Probabilistic Estimation of Chirp Instantaneous Frequency Using Gaussian Processes

We present a probabilistic approach for estimating chirp signal and its instantaneous frequency function when the true forms of the chirp and instantaneous frequency are unknown. To do so, we represent them by joint cascading Gaussian processes governed by a non-linear stochastic differential equation, and estimate their posterior distribution by using stochastic filters and smoothers. The model parameters are determined via maximum likelihood estimation. Theoretical results show that the estimation method has a bounded mean squared error. Experiments show that the method outperforms a number of baseline methods on a synthetic model, and we also apply the method to analyse a gravitational wave data.Comment: Submitted to IEEE Transactions on Signal Processin

Minding impacting events in a model of stochastic variance

We introduce a generalisation of the well-known ARCH process, widely used for generating uncorrelated stochastic time series with long-term non-Gaussian distributions and long-lasting correlations in the (instantaneous) standard deviation exhibiting a clustering profile. Specifically, inspired by the fact that in a variety of systems impacting events are hardly forgot, we split the process into two different regimes: a first one for regular periods where the average volatility of the fluctuations within a certain period of time is below a certain threshold and another one when the local standard deviation outnumbers it. In the former situation we use standard rules for heteroscedastic processes whereas in the latter case the system starts recalling past values that surpassed the threshold. Our results show that for appropriate parameter values the model is able to provide fat tailed probability density functions and strong persistence of the instantaneous variance characterised by large values of the Hurst exponent is greater than 0.8, which are ubiquitous features in complex systems.Comment: 18 pages, 5 figures, 1 table. To published in PLoS on

SLO-aware Colocation of Data Center Tasks Based on Instantaneous Processor Requirements

In a cloud data center, a single physical machine simultaneously executes dozens of highly heterogeneous tasks. Such colocation results in more efficient utilization of machines, but, when tasks' requirements exceed available resources, some of the tasks might be throttled down or preempted. We analyze version 2.1 of the Google cluster trace that shows short-term (1 second) task CPU usage. Contrary to the assumptions taken by many theoretical studies, we demonstrate that the empirical distributions do not follow any single distribution. However, high percentiles of the total processor usage (summed over at least 10 tasks) can be reasonably estimated by the Gaussian distribution. We use this result for a probabilistic fit test, called the Gaussian Percentile Approximation (GPA), for standard bin-packing algorithms. To check whether a new task will fit into a machine, GPA checks whether the resulting distribution's percentile corresponding to the requested service level objective, SLO is still below the machine's capacity. In our simulation experiments, GPA resulted in colocations exceeding the machines' capacity with a frequency similar to the requested SLO.Comment: Author's version of a paper published in ACM SoCC'1

A Fourier transform method for nonparametric estimation of multivariate volatility

We provide a nonparametric method for the computation of instantaneous multivariate volatility for continuous semi-martingales, which is based on Fourier analysis. The co-volatility is reconstructed as a stochastic function of time by establishing a connection between the Fourier transform of the prices process and the Fourier transform of the co-volatility process. A nonparametric estimator is derived given a discrete unevenly spaced and asynchronously sampled observations of the asset price processes. The asymptotic properties of the random estimator are studied: namely, consistency in probability uniformly in time and convergence in law to a mixture of Gaussian distributions.Comment: Published in at http://dx.doi.org/10.1214/08-AOS633 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Frequency and Phase Synchronization in Stochastic Systems

The phenomenon of frequency and phase synchronization in stochastic systems requires a revision of concepts originally phrased in the context of purely deterministic systems. Various definitions of an instantaneous phase are presented and compared with each other with special attention payed to their robustness with respect to noise. We review the results of an analytic approach describing noise-induced phase synchronization in a thermal two-state system. In this context exact expressions for the mean frequency and the phase diffusivity are obtained that together determine the average length of locking episodes. A recently proposed method to quantify frequency synchronization in noisy potential systems is presented and exemplified by applying it to the periodically driven noisy harmonic oscillator. Since this method is based on a threshold crossing rate pioneered by S.O. Rice the related phase velocity is termed Rice frequency. Finally, we discuss the relation between the phenomenon of stochastic resonance and noise-enhanced phase coherence by applying the developed concepts to the periodically driven bistable Kramers oscillator.Comment: to appear in the Chaos focus issue on "Control, communication, and synchronization in chaotic dynamical systems

Delay Performance of MISO Wireless Communications

Ultra-reliable, low latency communications (URLLC) are currently attracting significant attention due to the emergence of mission-critical applications and device-centric communication. URLLC will entail a fundamental paradigm shift from throughput-oriented system design towards holistic designs for guaranteed and reliable end-to-end latency. A deep understanding of the delay performance of wireless networks is essential for efficient URLLC systems. In this paper, we investigate the network layer performance of multiple-input, single-output (MISO) systems under statistical delay constraints. We provide closed-form expressions for MISO diversity-oriented service process and derive probabilistic delay bounds using tools from stochastic network calculus. In particular, we analyze transmit beamforming with perfect and imperfect channel knowledge and compare it with orthogonal space-time codes and antenna selection. The effect of transmit power, number of antennas, and finite blocklength channel coding on the delay distribution is also investigated. Our higher layer performance results reveal key insights of MISO channels and provide useful guidelines for the design of ultra-reliable communication systems that can guarantee the stringent URLLC latency requirements.Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl