Continuous Time Research Articles

The influencing factors of participation in time banking volunteer service for older adults among university students in Nanjing, China.

This study aims to identify factors influencing university students' participation in time banking volunteer services for older adults and provides evidence to promote the involvement. Conducted in November 2022, we utilized a convenience sampling method to recruit students from the School of Aging Service and Management at Nanjing University of Chinese Medicine, China. Data was collected through an online questionnaire focusing on various aspects related to time banking volunteer services for older adults. Factor analysis was employed to extract variables, and logistic regression was applied to identify key determinants. A significant majority (82.67%) of participants expressed willingness to engage in volunteer services for older adults. Factor analysis uncovered six influential factors explaining 62.55% of the variance. Logistic regression highlighted four key determinants of students' willingness: value judgment (OR = 4.392, CI = 2.897-6.658), social support (OR = 1.262, CI = 0.938-1.975), social influence (OR = 1.777, CI = 1.598-3.799), and socioeconomic conditions (OR = 1.174, CI = 1.891-3.046). To foster sustainability and continuous time banking among university students majoring in aging service and management, a multifaceted support involving governmental, social, and university is recommended.

A Bayesian functional approach to test models of life course epidemiology over continuous time.

Life course epidemiology examines associations between repeated measures of risk and health outcomes across different phases of life. Empirical research, however, is often based on discrete-time models that assume that sporadic measurement occasions fully capture underlying long-term continuous processes of risk. We propose (i) the functional relevant life course model (fRLM), which treats repeated, discrete measures of risk as unobserved continuous processes, and (ii) a testing procedure to assign probabilities that the data correspond to conceptual models of life course epidemiology (critical period, sensitive period and accumulation models). The performance of the fRLM is evaluated with simulations, and the approach is illustrated with empirical applications relating body mass index (BMI) to mRNA-seq signatures of chronic kidney disease, inflammation and breast cancer. Simulations reveal that fRLM identifies the correct life course model with three to five repeated assessments of risk and 400 subjects. The empirical examples reveal that chronic kidney disease reflects a critical period process and inflammation and breast cancer likely reflect sensitive period mechanisms. The proposed fRLM treats repeated measures of risk as continuous processes and, under realistic data scenarios, the method provides accurate probabilities that the data correspond to commonly studied models of life course epidemiology. fRLM is implemented with publicly-available software.

Adaptive robust bearing-based formation control for multi-agent systems

The problem of bearing-based formation control with disturbance rejection has been studied by quite a few papers under various assumptions on the disturbances such as constant disturbances, trigonometric polynomial disturbances or bounded uniformly continuous disturbances with known bounds. In this paper, we further study the same problem with the disturbances being bounded piecewise continuous time functions. We first consider the case where the bounds of the disturbances are known. We show that the problem can be solved by a distributed static state feedback control law. Then we further consider the case where the bounds of the disturbances are unknown. We manage to solve this problem by introducing the adaptive control technique to deal with the unknown bounds of the disturbances. Our results include all the existing results on the bearing-based formation control with disturbance rejection as special cases. Moreover, we present a sufficient condition on the initial values of the closed-loop system for each case that prevents the collision.

An optimization model for detailed scheduling of heterogeneous fleet of log trucks considering synchronization

ABSTRACT Log transportation accounts for a significant portion of the total delivered cost of logs due to the considerable number of truckloads between origins and destinations. Hence, an efficient transportation plan at the operational level can generate cost savings for forest companies. In this paper, a mixed integer linear programming model is developed for daily routing and scheduling of heterogeneous trucks considering synchronization constraints. Continuous time representation is used for modeling the problem to generate accurate schedules and to synchronize the trucks and loaders at cut blocks and sort yards. Compatibility requirements, overtime, and decisions related to the trucking contractors are incorporated in the model. The outputs of the model include the number of trucks utilized by each contractor, the arrival times and waiting times of trucks at each location, the detailed schedule of loaders, and the amount of overtime assigned to the drivers. To validate the model, it is applied to test problems from a case of a Canadian forest company, where transportation activities are contracted out. Results show it is more economical to pay overtime than dispatching additional trucks to carry logs. Additionally, variable costs and maximum driving time have the most impact on the total transportation cost.

