Jump Process Research Articles

Detecting And Predicting Price Jumps With Consecutive Signature Distance

In order to estimate the hidden states of dynamical systems, Jump Models cluster financial observations along time series and impose a cost on jumping from one cluster to another. While these models can detect abrupt changes in the underlying time series, they suffer from two major drawbacks when it comes to detecting price jumps: (1) they cannot detect two (or more) consecutive jumps; (2) they cannot dissociate high volatility from jumps. To remedy these drawbacks, Bloch and Liao consider two seemingly unrelated problems: (1) Detecting and predicting price jumps by identifying whether a new observation results in a price jump relative to previous observations; (2) Anomaly detection of segments of a time series, that is, fixed size segments of a time series are treated as a normal corpus, and search for outliers. It is observed that while these problems are clearly different, the former can be reformulated in terms of the latter and they can therefore associate jump indicators to data-driven metrics for anomaly detection. Bloch and Liao propose a three-step process: (1) jump detection: the variance norm is combined with path signatures to come up with a data-driven jump indicator; (2) training: Bloch and Liao use this Variance Norm Jump Indicator as an input feature for Jump Models; (3) prediction: the authors use new incoming data to predict its hidden state. This approach aims at enhancing the model�s accuracy and predictive capabilities by leveraging the strengths of variance norm on detecting data points after the jump as outliers from previous distribution. Bloch and Liao conducted an extensive analysis on simulated data, examining the structure, benefits and limitations of the approach, and found that they could retrieve the true hidden states with high accuracy without using future information.

Nonlocal-in-time finite-velocity diffusion approach on a ring.

The ubiquitous telegrapher's equationis presented in the context of a non-local-in-time master equationon the lattice. From the exact solution of this transport equation, for different hopping models, the second moment in the infinite lattice and the time evolution of the probability in the ring have been analyzed as a function of the two characteristic timescales appearing in the memory kernel of the finite-velocity approach: the rate of energy loss and the timescale characterizing the jumping process in the lattice. We have demonstrated how these timescales characterize the constraint to find positive solutions, the time variation of entropy and therefore the approach to the disordered stationary state on the ring. This lattice model provides an analytic treatment. Thus, this result is relevant in the study of Shannon entropy, transport of information, and waves in lattices and sheds light on the functional role of the loss of energy in the finite-velocity diffusion dynamics.

Fuzzy Resilient Control of DC Microgrids with Constant Power Loads Based on Markov Jump Models

This paper addresses the fuzzy resilient control of DC microgrids with constant power loads. The DC microgrid is subject to abrupt parameter changes which are described by the Markov jump model. Due to the constant power loads, the DC microgrid exhibits nonlinear dynamics which are characterized by a T-S fuzzy model. According to the parallel distributed compensation principle, mode-dependent fuzzy resilient controllers are designed to stabilize the resultant T-S fuzzy Markov jump DC microgrid. The “resilient” means the controller could cope with the uncertainty caused by the inaccurate execution of the control laws. This uncertainty is governed by a Bernoulli distributed random variable and thus may not occur. Then, the mean square exponential stability is analyzed for the closed-loop system by using the mode-dependent Lyapunov function. Since the stability conditions are not convex, a design algorithm is further derived to calculate the fuzzy resilient controller gains. Finally, simulations are provided to test the effectiveness of the proposed results.

Research on the biomimetic quadruped jumping robot based on an efficient energy storage structure

AbstractThe ability of quadruped robots to overcome obstacles is a critical factor that limits their practical application. Here, a design concept and a control algorithm are presented that aim at enhancing the explosive force of quadruped robots during jumping by utilizing elastic energy storage components. The hind legs of the quadruped robot are designed as energy storage units. Tension springs are utilized as components for storing energy and are installed in a parallel structure on the hind leg. Energy is stored during the compression process of the robot’s torso and released during the jumping phase. The optimal foot force is calculated using a single rigid body model. The mapping relationship between the force applied to the foot and the resulting joint torque is established by developing a dynamic model of the hind legs. Simulation experiments were conducted using the Webots physics engine to compare the impact of varying spring stiffness on joint torque during the jumping process. This study determined the optimal spring stiffness under specific conditions. The hind legs’ torque saving ratio reaches 19%, and the energy-saving ratio reaches 13%, which validates the effectiveness and feasibility of integrating elastic energy storage components.

