Time Instants Research Articles

Timing-accurate scheduling and allocation for parallel I/O operations in real-time systems

In industrial real-time systems, the I/O operations are often required to be both timing predictable, i.e., finish before the deadline to ensure safety, and timing accurate, i.e., start at or close to an ideal time instant for optimal I/O performance. However, for I/O-extensive systems, such strict timing requirements raise significant challenges for the scheduling of I/O operations, where execution conflicts widely exist if the I/O operations are scheduled at their ideal time instants. Existing methods mainly focus on one I/O device and apply simple heuristics to schedule I/O operations, which cannot effectively resolve execution conflicts, hence, undermining both timing predictability and accuracy. This paper proposes novel scheduling and allocation methods to maximize the timing accuracy while guaranteeing the predictability of the system. First, on one I/O device, a fine-grained schedule using Mixed Integer Linear Programming (MILP) is constructed that optimizes the timing accuracy of the I/O operations. Then, for systems containing multiple I/O devices of the same type, two novel allocations are proposed to realize parallel timing-accurate I/O control. The first utilizes MILP to further improve the timing accuracy of the system, whereas the second is a heuristic that provides competitive results with low overheads. Experimental results show the proposed methods outperform the state-of-the-art in terms of both timing predictability and accuracy by 37% and 25% on average (up to 5.56x and 33%), respectively.

Experimental investigation on gap resonance between two floating vessels

This paper explains the influence of gap resonance phenomena in floating vessels having unequal draughts. Two separate model configurations are considered here: one is a vessel having a shallow draught at the weather side (SW), and the other is a deep draught vessel that comes at the weather side. An experimental investigation was carried out in beam sea conditions, where the vessel could only move freely in the heave and roll directions. By beam sea, we mean the incident waves come at a right angle to the broadside of the vessels. Regular wave tests reveal that even though only a slight difference in the gap resonance frequency is observed for the two configurations, the wave amplification at resonance is 57% higher for SW. The reason for this behavior is explained using the instantaneous velocity and vorticity obtained from the particle image velocimetry analysis for a selected test case. Furthermore, the turbulent characteristics of the flow inside the gap for the configurations are compared at different time instances. The horizontal force acting on the vessels and motions (heave and roll) of the vessels in the beam sea condition are also reported in the study.

Modeling insect growth regulators for pest management.

Insect growth regulators (IGRs) have been developed as effective control measures against harmful insect pests to disrupt their normal development. This study is to propose a mathematical model to evaluate the cost-effectiveness of IGRs for pest management. The key features of the model include the temperature-dependent growth of insects and realistic impulsive IGRs releasing strategies. The impulsive releases are carefully modeled by counting the number of implements during an insect's temperature-dependent development duration, which introduces a surviving probability determined by a product of terms corresponding to each release. Dynamical behavior of the model is illustrated through dynamical system analysis and a threshold-type result is established in terms of the net reproduction number. Further numerical simulations are performed to quantitatively evaluate the effectiveness of IGRs to control populations of harmful insect pests. It is interesting to observe that the time-changing environment plays an important role in determining an optimal pest control scheme with appropriate release frequencies and time instants.

Truncating ground motions using the VMD-Hilbert transform for nonlinear dynamic analyses

Nonlinear dynamic analyses of engineered structures under long-duration ground motions usually require significant computational time, especially when performing incremental dynamic analyses or when developing fragility curves. This study proposes a truncation method of seismic records to reduce the computation cost of nonlinear structural analyses based on the Variational Mode Decomposition and the Hilbert Transform. The truncation-starting and -ending time instants are identified using the relative cumulative spectral energy, which is used to represent the Hilbert spectrum energy variation over time. The effectiveness of the proposed method is verified by the elastic pseudo-response spectrum, three different inelastic single-degree-of-freedom models and a multi-degree-of-freedom system. The proposed method, compared with the Arias intensity-based method, proves to be effective, not only for short-period structures, but also for medium- and long-period structures, allowing for reduction of ground motion duration of about 65% on average.

