Jump Process Research Articles

Markov Jump Processes in Estimating Sharing of Identity by Descent

Markov Jump Processes in Estimating Sharing of Identity by Descent

Probabilistic Resistive Switching Device Modeling Based on Markov Jump Processes

In this work, a versatile mathematical framework for multi-state probabilistic modeling of Resistive Switching (RS) devices is proposed for the first time. The mathematical formulation of memristor and Markov jump processes are combined and, by using the notion of master equations for finite-states, the inherent probabilistic time-evolution of RS devices is sufficiently modeled. In particular, the methodology is generic enough and can be applied for $N$ states; as a proof of concept, the proposed framework is further stressed for both two-state RS paradigm, namely $N=2$, and multi-state devices, namely $N=4$. The presented I-V results demonstrate in a qualitative and quantitative manner, adequate matching with other modeling approaches.

Nonlinear dynamic correlation between geopolitical risk and oil prices: A study based on high-frequency data

This study investigates the nonlinear dynamic correlations between geopolitical risk (GPR) and oil prices using nonlinear Granger causality and DCC-MVGARCH methods based on high-frequency data. The relationship between GPR and oil prices is found to have a complex nonlinear relationship rather than a simple linear one. Further, a bidirectional nonlinear Granger causality is found to consistently exist between GPR and oil volatility across different components of realized volatility. In terms of returns, GPR has relatively weak unidirectional nonlinear Granger causation with oil returns. The dynamic correlation analysis shows that GPR mainly affects oil volatility rather than returns. Moreover, GPR mainly affects oil volatility through the jump component of the oil market after the financial crisis, and there is a strong positive correlation between GPR and volatility jumps. Our findings innovatively suggest that GPR can potentially be utilized to improve models of volatility jumps and provide reference for investors and price analysts in oil markets who want to design sensible risk-management strategies.

Study of a new water jet thruster for robotic returnable jumping

A novel water jet thruster which is capable of conducting two sequential jumps is proposed for the amphibious jumping robot. The proposed water jet thruster adopted a unique structural design with a double-layered tank. Liquid nitrogen was injected to the tank to pressure the propellant water and generate propulsive force, which is safe and effective for both aquatic and terrestrial environment. Then a theoretical jumping model was built to evaluate the performances of two jumping actions. According to the tethered thrust measurement and free jumping experiments, the estimation from the model met well with their experimental verifications. Moreover, CFD simulation was conducted to compare the emission process of inner and outer chambers in detail. We believe the demonstration of the novel thruster would drive the innovation of future amphibious robots that capable of leaping from both aquatic and terrestrial environments.

Kinetic Model of Softening of Glasses

A liquid-glass transition (vitrification) has been analyzed in terms of the softening of a solid phase through diffusion jumps. It has been shown that the assumption of a Gibbs momentum distribution (in fact, local thermalization) in glass automatically results in the existence of diffusion in glasses at any temperatures. In view of this conclusion, the possibility of a virtual “thermodynamic” transition responsible for vitrification is questionable. A model of jumps of “hot” particles has been proposed that predicts the existence of two characteristic temperatures TA and TB and describes qualitative changes in the temperature dependence of the viscosity of a liquid upon cooling (“Arrhenius”—“super-Arrhenius”—“Arrhenius”). The temperatures TA and TB are related to the number of particles in the first coordination sphere and the number of particles in the region of structural correlations (intermediate order region) in disordered media. The concept of ergodicity is discussed in application to glasses.

Electrical Properties in Large Frequency and Temperature Ranges of Sr0.6Ca0.4TiO3 Ceramics

Abstract: Lead-free Sr0.6Ca0.4TiO3 (SCT) ceramic was prepared by the solid state reaction route. X-Ray diffraction technique showed the phase purity and identified the orthorhombic perovskite structure of the material. Scanning Electronic Microscopy observation evidenced homogeneous morphology and dense microstructure for the ceramic. The dielectric and conductivity properties of the sample were studied using complex impedance measurement technique in a wide range of frequencies and temperatures: from 100 Hz to 1.8 GHz and from 25°C to 550°C. The ceramic exhibits a stable dielectric permittivity and low dielectric losses in frequency and temperature up to 200°C. This is very interesting in view of developing high-quality lead-free ceramic capacitors for applications requiring high temperatures; for example, in cars. The increase in dielectric permittivity for temperatures higher than 200°C may be related to oxygen vacancies that are heat-activated in the material. Dielectric losses show the existence of a dielectric relaxation at low temperatures and low frequencies. Conductivity measurement investigated at high temperatures show on one hand high AC conductivity values attributed to the high temperature jumping process and on the other hand two electrical conductivity mechanisms above 400° C in the material. Keywords: Strontium calcium titanate, Ceramic, Structure, Dielectric properties, Conductivity.