Particle–droplet coalescence and jumping on superhydrophobic surfaces—A direct numerical simulations study

We report here multiphase direct numerical simulations of a recently discovered passive mechanism of self-cleaning on superhydrophobic surfaces. The removal of contaminants is governed by coalescence of a single droplet with a particle of micrometer size, where the droplet initiates spontaneous spreading on the particle and drives particle–droplet jumping. We use an in-house volume of fluid–immersed boundary numerical framework, introduce and thoroughly analyze capillary forces at the particle–droplet contact line, and validate our simulations in relation to previous experimental results. We then perform a comprehensive investigation over a number of different parameters regarding the interaction physics of the droplet with the particle and the substrate. We systematically vary particle, droplet, and surface physical and wetting properties and unveil a range of scenarios related to different energy dissipation mechanisms as a function of the substrate contact angles and contact-angle hysteresis. Detailed parameter studies establish the connection between the droplet, substrate and particle properties, and the outcome and efficiency of the particle-launching process. We particularly highlight the effects of the particle–droplet size ratio and the wettability of the particle. We reveal and discuss the corresponding dissipation mechanisms and quantify the energy efficiencies of the jumping process in the treated parameter space.

Study on the partial discharge characteristics induced by the motion of cellulose particles in transformer oil

AbstractCellulose particles present a significant concern within the oil‐paper insulation of transformers, posing potential risks to insulation performance. Under the influence of the electric field, the movement of cellulose particles can compromise the transformer's insulation, leading to potential failure. An experimental platform was established to synchronously record particle motion images, partial discharge (PD) pulses, and electric voltage waveforms in oil, aiming to observe the PD characteristics resulting from particle motion under alternating current (AC) voltage and investigate the relationship between different particle motion modes, motion positions, and PD signals. The findings reveal that the phase distribution of PD signals is correlated with the particle motion mode. Specifically, the phase distribution of PD pulses during the back‐and‐forth motion mode is between 4°–94° and 182°–275°. In the suspended oscillation motion mode, the PD pulses phase is concentrated between 20°–84° and 203°–268°. The generation of PD pulses is closely linked to the particle's motion position. PD pulses occur when the particle remains on the electrode during the back‐and‐forth motion mode, generally, PD pulses rarely occur during the jumping process between the two electrodes. In the suspended oscillation motion mode, PD pulses occur when the particle moves upward, but generally do not occur during downward movement. Furthermore, the Pulse Sequence Analysis technique was used to employ the PD characteristics caused by particle motion in transformer oil. The simulation calculations of the electric field distribution for two different particle motion modes show that the particle's motion can cause distortion of the electric field distribution, leading to the generation of PD. The study of the PD characteristics at different particle motion modes and positions obtained contributes to a deeper understanding of the PD induced by cellulose particle motion under AC voltage and provides a reference for the insulation evaluation of transformers.

Reversible kink instability drives ultrafast jumping in nematodes and soft robots.

Entomopathogenic nematodes (EPNs) exhibit a bending-elastic instability, or kink, before becoming airborne, a feature hypothesized but not proven to enhance jumping performance. Here, we provide the evidence that this kink is crucial for improving launch performance. We demonstrate that EPNs actively modulate their aspect ratio, forming a liquid-latched closed loop over a slow timescale O (1 s), then rapidly open it O (10 µs), achieving heights of 20 body lengths (BL) and generating ∼ 10 4 W/Kg of power. Using jumping nematodes, a bio-inspired Soft Jumping Model (SoftJM), and computational simulations, we explore the mechanisms and implications of this kink. EPNs control their takeoff direction by adjusting their head position and center of mass, a mechanism verified through phase maps of jump directions in simulations and SoftJM experiments. Our findings reveal that the reversible kink instability at the point of highest curvature on the ventral side enhances energy storage using the nematode's limited muscular force. We investigated the impact of aspect ratio on kink instability and jumping performance using SoftJM, and quantified EPN cuticle stiffness with AFM, comparing it with C. elegans . This led to a stiffness-modified SoftJM design with a carbon fiber backbone, achieving jumps of ∼25 BL. Our study reveals how harnessing kink instabilities, a typical failure mode, enables bidirectional jumps in soft robots on complex substrates like sand, offering a novel approach for designing limbless robots for controlled jumping, locomotion, and even planetary exploration.

