Arbitrary Time Research Articles

Direct Sampling for Spatially Variable Extreme Event Generation in Resampling‐Based Stochastic Weather Generators

AbstractResampling‐based weather generators simulate new time series of weather variables by reordering the observed values such that the statistics of the simulated data are consistent with the observed ones. These generators are fully data‐driven, easy to implement, and capable of reproducing the dynamics among weather variables. However, although the simulated time series is new, the weather fields produced at arbitrary time steps are replicas of those found in observations, limiting the spatial variability of simulations and preventing the generation of extreme weather fields beyond the range of observed values. To address these limitations, we propose the integration of the Direct Sampling algorithm—a data‐driven method for producing simulations—into resampling‐based weather generators. By incorporating Direct Sampling as a post‐processing step on the outputs of the weather generator, we enhance the spatial variability of the generated weather fields and enable the generation of extreme weather fields. We introduce an approach for generating out‐of‐sample extreme weather fields using Direct Sampling. This method involves utilizing a set of control points in conjunction with Direct Sampling, where the values of these control points are informed by return period analysis. The proposed approach is validated using precipitation, temperature, and cloud cover weather fields in a region of northwest India. The experimental results confirm that Direct Sampling enhances the spatial variability of the weather fields and facilitates the generation of out‐of‐sample precipitation fields that accurately adhere to the spatial statistics provided by return precipitation level maps, as well as the observed precipitation weather field employed in the analysis.

Expanding the Design Space of Constraints in Auxiliary-Field Quantum Monte Carlo.

We formulate and characterize a new constraint for auxiliary-field quantum Monte Carlo (AFQMC) applicable for general fermionic systems, which allows for the accumulation of phase in the random walk but disallows walkers with a magnitude of phase greater than π with respect to the trial wave function. For short imaginary times, before walkers accumulate sizable phase values, this approach is equivalent to exact free projection, allowing one to observe the accumulation of bias associated with the constraint and thus estimate its magnitude a priori. We demonstrate the stability of this constraint over arbitrary imaginary times and system sizes, highlighting the removal of noise due to the fermionic sign problem. Benchmark total energies for a variety of weakly and strongly correlated molecular systems reveal a distinct bias with respect to standard phaseless AFQMC, with a comparative increase in accuracy given sufficient quality of the trial wave function for the set of studied cases. We then take this constraint, termed linecut AFQMC (lc-AFQMC), and systematically release it (lcR-AFQMC), providing a route to obtain a smooth bridge between constrained AFQMC and the exact free projection results.

Correction to: Novel neural adaptive terminal sliding mode control for TCP network systems with arbitrary convergence time

Correction to: Novel neural adaptive terminal sliding mode control for TCP network systems with arbitrary convergence time

Symmetry-informed surrogates with data-free constraint for real-time acoustic wave propagation

A deep neural network is developed as a symmetry-informed surrogate model to estimate the stress of acoustic waves at any arbitrary location, time, and wave excitation width, as a kind of implicit representation of acoustic wave propagation. To improve the model performance, we suggest a physic-informed training residual by employing the symmetry constraint of acoustics. Compared to the FEM simulation using COMSOL Multiphysics, the R2 score of the surrogate model was greater than 98%, and its inference performance was about 215 times faster. The proposed residual can be characterized by three benefits: no architectural changes to the surrogate model are required, no labeled data or reference solutions are necessary, and the generalization ability of the surrogate model is enhanced in all input directions. Numerical investigation validates the superior generalization of the model trained with the symmetry constraint, along with the examination of the regularization rate and sampling approach, the additional hyperparameters induced by the proposed residual. Furthermore, we demonstrate the potential viability of real-time simulations from surrogate models through a practical application of the trained model for flaw detection. The results indicate that the capability of the data-driven surrogate model for generalized implicit representation can be enhanced by adopting the physic-informed training residual.

Free-will arbitrary time consensus of heterogeneous nonlinear multi-agent systems

This paper addresses several kinds of free-will arbitrary time (FWAT) consensus problems for heterogeneous nonlinear multi-agent systems (MASs). For first-order MASs, both leaderless and leader-following FWAT consensus are studied. Based on the FWAT control technology, some novel distributed control protocols are proposed, under which FWAT consensus of first-order MASs is achieved within the arbitrary pre-specified time and maintained after then. Then, the backstepping method is employed to design the controller for second-order heterogeneous nonlinear MASs. FWAT consensus of second-order MASs can also be guaranteed by using the proposed controller. Finally, simulation examples are presented to illustrate the effectiveness of theoretical analysis.