Slow passage through the Busse balloon – predicting steps on the Eckhaus staircase

Abstract Motivated by the impact of worsening climate conditions on vegetation patches, we study dynamic instabilities in an idealised Ginzburg–Landau model. Our main results predict time instances of sudden drops in wavenumber and the resulting target states. The changes in wavenumber correspond to the annihilation of individual vegetation patches when resources are scarce and cannot support the original number of patches. Drops happen well after the primary pattern has destabilised at the Eckhaus boundary and key to distinguishing between the disappearance of 1,2 or more patches during the drop are complex spatio-temporal resonances in the linearisation at the unstable pattern. We support our results with numerical simulations and expect our results to be conceptually applicable universally near the Eckhaus boundary, in particular in more realistic models.

A Discrete Risk-Theory Approach to Manage Equity-Linked Policies in an Incomplete Market

We construct a model where, at each time instance, risky securities can only take a limited number of values and the equity-linked policy sold by the insurer to policyholders pays benefits linked to these securities. Since the number of states in the model exceeds the number of securities in the (incomplete) market, the martingale measure is not unique, posing a problem in pricing insurance instruments. In this framework, we consider how a super-replicating strategy violates the assumption of absence of arbitrage, yet simultaneously allows the insurance company to fully hedge against financial risk. Since the super-replicating strategy, when considered alone, would be too costly for any rational insured person, through the definition of the safety loading, we demonstrate how the insurer can still hedge against financial risk, albeit at the expense of increasing its exposure to demographic risk. This approach does not aim to show how the pricing of the index-linked policy can actually be performed but rather highlights how risk theory-based approaches (via the definition of the profit and loss random variable) enable the management of the trade-off between financial risk and demographic risk.

Probabilistic Analysis of Random Check Intrusion Detection System

The ubiquitous adoption of network-based technologies has left organizations vulnerable to malicious attacks. It has become vital to have effective intrusion detection systems (IDS) that protect the network from attacks. In this paper, we study the intrusion detection problem through the lens of probability theory. We consider a situation where a network receives random malicious signals at discrete time instances, and an IDS attempts to capture these signals via a random check process. We aim to develop a probabilistic framework for intrusion detection under the given scenario. Concretely, we calculate the detection rate of a network attack by an IDS and determine the expected number of detections. We perform extensive theoretical and experimental analyses of the problem. The results presented in this paper would be helpful tools for designing and analyzing intrusion detection systems. We propose a probabilistic framework that could be useful for IDS experts; for a network-based IDS that monitors in real-time, analyzing the entire traffic flow can be computationally expensive. By probabilistically sampling only a fraction of the network traffic, the IDS can still perform its task effectively while reducing the computational cost. However, checking only a fraction of the traffic increases the possibility of missing an attack. This research can help IDS designers achieve appropriate detection rates while maintaining a low false alarm rate. The groundwork laid out in this paper could be used for future research on understanding the probabilities related to intrusion detection.

Generating preferential attachment graphs via a Pólya urn with expanding colors

AbstractWe introduce a novel preferential attachment model using the draw variables of a modified Pólya urn with an expanding number of colors, notably capable of modeling influential opinions (in terms of vertices of high degree) as the graph evolves. Similar to the Barabási-Albert model, the generated graph grows in size by one vertex at each time instance; in contrast however, each vertex of the graph is uniquely characterized by a color, which is represented by a ball color in the Pólya urn. More specifically at each time step, we draw a ball from the urn and return it to the urn along with a number of reinforcing balls of the same color; we also add another ball of a new color to the urn. We then construct an edge between the new vertex (corresponding to the new color) and the existing vertex whose color ball is drawn. Using color-coded vertices in conjunction with the time-varying reinforcing parameter allows for vertices added (born) later in the process to potentially attain a high degree in a way that is not captured in the Barabási-Albert model. We study the degree count of the vertices by analyzing the draw vectors of the underlying stochastic process. In particular, we establish the probability distribution of the random variable counting the number of draws of a given color which determines the degree of the vertex corresponding to that color in the graph. We further provide simulation results presenting a comparison between our model and the Barabási-Albert network.

