Jump Process Research Articles (Page 4)

DeepNet Jump Models: Detecting and Predicting Price Jumps with Mahalanobis Distance and Signatures

We introduce a novel option pricing model that features stochastic interest rates along with an underlying price process driven by stochastic string shocks combined with pure jump Lévy processes. Substituting the Brownian motion in the Black–Scholes model with a stochastic string leads to a class of option pricing models with expiration-dependent volatility. Further extending this Generalized Black–Scholes (GBS) model by adding Lévy jumps to the returns generating processes results in a new framework generalizing all exponential Lévy models. We derive four distinct versions of the model, with each case featuring a different jump process: the finite activity lognormal and double–exponential jump diffusions, as well as the infinite activity CGMY process and generalized hyperbolic Lévy motion. In each case, we obtain closed or semi-closed form expressions for European call option prices which generalize the results obtained for the original models. Empirically, we evaluate the performance of our model against the skews of S&P 500 call options, considering three distinct volatility regimes. Our findings indicate that: (a) model performance is enhanced with the inclusion of jumps; (b) the GBS plus jumps model outperform the alternative models with the same jumps; (c) the GBS-CGMY jump model offers the best fit across volatility regimes.

Abstract Half‐metallic ferromagnets (HMFs) exhibit semiconductor behavior for one spin projection and metal characteristics for the other, which have promising applications in spintronics. It is a great challengeable for HMFs to have wide spin energy gap, large saturation magnetization (MS), and high Curie temperature (TC) simultaneously. Here, we report the Sr1.5Mn0.5Fe0.5Hf1.5O6 (SMFHO) double perovskite compounds synthesized by solid‐state reaction and display a magnetic TC up to 804 K due to the strong Mn3+(↑)Fe3+(↑) spin interactions, which is the reported record in perovskite‐type HMFs so far. The measured MS value at 300 K was 4.87 μB/f.u., and it further increased up to 6.09 μB/f.u. at 2 K. The SMFHO powders exhibited butterfly‐shaped magnetoresistance (MR)–H curve at 2 K, and the MR (2 K, 7 T) value was measured as −3.86% due to the intergranular magnetic tunneling effect. Variation of the resistivity of the SMFHO ceramics versus temperature exhibits a semiconductor behavior, and the electrical transport properties of the SMFHO ceramics are well studied by Mott's range jump model, thermally activated semiconductor conductance model and small polaron jumping model, respectively. The optical absorption spectrum of the SMFHO powders demonstrates an indirect optical bandgap of 3.56 eV. Our present work demonstrates the intriguing properties of the SMFHO oxides where high TC, wide energy gap, and large MS value are preserved at the same time, which open the way to their promising applications in advanced spintronic devices at or beyond room temperature.

Abstract. At present, research on bionic jumping robots mainly focuses on imitating various jumping animals, such as kangaroos, frogs, or locusts. These bionic objects have good jumping ability. The goat, as one of these with a moderate size and a strong jumping ability, is very suitable as a prototype to imitate jumping. In this study, first, a simplified serial joint model that imitates a goat's hindlimb is proposed with a comparison analysis of its physiological structure. Then, a jumping leg mechanism that imitates a goat's hindlimb was designed. Second, the kinematics of the goat-inspired jumping leg were constructed to describe the relationship between joint angles and foot positions. Additionally, we used a cubic polynomial to plan the trajectory of the jumping process to achieve a smooth jumping movement based on the characteristics of the goat's jumping, with position and speed constraints during the jump. Thus, we established a smooth jumping trajectory model of the goat-inspired jumping leg. Finally, experiments on the jumping of the goat-inspired jumping leg were conducted. The goat-inspired jumping leg has good jumping performance. In this study, we took the goat's hindlimbs as the bionic model, proposed the goat-inspired jumping leg mechanism, and presented the jumping trajectory planning theory for smooth jumping of the goat-inspired jumping leg. These provide new ideas for the study of bionic jumping legs and can effectively promote further development of bionic jumping robots.

