions on the Cu matrix, thus reducing the local and bulk temperature rise. The two-layer composite brake-pad showed performance intermediate to the two single-layer brake pads. No advantage due to higher thermal conductivities in Fe deficient composite was observed as the two composite layers, showed similar Fe contents in their matrix phases.

A Class of Recursive Optimal Stopping Problems with Applications to Stock Trading

In this paper, we introduce and solve a class of optimal stopping problems of recursive type. In particular, the stopping payoff depends directly on the value function of the problem itself. In a multidimensional Markovian setting, we show that the problem is well posed in the sense that the value is indeed the unique solution to a fixed point problem in a suitable space of continuous functions, and an optimal stopping time exists. We then apply our class of problems to a model for stock trading in two different market venues, and we determine the optimal stopping rule in that case.

Prophet Inequalities for Independent and Identically Distributed Random Variables from an Unknown Distribution

A central object of study in optimal stopping theory is the single-choice prophet inequality for independent and identically distributed random variables: given a sequence of random variables [Formula: see text] drawn independently from the same distribution, the goal is to choose a stopping time τ such that for the maximum value of α and for all distributions, [Formula: see text]. What makes this problem challenging is that the decision whether [Formula: see text] may only depend on the values of the random variables [Formula: see text] and on the distribution F. For a long time, the best known bound for the problem had been [Formula: see text], but recently a tight bound of [Formula: see text] was obtained. The case where F is unknown, such that the decision whether [Formula: see text] may depend only on the values of the random variables [Formula: see text], is equally well motivated but has received much less attention. A straightforward guarantee for this case of [Formula: see text] can be derived from the well-known optimal solution to the secretary problem, where an arbitrary set of values arrive in random order and the goal is to maximize the probability of selecting the largest value. We show that this bound is in fact tight. We then investigate the case where the stopping time may additionally depend on a limited number of samples from F, and we show that, even with o(n) samples, [Formula: see text]. On the other hand, n samples allow for a significant improvement, whereas [Formula: see text] samples are equivalent to knowledge of the distribution: specifically, with n samples, [Formula: see text] and [Formula: see text], and with [Formula: see text] samples, [Formula: see text] for any [Formula: see text].

Axion fragmentation on the lattice

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 $$ \mathcal{O}(1) $$ O 1 difference. We finally speculate on the generation of bubbles with different VEVs of the axion field, and discuss their cosmological consequences.

Detecting a Novel Walking-Based Performance Fatigability Marker With Accelerometry in Older Adults

Walking-based performance fatigability measures (e.g., lap-time difference) may not adequately capture performance deterioration as self-pacing is a common compensatory strategy in those with low activity tolerance. To overcome this limitation, we developed a new approach with accelerometry (ActiGraph GT3X+, sampling=80 Hz, non-dominant wrist) during fast-paced 400m-walk (N=57, age=78.7±5.7 years, women=53%). Cadence (steps/second) was estimated using raw accelerometer data (R “ADEPT”). Penalized regression splines (R “mgcv”) were used to estimate the individual-level smoothed cadence trajectories. “Time-to-slow-down” was defined as first time-point where the full confidence interval of change in cadence<0. Five participants were censored at stopping time (not slowdown or complete walk). Median “time-to-slow-down” was 1.86 minutes (IQR=0.98-2.73, range=0.57-6.25). Participants with longer “time-to-slow-down” had slower starting cadence, longer 400m-walk time, and greater perceived fatigability (Pittsburgh Fatigability Scale), p’s<0.05 (linear regression). Our preliminary findings revealed that detecting accelerometry-based performance fatigability/deterioration in older adults is feasible and needs to account for initial pace.