Reduced order modeling of delta operator systems by optimal frequency fitting approach

The delta operator modeling provides a unified framework for both continuous-time and discrete-time modeling in system theory. At high sampling rate, the shift operator fails to provide meaningful information whereas, the delta operator parameterized system provides the same results as of continuous time systems. In this paper reduced order modeling of delta operator parameterized systems is considered. A complex domain (δ) optimal frequency matching (OFM) technique is proposed and frequency points are optimized using Particle Swarm Optimization (PSO) algorithm. This OFM is then utilized to find the reduced order model of the higher order system. PSO algorithm is a robust, global optimization technique, used to find these OFMs and thereby used to find the coefficients of the reduced order model by minimizing a cost function developed based on the responses of the higher order model and that of the reduced order model when both are excited by pseudo random binary sequences (PRBS). The performance characteristics are evaluated in software simulation using MATLAB considering example of higher order system in delta domain and time & frequency responses of the corresponding reduced model.

Robust optimal control of the multi‐input systems with unknown disturbance based on adaptive integral reinforcement learning Q‐function

AbstractConsidering overshoot and chatter caused by the unknown interference, this article studies the adaptive robust optimal controls of continuous‐time (CT) multi‐input systems with an approximate dynamic programming (ADP) based Q‐function scheme. An adaptive integral reinforcement learning (IRL) scheme is proposed to study the optimal solutions of Q‐functions. First, multi‐input value functions are presented, and Nash equilibrium is analyzed. A complex Hamilton–Jacobi–Issacs (HJI) equation is constructed with the multi‐input system and the zero‐sum‐game‐based value function. It is a challenging task to solve the HJI equation for nonlinear system. Thus, A transformation of the HJI equation is constructed as a Q‐function. The neural network (NN) is applied to learn the solution of the transformed Q‐functions based on the adaptive IRL scheme. Moreover, an error information is added to the Q‐function for the issue of insufficient initial incentives to relax the persistent excitation (PE) condition. Simultaneously, an IRL signal of the critic networks is introduced to study the saddle‐point intractable solution, such that the system drift and NN derivatives in the HJI equation are relaxed. The convergence of weight parameters is proved, and the closed‐loop stability of the multi‐system with the proposed IRL Q‐function scheme is analyzed. Finally, a two‐engine driven F‐16 aircraft plant and a nonlinear system are presented to verify the effectiveness of the proposed adaptive IRL Q‐function scheme.

Influence of Alevinage Time in the Optimization of Tambaqui Biomass Production in Semi-Intensive Fish Farming in the Northern Region of Amazonas

Objective: To evaluate the weight mix for the market obtained with variation in the pre-fixed fingerlings time, for the cultivation of tambaqui (Colossoma macropomum) in a semi-dug tank. Theoretical framework: The parameters evaluated regarding resources are, the tanks, each of which has its own capacity, its own state variable, which includes fish biomass, growth function and mortality rate. And identifying potential alternatives and making better decisions that optimize biomass production are important, but that take into account the reduction of its environmental impact. Method: The model incorporates two types of input variables. The discrete event variable, which comprises the number of fish in each batch, the number of tanks available, the time between the arrival of fingerlings in the system and the frequency of classification by weight for the market. The second refers to the continuous time variable, involving the weight of the fish, dissolved oxygen (DO) available to the fish, and feed consumption. Results and conclusions: The analysis showed that the decision variables are the quantities of fish, with the premise of final weight of 0.5 kg, 1 kg and 2 kg which are related to the hatching time pre-fixed at entry as “30, 40, 50, 60, 70, 80, 90, 100 days” in phase I, results in the optimization of production, target weight for the market as a function of time, in layout scenarios of 5 and 10 tanks, with the premise of harvesting in both, with Mix weight with 0.5kg, 1kg and 0.5kg, 1kg, 2kg to maximize net profit. Considering that the transition between growth phases is a stochastic process, which satisfies the Markov property. It was possible to define the balance between the input and output of the system. Research implications: The study is of great relevance, as it describes a sequential queue through the growth phases in relation to time, capable of determining the optimization of production with weight mix to maximize net profit. Originality/value: The research reveals that it is possible to use queuing theory analyzes in stochastic processes, evaluating the transition between time phases, which satisfies the Markov property.

Hybrid continuous-discrete time control strategy to optimize thermal network dynamic storage and heat-electricity integrated energy system dynamic operation

The heat-electricity integrated energy system (HE-IES) presents a promising opportunity for increasing renewable energy generation by fully utilizing the dynamic heat storage capabilities of the thermal network (TN). However, the dynamic characteristics of the TN and the response characteristics of devices in the HE-IES present challenges to system operation and control. To address these challenges, this study proposes a novel multi-layer control strategy that divides the system based on the component response status. The first layer aims to minimize the operating costs of the HE-IES, disregarding any dynamic effects. The second layer optimizes the dynamic operation of thermal subsystems by employing a TN’s Taylor expansion model and continuous-time generalized predictive control. The third layer focuses on optimizing the power subsystem to enhance the share of renewable energy generation, using discrete-time model predictive control. To the best of our knowledge, this is the first study that utilizes continuous time models to control the dynamic operation of TNs and their thermal subsystems. Through case analysis, the proposed model achieves a 34.5% reduction in operating costs compared to a single-layer control strategy and a 2.7% reduction compared to a discrete-time multi-layer control strategy. These findings highlight the favorable economic performance of the proposed model. Additionally, the utilization of continuous-time model allows for effective capturing dynamic performance of the TN and enhances its role in system operation.