Computational complexity of jumping block puzzles

In this paper, we investigate the optimal control problems for a class of neutral stochastic integrodifferential equations (NSIDEs) with infinite delay driven by Poisson jumps and the Rosenblat process in Hilbert space involving concrete-fading memory-phase space, in which we define the advanced phase space for infinite delay for the stochastic process. First, we introduce conditions that ensure the existence and uniqueness of mild solutions using stochastic analysis theory, successive approximation, and Grimmer’s resolvent operator theory. Next, we prove exponential stability, which includes mean square exponential stability, and this especially includes the exponential stability of solutions and their maps. Following that, we discuss the existence requirements of an optimal pair of systems governed by stochastic partial integrodifferential equations with infinite delay. Then, we explore examples that illustrate the potential of the main result, mainly in the heat equation, filter system, traffic signal light systems, and the biological processes in the human body. We conclude with a numerical simulation of the system studied. This work is a unique combination of the theory with practical examples and a numerical simulation.

Stochastic captive jump processes are explicitly constructed in continuous time, whose non-linear dynamics are strictly confined by bounded domains that can be time-dependent. By introducing non-anticipative path-dependency, the framework offers the possibility of generating multiple inner tunnels within a master domain, such that a captive jump process is allowed to proceed either within a single inner tunnel or jump in between tunnels without ever penetrating the outermost shell. If a captive jump process is a continuous martingale or a pure-jump process, the uppermost confining boundary is non-decreasing, and the lowermost confining boundary is non-increasing. Under certain conditions, it can be shown that captive jump processes are invariant under monotonic transformations, enabling one to construct and study systems of increasing complexity using simpler building blocks. Amongst many applications, captive jump processes may be considered to model phenomena such as electrons transitioning from one orbit (valence shell) to another, quantum tunnelling where stochastic wave-functions can “penetrate” inner boundaries (i.e., walls) of potential energy, non-linear dynamical systems involving multiple attractors, and sticky concentration behaviour of pathogens in epidemics. We provide concrete, worked-out examples, and numerical simulations for the dynamics of captive jump processes within different geometries as demonstrations.

The motion process and force of the jumper crossing a multiphase environment are of great significance to the research of small amphibious robots. Here, CFD (Computational Fluid Dynamics)-based simulation analysis for motions through multiphase environments (water-air multiphase) is successfully realized by UDF (user-defined function). The analytical model is first established to investigate the jumping response of the jumpers with respect to the jump angle, force, and water depth. The numerical model of the jumper and its surrounding fluid domain is conducted to obtain various dynamic parameters in the jumping process, such as jumping height and speed. Satisfactory agreements are obtained by comparing the error of repeated simulation results (5%). Meanwhile, the influence of the jumper's own attributes, including mass and structural size, on the jumping performance is analyzed. The flow field information, such as wall shear and velocity when the jumper approaches and breaks through the water surface, is finally extracted, which lays a foundation for the structural design and dynamic underwater analysis of the amphibious robot.

The performance of stilling basins including a negative step was analyzed addressing its effect on the energy dissipation efficiency, dimensions and structural properties of the hydraulic jump, streambed pressures and pressure fluctuations. Six different cases were simulated, considering two possible relative heights for the step and three possible Froude numbers. The results show that the step yields to lower subcritical depths, allowing smaller basin dimensions. Nevertheless, it tends to slightly increase the roller length of the jump. Concerning the relative energy dissipation, results confirm the improvement derived from the step presence. The internal flow occurring in the jump was also analyzed, and more specifically the subzones generated upstream and downstream the impingement point. The results prove the contribution of the negative step in the stabilization of hydraulic jumps in the stilling basin. In particular, a general decrease of the streambed pressure is observed. In addition, pressure fluctuations are significantly reduced due to the negative step size influence on the hydraulic jump. Furthermore, the effectiveness of the computational fluid dynamics (CFD) techniques to simulate stilling basin flows and to adequately characterize the hydraulic jump performance was confirmed.

In this study we have synthesized the iron and bismuth co-substituted BaTiO3 ceramic, with the general formula: Ba0.95Bi0.05Ti1-xFexO3 for x=0.00 to 1.00, by solid state route. The impedance and electrical properties of these materials were investigated. The dispersion in conductivity in these ceramics can be described by Jonscher's power law and suggests a mechanism of conduction that is related to the Correlated Barrier Jump (CBH) model, according to which charge transport occurs between localized states due to a jump of the potential barriers. The conductivity results confirmed the semi-conductor behavior of these ceramics at high frequency region. The Nyquist plots for the different ceramics confirmed the simple electrical relaxation phenomena with the presence of a Debye-type relaxation phenomenon for x<040 of Fe content. While above this rete, the relaxation behavior is transformed into a Non-Debye phenomenon.

