Time-scale Approach Research Articles

Vehicular edge cloud computing content caching optimization solution based on content prediction and deep reinforcement learning

In conventional studies on vehicular edge computing, researchers frequently overlook the high-speed mobility of vehicles and the dynamic nature of the vehicular edge environment. Moreover, when employing deep reinforcement learning to address vehicular edge challenges, insufficient attention is given to the potential issue of the algorithm converging to a local optimal solution. This paper presents a content caching solution tailored for vehicular edge cloud computing, integrating content prediction and deep reinforcement learning techniques. Given the swift mobility of vehicles and the ever-changing nature of the vehicular edge environment, the study proposes a content prediction model based on Informer. Leveraging the Informer prediction model, the system anticipates the vehicular edge environment dynamics, thereby informing the caching of vehicle task content. Acknowledging the diverse time scales involved in policy decisions such as content updating, vehicle scheduling, and bandwidth allocation, the paper advocates a dual time-scale Markov modeling approach. Moreover, to address the local optimality issue inherent in the A3C algorithm, an enhanced A3C algorithm is introduced, incorporating an ɛ-greedy strategy to promote exploration. Recognizing the potential limitations posed by a fixed exploration rate ɛ, a dynamic baseline mechanism is proposed for updating ɛ dynamically. Experimental findings demonstrate that compared to alternative content caching approaches, the proposed vehicle edge computing content caching solution substantially mitigates content access costs. To support research in this area, we have publicly released the source code and pre-trained models at https://github.com/JYAyyyyyy/Informer.git.

STABILITY AND BIFURCATION ANALYSIS OF A SIMPLE DELAYED p53-Mdm2 GENE NETWORK MODEL WITH DIFFUSION

p53 is a star protein in cancer biology, and its oscillatory dynamics have received much attention. However, most studies do not consider spatial effects. For this reason, we introduce the diffusion term in a classical p53-Mdm2 autoregulatory loop model. First, the equation is linearized at the positive equilibrium so that we can discuss the local asymptotic stability of this equilibrium. By taking the delay as a bifurcation parameter, the positive equilibrium transitions from stable to unstable and occurs a Hopf bifurcation. Second, we determine the stability of the bifurcating period solution by using a multiple time scales approach. Finally, the theoretical analysis is verified by the numerical simulations. Our study contributes to providing new insight in the controlling of p53 dynamics.

Gravitational wave turbulence: A multiple time scale approach for quartic wave interactions

Gravitational wave turbulence: A multiple time scale approach for quartic wave interactions

Resource Scheduling for eMBB and URLLC Multiplexing in NOMA-Based VANETs: A Dual Time-Scale Approach

Resource Scheduling for eMBB and URLLC Multiplexing in NOMA-Based VANETs: A Dual Time-Scale Approach

Transcriptional and epigenetic changes during tomato yellow leaf curl virus infection in tomato

BackgroundGeminiviruses are DNA plant viruses that cause highly damaging diseases affecting crops worldwide. During the infection, geminiviruses hijack cellular processes, suppress plant defenses, and cause a massive reprogramming of the infected cells leading to major changes in the whole plant homeostasis. The advances in sequencing technologies allow the simultaneous analysis of multiple aspects of viral infection at a large scale, generating new insights into the molecular mechanisms underlying plant-virus interactions. However, an integrative study of the changes in the host transcriptome, small RNA profile and methylome during a geminivirus infection has not been performed yet. Using a time-scale approach, we aim to decipher the gene regulation in tomato in response to the infection with the geminivirus, tomato yellow leaf curl virus (TYLCV).ResultsWe showed that tomato undergoes substantial transcriptional and post-transcriptional changes upon TYLCV infection and identified the main altered regulatory pathways. Interestingly, although the principal plant defense-related processes, gene silencing and the immune response were induced, this cannot prevent the establishment of the infection. Moreover, we identified extra- and intracellular immune receptors as targets for the deregulated microRNAs (miRNAs) and established a network for those that also produced phased secondary small interfering RNAs (phasiRNAs). On the other hand, there were no significant genome-wide changes in tomato methylome at 14 days post infection, the time point at which the symptoms were general, and the amount of viral DNA had reached its maximum level, but we were able to identify differentially methylated regions that could be involved in the transcriptional regulation of some of the differentially expressed genes.ConclusionWe have conducted a comprehensive and reliable study on the changes at transcriptional, post-transcriptional and epigenetic levels in tomato throughout TYLCV infection. The generated genomic information is substantial for understanding the genetic, molecular and physiological changes caused by TYLCV infection in tomato.