Cluster target tracking based on multi-sensor continuous-discrete PMBM filter

Coordination effectively enhances the detection capabilities of sensors towards cluster targets. However, due to the dense distribution of cluster members and the cooperative interaction among them, continuous tracking of these targets becomes challenging. To address these issues, we propose a novel multi-sensor continuous-discrete Poisson multi-Bernoulli mixture filter, abbreviated as MS-CDPMBM-CT filter. Based on the cooperative interaction rules, we use the multivariate stochastic differential equation (SDE) to model the dynamics of cluster members in continuous time. To adapt to the Bayesian recursive process, we derive a Gaussian state transition form of the above model in the state space. In addition, by utilizing a cluster structure undirected graph and a multi-dimensional assignment (MDA) algorithm, we improve the multi-sensor continuous-discrete PMBM filter, which can iteratively estimate the posterior probability density of the target based on the continuous time state model and discrete multi-sensor measurements. During prediction, the cluster structure is exploited to provide cooperative interaction inputs that constrain member motions. During the update, the partitioning problem of multi-sensor measurements is transformed into the MDA problem for updating the global hypotheses. Simulation experiments show that the proposed method can better adapt to the cluster interaction behavior, distinguish the members within the cluster, and achieve high filtering accuracy.

Immediate neural effects of acupuncture manipulation time for stroke with motor dysfunction: a fMRI pilot study.

Acupuncture is widely utilized as a beneficial intervention for the treatment of motor dysfunction after stroke, and its effectiveness depends on the stimulation dose. Manipulation time is an important factor affecting the dose. This trial aimed use fMRI to explore the immediate neural effects in stroke patients with motor dysfunction by different acupuncture manipulation times, to reveal the neural mechanism of acupuncture manipulation. Thirty participants were divided into three groups according to different acupuncture times. Each group received the same acupoint prescription, although the continuous manipulation time of each acupoint in three groups was 1-min, 2-min, and 3-min, respectively. The NIHSS, FMA and fMRI-BOLD in each participant we obtained before and after acupuncture manipulation. Then, we used the regional homogeneity (ReHo) algorithm to analyze the changes of brain function and to compare the neural effects at different acupuncture manipulation times. There were no significant differences in NIHSS and FMA scores between and within groups. Longitudinal analysis of ReHo values indicated that the right inferior frontal gyrus was activated in the 1-min group, the right insula in the 2-min group, and the right inferior temporal gyrus in the 3-min group. Compared with the 1-min group, the 2-min group showed the ReHo values of the right precentral gyrus was decreased, and the 3-min group showed the left cerebellum posterior lobe was increased, the right posterior cingulate gyrus and the right anterior cingulate gyrus were decreased. Compared with the 2-min group, the 3-min group showed the ReHo values of the right cerebellum anterior lobe was increased. Our findings suggest that acupuncture at different manipulation times caused different changes of the neural effects in stroke patients, and the volume of activated voxel clusters is positively correlated with the manipulation time. Longer acupuncture manipulation could drive SMN and DMN in stroke patients, which may be the potential neurological mechanism of acupuncture manipulation affecting the recovery of motor dysfunction.

On the Relative Stability of Linear Time Invariant Systems

In this paper, state space representation based approach to relative stability of Linear Time Invariant (LTI) systems is discussed. Specifically, given a bound on the output, relative Bounded Input-Bounded Output (BIBO) stability of LTI systems is discussed. The bound on dominant pole is first determined using input-output description of LTI system. Using state space representation of homogeneous (no external input) LTI system, the components of state vector are upper bound. The results are applied to Continuous Time Markov Chains (i.e. homogeneous stochastic linear systems). Finally, using state space representation of arbitrary (with external input) Linear Time Invariant systems, the location of dominant pole is bounded. Using the upper bound, the location of line (parallel to imaginary-axis jω and to the left of it) is utilized for determining relative stability.

