Related papers: Analysis of persistent and antipersistent time ser…
We study the computational efficiency of approaches, based on Hilbert's Nullstellensatz, which use systems of linear equations for detecting non-colorability of graphs having large girth and chromatic number. We show that for every…
Topological data analysis is an emerging area in exploratory data analysis and data mining. Its main tool, persistent homology, has become a popular technique to study the structure of complex, high-dimensional data. In this paper, we…
We assess the detectability of a nanohertz gravitational wave (GW) background with respect to additive red and white noise in the timing of millisecond pulsars. We develop detection criteria based on the cross-correlation function summed…
Time series graphical models have recently received considerable attention for characterizing (conditional) dependence structures in multivariate time series. In many applications, the multivariate series exhibit variable-partitioned…
We study the problem of periodicity detection in massive data sets of photometric or radial velocity time series, as presented by ESA's Gaia mission. Periodicity detection hinges on the estimation of the false alarm probability (FAP) of the…
The processes governing protostellar mass growth remain debated, although episodic accretion is now understood as a key feature of protostellar evolution across all masses. Luminosity bursts have been observed in both low- and high-mass…
Radial velocity (RV) searches for Earth-mass exoplanets in the habitable zone around Sun-like stars are limited by the effects of stellar variability on the host star. In particular, suppression of convective blueshift and brightness…
We present a unified pipeline for univariate time series classification via complex networks and persistent homology. A time series is mapped to a graph through one of five constructions across three families (visibility (natural and…
In transportation applications such as real-time route guidance, ramp metering, congestion pricing and special events traffic management, accurate short-term traffic flow prediction is needed. For this purpose, this paper proposes several…
The aim of this paper is to characterize an important class of marked digraphs, called structurally observable graphs (SOGs), and to solve two minimum realization problems. To begin with, by exploring structural observability of large-scale…
This paper addresses the problem of detecting and characterizing local variability in time series and other forms of sequential data. The goal is to identify and characterize statistically significant variations, at the same time…
This paper proposes a hybrid Gaussian process (GP) approach to robust economic model predictive control under unknown future disturbances in order to reduce the conservatism of the controller. The proposed hybrid GP is a combination of two…
We consider the problem of breaking a multivariate (vector) time series into segments over which the data is well explained as independent samples from a Gaussian distribution. We formulate this as a covariance-regularized maximum…
Persistent homology (PH) is a recently developed theory in the field of algebraic topology to study shapes of datasets. It is an effective data analysis tool that is robust to noise and has been widely applied. We demonstrate a general…
Gaussian processes (GPs) are non-parametric probabilistic regression models that are popular due to their flexibility, data efficiency, and well-calibrated uncertainty estimates. However, standard GP models assume homoskedastic Gaussian…
Temporal graphs are used to abstractly model real-life networks that are inherently dynamic in nature. Given a static underlying graph $G=(V,E)$, a temporal graph on $G$ is a sequence of snapshots $G_t$, one for each time step $t\geq 1$. In…
Constraint-based methods and noise-based methods are two distinct families of methods proposed for uncovering causal graphs from observational data. However, both operate under strong assumptions that may be challenging to validate or could…
Given a network, the critical node detection problem finds a subset of nodes whose removal disrupts the network connectivity. Since many real-world systems are naturally modeled as graphs, assessing the vulnerability of the network is…
We address highly dynamic distributed systems modeled by time-varying graphs (TVGs). We interest in proof of impossibility results that often use informal arguments about convergence. First, we provide a distance among TVGs to define…
Motivated by empirical evidence from the joint behavior of realized volatility time series, we propose to model the joint dynamics of log-volatilities using a multivariate fractional Ornstein-Uhlenbeck process. This model is a multivariate…