Remote Sensing of Multitemporal Functional Lake‐To‐Channel Connectivity and Implications for Water Movement Through the Mackenzie River Delta, Canada

AbstractThe Mackenzie River Delta in Canada is a mediator of hydrological transport between the expansive Mackenzie River watershed and the Beaufort Sea. Within the delta, lakes frequently act as water and sediment traps, limiting or delaying the movement of material to the coastal ocean. The degree to which this filtering takes place depends on the ease with which sediment‐laden water is transported from distributary channels into deltaic lakes, referred to as functional lake‐to‐channel connectivity, which varies both spatially and temporally. Tracking of connectivity has previously been limited to either small regions of the delta or has focused on a snapshot of connectivity at a single instance in time. Here we describe an algorithm that uses Landsat imagery to track summertime functional lake‐to‐channel connectivity of 10,362 lakes between 1984 and 2022 on an image‐by‐image basis. We calculate a total average connected lake area of 1400.7 km2 during the 2 weeks after peak discharge, 763.6 km2 higher than previous estimates, suggesting a larger influence of connected lakes on water movement through the delta than previously estimated. We also identify water level thresholds that lead to the initiation of high sediment river water movement into 5,989 lakes (908 lakes with uncertainty ≤±0.5 m), and identify an additional 2899 lakes whose connectivity does not vary at all. As the Arctic hydrological cycle responds to climate change, this work lays a foundation for tracking the movement of water, and the matter it carries, from the Mackenzie River watershed to the Beaufort Sea.

Sliding Surface-Based Path Planning for Unmanned Aerial Vehicle Aerobatics

This paper exploits the concept of nonlinear sliding surfaces to be used as a basis in the development of aerial path planning projects involving aerobatic three-dimensional path curves in the presence of disturbances. This approach can be used for any kind of unmanned aerial vehicle aimed at performing aerobatic maneuvers. Each maneuver is associated with a nonlinear surface on which an aerial vehicle could be driven to slide. The surface design exploits the properties of Viviani’s curve and the Hopf bifurcation. A vector form of the super twisting algorithm steers the vehicle to the prescribed surfaces. A suitable switching control law is proposed to shift between surfaces at different time instants. A practical stability analysis that involves the descriptor approach allows for determining the controller gains. Numerical simulations are developed to illustrate the accomplishment of the suggested aerobatic flight.

Event-triggered robust cooperative output regulation for a class of linear multi-agent systems with an unknown exosystem

This paper investigates the robust cooperative output regulation problem for a class of heterogeneous uncertain linear multi-agent systems with an unknown exosystem via event-triggered control (ETC). By utilizing the internal model approach and the adaptive control technique, a distributed adaptive internal model is constructed for each agent. Then, based on this internal model, a fully distributed ETC strategy composed of a distributed event-triggered adaptive output feedback control law and a distributed dynamic event-triggering mechanism is proposed, in which each agent updates its control input at its own triggering time instants. It is shown that under the proposed ETC strategy, the robust cooperative output regulation problem can be solved without requiring either the global information associated with the communication topology or the bounds of the uncertain or unknown parameters in each agent and the exosystem. A numerical example is provided to illustrate the effectiveness of the proposed control strategy.

Spatio-temporal water height prediction for dam break flows using deep learning

Spatio-temporal prediction of the water height for dam break flow is of great significance in flood control projects. In this article, we propose a novel deep learning model named AE-LSTM-ATT that combines AutoEncoder (AE) and Long Short-Term Memory with Attention (LSTM-ATT) to predict the dynamic behavior of the dam-break water height field in spatial and temporal dimensions. The prediction performance of the AE-LSTM-ATT model was demonstrated using dam-break flow cases with different initial heights of the water column. The AE first compresses high-dimensional inputs into low-dimensional latent space using its encoder to enable a fast computation process. Then, the latent space is adopted as an input for the LSTM-ATT to predict low-dimensional representations at future time instances that can be restored to the water height field by the decoder of the AE. The major findings of this article include three parts: (1) AE-LSTM-ATT model can successfully achieve the spatio-temporal prediction of the water height for dam break flows with high precision; (2) The proposed AE presents much better performance than those of the widely used Principal Component Analysis (PCA) and Kernel Principal Component Analysis (KPCA) in the dimension reduction; (3) The developed LSTM-ATT performs far better than the commonly used Recurrent Neural Network (RNN) and Long Short-Term Memory (LSTM) in the time-series prediction. These promising results suggest that the proposed AE-LSTM-ATT model can play an essential role in capturing and advancing the spatio-temporal features of dam-break water height, which can be applied in the field of real-time decision making for dam-break floods.