A multiple time scale approach for anisotropic inertial wave turbulence

Wave turbulence is the study of the long-time statistical behaviour of equations describing a set of weakly nonlinear interacting waves. Such a theory, which has a natural asymptotic closure, allows us to probe the nature of turbulence more deeply than the exact Kolmogorov laws by rigorously proving the direction of the cascade and the existence of an inertial range, predicting stationary spectra for conserved quantities, or evaluating the Kolmogorov constant. An emblematic example is given by fast rotating fluids for which a wave turbulence theory has been derived by Galtier (Phys. Rev. E, vol. 68, issue 1, 2003, p. 015301). This work involves non-trivial analytical developments for a problem that is anisotropic by nature. We propose here a new path for the derivation of the kinetic equation by using the anisotropy at the beginning of the analysis. We show that the helicity basis is not necessary to obtain the wave amplitude equation for the canonical variables that involve a combination of poloidal and toroidal fields. The multiple time scale method adapted to this anisotropic problem is then used to derive the kinetic equation that is the same as the original work when anisotropy is eventually taken into account. This result proves the commutativity between asymptotic closure and anisotropy. In addition, the multiple time scale method informs us that the kinetic equation can be derived without imposing restrictions on the probability distribution of the wave amplitude such as quasi-Gaussianity, or on the phase such as random phase approximation that naturally occurs dynamically.

Distributed State Estimation With Deep Neural Networks for Uncertain Nonlinear Systems Under Event-Triggered Communication

This work explores the distributed state estimation problem for an uncertain, nonlinear, and continuous-time system. Given a sensor network, each agent is assigned a deep neural network (DNN) which is used to approximate the system's dynamics. Each agent updates the weights of their DNN through a multiple timescale approach, i.e., the outer layer weights are updated online with a Lyapunov-based gradient descent update law, and the inner layer weights are updated concurrently using a supervised learning strategy. To promote the efficient use of network resources, the distributed observer uses event-triggered communication. A nonsmooth Lyapunov analysis demonstrates that the distributed event-triggered observer achieves uniformly ultimately bounded state reconstruction. A simulation example of a 5-agent sensor network estimating the state of a two-link robotic manipulator tracking a desired trajectory is provided to validate the result and showcase the performance improvements afforded by DNNs.

A multiple timescale approach of bispectral correlation

The paper develops an approximate semi-analytical solution for the computation of the third statistical cross-moments of modal responses in a stochastic dynamic analysis. These moments would require heavy twofold numerical integration in a general context but are drastically simplified in the proposed formulation by taking advantage of the assumed distinctness between the low characteristic frequency of the loading and the natural frequencies of the structure. This condition is typically respected and acknowledged in wind engineering where the buffeting analysis of large structures hinges on the Background/Resonant decomposition. As such, the proposed formulation extends to third statistical order the existing developments for the estimation of the modal variances and covariances. It allows the third order spectral analysis of large structures to be conducted within a reasonable amount of time. It also reveals the existence of three main components to the response: background, bi-resonant and tri-resonant. The latter one is specific to this very own problem and is shown to be important when the sum of two natural frequencies is equal to a third one, although the structural behavior is linear. Mathematics highlight this and other findings which are then illustrated on a minimum working example, easily reproducible by readers. Overall, it clearly demonstrates the benefits of the proposed decomposition in terms of both behavioral comprehension and computational consumption.

