搜索结果：Regenerative

This paper presents a regenerative variant of the classical Ulam-von Neumann Markov chain Monte Carlo algorithm for the approximation of the matrix inverse. The algorithm presented in this paper, termed regenerative Ulam-von Neumann algorithm, utilizes the regenerative structure of classical, non-truncated Neumann series defined by a non-singular matrix and produces an estimator of the matrix inverse via ratios of unbiased estimators of the regenerative quantities. The accuracy of the proposed algorithm depends on a single parameter that controls the total number of simulated Markov transitions, thus avoiding the challenge of balancing between the total number of Markov chain replications and their length as in the classical Ulam-von Neumann algorithm. To efficiently utilize Markov chain transition samples in the calculation of the regenerative variables, the proposed algorithm automatically quantifies the contribution of each Markov transition to all regenerative quantities by a carefully designed updating scheme that utilized three separate matrices containing the current weights, total weights, and regenerative cycle count, respectively. A probabilistic analysis of the performan

This thesis presents Regenerative Rejection Sampling (RRS), a novel approximate sampling algorithm inspired by classical Rejection Sampling and Markov Chain Monte Carlo methods. The method constructs a continuous-time regenerative process whose stationary distribution coincides with a target density known only up to a normalizing constant. Unlike standard Rejection Sampling, RRS does not require the existence of a finite constant that upper-bounds the likelihood ratio. As a result, its total variation convergence rate remains exponential for a larger class of scenarios compared to, for example, the Independent Metropolis-Hastings sampler, which requires a finite bounding constant. To explain the workings of the method, we first present a detailed review of renewal and regenerative processes, including their limit theorems, stationary versions, and convergence properties under standard conditions. We explain a coupling proof for exponential convergence of regenerative processes, under the assumption of a spread-out cycle length distribution. We then introduce the RRS algorithm, and derive its convergence rate. Its performance is compared theoretically and empirically with classical

We prove a version of the Dvoretzky-Kiefer-Wolfowitz inequality for Markov chains with a regenerative structure. Suppose we have a regenerative Markov chain with stationary distribution $π$. Given a functional $θ$ on the state space and a confidence level $1-δ$, our result provides a uniform $1-δ$ confidence band for the CDF of $θ$ under $π$ based on the empirical CDF. By inversion, we get a $1-δ$ confidence band for the quantile function of $θ$ under $π$. Our bounds are fully explicit and nearly optimal. In addition, they are data-dependent in the following sense: in the formula for the width of the confidence band, the leading term can be computed directly from the sample path without any a priori information about the convergence rate of the chain. A convergence bound is required, but it contributes to the width of the confidence band only through a lower-order term. For this reason, our result is attractive for Markov chains whose convergence rate is much quicker in practice than what can be proved in theory. Data-dependent bounds of this type are called empirical concentration inequalities in the literature. Thus, our result is an empirical concentration inequality for the emp

We study regenerative processes time-changed by state-dependent inverse subordinators. The construction assigns possibly different independent subordinators to measurable classes of excursions and builds a random clock from the corresponding occupation times. Although the resulting process is generally not regenerative, we prove that its transformed excursion point process is again Poisson, using an excursion-wise marking-and-mapping procedure. We apply this to study occupation-time asymptotics. Under regular variation assumptions on the transformed excursion lifetime tails, we prove a multiscale joint occupation-time limit theorem, including generalized arcsine laws and Darling--Kac type limits.

The regenerative satellite access network (SAN) architecture deploys next-generation NodeB (gNBs) on satellites to enable enhanced network management capabilities. It supports two types of regenerative payload, on-board gNB and on-board gNB-Distributed Unit (gNB-DU). Measurement results based on our prototype implementation show that the on-board gNB offers lower latency, while the on-board gNB-DU is more cost-effective, and there is often a trade-off between Quality-of-Service (QoS) and operational expenditure (OPEX) when choosing between the two payload types. However, current SAN configurations are static and inflexible -- either deploying the full on-board gNB or only the on-board gNB-DU. This rigidity can lead to resource waste or poor user experiences. In this paper, we propose Flexible SAN (FlexSAN), an adaptive satellite access network architecture that dynamically configures the optimal regenerative payload based on real-time user demands. FlexSAN selects the lowest OPEX payload configuration when all user demands are satisfied, and otherwise maximizes the number of admitted users while ensuring QoS for connected users. To address the computational complexity of dynamic pa