Jumping archer fish exhibit multiple modes of fin–fin interaction

Aquatic organisms jumping for aerial prey require high-performance propulsion, accurate aim, and trajectory control to succeed. Archer fish, capable of jumping up to twice their body length out of the water, address these considerations through multifaceted fin and body kinematics. In this study, we utilized 3D synthetic aperture particle image velocimetry to visualize the wakes of archer fish throughout the jumping process. We found that multiple modes of interaction between the anal and caudal fins occur during jump behaviors. Time-resolved volumetric measurements presented herein illustrate the hydrodynamics of each interaction mode in detail. Additionally, regardless of which fin uses and interactions were exhibited during a jump, we found similar relationships between the cumulative impulse of multiple propulsive vortices in the wake and the instantaneous ballistic momentum of the fish. Our results suggests that fin use may compensate for variations in individual kinematic events and in the aiming posture assumed prior to jumping and highlight how interactions between tailbeats and other fins help the archer fish reach necessary prey heights in a spatially- and visually-constrained environment. In the broader context of bioinspired propulsion, the archer fish exemplifies that multiple beneficial hydrodynamic interactions can be generated in a high-performance scenario using a single set of actuators.

Fixed time output feedback containment for uncertain nonlinear multiagent systems with switching communication topologies

This paper presents a fixed time containment protocol within output feedback framework for uncertain nonlinear multiagent systems (MASs) exposed to unknown leader dynamics under switching communication topologies. To characterize dynamic communication links among agents in uncertain environments, a Markov jumping process with partially known transition probability is introduced to circumvent the difficulties of requiring the exact elements of transition rates as a prior. Then, in order to eliminate the necessity of broadcasting local velocity states between neighboring agents over the wireless and reject the comprehensive uncertainties including unknown model nonlinearities, external disturbances as well as switching topology jumps, a fixed time extended state observer (FTESO) only using the relative position information as input data is established for follower agents to achieve a uniform fast and precise estimation capability. A fixed time output feedback containment protocol by means of observer is presented to ensure that individual follower is guided into the geometric area constituted by a fleet of unknown leaders with a consistent convergence time irrelevant of initial conditions. The outstanding features of the developed algorithm are threefold: First, a prescribed fixed time containment consensus with reduced communication burden and enhanced robustness can be implemented. Second, a Markov jumping process with a partially known transition probability is considered to stimulate switching communication topologies. Third, a FTESO is constructed for each agent to realize a fixed-time estimation without requiring accurate modeling information. Finally, the fixed time stabilization of cascaded system is illuminated by applying the Lyapunov-based methods and bi-limit homogeneity. Simulation examples validate the feasibility and strengths of developed control protocol.

Jump Models with Delay—Option Pricing and Logarithmic Euler–Maruyama Scheme

In this paper, we obtain the existence, uniqueness, and positivity of the solution to delayed stochastic differential equations with jumps. This equation is then applied to model the price movement of the risky asset in a financial market and the Black–Scholes formula for the price of European option is obtained together with the hedging portfolios. The option price is evaluated analytically at the last delayed period by using the Fourier transformation technique. However, in general, there is no analytical expression for the option price. To evaluate the price numerically, we then use the Monte-Carlo method. To this end, we need to simulate the delayed stochastic differential equations with jumps. We propose a logarithmic Euler–Maruyama scheme to approximate the equation and prove that all the approximations remain positive and the rate of convergence of the scheme is proved to be 0.5.

Evaluation of classification performance in human lower limb jump phases of signal correlation information and LSTM models

The recognition of the human lower limb jump phases plays an important role in measuring the degree of rehabilitation and the control of the exoskeleton. However, one of the challenges is that the recognition accuracy using sEMG signal is low. In this paper, we propose two types of long–short term memory network (LSTM) models for offline and online recognition of jump sequences. The recognition accuracies of bidirectional LSTM and convolutional LSTM (ConvLSTM) for sEMG reach 97.84% and 97.44%, respectively. When the offline analysis model is used with sEMG sequence of the jump process, the misclassification only occurs in the adjacent phases. From the Pearson correlation coefficients (PCCs) of sEMG and IMU signals, the complex network of muscles and kinematics is built to analyze the coupling of muscle and motion in the jumping process. Taking the sequence composed of PCC matrix with sensor information confusion as the input, ConvLSTM model can acquire spatiotemporal features and the accuracy of the online model can reach 98.13%. In this paper, the number and length of analysis windows that influence the model performance are studied. The synthesis method of Euler angle signals facilitates the recognition of human movement intention.