Fixed-time terminal sliding mode control with arbitrary convergence time for a class of chaotic systems applied to a nonlinear finance model

Fixed-time terminal sliding mode control with arbitrary convergence time for a class of chaotic systems applied to a nonlinear finance model

Minimizing age of information under arbitrary arrival model with arbitrary packet size

We consider a single source–destination pair, where information updates (in short, updates) arrive at the source at arbitrary time instants. For each update, its size, i.e. the service time required for complete transmission to the destination, is also arbitrary. At any time, the source may choose which update to transmit, while incurring transmission cost that is proportional to the duration of transmission. We consider the age of information (AoI) metric that quantifies the staleness of the update (information) at the destination. At any time, AoI is equal to the difference between the current time, and the arrival time of the latest update (at the source) that has been completely transmitted (to the destination). The goal is to find a causal (i.e. online) scheduling policy that minimizes the sum of the AoI and the transmission cost, where the possible decisions at any time are (i) whether to preempt the update under transmission upon arrival of a new update, and (ii) if no update is under transmission, then choose which update to transmit (among the available updates). In this paper, we propose a causal policy called SRPT+ that at each time, (i) preempts the update under transmission if a new update arrives with a smaller size (compared to the remaining size of the update under transmission), and (ii) if no update is under transmission, then from the set of available updates with size less than a threshold (which is a function of the transmission cost and the current AoI), begins to transmit the update for which the ratio of the reduction in AoI upon complete transmission (if not preempted in future) and the remaining size, is maximum. We characterize the performance of SRPT+ using a metric called the competitive ratio, i.e. the ratio of the cost of causal policy and the cost of an optimal offline policy (that knows the entire input in advance), maximized over all possible inputs. We show that the competitive ratio of SRPT+ is at most 5. In the special case when there is no transmission cost, we further show that the competitive ratio of SRPT+ is at most 3.

GsNeRF: Fast novel view synthesis of dynamic radiance fields

Synthesis of new views in dynamic 3D scenes is a challenging task in 3D vision. However, most current approaches rely on radiance fields built upon multi-view camera systems for dynamic scenes, which are expensive and time-consuming, and depend on implicit representations based on Neural Radiance Fields . In this study, we introduced a new representation method for dynamic scenes called GsNeRF, which allows for fast reconstruction of objects under motion by moving a single camera in the scene, and it can render high-quality views from arbitrary time frames and camera poses. We utilize five grids to represent the dynamic scene, employing tensor decomposition for each grid to reduce storage space usage. Since the primary task of the entire model is to optimize these planes, we enforce spatio-temporal continuity of these planes through a smoothness loss. GsNeRF is combined with a miniature MLP to regress color outputs and trained using volume rendering. Through testing on a series of synthetic and real datasets, our method reduces the training time by over 100 times compared to implicit methods and achieves better rendering quality compared to explicit methods. Our approach achieves a balance between memory usage, speed, and quality overall.

A multi-functional arbitrary timing generator based on a digital-to-time converter.

This paper proposes a new high-resolution digital-to-time converter architecture based on a field programmable gate array and digital-to-analog converter (DAC). A real-time algorithm of time--amplitude mapping is proposed, which converts the vertical resolution of the DAC to the timing resolution and realizes the ultra-high resolution timing signal generation. Moreover, the relationship between the timing resolution and the vertical resolution and the sampling rate of DAC is discussed. Based on this, arbitrarily distributed random timing signals and editable timing signal sequence functions are realized. This method is verified in the experiment on Xilinx XCKU040 and Texas Instrument DAC37J82. Furthermore, a timing resolution of 1ps is realized. A time range of 4.2ns to 999s, an editable sequence length of 1-128k, and excellent nonlinear performance are achieved. In addition, functions for arbitrarily distributed random timing signals and signal bursts are tested. This method can be flexibly deployed on existing hardware and satisfy almost all test requirements.

Analytical study of unsteady two-layer combined electroosmotic and pressure-driven flow through a cylindrical microchannel with slip-dependent zeta potential

For investigating dynamics of two-fluid co-flows at an arbitrary time, the unsteady two-layer pressure-driven electroosmotic flow in a cylindrical microchannel is studied. To propose a model of universal significance, the interfacial slip and slip-dependent zeta potential are incorporated. The momentum equations are analytically solved and the physical picture how the unsteady two-layer flow evolves into the steady state is provided by evaluating the transient velocities. The two-layer velocities or flow rates are computed at different slip coefficients, electrokinetic widths, viscosity ratios, density ratios, radius ratios and zeta potential ratios, thereby the resulting interactive influences are assessed. When considering slip-dependent zeta potential, the change in two-layer velocity with other parameters is more pronounced. The increasing rate of flow rate with slip coefficient augments with electrokinetic width and outer zeta potential, which decreases with radius ratio. This work establishes mechanisms for the enhancement of transporting efficiency in microdevices associated with multi-layer flows.