Regenerative braking (RB) significantly influences electric vehicle (EV) car-following (CF) dynamics, yet traditional traffic-flow models rarely capture these effects. We introduce a comprehensive empirical dataset comprising 197.5 hours of driving data from 25 drivers across eight EV models to systematically investigate regen-induced CF behaviors. Two primary CF patterns emerge: (i) steady-state scenarios where EVs use regenerative braking and subsequently re-accelerate to equilibrium speeds with larger spacing, and (ii) dynamic scenarios involving lead oscillations, characterized by a distinctive three-phase CF process-regenerative deceleration, transitional plateau, and rapid re-acceleration. The paper's main contribution is the development of an analytical framework that models these EV-specific CF behaviors and quantifies their impacts on traffic capacity. We derive closed-form expressions for the established $η$ function from the literature, explicitly quantifying EV driving deviations from stable CF defined by Newell's CF model and assessing their implications for roadway capacity. Validation against empirical data and simulation confirm the model's accuracy ($R^2=0.96$) in

Mitigating climate change requires transforming agriculture to minimize environ mental impact and build climate resilience. Regenerative agricultural practices enhance soil organic carbon (SOC) levels, thus improving soil health and sequestering carbon. A challenge to increasing regenerative agriculture practices is cheaply measuring SOC over time and understanding how SOC is affected by regenerative agricultural practices and other environmental factors and farm management practices. To address this challenge, we introduce an AI-driven Soil Organic Carbon Copilot that automates the ingestion of complex multi-resolution, multi-modal data to provide large-scale insights into soil health and regenerative practices. Our data includes extreme weather event data (e.g., drought and wildfire incidents), farm management data (e.g., cropland information and tillage predictions), and SOC predictions. We find that integrating public data and specialized models enables large-scale, localized analysis for sustainable agriculture. In comparisons of agricultural practices across California counties, we find evidence that diverse agricultural activity may mitigate the negative effects of tillage;

This document presents a compilation of results related to the theory of stochastic processes, with a specific focus on Markov processes, regenerative processes, renewal processes, and stationary processes. The relevance of these topics lies in the ability to identify regeneration points and the necessary conditions to ensure the stationarity of the process. The study begins with a review of Markov chains and continues with the analysis of processes that satisfy the strong Markov property. Subsequently, it delves into renewal processes, regenerative processes, and finally, stationary regenerative processes, highlighting the results presented by Thorisson [22]. This work is not intended to be exhaustive but aims to provide a solid foundation for further deepening the knowledge of these processes, given their broad range of applications in cryptography [16], queueing theory [15], and Monte Carlo methods [23]. Additionally, the importance of Poisson-type processes is emphasized due to their numerous applications (see [8]).

The problem of estimating the probability of a random process reaching a certain level is well known. In this article, two-sided estimates are established for the probability that a regenerative process reaches a high level. Two auxiliary results for geometric sums with delay will play an important role. Examples of application to random processes describing queue lengths in queueing theory are also given.

A new class of random composition structures (the ordered analog of Kingman's partition structures) is defined by a regenerative description of component sizes. Each regenerative composition structure is represented by a process of random sampling of points from an exponential distribution on the positive halfline, and separating the points into clusters by an independent regenerative random set. Examples are composition structures derived from residual allocation models, including one associated with the Ewens sampling formula, and composition structures derived from the zero set of a Brownian motion or Bessel process. We provide characterisation results and formulas relating the distribution of the regenerative composition to the L{é}vy parameters of a subordinator whose range is the corresponding regenerative set. In particular, the only reversible regenerative composition structures are those associated with the interval partition of $[0,1]$ generated by excursions of a standard Bessel bridge of dimension $2 - 2 α$ for some $α\in [0,1]$.

We consider Kingman's partition structures which are regenerative with respect to a general operation of random deletion of some part. Prototypes of this class are the Ewens partition structures which Kingman characterised by regeneration after deletion of a part chosen by size-biased sampling. We associate each regenerative partition structure with a corresponding regenerative composition structure, which (as we showed in a previous paper) can be associated in turn with a regenerative random subset of the positive halfline, that is the closed range of a subordinator. A general regenerative partition structure is thus represented in terms of the Laplace exponent of an associated subordinator. We also analyse deletion properties characteristic of the two-parameter family of partition structures.

Multiclass open queueing networks find wide applications in communication, computer and fabrication networks. Often one is interested in steady-state performance measures associated with these networks. Conceptually, under mild conditions, a regenerative structure exists in multiclass networks, making them amenable to regenerative simulation for estimating the steady-state performance measures. However, typically, identification of a regenerative structure in these networks is difficult. A well known exception is when all the interarrival times are exponentially distributed, where the instants corresponding to customer arrivals to an empty network constitute a regenerative structure. In this paper, we consider networks where the interarrival times are generally distributed but have exponential or heavier tails. We show that these distributions can be decomposed into a mixture of sums of independent random variables such that at least one of the components is exponentially distributed. This allows an easily implementable embedded regenerative structure in the Markov process. We show that under mild conditions on the network primitives, the regenerative mean and standard deviation es