The Performance of Jump Models to Price Commodity Options

This article investigates the sliding mode control (SMC) for discrete-time nonlinear semi-Markov jump models with a partly known semi-Markov kernel (SMK). The nonlinear system is characterized by the Takagi–Sugeno (T–S) fuzzy model, where the membership functions for fuzzy rules are designed to be related to the system mode. In view of the fact that the statistical characteristic of the SMK is difficult to fully obtain in practical engineering, the SMK is recognized to be partly known with less conservativeness than both semi-Markov jump models with completely known SMK and Markov jump models with partly known transition probabilities. On the basis of classical Lyapunov stability and fuzzy-model-based approach, novel convex mean-square stability is proposed for the underlying system by eliminating the nonlinear coupling terms with the aid of additional matrix variables. Afterward, a fuzzy SMC law strategy is constructed to guarantee the reachability of the discrete quasi-sliding mode. Finally, a robot arm model is simulated to verify the proposed fuzzy SMC strategy.

Due to the inherent vulnerability of Deep Neural Networks (DNNs), Adversarial Example (AE) attack has become a serious threat to intelligent systems, e.g., the failure cause of an image classification system. Different to existing works, in this paper we are interested in the generation of AEs for DNNs with defensive mechanisms. To make the attack more practical, we exploit a query-based method to generate image AEs in a black-box attack setting. Considering that the generation of AEs is inherently a constrained optimization problem, this paper first formulates three objectives regarding to defensive DNNs, i.e, attack effectiveness, attack evasiveness and attack coverage. Then, this paper proposes a query-efficient AE attack based on Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) to address the perturbation optimization problem. To improve the efficiency of search and query, AE-specific operators including block-level and pixel-level crossovers, discrete perturbation mutation and direction-driven reproduction are designed within the GA-based search framework. In addition, predication-based adaptation of reproduction-related parameters is implemented to speed up the search convergence. PSO-based jumping process is further devised to avoid stuck in local optimum. Benchmark-based experiments evaluated the efficiency of our method, which can achieve an attack success rate of 100% with averagely 52.95% reduced queries in contrast to existing black-box attacks on non-defensive models. For defensive DNN models, our method can obtain top attack performance with the query reduction up to 70.92% comparing with the candidates.

This article focuses on the dissipativity-based consensus tracking control (DBCTC) problems of time-varying delayed leader-following nonlinear multiagent systems (LFNMASs) with the event-triggered transmission strategy. The switching topologies of the LFNMASs are subject to the uncertain and partially unknown generally Markovian jumping process. The control inputs of the following agents are updated according to the proposed event-triggered transmission strategy, which could reduce the communication burden. Based on the event-triggered transmission condition and distributed consensus protocol, some dissipativity-based criteria obtained by adopting the delay-product-term Lyapunov-Krasovskii functional (DPTLKF) and higher order polynomial-based relaxed inequality (HOPRII) are proposed to guarantee the LFNMAS consensus. The validity of the main results is verified by two simulation examples.

Variational RANS modeling of hydraulic jumps

Periodic Jump processes commonly occur in complex industrial systems. As the systems vary dynamically between different stages, learning their dynamics in an unified model, so as to forecast and simulation accurately is challenging. In this study, we propose Autonomous jump Ordinary Differential Equation Net (AJ-ODENet) to learn the continuous-time periodic jump system. The model consists of several Hierarchical ODENets (H-ODENets) and a stage transition predictor. Each H-ODENet is an advanced version of ODENet to individually learn specific dynamics in each stage from irregularly sampled sequence data. The stage transition predictor realizes autonomous stage transition during open loop simulation. Furthermore, an encoder-decoder framework built on AJ-ODENet is employed on a real cooling system of data center to simulate some variables in runtime. With multivariate data given, such as server power and environmental temperature, the model can simulate the working patterns as in reality, and the relative error of the predicted energy consumption is within 5%. Furthermore, based on the model, we infer the optimal cooling temperature settings under different heat loads. The simulation results indicate that 6-25% of cooling energy consumption can be optimized.