Stochastic intervention control of mean-field jump system with noisy observation via L-derivatives with application to finance

In this paper, we investigate stochastic optimal intervention control of mean-field nonlinear random Poisson-jump-system with related noisy process. We derive the necessary conditions of optimality for partially observed optimal intervention control problems of mean-field type. The coefficients depend on the state of the solution process as well as of its probability distribution and the control variable. The proof of our main result is obtained by applying L-derivatives in the sense of Lions. In our control model, there are two models of jumps for the state process, the inaccessible ones which come from the random Poission process and the predictable ones which come from the intervention control. Finally, we apply our result to study conditional mean-variance portfolio selection problem with interventions, where the foreign exchange interventions are intended to contain excessive fluctuations in foreign exchange rates and to stabilize them.

Tumro: A Tunable Multimodal Wheeled Jumping Robot Based on the Bionic Mechanism of Jumping Beetles

The implementation of multimodal motion ensures the stable operation in complex terrain environments, thus providing an effective guarantee for system performance. The crawling‐jumping robot has the ability to navigate in various road conditions utilizing different modes of movement. However, the mobility of the current multimodal jumping robots remains somewhat constrained by their jumping capability and the recovery time after each jump. Drawing inspiration from the energy‐storage jumping mechanism of jumping beetles, a tuneable multimodal jumping robot (Tumro) capable of executing multimodal movements including wheeled locomotion and ground‐based jumping, which can achieve a jump height of up to 3 m and swiftly recover its wheeled crawling state without requiring posture correction post‐jump, is presented. Through a specific structural design, the robot can storage energy and switch motions to jump in the desired direction based on the preset angle according to actual demand. The jumping process is thoroughly analyzed, and the kinematics and dynamics models are derived in meticulous detail. In addition, the performance of the robot is comprehensively assessed from aspects of wheel action versus vertical jump capability, power consumption, and endurance across various motion modes. The simulation scene experiment demonstrates the robot's exceptional jumping capability and efficient wheeled mobility.

Study on the Bouncing Process Induced by Ice Shedding on Overhead Conductors under Strong Wind Conditions

Strong winds can lead to more complex ice shedding oscillation processes for overhead conductors, inducing flashovers, strand breakages and other accidents. This study analyzes the aerodynamic parameters of several typical icing features and establishes a numerical model for ice shedding on overhead conductors under strong wind conditions. The results show that for the same amount of icing, the resistance and lift force on the conductor changes with ice shape, wind attack angle and wind speed, which has a significant effect on the ice shedding jumping process. When the wind attack angle approaches 180°, the airflow resistance of the fan-shaped and D-shaped icing conductors significantly increases. And in the process of ice shedding response of transmission lines, the lateral amplitude may exceed 20 m, which increase the discharge risk of horizontally arranged conductors. Moreover, for the significant lateral oscillation of conductors by ice shedding under strong wind, the maximum horizontal displacement is approximately 1.6 times the difference in lateral position before and after ice shedding.

Using a simple model to systematically examine the influence of force-velocity profile and power on vertical jump performance with different constraints

ABSTRACT Power, and recently force-velocity (F-V) profiling, are well-researched and oft cited critical components for sports performance but both are still debated; some would say misused. A neat, applied formulation of power and linear F-V in the literature is practically useful but there is a dearth of fundamental explanations of how power and F-V interact with human and environmental constraints. To systematically explore the interactions of a linear F-V profile, peak power, gravity, mass, range of motion (ROM), and initial activation conditions, a forward dynamics point mass model of vertical jumping was parameterised from an athlete. With no constraints and for a given peak power, F-V favouring higher velocity performed better, but were impacted more under real-world conditions of gravity and finite ROM meaning the better F-V was dependent on constraints. Increasing peak power invariably increased jump height but improvement was dependent on the initial F-V and if it was altered by changing maximal force or velocity. When mass was changed along with power and F-V there was a non-linear interaction and jump improvement could be almost as large for a F-V change as an increase in power. An ideal F-V profile cannot be identified without knowledge of mass and ROM.

Design and Experimentation of Tensegrity Jumping Robots

Jumping robots possess the capability to surmount formidable obstacles and are well-suited for navigating through complex terrain environments. However, most of the existing jumping robots face challenges in achieving stable jumping and they also have low energy utilization efficiency, which limits their practical applications. In this work, a two-module jumping robot based on tensegrity structure is put forward. Firstly, the structural design and jumping mechanism of the robot are elaborated in the article. Then, dynamic models, including the two modules’ simultaneous jumping and step-up jumping process of the robot, are established utilizing the Lagrange dynamic modeling method. On this basis, the effects of parameters, including the stiffness of elastic cables and the initial tilt angle of the robot, on the jumping performance of the robot can be obtained. Finally, simulations are carried out and a prototype is developed to verify the rationality of the tensegrity-based jumping robot proposed in this work. The experiment results show that our jumping robot can achieve a stable jumping process and the step-up jumping of each module of the prototype can have higher energy efficiency than that of simultaneous jumping of each module, which enables the robot a better jumping performance. This research serves as a valuable reference for the design and analysis of jumping robots.