Bubble tracking method based on Kuhn-Munkres algorithm for boiling two-phase flow study

The study of bubble dynamics is important in various engineering applications as it can provide a fundamental understanding of the bubbly flow behavior. This paper presents a novel method for tracking bubble trajectories and classifying bubble behaviors, including formation, extinction, continuous movement, fragmentation, and coalescence. The method is based on the theory of perfect matching in bipartite graphs. By establishing the perfect matching between bubbles identified at adjacent time instants, judging the continuity of bubble motion, and simply calculating the number of bubbles in the neighbor of matching bubbles at adjacent time instants, the method can deal with the challenging situation where the bubble position and volume significantly change between two adjacent time instants. The method is validated in a simulated vertical pipe boiling flow, showing that the tracking accuracy is 100% and classification accuracies for continuous movement, fragmentation, and coalescence events are estimated to be larger than 90% in a wide range of time steps between two adjacent time instants.

A Study of the Stability of Integro-Differential Volterra-Type Systems of Equations with Impulsive Effects and Point Delay Dynamics

This research relies on several kinds of Volterra-type integral differential systems and their associated stability concerns under the impulsive effects of the Volterra integral terms at certain time instants. The dynamics are defined as delay-free dynamics contriobution together with the contributions of a finite set of constant point delay dynamics, plus a Volterra integral term of either a finite length or an infinite one with intrinsic memory. The global asymptotic stability is characterized via Krasovskii–Lyapuvov functionals by incorporating the impulsive effects of the Volterra-type terms together with the effects of the point delay dynamics.

Revenue maximization for multiple advertisements placement on a web banner using a pixel-price model

The aim of this paper is to optimize the allocation of multiple advertisements on a Web banner, where the price of an advertisement depends on the location at the banner. This problem can be defined as a two-dimensional single orthogonal knapsack problem with a location-based pixel-price model. A formulation is proposed in which the problem is specified as a 0–1 integer programming problem. As this problem is NP-complete, we mainly focus on a heuristic approach to solve the problem. We propose two new heuristic algorithms: the reactive GRASP algorithm and the partitioning left-justified algorithm. Next to that, we present an exact algorithm that is able to solve small problem instances in a reasonable time. These newly presented algorithms are compared with respect to efficiency and effectiveness to existing algorithms that solve the problem without a location-based pixel-price model. To test the quality of the algorithms, we have executed two experiments. The results of these experiments show that overall the reactive GRASP algorithm is the most effective algorithm, whereas the greedy stripping algorithm is the most efficient.

Event-triggered boundary control of an unstable reaction diffusion PDE with input delay

In chemical, biological, or population (epidemiological) processes the feedback action may be considerably delayed by time-consuming chemical measurements or biological tests. With such large delays on the control action in mind, and motivated by the fact that in some of these systems only piecewise-constant inputs can be applied between time instants at which measurements trigger changes in control, we consider the problem of event-triggered stabilization of 1-D reaction–diffusion PDE systems with input delay. The approach relies on reformulating the delay problem as an actuated transport PDE which cascades into the reaction–diffusion PDE, and on the emulation of backstepping control. The paper proposes a static (state-dependent) triggering condition which establishes the time instants at which the control value needs to be updated. It is shown that under the proposed event-triggered boundary control, there exists a minimal dwell-time (independent of the initial conditions) between two triggering times which allows to guarantee the well-posedness of the closed-loop system, and the exponential stability. The stability analysis is based on Input-to-State stability theory for PDEs and small-gain arguments. A simulation example is presented to validate the theoretical results.