Estimation of [formula omitted], [formula omitted] and portfolio weights in a pure-jump model with long memory in volatility

We investigate a bivariate pure-jump model of stock prices with long memory in volatility, using a marked log-Gaussian Cox process. We show that, due to the non-synchronicity of transactions, the ordinary least squares estimator of the slope in a contemporaneous regression of returns on returns converges to different targets depending on the sampling frequency. Therefore, we propose a transaction-level estimator that makes full use of data in the complete continuous-time record, and show that the estimator of the slope has slow convergence with rate determined by the memory parameter in volatility.

Evolution of deepwater turbidite bedforms in the Huaguang channel–lobe transition zone revealed by 3D seismic data in the Qiongdongnan Basin, South China Sea

The theoretical model of turbidite bedform evolution has been verified based on laboratory tests and outcrop surveys. However, the evolution of the bedforms associated with flow regime variation within the channel–lobe transition zone (CLTZ) is poorly documented and generally extremely poorly understood. In this study, a combination of seismic sedimentological and topographic analyses, based on high-resolution 3D seismic data within the Qiongdongnan Basin of the South China Sea, was used. Continuous bedforms varied with the depositional elements within the CLTZ of the Huaguang leveed channel system along the flow direction. The depositional elements within the CLTZ change from the main channel to the distributary channels as well as to the sub-distributary channels. Numerous bifurcation and confluence points of gravity flows illustrated the complexity of the drainage network within the CLTZ. The average asymmetry index of the bedforms increased from 0.8 to 1.6, with the average wavelength increasing from 803 m to 1545 m along the thalweg of the channels. Crevasse splays at the starting reach of the CLTZ are likely to form the initial state of the new CLTZ in the future, because the slope gradient starting from the avulsion point was higher than that inside the channel. The deep scours at the bifurcation points and high steps at the confluence points demonstrate the critical roles of supercritical flows and hydraulic jumps in reworking the bedforms of the CLTZ. The high steps at confluence points were simultaneously formed along the margin and thalweg of the main channel. The acceleration mechanisms of flow velocity forming the high steps were the increase of the elevation difference along the internal slope of the main channel margin and promotion of discharge along the main channel thalweg. This paper presents newly completed deepwater observations of the present seafloor bedforms based on the turbidity currents within the CLTZ. These observations update the evolution model of local supercritical flows and hydraulic jumps under the global decreasing trend of the Froude numbers within CLTZs.

Numerical modeling of the hydraulic jump location using 2D Iber software

In the recent years, numerical modeling of free surface flows has experienced a rapid and important development. Several programs and software have been used to simulate free surface flows. Transition from supercritical to subcritical flow regime leads to formation of hydraulic jumps. Numerical modeling of hydraulic jumps has taken an important part in this domain. This work aims to assess the efficiency of Iber software in the simulation of hydraulic jump in a rectangular channel. The location and displacement of the hydraulic jump were simulated by 2D Iber software. The data of these simulations were obtained from the experimental tests carried out at the laboratory. The results of the simulated hydraulic jump surface profiles showed a good agreement with those measured experimentally. The velocity distribution is presented in this study. Numerical simulation results satisfactorily predicted the hydraulic jump location, which gives confidence using of Iber software in the simulation of hydraulic jump.

Estimating Jump Activity Using Multipower Variation

Realized multipower variation, originally introduced to eliminate jumps, can be extremely useful for inference in pure-jump models. This article shows how to build a simple and precise estimator of the jump activity index of a semimartingale observed at a high frequency by comparing different multipowers. The novel methodology allows to infer whether a discretely observed process contains a continuous martingale component. The empirical part of the article undertakes a nonparametric analysis of the jump activity of bitcoin and shows that bitcoin is a pure jump process with high jump activity, which is critically different from conventional currencies that include a Brownian motion component.

