Jump Process Research Articles

Jump-diffusion algorithms are applied to sampling from Bayesian posterior distributions. We consider a class of random sampling algorithms based on continuous-time jump processes. The semigroup theory of random processes lets us show that limiting cases of certain jump processes acting on discretized spaces converge to diffusion processes as the discretization is refined. One of these processes leads to the familiar Langevin diffusion equation; another leads to an entirely new diffusion equation.

We consider partial differential equations (PDEs) characterized by an upper barrier that depends on the solution itself and a fixed lower barrier, while accommodating a non-local driver. First, we show a Feynman–Kac representation for the PDE when the driver is local. Specifically, we relate the non-linear Snell envelope, arising from an optimal stopping problem—where the underlying process is the first component in the solution to a stopped backward stochastic differential equation (BSDE) with jumps and a constraint on the jumps process—to a viscosity solution for the PDE. Leveraging this Feynman–Kac representation, we subsequently prove existence and uniqueness of viscosity solutions in the non-local setting by employing a contraction argument. This approach also introduces a novel form of non-linear Snell envelope and expands the probabilistic representation theory for PDEs.

The mechanism of fibrosis at the patella-patellar tendon junction (PPTJ) was investigated using a rabbit overuse jumping model. Thirty-two female New Zealand White rabbits were randomly divided into control and jumping groups, and each group was further divided into four groups at 2, 4, 6, and 8 wk. The rabbit in the jumping group jumped 150 times/day, 5 days/wk. The PPTJ was removed at the corresponding time point and subjected to hematoxylin and eosin, safranin O, and immunohistochemical staining. Significant differences were observed in histological changes and fibrosis-related factors between the jumping and control groups (P < 0.01). Comparison within the jumping group indicated that the changes in the fibrocartilage zone thickness and proteoglycan area were pronounced at week 6; the expressions of transforming growth factor β (TGF-β1), Smad3, CTGF, α-SMA, COL-I, and COL-III peaked at week 6 (P < 0.05). The jumping load can lead to morphological and fibrotic changes in the patella-patellar tendon junction, with peak changes occurring at week 6. The fibrosis in the patella-patellar tendon junction may be associated with increased secretion of TGF-β1 and Smad3 due to jump loading, which upregulates CTGF expression and thus promotes the synthesis of α-SMA, COL-I, and COL-III.NEW & NOTEWORTHY The temporal pattern of fibrosis in the patella-patellar tendon junction (PPTJ) was determined by observing changes in histology and fibrosis-related factors at different time points in an overused jumping rabbit model. The results revealed that 1) the peak fibrotic changes in the PPTJ occurred at week 6 of jump training; 2) fibrosis in PPTJ may be associated with the changes in TGF-β1/Smad3. This study contributes to the development of targeted early interventions.

Asynchronous Dynamic Output Feedback Control for Discrete Nonlinear Networked Semi-Markov Jump Models With Cyber Attacks and Applications

The paper presents the features of the design and possible application areas of the cam mechanism of a jumping robot. The design and technological parameters of the robot are substantiated according to its mass, the stiffness of the spring, the impact system, as well as the profile surface of the cam using the environment of Autodesk Inventor.Directions for the development of jumping robot designs are highlighted, and the feasibility of developing cam mechanisms for robots is substantiated, considering the direction of its jump according to the distribution of forces and applied loads.The calculation of the forces, power, and structural parameters of the impact system is presented, and all stages of the jumping process are thoroughly analyzed. These stages include the compression of the spring by a lever-type device, the removal of the compressing device, the release of the spring, and the final ballistic phase (flight phase).

A model of jumps in pro ts of a construction company based on the mathematical theory of catastrophes is proposed. The model makes it possible to calculate changes in pro ts for six (seven) factors that determine the economic security of the enterprise. We consider a 6-factor model known as the Star catastrophe. This model represents a typical sprout of catastrophes, i.e. it describes the bulk of similar construction companies. The typicality of the sprout and their universal deformations allows us to talk about the su cient adequacy of the proposed model, since atypical sprouts are related from the point of view of mathematics to exceptional phenomena, rarely encountered in the economy

This work investigates the protocol-based synchronization of inertial neural networks (INNs) with stochastic semi-Markovian jumping parameters and image encryption application. The semi-Markovian jumping process is adopted to characterize INNs under sudden complex changes. To conserve the limited available network bandwidth, an adaptive event-driven protocol (AEDP) is developed in the corresponding semi-Markovian jumping INNs (S-MJINNs), which not only reduces the amount of data transmission but also avoids the Zeno phenomenon. The objective is to construct an adaptive event-driven controller so that the drive and response systems maintain synchronous relationships. Based on the appropriate Lyapunov functional, integral inequality, and free weighting matrix, novel criteria are derived to realize the synchronization. Moreover, the desired adaptive event-driven controller is designed under a semi-Markovian jumping process. The proposed method is demonstrated through a numerical example and an image encryption process.

Observer-Based Stabilization of Networked IT2 Fuzzy Semi-Markov Jump Models With Redundant Channels and Applications to Tunnel Circuit Model

This study aims to investigate the key lower limb joint biomechanical factors affecting the performance of vertical jumping in high-level sprinters, focusing on analysing the torque, power output and stiffness of the hip, knee and ankle joints during the vertical jumping process. The relationship between the joint biomechanical parameters and the key indexes of vertical jump performance, including ground contact time, free height and reaction power index, was systematically analysed through the simultaneous acquisition of 3D kinematic and kinetic data of the sprinters. The results showed that different lower limb joints play key roles in different phases of the long jump. During the centrifugal phase (landing), knee stiffness had a significant effect on ground contact time, with athletes with greater stiffness demonstrating shorter contact times, thus contributing to a quicker entry into the centripetal phase (jumping). In contrast, during the centripetal phase, ankle power output was highly correlated with free height and explosive performance, showing the decisive role of the ankle joint in vertical mobility at the start of the jump. The hip joint also plays a role in coordinating upper and lower limb movements and enhancing power transfer throughout the exercise process, but its influence is more indirect. This study provides biomechanical empirical evidence for the training of sprinters, especially by enhancing knee joint stiffness and ankle joint power output, athletes can effectively improve the performance of vertical jump manoeuvres. These findings provide a scientific basis for coaches and athletes to optimise their training programmes and improve their performance in competitions, and provide a reference direction for future related research.

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.

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.

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.

Abstract The 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.

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.

Abstract Cellulose 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.

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.

In this extended abstract, we describe CoRe Challenge 2022/2023, an international competition series aiming to construct the technical foundation of practical research for Combinatorial Reconfiguration. This competition series targets one of the most well-studied reconfiguration problems, called the independent set reconfiguration problem under the token jumping model, which asks a step-by-step transformation between two given independent sets in a graph. Theoretically, the problem is PSPACE-complete, which implies that there exist instances such that even a shortest transformation requires super-polynomial steps with respect to the input size under the assumption of $NP \neq PSPACE$. The competition series consists of four tracks: three tracks take two independent sets of a graph as input, and ask the existence of a transformation, a shortest transformation, a longest transformation between them; and the last track takes only a number of vertices as input, and asks for an instance of the specified number of vertices that needs a longer shortest transformation steps. We describe the background of the competition series and highlight the results of the solver and graph tracks.

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.

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.

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.