An Expository Examination of Temporally Evolving Graph-Based Approaches for the Visual Investigation of Autonomous Driving

With the continuous advancement of autonomous driving technology, visual analysis techniques have emerged as a prominent research topic. The data generated by autonomous driving is large-scale and time-varying, yet more than existing visual analytics methods are required to deal with such complex data effectively. Time-varying diagrams can be used to model and visualize the dynamic relationships in various complex systems and can visually describe the data trends in autonomous driving systems. To this end, this paper introduces a time-varying graph-based method for visual analysis in autonomous driving. The proposed method employs a graph structure to represent the relative positional relationships between the target and obstacle interferences. By incorporating the time dimension, a time-varying graph model is constructed. The method explores the characteristic changes of nodes in the graph at different time instances, establishing feature expressions that differentiate target and obstacle motion patterns. The analysis demonstrates that the feature vector centrality in the time-varying graph effectively captures the distinctions in motion patterns between targets and obstacles. These features can be utilized for accurate target and obstacle recognition, achieving high recognition accuracy. To evaluate the proposed time-varying graph-based visual analytic autopilot method, a comparative study is conducted against traditional visual analytic methods such as the frame differencing method and advanced visual analytic methods like visual lidar odometry and mapping. Robustness, accuracy, and resource consumption experiments are performed using the publicly available KITTI dataset to analyze and compare the three methods. The experimental results show that the proposed time-varying graph-based method exhibits superior accuracy and robustness. This study offers valuable insights and solution ideas for developing deep integration between intelligent networked vehicles and intelligent transportation. It provides a reference for advancing intelligent transportation systems and their integration with autonomous driving technologies.

Aperiodic intermittent sampling for nonlinear discrete-time event-based model predictive control

ABSTRACT In this article, an aperiodic intermittent sampling method is designed in event-based model predictive control for nonlinear discrete systems subject to external disturbances. The proposed aperiodic intermittent sampling is applied to find the appropriate triggering instant satisfying the desired sub-optimal performance. In the proposed event-based MPC, selection of the sampling instants is based on the prediction of the worst case induced by disturbances and the mapping principle with updated state feedback. With the proposed event-based MPC, the measurement frequency and the triggering rate can be reduced by sampling the system states only at certain time instants. Recursive feasibility and robust stability are established under sufficient conditions.

Stochastic resetting with refractory periods: pathway formulation and exact results

We look into the problem of stochastic resetting with refractory periods. The model dynamics comprises diffusive and motionless phases. The diffusive phase ends at random time instants, at which the system is reset to a given position—where the system remains at rest for a random time interval, termed the refractory period. A pathway formulation is introduced to derive exact analytical results for the relevant observables in a broad framework, with the resetting time and the refractory period following arbitrary distributions. For the paradigmatic case of Poissonian distributions of the resetting and refractory times, in general with different characteristic rates, closed-form expressions are obtained that successfully describe the relaxation to the steady state. Finally, we focus on the single-target search problem, in which the survival probability and the mean first passage time to the target can be exactly computed. Therein, we also discuss optimal strategies, which show a non-trivial dependence on the refractory period.

Lead fractions from SAR-derived sea ice divergence during MOSAiC

Abstract. Leads and fractures in sea ice play a crucial role in the heat and gas exchange between the ocean and atmosphere, impacting atmospheric, ecological, and oceanic processes. We estimated lead fractions from high-resolution divergence obtained from satellite synthetic aperture radar (SAR) data and evaluated them against existing lead products. We derived two new lead fraction products from divergence with a spatial resolution of 700 m calculated from daily Sentinel-1 images. For the first lead product, we advected and accumulated the lead fractions of individual time instances. With those accumulated divergence-derived lead fractions, we comprehensively described the presence of up to 10 d old leads and analyzed their deformation history. For the second lead product, we used only divergence pixels that were identified as part of linear kinematic features (LKFs). Both new lead products accurately captured the formation of new leads with widths of up to a few hundred meters. We presented a Lagrangian time series of the divergence-based lead fractions along the drift of the Multidisciplinary drifting Observatory for the Study of Arctic Climate (MOSAiC) expedition in the central Arctic Ocean during winter 2019–2020. Lead activity was high in fall and spring, consistent with wind forcing and ice pack consolidation. At larger scales of 50–150 km around the MOSAiC expedition, lead activity on all scales was similar, but differences emerged at smaller scales (10 km). We compared our lead products with six others from satellite and airborne sources, including classified SAR, thermal infrared, microwave radiometer, and altimeter data. We found that the mean lead fractions varied by 1 order of magnitude across different lead products due to different physical lead and sea ice properties observed by the sensors and methodological factors such as spatial resolution. Thus, the choice of lead product should align with the specific application.