This paper is devoted to the issue of observer-based adaptive sliding mode control of distributed delay systems with deterministic switching rules and stochastic jumping process, simultaneously, through a neural network approach. Firstly, relying on the designed Lebesgue observer, a sliding mode hyperplane in the integral form is put forward, on which a desired sliding mode dynamic system is derived. Secondly, in consideration of complexity of real transition rates information, a novel adaptive dynamic controller that fits to universal mode information is designed to ensure the existence of sliding motion in finite-time, especially for the case that the mode information is totally unknown. In addition, an observer-based neural compensator is developed to attenuate the effectiveness of unknown system nonlinearity. Thirdly, an average dwell-time approach is utilized to check the mean-square exponential stability of the obtained sliding mode dynamics, particularly, the proposed criteria conditions are successfully unified with the designed controller in the type of mode information. Finally, a practical example is provided to verify the validity of the proposed method.

The phenomenon of droplet coalescence and jumping has received increasing attention due to its potential applications in the fields of condensation heat transfer and surface self-cleaning. Basic research on the process and mechanism of coalescence-induced droplet jumping has been carried out, and some universal laws have been established. However, it is found that the focus of these studies is based on two identical droplets, and the coalescence-induced jumping with different radii is rarely investigated, which is commonly encountered in nature. Therefore, it is essential to proceed with the research of coalescence and jumping of droplets with unequal radii. In this paper, molecular dynamics (MD) simulations are performed to reveal the effects of radius ratio and radius of small droplets on jumping velocity. The results show that as the increasing of radius ratio with an unchanged small droplet radius of 8.1 nm, the jumping velocity increases then decreases, which indicates there is an optimal radius ratio to maximize the jumping velocity. Additionally, it is found that if the small droplet radius is changed, the critical radius ratio for characterizing whether the coalesced droplet jumping increases with increasing the small droplet radius. Furthermore, according to energy conservation, the conversion efficiency of energy is discussed. The results show that when the radius ratio is greater than 1.3 with three different small droplet radii, the energy conversion efficiency rapidly decreases to below 1.0%; and the critical radius ratios are consistent with the result obtained from the velocity analysis. This work broadens the understanding of the more general phenomenon of coalescence-induced droplet jumping and can better guide industrial applications.

In this paper, we investigate the problem of a dynamic event-triggered robust controller design for flexible robotic arm systems with continuous-time phase-type semi-Markov jump process. In particular, the change in moment of inertia is first considered in the flexible robotic arm system, which is necessary for ensuring the security and stability control of special robots employed under special circumstances, such as surgical robots and assisted-living robots which have strict lightweight requirements. To handle this problem, a semi-Markov chain is conducted to model this process. Furthermore, the dynamic event-triggered scheme is used to solve the problem of limited bandwidth in the network transmission environment, while considering the impact of DoS attacks. With regard to the challenging circumstances and negative elements previously mentioned, the adequate criteria for the existence of the resilient H∞ controller are obtained using the Lyapunov function approach, and the controller gains, Lyapunov parameters and event-triggered parameters are co-designed. Finally, the effectiveness of the designed controller is demonstrated via numerical simulation using the LMI toolbox in MATLAB.

Seeing the root of the problem of student independence during the Covid-19 pandemic, implementing the effectiveness of learning with the Seven Jumps model assisted by the whatsapp group during the Covid-19 Pandemic is the aim of this research. This type of research approach is a qualitative and quantitative experiment carried out online with the Seven Jumps learning model assisted by WhatsApp groups. Data was collected by questionnaires, observation sheets and tests. Valid device tests come from expert perceptions, test the effectiveness of learning with statistical tests of the effect of regression and comparative t tests. The results showed that the root problems and constraints for student independence in utilizing information technology to achieve the expected competencies were: low self-motivation to learn, self-assessment ability, self-discipline, self-control, responsibility, pattern-learning ability, self-reliance in designing appropriate learning objectives, design implementation strategies, monitoring the progress of learning outcomes, coordination of learning methods, and the need for guidance in finding learning resources, implementing independent learning with the Seven Jumps model assisted by the whatsapp group is effective. This is indicated by: a) there is a positive influence of independent learning on problem solving ability of 60.8%, b) The gain test to measure the effectiveness of the pretest and posttest is 0.52 in the medium category and the effectiveness is sufficient. The Seven Jumps method can be implemented boldly during the Covid-19 Pandemic.