New Class of Discrete-Time Memristor Circuits: First Integrals, Coexisting Attractors and Bifurcations Without Parameters

The use of ideal memristors in a continuous-time (CT) nonlinear circuit is known to greatly enrich the dynamic behavior with respect to the memristorless counterpart, which is a crucial property for applications in future analog electronic circuits. This can be explained via the flux–charge analysis method (FCAM), according to which CT circuits with ideal memristors have for structural reasons first integrals (or invariants of motion, or conserved quantities) and their state space can be foliated in infinitely many invariant manifolds where they can display different dynamics. The paper introduces a new discretization scheme for the memristor which, differently from those adopted in the literature, guarantees that the first integrals of the CT memristor circuits are preserved exactly in the discretization, and that this is true for any step size. This new scheme makes it possible to extend FCAM to discrete-time (DT) memristor circuits and rigorously show the existence of invariant manifolds and infinitely many coexisting attractors (extreme multistability). Moreover, the paper addresses standard bifurcations varying the discretization step size and also bifurcations without parameters, i.e. bifurcations due to varying the initial conditions for fixed step size and circuit parameters. The method is illustrated by analyzing the dynamics and flip bifurcations with and without parameters in a DT memristor–capacitor circuit and the Poincaré–Andronov–Hopf bifurcation in a DT Murali–Lakshmanan–Chua circuit with a memristor. Simulations are also provided to illustrate bifurcations in a higher-order DT memristor Chua’s circuit. The results in the paper show that DT memristor circuits obtained with the proposed discretization scheme are able to display even richer dynamics and bifurcations than their CT counterparts, due to the coexistence of infinitely many attractors and the possibility to use the discretization step as a parameter without destroying the foliation in invariant manifolds.

Unsolved problem about stability of stochastic difference equations with continuous time and distributed delay

Despite the fact that the theory of stability of continuous-time difference equations has a long history, is well developed and very popular in research, there is a simple and clearly formulated problem about the stability of stochastic difference equations with continuous time and distributed delay, which has not been solved for more than 13 years. This paper offers to readers some generalization on this unsolved problem in the hope that it will help move closer to its solution.

Dense Continuous-Time Optical Flow from Event Cameras.

We present a method for estimating dense continuous-time optical flow from event data. Traditional dense optical flow methods compute the pixel displacement between two images. Due to missing information, these approaches cannot recover the pixel trajectories in the blind time between two images. In this work, we show that it is possible to compute per-pixel, continuous-time optical flow using events from an event camera. Events provide temporally fine-grained information about movement in pixel space due to their asynchronous nature and microsecond response time. We leverage these benefits to predict pixel trajectories densely in continuous time via parameterized Bézier curves. To achieve this, we build a neural network with strong inductive biases for this task: First, we build multiple sequential correlation volumes in time using event data. Second, we use Bézier curves to index these correlation volumes at multiple timestamps along the trajectory. Third, we use the retrieved correlation to update the Bézier curve representations iteratively. Our method can optionally include image pairs to boost performance further. To the best of our knowledge, our model is the first method that can regress dense pixel trajectories from event data. To train and evaluate our model, we introduce a synthetic dataset (MultiFlow) that features moving objects and ground truth trajectories for every pixel. Our quantitative experiments not only suggest that our method successfully predicts pixel trajectories in continuous time but also that it is competitive in the traditional two-view pixel displacement metric on MultiFlow and DSEC-Flow. Open source code and datasets are released to the public.

Transcriptomics and metabolomics revealed the synthesis and potential role of flavonoids in pea roots under continuous cropping obstacles

AbstractWith the continuation of intensive and monoculture production in modern agriculture, the harm of continuous cropping obstacles is becoming more prominent. Pea has important nutritional and economic value, but it is easy to have continuous cropping obstacles in production. However, there is limited knowledge of the regulatory mechanisms of pea to cope with continuous cropping obstacles. In this study, we found that the number of differential expressed genes (DEGs) and differential metabolites (DAMs) increased in the pea roots with increasing continuous cropping times, and the number of DEGs and DAMs in roots of sensitive pea was more than that of continuous cropping tolerant pea. Comprehensive analysis of the omics data revealed that the flavonoid and isoflavonoid biosynthesis pathways play key roles in the response of pea roots to the continuous cropping obstacles. Most of the DEGs involved in these two pathways were up‐regulated. Meanwhile, most of the flavonoid compounds and total flavonoid content increased. With increasing continuous cropping times, the isoflavones category in DAMs increased, and the isoflavones category in the roots of continuous cropping tolerant pea were higher than in sensitive pea. Additionally, the isoflavonoid (biochanin A, calycosin, genistein) in the roots of continuous cropping tolerant pea have the ability to inhibit the growth of fungi in pea soil and possess antioxidant activity. These findings revealed the important role of flavonoids in pea continuous cropping obstacles and laid a foundation for effectively alleviating pea continuous cropping obstacles in the future.