The best of both worlds: Combining population genetic and quantitative genetic models

Numerous traits under migration–selection balance are shown to exhibit complex patterns of genetic architecture with large variance in effect sizes. However, the conditions under which such genetic architectures are stable have yet to be investigated, because studying the influence of a large number of small allelic effects on the maintenance of spatial polymorphism is mathematically challenging, due to the high complexity of the systems that arise. In particular, in the most simple case of a haploid population in a two-patch environment, while it is known from population genetics that polymorphism at a single major-effect locus is stable in the symmetric case, there exist no analytical predictions on how this polymorphism holds when a polygenic background also contributes to the trait. Here we propose to answer this question by introducing a new eco-evo methodology that allows us to take into account the combined contributions of a major-effect locus and of a quantitative background resulting from small-effect loci, where inheritance is encoded according to an extension to the infinitesimal model. In a regime of small variance contributed by the quantitative loci, we justify that traits are concentrated around the major alleles, according to a normal distribution, using new convex analysis arguments. This allows a reduction in the complexity of the system using a separation of time scales approach. We predict an undocumented phenomenon of loss of polymorphism at the major-effect locus despite strong selection for local adaptation, because the quantitative background slowly disrupts the rapidly established polymorphism at the major-effect locus, which is confirmed by individual-based simulations. Our study highlights how segregation of a quantitative background can greatly impact the dynamics of major-effect loci by provoking migrational meltdowns. We also provide a comprehensive toolbox designed to describe how to apply our method to more complex population genetic models.

Electric discharge initiation in water with gas bubbles: A time scale approach

High voltage nanosecond pulse driven electric discharges in de-ionized water with an argon bubble suspended between two electrodes were experimentally investigated. Two electrode configurations were used to temporally resolve the time scales of the discharge from the applied voltage rise time (7 ns), through the end of the first pulse (∼30 ns), and longer (>50 ns). We found that, in positive and negative applied voltage polarities, discharge initiates in the water at the tip of the anode. The discharge in the water rapidly extends (∼104 m/s) to the apex of the bubble and light emitted from inside the bubble begins to form. The steep rate of rise of the applied voltage (dV/dt<4 kV/ns) and the short time for the development of discharge in the water suggest that cavitation is a likely mechanism for discharge initiation and propagation in water. In addition, the short duration of the applied voltage pulse results in only a partial Townsend discharge inside the bubble.

A time-scale transformation approach to prescribed-time stabilisation of non-holonomic systems with inputs quantisation

This article addresses the problem of global stabilisation using state feedback for a kind of uncertain non-holonomic systems in chained form. Two distinct characteristics of this study are that the considered system suffers from the input-quantised actuator, and the system states are expected to converge to zero in prescribed finite time. To address these, a time-scale transformation, that can change the original stabilisation into the finite-time stabilisation of the transformed one, is first introduced. Then, under the new framework of equivalent transformation, a quantised state feedback controller that achieves of the performance requirements is developed with the aid of the recursive technique. Finally, simulation results of a unicycle-type mobile robot are provided to confirm the efficacy of the proposed approach.

Fast reactions with non-interacting species in stochastic reaction networks.

We consider stochastic reaction networks modeled by continuous-time Markov chains. Such reaction networks often contain many reactions, potentially occurring at different time scales, and have unknown parameters (kinetic rates, total amounts). This makes their analysis complex. We examine stochastic reaction networks with non-interacting species that often appear in examples of interest (e.g. in the two-substrate Michaelis Menten mechanism). Non-interacting species typically appear as intermediate (or transient) chemical complexes that are depleted at a fast rate. We embed the Markov process of the reaction network into a one-parameter family under a two time-scale approach, such that molecules of non-interacting species are degraded fast. We derive simplified reaction networks where the non-interacting species are eliminated and that approximate the scaled Markov process in the limit as the parameter becomes small. Then, we derive sufficient conditions for such reductions based on the reaction network structure for both homogeneous and time-varying stochastic settings, and study examples and properties of the reduction.