Nonlocality, nonlinearity, and time inconsistency in stochastic differential games

AbstractThis paper studies the well‐posedness of a class of nonlocal fully nonlinear parabolic systems, which nest the equilibrium Hamilton–Jacobi–Bellman (HJB) systems that characterize the time‐consistent Nash equilibrium point of a stochastic differential game (SDG) with time‐inconsistent (TIC) preferences. The nonlocality of the parabolic systems stems from the flow feature (controlled by an external temporal parameter) of the systems. This paper proves the existence and uniqueness results as well as the stability analysis for the solutions to such systems. We first obtain the results for the linear cases for an arbitrary time horizon and then extend them to the quasilinear and fully nonlinear cases under some suitable conditions. Two examples of TIC SDG are provided to illustrate financial applications with global solvability. Moreover, with the well‐posedness results, we establish a general multidimensional Feynman–Kac formula in the presence of nonlocality (time inconsistency).

Reservoir computing using self-sustained oscillations in a locally connected neural network

Understanding how the structural organization of neural networks influences their computational capabilities is of great interest to both machine learning and neuroscience communities. In our previous work, we introduced a novel learning system, called the reservoir of basal dynamics (reBASICS), which features a modular neural architecture (small-sized random neural networks) capable of reducing chaoticity of neural activity and of producing stable self-sustained limit cycle activities. The integration of these limit cycles is achieved by linear summation of their weights, and arbitrary time series are learned by modulating these weights. Despite its excellent learning performance, interpreting a modular structure of isolated small networks as a brain network has posed a significant challenge. Here, we investigate how local connectivity, a well-known characteristic of brain networks, contributes to reducing neural system chaoticity and generates self-sustained limit cycles based on empirical experiments. Moreover, we present the learning performance of the locally connected reBASICS in two tasks: a motor timing task and a learning task of the Lorenz time series. Although its performance was inferior to that of modular reBASICS, locally connected reBASICS could learn a time series of tens of seconds while the time constant of neural units was ten milliseconds. This work indicates that the locality of connectivity in neural networks may contribute to generation of stable self-sustained oscillations to learn arbitrary long-term time series, as well as the economy of wiring cost.

Projective lag quasi-synchronization of coupled systems with mixed delays and parameter mismatch: a unified theory

This paper investigates the projective lag quasi-synchronization by feedback control of a coupled dynamical system with delays and parameter mismatches on arbitrary time domains. Being formulated on time scales, our results are valid simultaneously for continuous- and discrete-time models as well as for any non-standard time domain. Furthermore, the controller design respects the structure of the equations so that we can characterize the stabilization by a limited controller action. Our proofs rely on the unified matrix-measure theory and the generalized Halanay inequality on time scales. We validate our theoretical results with several simulation examples on various time domains.

Analysis of a GIX/M/1 queue with two-stage vacation policy using shift operator method

In this paper, we investigate a GI X /M/1 queue with the two-stage vacation policy. The system will first enter a working vacation once the system becomes empty in the normal busy period, during which the service rate will be switched to a lower rate. After this working vacation, if the system is nonempty, the service rate will be switched to the normal rate immediately; otherwise, the system will enter multiple vacations during which the service rate reduces to zero until the system is nonempty after one vacation and a new normal busy period starts. The distinguishing feature of this paper is the use of a general algorithm for solving the difference equation based on the right shift operator method to obtain the queue length distribution at pre-arrival time and arbitrary time. Moreover, the sojourn time of arbitrary customer is analyzed. Finally, several typical numerical examples are provided to validate our computational algorithm.

3D Impedance Analysis on Dissolution Behavior of Additive-Manufactured Al-12%Si Alloy

Laser Powder Bed Fusion (LBPF) is one of the additive manufacturing techniques using a laser beam to melt and fuse layers of metal powder particles forming various metal products with complex shapes. Because the Al-Si alloy manufactured by LPBF has good mechanical properties compared to conventionally cast Al alloys, it is important to investigate the dissolution behavior of Al-Si alloy manufactured by LPBF for wider usage in industry.In the present study, the film resistance of oxide film formed on additive-manufactured Al-12%Si alloys were investigated by a three-dimensional(3D) impedance spectroscopy1-5. This method allows for the estimation of the film resistance with time information because the impedance is plotted on the 3D diagram whose axes are real, imaginary and time, namely, the instantaneous impedance at arbitrary time can be determined from 3D impedance. To investigate the dissolution behavior of additive-manufactured Al alloys, the non-annealed sample (Al-12Si) and annealed samples at different temperatures ranging from 200 to 350 ℃ (Al-12Si300) and 530 ℃ (Al-12Si530) with arbitrary holding time were used for the electrochemical measurements. The 3D impedance of Al-12Si, Al-12Si300 and Al-12Si530 could be successively measured in the immersion conditions. The 3D impedance of Al-12Si and Al-12Si300 demonstrated that the impedance of both samples was increased with time. The 3D impedance of Al-12Si530 indicated small values during measurement. These results imply that the increase of impedance of Al-12Si and Al-12Si300 is associated with the formation of oxide film on the surface. The film resistance estimated from impedance spectra determined from 3D impedance and the morphology of samples after the measurement were correlated discussed.