Fast Rare Events in Exit Times Distributions of Jump Processes.

Rare events in the first-passage distributions of jump processes are capable of triggering anomalous reactions or series of events. Estimating their probability is particularly important when the jump probabilities have broad-tailed distributions, and rare events are therefore not so rare. We formulate a general approach for estimating the contribution of fast rare events to the exit probabilities in the presence of fat-tailed distributions. Using this approach, we study three jump processes that are used to model a wide class of phenomena ranging from biology to transport in disordered systems, ecology, and finance: discrete time random walks, Lévy walks, and the Lévy-Lorentz gas. We determine the exact form of the scaling function for the probability distribution of fast rare events, in which the jump process exits from an interval in a very short time at a large distance opposite to the starting point. In particular, we show that events occurring on timescales orders of magnitude smaller than the typical timescale of the process can make a significant contribution to the exit probability. Our results are confirmed by extensive numerical simulations.

Shortage Policies for a Jump Process with Positive and Negative Batch Arrivals in a Random Environment

We study a continuous-review stock management of a retailer for a single item in a limited storage (buffer) in a random environment. The stock level fluctuates according to two independent compound Poisson processes with discrete amounts of items (batches) that enter and leave the storage facility. The storage facility is controlled by a three-parameter base-stock replenishment policy. All items exceeding the storage capacity are transferred to an unlimited foreign facility. In addition, a restricted backlogging possibility is permitted; additional demands for items are lost sales. We further assume a random shelf life, the possibility of total inventory collapse, and a random lead time. Applying Markov theory, we derive the optimal control parameters minimizing the long-run expected total cost. A sensitivity analysis is conducted focusing on the comparison between the pure lost-sales policy and a partial backordering policy. Accordingly, we identify cases where one policy is cost effective compared to the other, particularly with respect to the batch patterns (sign, rate, average, and variability), and the associated costs.

Molecular Origin of Distinct Hydration Dynamics in Double Helical DNA and RNA Sequences.

Water molecules are essential to determine the structure of nucleic acids and mediate their interactions with other biomolecules. Here, we characterize the hydration dynamics of analogous DNA and RNA double helices with unprecedented resolution and elucidate the molecular origin of their differences: first, the localization of the slowest hydration water molecules─in the minor groove in DNA, next to phosphates in RNA─and second, the markedly distinct hydration dynamics of the two phosphate oxygen atoms OR and OS in RNA. Using our Extended Jump Model for water reorientation, we assess the relative importance of previously proposed factors, including the local topography, water bridges, and the presence of ions. We show that the slow hydration dynamics at RNA OR sites is not due to bridging water molecules but is caused by both the larger excluded volume and the stronger initial H-bond next to OR, due to the different phosphate orientations in A-form double helical RNA.

Event-triggered sliding mode control for singular discrete-time fuzzy Markov jump networked systems

In this present paper, the event-triggered sliding mode control (SMC) issue for a type of singular networked Markov jump systems with partly unknown transition probabilities (TPs) is mainly investigated, and it is modeled by discrete-time Takagi–Sugeno fuzzy systems. To save network resources, a mode-dependent event-triggered scheme (ETS) is applied to improve transmission efficiency. Subsequently, a common sliding surface is designed, which can effectively reduce the impact of the jumping process. Therein, the stochastic admissibility criterion for the system with [Formula: see text] performance [Formula: see text] is derived in the sense of partly unknown TPs. Moreover, a novel SMC law that guarantees the reachability of the quasi-sliding mode is given in view of the reaching condition. Finally, the validity of the presented theorems is demonstrated by a numerical example.

Homotopic ADP based [formula omitted] integral sliding mode secure control for Markov jumping cyber-physical systems

This paper addresses the sliding mode secure control problem for continuous-time cyber-physical systems (CPSs) subject to unmatched disturbances and actuator deception attacks. To capture different operating conditions and account for random component failures in CPSs, a Markov jumping model is introduced to characterize the system's component matrices. Next, a novel model-free integral sliding mode function and a corresponding sliding mode controller are presented to mitigate the impact of external disturbances and deception attacks on Markov jumping cyber-physical systems. An algorithm based on adaptive dynamic programming (ADP) and homotopic policy iteration (PI) is applied to develop the sliding mode controller, called the online homotopic ADP algorithm, which avoids the requirement for an initial stabilizing matrix compared to existing PI algorithms. Lastly, the mode-independent integral sliding mode control scheme is studied to a two-mode Markov jumping vertical take-off and landing helicopter system, providing guaranteed reachability of sliding variables and stability of sliding mode dynamics. Importantly, this is achieved without any reliance on knowledge of system dynamics.