Learning and Adaptation for Millimeter-Wave Beam Tracking and Training: A Dual Timescale Variational Framework

Millimeter-wave vehicular networks incur enormous beam-training overhead to enable narrow-beam communications. This paper proposes a learning and adaptation framework in which the dynamics of the communication beams are learned and then exploited to design adaptive beam-tracking and training with low overhead: on a long-timescale, a deep recurrent variational autoencoder (DR-VAE) uses noisy beam-training feedback to learn a probabilistic model of beam dynamics and enable predictive beam-tracking; on a short-timescale, an adaptive beam-training procedure is formulated as a partially observable (PO-) Markov decision process (MDP) and optimized via point-based value iteration (PBVI) by leveraging beam-training feedback and a probabilistic prediction of the strongest beam pair provided by the DR-VAE. In turn, beam-training feedback is used to refine the DR-VAE via stochastic gradient ascent in a continuous process of learning and adaptation. The proposed DR-VAE learning framework learns accurate beam dynamics: it reduces the Kullback-Leibler divergence between the ground truth and the learned model of beam dynamics by ~95% over the Baum-Welch algorithm and a naive learning approach that neglects feedback errors. Numerical results on a line-of-sight scenario with multipath and 3D beamforming reveal that the proposed dual timescale approach yields near-optimal spectral efficiency, and improves it by 130% over a policy that scans exhaustively over the dominant beam pairs, and by 20% over a state-of-the-art POMDP policy. Finally, a low-complexity policy is proposed by reducing the POMDP to an error-robust MDP, and is shown to perform well in regimes with infrequent feedback errors.

Time-scale-chirp_rate operator for recovery of non-stationary signal components with crossover instantaneous frequency curves

The objective of this paper is to introduce an innovative approach for the recovery of non-stationary signal components with possibly crossover instantaneous frequency (IF) curves from a multi-component blind-source signal. The main idea is to incorporate a chirp rate parameter with the time-scale continuous wavelet-like transformation, by considering the quadratic phase representation of the signal components. Hence-forth, even if two IF curves cross, the two corresponding signal components can still be separated and recovered, provided that their chirp rates are different. In other words, signal components with the same IF value at any time instant could still be recovered. To facilitate our presentation, we introduce the notion of time-scale-chirp_rate (TSC_R) recovery transform or TSC_R recovery operator to develop a TSC_R theory for the 3-dimensional space of time, scale, chirp rate. Our theoretical development is based on the approximation of the non-stationary signal components with linear chirps and applying the proposed adaptive TSC_R transform to the multi-component blind-source signal to obtain fairly accurate error bounds of IF estimations and signal components recovery. Several numerical experimental results are presented to demonstrate the out-performance of the proposed method over all existing time-frequency and time-scale approaches in the published literature, particularly for non-stationary source signals with crossover IFs.

Output feedback control design using Extended High-Gain Observers and dynamic inversion with projection for a small scaled helicopter

This paper presents the output feedback control design for a tracking problem of a small-scale helicopter in the presence of uncertainties. The dynamics of the helicopter is an underactuated mechanical system and the form of control inputs is nonaffine. A time-scale approach is suggested to cope with underactuated mechanical systems to overcome lack of the number of inputs. A newly developed dynamic inversion with projection is used to deal with nonaffine control inputs to increase the region of attraction as compared to linearized inputs, i.e., an affine control input form and to deal with actuator’s constraints and peaking in estimates from an Extended High-Gain Observer. The Extended High-Gain Observer is employed to quickly estimate model uncertainties and external disturbances. The singular perturbation method is used to analyze the stability of the closed-loop system in a multi-time scale structure. Based on the stability analysis, the design procedure for the proposed algorithm is presented for practical implementation. The effectiveness of the proposed control algorithm is shown via numerical simulations as well as experimental tests with a small-scale helicopter in an outdoor environment.