Oscillation of noncanonical fourth-order dynamic equations

We present two sufficient conditions for the oscillatory behaviour of a class of noncanonical fourth-order dynamic equations on arbitrary time scales. An illustrative example is included to show that new criteria improve related results reported in the literature.

Distributed adaptive fault tolerant formation control for multiple underwater vehicles: Free-will arbitrary time approach

This note examines the distributed free-will arbitrary time (FwAT) fault-tolerant formation control for heterogeneous multiple autonomous underwater vehicles (AUVs) operating under actuator faults, uncertainties, and exogenous disturbances. The established formation control protocol is free from initial conditions and provides higher tracking accuracy, singularity-free and smooth control signal, while the convergence time of the system is non-conservative. An adaptive nonsingular sliding mode is then developed in which the bound of lumped uncertainty is not necessary to know in advance. Due to the need for a rapid and immediate response in fixed-time control, the actuators are prone to saturation as a result of the high control torque required and to overcome this issue, an input saturation compensator is designed and incorporated into the control framework. Stability analysis under the developed control law is thoroughly performed using the Lyapunov stability theory. Finally, simulations and comparisons are demonstrated in order to verify the effectiveness of the proposed distributed formation control algorithm for a group of AUVs.

Scheduling coflows for minimizing the total weighted completion time in heterogeneous parallel networks

Coflow is a network abstraction used to represent communication patterns in data centers. The coflow scheduling problem encountered in large data centers is a challenging NP-hard problem. Many previous studies on coflow scheduling mainly focus on the single-core model. However, with the growth of data centers, this single-core model is no longer sufficient. This paper addresses the coflow scheduling problem within heterogeneous parallel networks, which feature an architecture consisting of multiple network cores running in parallel. In this paper, two polynomial-time approximation algorithms are developed for the flow-level scheduling problem and the coflow-level scheduling problem in heterogeneous parallel networks, respectively. For the flow-level scheduling problem, the proposed algorithm achieves an approximation ratio of O(log⁡m/log⁡log⁡m) when all coflows are released at arbitrary times, where m represents the number of network cores. On the other hand, in the coflow-level scheduling problem, the proposed algorithm achieves an approximation ratio of O(m(log⁡m/log⁡log⁡m)2) when all coflows are released at arbitrary times. Moreover, we propose a heuristic algorithm for the flow-level scheduling problem. Simulation results using synthetic traffic traces validate the performance of our algorithms and show improvements over the previous algorithm.

Spike formation theory in three-dimensional flow separation

We develop a frame-invariant theory of material spike formation during flow separation over a no-slip boundary in three-dimensional flows with arbitrary time dependence. Based on the exact evolution of the largest principal curvature on near-wall material surfaces, our theory identifies fixed and moving separation. Our approach is effective over short time intervals and admits an instantaneous limit. As a byproduct, we derive explicit formulas for the evolution of the Weingarten map and the principal curvatures of any surface advected by general three-dimensional flows. The material backbone we identify acts first as a precursor and later as the centrepiece of Lagrangian flow separation. We discover previously undetected spiking points and curves where the separation backbones connect to the boundary and provide wall-based analytical formulas for their locations. We illustrate our results on several steady and unsteady flows.

Arbitrary-time thermodynamic uncertainty relation from fluctuation theorem.

The thermodynamic uncertainty relation (TUR) provides a universal entropic bound for the precision of the fluctuation of the charge transfer, for example, for a class of continuous-time stochastic processes. However, its extension to general nonequilibrium dynamics is still an unsolved problem. We derive TUR for an arbitrary finite time from exchange fluctuation theorem under a geometric necessary and sufficient condition. We also generally show a necessary and sufficient condition of multidimensional TUR in a unified manner. As a nontrivial practical consequence, we obtain universal scaling relations among the mean and variance of the charge transfer in short time regime. In this manner, we can deepen our understanding of a link between two important rigorous relations, i.e., the fluctuation theorem and the thermodynamic uncertainty relation.