The Gibbs sampler of Park and Casella is one of the most popular MCMC methods for sampling from the posterior density of the Bayesian Lasso regression. As with many Markov chain samplers, their Gibbs sampler lacks a theoretically sound method of output analysis --- a method for estimating the variance of a given ergodic average and estimating how closely the chain is sampling from the stationary distribution, that is, the burn-in. In this paper, we address this shortcoming by identifying regenerative structure in the sampler of Park and Casella, thus providing a theoretically sound method of assessing its performance. The regenerative structure provides both a strongly consistent variance estimator, and an estimator of (an upper bound on) the total variation distance from the target posterior density. The result is a simple and theoretically sound way to assess the stationarity of the Park and Casella and, more generally, other MCMC samplers, for which regenerative simulation is possible. We perform a numerical study in which we validate the standard errors calculated by our regenerative method by comparing it with the standard errors calculated by an AR(1) heuristic approximation.

We study a type of Online Linear Programming (OLP) problem that maximizes the objective function with stochastic inputs. The performance of various algorithms that analyze this type of OLP is well studied when the stochastic inputs follow some i.i.d distribution. The two central questions to ask are: (i) can the algorithms achieve the same efficiency if the stochastic inputs are not i.i.d but still stationary, and (ii) how can we modify our algorithms if we know the stochastic inputs are trendy, hence not stationary. We answer the first question by analyzing a regenerative type of input and show the regrets of two popular algorithms are bounded by the same orders as their i.i.d counterparts. We discuss the second question in the context of linearly growing inputs and propose a trend-adaptive algorithm. We provide numerical simulations to illustrate the performance of our algorithms under both regenerative and trendy inputs.

Chip-based optical amplifiers can significantly expand the functionalities of photonic devices. In particular, optical-parametric amplifiers (OPAs), with engineerable gain-spectra, are well-suited for nonlinear-photonic applications. Chip-based OPAs typically require long waveguides that occupy a large footprint, and high pump powers that cannot be easily produced with chip-scale lasers. We theoretically and experimentally demonstrate a microresonator-assisted regenerative OPA that benefits from the large nonlinearity enhancement of microresonators and yields a high gain in a small footprint. We achieve 30-dB parametric gain with only 9 mW of cw-pump power and show that the gain spectrum can be engineered to cover telecom channels inaccessible with Er-based amplifiers. We further demonstrate the amplification of Kerr-soliton comb lines and the preservation of their phase properties. Additionally, we demonstrate amplification by injection locking of optical-parametric oscillators, which corresponds to a regenerative amplifier pumped above the oscillation threshold. Novel dispersion engineering techniques such as coupled cavities and higher-order-dispersion phase matching can further

In this paper we present a robust mixed integer optimization model to utilize regenerative braking energy produced by trains in a railway network. An electric train produces regenerative energy during braking, which is often lost in present technology. To utilize this energy we calculate a timetable which maximizes the total overlapping time between the braking and accelerating phases of suitable train pairs, so that the regenerative energy of a braking train can be transferred to a suitable accelerating one. We apply our optimization model to different instances of a railway network for a time horizon spanning six hours. For each instance, our model finds an optimal timetable very quickly (largest running time being 86.64 seconds). Compared to the existing timetables, we observe significant increase in utilization of regenerative energy for every instance.

This paper presents a unique flywheel-based regenerative energy recovery, storage and release system developed at the author's laboratory. It can recover and store regenerative energy produced by braking a motion generator with intermittent rotary velocity such as the rotor of a wind turbogenerator subject to intermittent intake wind and the axels of electric and hybrid gas-electric vehicles during frequent coasting and braking. Releasing of the stored regenerative energy in the flywheel is converted to electricity by the attached alternator. A proof-of-concept prototype called the SJSU-RBS was designed, built and tested by author's students with able assistance of a technical staff in his school.

Consider a stochastic process $\mathfrak{X}$, regenerative at a state $x$ which is instantaneous and regular. Let $L$ be a regenerative local time for $\mathfrak{X}$ at $x$. Suppose furthermore that $\mathfrak{X}$ can be approximated by discrete time regenerative processes $\mathfrak{X}^n$ for which $x$ is accesible. We give conditions on $\mathfrak{X}$ and $\mathfrak{X}^n$ so that the naturally defined local time of $\mathfrak{X}^n$ converges weakly to $L$. This limit theorem generalizes previous invariance principles that have appeared in the literature.

In this paper, we give a necessary and sufficient condition for mean stability of switched linear systems having a Markov regenerative process as its switching signal. This class of switched linear systems, which we call Markov regenerative switched linear systems, contains Markov jump linear systems and semi-Markov jump linear systems as special cases. We show that a Markov regenerative switched linear system is $m$th mean stable if and only if a particular matrix is Schur stable, under the assumption that either $m$ is even or the system is positive.