Dynamic consensus and extended high gain observers as a tool to achieve practical frequency synchronization in power systems under unknown time-varying power demand

In this paper, we consider the frequency synchronization problem in a network of lossless, connected, and network-reduced power system. Frequency synchronization is an important problem in power systems as frequency deviation can lead to degraded power quality, tripping of generators, etc. We present a load-estimator-based consensus algorithm in a network of fourth-order generator models that achieves practical frequency synchronization in the presence of unknown time-varying power demand. We do not assume that the demand is generated by a known model. We follow a multiple time-scale approach for the stability analysis. It is shown that synchronization is achieved for the case of constant power demand, by showing that the system is exponentially stable. For the case of time-varying power demand, we show the error trajectories are ultimately bounded, and the synchronization error is proportional to an upper bound on the derivative of the time-varying power demand. We simulate the controller performance on a four area network which is equivalent to the IEEE New England 39-Bus system.

Measuring the global economic impact of the coronavirus outbreak: Evidence from the main cluster countries

This study measures the global economic impact of the coronavirus outbreak. This pandemic is characterized by demand and supply shocks, leading to restrictions on trade, product and service transactions, and capital flow mobility. We investigate its impact on currency markets, stock market performance, and investor fear sentiment. We employ an empirical, time-scale approach based on the continuous wavelet transform—appropriate for time-series characteristics during times of turmoil. Based on daily data for four main cluster countries (China, France, Italy, and the USA), our results show that the impact of the pandemic's evolution on the main economic indicators in China exhibits a different pattern from France, Italy, and the USA. For China, our results show that the pandemic evolution co-moves with the main economic indicators only in the short term (one week). The effect is more persistent in other countries. We also show that the main economic indicators are more sensitive to pandemic evolution assessed by the number of deaths rather than number of cases, and that currency and financial markets are affected in different timescales. These findings might assist policymakers in addressing the feedback loop between currency markets and capital flows and help investors find alternative assets to hedge against heath shocks.

Continuous-time distributed Nash equilibrium seeking algorithms for non-cooperative constrained games

This paper studies the Nash equilibrium seeking problem for non-cooperative games subject to set and nonlinear inequality constraints. The cost function for each player and the constrained function are determined by all the players’ decision variables. Each player is assigned a constrained set while all the players are subject to a coupling nonlinear inequality constraint. A continuous-time distributed seeking algorithm using local information interaction is proposed, where the players deliver/receive information unidirectionally over a directed network. In particular, a distributed observer is first introduced for each player to estimate all the others’ decision variables. Then, by using these estimates, a seeking algorithm is synthesized with a projection operator. Based on the time-scale separation approach, it is shown that the proposed continuous-time distributed seeking algorithm guarantees the convergence of the strategy profile to an arbitrarily small neighborhood of the generalized Nash equilibrium satisfying a KKT condition. An illustrative example is finally presented to validate the theoretical results.

Flow Optimization in Dynamic Networks on Time Scales

Network flow optimization has a wide range of real world applications such as in transportation, in electric, in civil engineering, in industrial engineering and in communication networks and so on. In the minimum cost network flow model, the goal is to find the values of the decisions variables that minimize the total cost of flows over the given network. In this work, a new formulation of flow optimization in dynamic networks using time scales approach has been presented. The continuous network model and the quantum case model are also obtained as special cases. The formulation has been given for both dynamic models and time scales models. Moreover, the new approach provides the exact optimal solution for this type of optimization problems. Furthermore, a new version of some duality theorems for time scales flow optimization in dynamic networks has been introduced.

Information Diffusion and Spillover Dynamics in Renewable Energy Markets

The aim of this paper is to analyze the connectedness between renewable energy (RE) sectors, the oil & gas sector and other assets using time-scale spillover approach. We find that the RE bioenergy firms are the most connected to oil & gas firms and oil prices. The bond market transmits spillover to the RE sectors, while it receives spillover from the oil & gas sector. Moreover, short-run connectedness drives the dynamic total connectedness. Since changes in bond rates mainly spillover to RE firms and not to oil & gas firms, policy makers should also be aware that changes in interest rates may impact the societal transition to a RE based energy system. Since a shock that increases connectedness in the short run will deter investors from investing in RE assets, it is important for climate policy makers to develop policies that reduce the effect of increased connectedness on RE investments.