The Influence of CRTS II Slab Ballastless Track Upper Arch Deformation on the Wheel Jumping Law of High-Speed Vehicle

To study the impact of upwarp deformation in the ballastless track on the jumping behavior of the high-speed vehicle, utilizing UM and ANSYS joint simulation, a vertical vibration model of high-speed vehicle on CRTS II slab ballastless track was developed based on the non-Hertz wheel–rail contact model of virtual penetration theory. By using the single-wave cosine curve simulating the characteristics of upwarp deformation in the track slab, we calculated the whole process of wheel jumping. This allowed us to analyze how the amplitude and wavelength of the track slab upward deformation influence the vibration response of the vehicle–track system. Our findings indicate that when a wheel passes through the arch section of the track slab, the entire wheel jumping process consists of distinct stages: “wheel–rail bonding, wheel–rail separation, wheel–rail impact (one or more times), and wheel–rail bonding.” As the amplitude of upwarp deformation increases and the wavelength decreases, significant changes occur in several parameters, including the vertical force between the wheel and rail, wheel unloading rate, wheel jump height, frequency, duration, and vertical displacement of the rail. Additionally, when the wavelength is between 2 and 6[Formula: see text]m and the amplitude is 8[Formula: see text]mm, the vertical force between the wheel and rail becomes zero, the wheel load reduction rate is one, and the wheel jumps. When the wavelength is less than 3[Formula: see text]m, the wheel jump height exceeds the flange height, increasing the risk of derailment. Meanwhile, during the first wheel–rail impact, the wheel–rail vertical force and the rail vertical displacement reach their maximum, potentially impacting rail service performance negatively. Finally, compared to the amplitude of the track slab camber deformation, its wavelength has a greater impact on the entire process of wheel jumping. It is recommended that attention be paid to the change in the wavelength of the track slab camber during the maintenance and repair of the ballastless track.

Characterization of Heat Kernel Lower Bounds for Symmetric Jump Processes

This paper is devoted to symmetric mixture stable-like processes on metric measure space.Assume that the process enjoys upper bounds of heat kernel,characterization of near diagonal lower bounds of heat kernel is given.different from previous work which is usually based on regularity of elliptic harmonic functions,here we make full use of smooth properties of functions space associated with the generator of the process.

Progress in Ski Jumping Technology Based on Biomechanical Sport Research Methods

(1) Background: Previous studies have compared research into ski jumping in different motor processes, but there is a lack of comparative analysis of the biomechanical research methods used to investigate different ski jumping sports. (2) Content: Our study compared the advantages and disadvantages of six research methods and proposes future research directions. Motion video collection and analysis show that controlling angular momentum and achieving stable flight attitude in the take-off process are the most critical factors in ski jumping performance. Most research on force platforms focuses on dynamic performance at the time of take-off, but there are few training sites with an embedded force platform, and so, more empirical research is required. Wearable inertial measurement units, including gyroscopes and accelerometers, can be used to determine a series of forces, calculate the joint angle, and speculate the position of the centroid during motion. Surface EMG studies are primarily used to compare the activity characteristics of the lower limb muscles in the actual field of the jump, the exercise simulation, and the lack of complete training process data. Wind tunnel measurement can satisfy fluid mechanics simulation experiments and provide theoretical support for optimizing special ski jumping technology. Based on the theory of computational fluid dynamics, the optimal drag reduction posture data of ski jumpers can be derived using computer simulations. (3) Conclusions: Due to the wide range of ski jumping sports, the present research focused on the kinematics and dynamics of different movement stages, lacking the study of the complete exercise training process. The range of wearable inertial measurement and sensor equipment can cover the whole process of ski jumping, including kinematics and dynamics data, and is a feasible and reliable test method for monitoring ski jump training in natural environments. The simultaneous testing of surface electromyography, kinematics, and dynamics requires further exploration. (4) Future direction of development: Under computational fluid dynamics, wearable inertial measurement units and global navigation satellite systems (GNSSs), intelligent wind tunnel experimental training areas will become essential tools for ski jumping research.