RHMX: Bus arrival time prediction via mixed model

With the widespread use of information technologies such as IoT and big data in the transportation business, traditional passenger transportation has begun to transition and upgrade into intelligent transportation, providing passengers with a better riding experience. Giving precise bus arrival times is a critical link in achieving urban intelligent transportation. As a result, a mixed model-based bus arrival time prediction model (RHMX) was suggested in this work, which could dynamically forecast bus arrival time based on the input data. First, two sub-models were created: bus station stopping time prediction and interstation running time prediction. The former predicted the stopping time of a running bus at each downstream station in an iterative manner, while the latter projected its running time on each downstream road segment (stations as the break points). Using the two models, a group of time series data on interstation running time and bus station stopping time may be predicted. Following that, the time series data from the two sub-models was fused using long short-term memory (LSTM) to generate an approximate bus arrival time. Finally, using Kalman filtering, the LSTM prediction results were dynamically updated in order to eliminate the influence of aberrant data on the anticipated value and obtain a more precise bus arrival time. The experimental findings showed that the suggested model's accuracy and stability were both improved by 35% and 17%, respectively, over AutoNavi and Baidu.

The Lindy effect in psychology: Network dynamics reinforce depression over time

This paper studies the factors that sustain mental disorders by taking a network approach. The network theory suggests that mental disorders are networks of symptoms that causally interact (Borsboom, 2017). Symptom networks share certain dynamics with other complex systems: abrupt transitions between stable states, critical slowing down and hysteresis (Cramer et al., 2016). These findings suggest that symptom networks that have transitioned to a pathological state tend to remain that state. We argue that this tendency leads to the Lindy effect in symptom networks. The Lindy effect means that the conditional probability of surviving beyond a time point, given survival until that time point, increases over time (Taleb, 2014). In other words, time benefits future survival. A symptom network is considered to have survived until a time point if it has remained in a pathological state until that point. We first show how the Lindy effect is formalised by examining the stopping time distribution of Brownian motion with an absorbing barrier (Cook, 2012; Taleb, 2018). Specifically, we describe the hazard function of the stopping time distribution and make a distinction between "strong Lindy" and "weak Lindy". Strong Lindy is a monotonically decreasing hazard function whereas weak Lindy means an inverted-U shaped hazard function. Then, major depressive disorder (MDD) networks were simulated, manipulating the level of symptom connectivity. As before, the presence of the Lindy effect in these networks were tested using hazard functions, and in addition, survival probabilities conditioned on time. Afterwards, we fit a distribution to the network lifetimes. The lifetime distribution of strongly connected networks were heavy tailed and showed the Lindy effect; the longer a network had been depressed, the more likely it was to remain depressed. The lifetime distribution of weakly connected networks were light tailed and did not show the Lindy effect. After discussing caveats and alternative explanations of the findings, we conclude that network dynamics and the resulting Lindy effect can explain several findings in psychology such as the chronicity of depression (Swaminath, 2009) and the frequency distribution of remission times (Simon, 2000; Patten et al., 2010).

Optimal Modulation of Regenerative Braking in Through-The-Road Hybridized Vehicles

Regenerative braking can significantly improve the energy efficiency of hybrid and electric vehicles, and many studies have been carried out in order to improve and optimize the energy recovery of the braking energy. In the paper, the optimization of regenerative braking by means of braking force modulation is analysed, with specific application to the case of cars converted into Through-the-road (TTR) hybrid vehicles, and an optimal modulation strategy is also proposed. Car hybridization is an emerging topic since it may be a feasible, low-cost, intermediate step toward the green transition of the transport system with a potential positive impact in third-world countries. In this case, the presence of two in-wheel-motors installed on the rear axle and of the original mechanical braking system mounted on the vehicle can result in limited braking energy recovery in the absence of proper braking management strategies. A vehicle longitudinal model has been integrated with an algorithm of non-linear constrained optimization to maximize the energy recovery for various starting speed and stopping time, also considering the efficiency map and power limitations of the electric components. In the best conditions, the recovery can reach about 40% of the vehicle energy, selecting the best deceleration at each speed and proper modulation, and with a realistic estimate of the grip coefficient.