Zero-sum stochastic games in continuous-time with risk-sensitive average cost criterion on a countable state space

We consider zero-sum stochastic games in continuous time with controlled Markov chains and with risk-sensitive average cost criterion. Here the transition and the cost rates may be unbounded. We prove the existence of the value of the game and a saddle-point equilibrium in the class of all stationary strategies under a Lyapunov stability condition. This is accomplished by establishing the existence of a principal eigenpair for the corresponding Hamilton-Jacobi-Isaacs (HJI) equation. This, in turn, is established by using a nonlinear version of Krein-Rutman theorem. We then obtain a characterization of the saddle-point equilibrium in terms of the corresponding HJI equation. Finally, we use a controlled population system to illustrate our results.

Self-Supervised Temporal Graph Learning With Temporal and Structural Intensity Alignment.

Temporal graph learning aims to generate high-quality representations for graph-based tasks with dynamic information, which has recently garnered increasing attention. In contrast to static graphs, temporal graphs are typically organized as node interaction sequences over continuous time rather than an adjacency matrix. Most temporal graph learning methods model current interactions by incorporating historical neighborhood. However, such methods only consider first-order temporal information while disregarding crucial high-order structural information, resulting in suboptimal performance. To address this issue, we propose a self-supervised method called S2T for temporal graph learning, which extracts both temporal and structural information to learn more informative node representations. Notably, the initial node representations combine first-order temporal and high-order structural information differently to calculate two conditional intensities. An alignment loss is then introduced to optimize the node representations, narrowing the gap between the two intensities and making them more informative. Concretely, in addition to modeling temporal information using historical neighbor sequences, we further consider structural knowledge at both local and global levels. At the local level, we generate structural intensity by aggregating features from high-order neighbor sequences. At the global level, a global representation is generated based on all nodes to adjust the structural intensity according to the active statuses on different nodes. Extensive experiments demonstrate that the proposed model S2T achieves at most 10.13% performance improvement compared with the state-of-the-art competitors on several datasets.

An SIS epidemic model with individual variation

<abstract><p>We study an extension of the stochastic SIS (Susceptible-Infectious-Susceptible) model in continuous time that accounts for variation amongst individuals. By examining its limiting behaviour as the population size grows we are able to exhibit conditions for the infection to become endemic.</p></abstract>

Note on control for hybrid stochastic systems by intermittent feedback rooted in discrete observations of state and mode with delays

<abstract> <p>For a hybrid stochastic system, most existing feedback controllers need to observe modes at continuous times, which is feasible when the system's mode is observable and does not incur any cost. However, in most cases, the mode is not readily apparent, and identifying it always incurs a certain expense. Therefore, in order to reduce control costs, when designing a feedback controller, both the state and the mode should be observed at discrete moments. This paper introduces an intermittent feedback controller for stabilizing an unstable hybrid stochastic system through discrete delayed observations of state and mode. By utilizing M-matrix theory, intermittent control approach, and the comparison principle, we propose sufficient conditions for the stabilization theory of hybrid stochastic systems. An illustrative example is taken to validate the proposed theory.</p> </abstract>

Research on Simulation Approximate Solution Strategy for Complex Kinematic Models

Abstract In order to meet the needs of military, road construction, multimedia industry and other aspects, UAVs are gradually given more functions. As the basic function of UAV applications, the fixed-point delivery problem model has higher and higher accuracy requirements. However, in the actual scene, the UAV delivery problem is affected by the interaction of various factors such as flight height, air resistance, and dive angle, which makes it difficult to achieve high stability and high hit accuracy. This paper will analyze the complex motion model based on the fixed-point delivery of explosives by UAV, study the relationship between the stability of UAV delivery and the hit accuracy, and analyze the influence of relevant parameters on the problem by using modeling. In this paper, a multivariate nonlinear continuous time change model is proposed, and a continuous time slice discretization idea operation model is introduced to approximate the time slice splitting inside the UAV launch motion. Secondly, the design quantified evaluation index reaction the initial velocity of the explosive, the launch Angle, the height off the ground and other parameters to analyze the model. Finally, the best scheduling strategy is obtained and verified by using the idea of variable traversal and trial- and-error simulation. The experimental results show that the variation of UAV flying height, speed, depression and other interference factors is consistent with the prediction of score and hit accuracy, according to the environment setting of this model, when the UAV is 300 meters above the ground and 290 meters away from the target horizontal position, the delivery speed is 250m/s, and the pitch angle is about 27°, the fixed-point delivery of explosives is the best strategy.