STATE-FEEDBACK CONTROL OF DISCRETE-TIME STOCHASTIC LINEAR SYSTEMS WITH MARKOVIAN SWITCHING

This paper is concerned with the stabilization problem via state-feedback control of discrete-time jumping systems with stochastic multiplicative noises. The jumping process of the system is driven by a discrete-time Markov chain with finite states and partially known transition probabilities. Sufficient conditions are established in terms of tractable linear matrix inequalities to design a mode-dependent stabilizing state-feedback controller. A numerical example is provided to validate the effectiveness of the obtained result.

Variance Swap Pricing under Hybrid Jump Model

Variance Swap Pricing under Hybrid Jump Model

Robust Filtering Algorithm for Markov Jump Processes with High-Frequency Counting Observations

We present an algorithm for estimating the state ofMarkov jump processes, given the counting observations. A characteristic feature of the class of considered observation systems is that the frequency of jumps in incoming observations significantly exceeds the intensity of the change of states of the estimated process. This property makes it possible for the filtering algorithm to process incoming observations using their diffusion approximation. The estimates proposed in this work have the stability property concerning inaccurate knowledge of the distribution of the observed process. To illustrate the robust qualities of the estimates, we present a solution for the applied problem of monitoring the state of an RTP connection based on observations of the packet flow recorded at the receiving node.

An Empirical Examination of the Term Structure Fundamentals of Credit Spreads

Using an exponential model of jumps to default, this research investigates the fundamentals that determine the spreads required by investors for corporate credit risk at different maturities. The empirical results indicate that credit default swap (CDS) prices across the term spectrum are strongly associated with interrelated probabilities of cash, income, and valuation insolvency, as well as with market-based measures of systematic risk. Although the financial functions best-fitting CDS prices are found to vary somewhat by maturity, an integrated model with constant parameters across time, company, and term is found to explain about 50% of individual credit spreads both in sample and ex post. <b>TOPICS:</b>Credit risk management, credit default swaps <b>Key Findings</b> • Using nonnegative least squares procedures to find the structural model forms which best fit credit spreads across the term structure, this empirical research explains more than half of individual credit default swap prices in and out of sample. • Credit default swap prices with shorter terms (like 1–3 years) are found to be most strongly determined by the probability of a company generating negative income and running out of cash, but the likelihood of cash and income insolvency is discovered to have important impacts at longer maturities of 5–10 years. • The 378,401 individual credit spreads in the sample over the 2008–2019 interval are found to incorporate time-varying systematic risk premiums (estimated from market prices), as well as reflect the integrated risks of income, cash, and valuation insolvency on any day.

Stationary stochastic Higher Spin Six Vertex Model and q-Whittaker measure

In this paper we consider the Higher Spin Six Vertex Model on the lattice $${\mathbb {Z}}_{\ge 2} \times {\mathbb {Z}}_{\ge 1}$$ . We first identify a family of translation invariant measures and subsequently we study the one point distribution of the height function for the model with certain random boundary conditions. Exact formulas we obtain prove to be useful in order to establish the asymptotic of the height distribution in the long space-time limit for the stationary Higher Spin Six Vertex Model. In particular, along the characteristic line we recover Baik–Rains fluctuations with size of characteristic exponent 1/3. We also consider some of the main degenerations of the Higher Spin Six Vertex Model and we adapt our analysis to the relevant cases of the q-Hahn particle process and of the Exponential Jump Model.

A combined series-elastic actuator & parallel-elastic leg no-latch bio-inspired jumping robot

Compared with the catapult mechanism widely employed by small jumping robots, recently proposed jumping strategies based on series-elastic actuators (SEA) without latch mechanisms perform better in terms of agility, structural robustness and maneuverability. However, in some practical applications, they have difficulty in effectively storing energy before the push-off. This paper presents a novel no-latch jumping strategy inspired by frogs, achieving highly effective energy storage. The jumping strategy combines an SEA with a parallel-elastic linkage, which allows one motor to rotate in one direction to store the elastic energy and automatically trigger its release. Combined with this strategy, a frog-inspired robotic leg mechanism is designed. The jumping process is analysed in detail and the kinematic and dynamic models are derived. Bars’ dimensions and springs’ parameters are determined by the optimization to maximize the energy-storing capacity. The simulation is performed to predict the jumping performance. A 100.7 g prototype is fabricated and jumps to a height of 1.3 m with slight aerial body rotation. The energy-storing capacity of the robot is 18.1 J/Kg.