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Climate changepoint (homogenization) methods abound today, with a myriad of techniques existing in both the climate and statistics literature. Unfortunately, the appropriate changepoint technique to use remains unclear to many. Further…
The world surrounding us is subject to constant change. These changes, frequently described as concept drift, influence many industrial and technical processes. As they can lead to malfunctions and other anomalous behavior, which may be…
Dynamical systems are frequently used to model biological systems. When these models are fit to data it is necessary to ascertain the uncertainty in the model fit. Here we present prediction deviation, a new metric of uncertainty that…
Change detection is an important problem in vision field, especially for aerial images. However, most works focus on traditional change detection, i.e., where changes happen, without considering the change type information, i.e., what…
Complex numerical weather prediction models incorporate a variety of physical processes, each described by multiple alternative physical schemes with specific parameters. The selection of the physical schemes and the choice of the…
Due to lack of scientific understanding, some mechanisms may be missing in mathematical modeling of complex phenomena in science and engineering. These mathematical models thus contain some uncertainties such as uncertain parameters. One…
Equilibrium is a rather ideal situation, the exception rather than the rule in Nature. Whenever the external or internal parameters of a physical system are varied its subsequent relaxation to equilibrium may be either impossible or take…
Classical anomaly detection is principally concerned with point-based anomalies, anomalies that occur at a single data point. In this paper, we present a new mathematical model to express range-based anomalies, anomalies that occur over a…
Many forecasts consist not of point predictions but concern the evolution of quantities. For example, a central bank might predict the interest rates during the next quarter, an epidemiologist might predict trajectories of infection rates,…
Nonlinearity in many systems is heavily dependent on component variation and environmental factors such as temperature. This is often overcome by keeping signals close enough to the device's operating point that it appears approximately…
A validated simulation model primarily requires performing an appropriate input analysis mainly by determining the behavior of real-world processes using probability distributions. In many practical cases, probability distributions of the…
Point processes often have a natural interpretation with respect to a continuous process. We propose a point process construction that describes arrival time observations in terms of the state of a latent diffusion process. In this…
Observation of other people's choices can provide useful information in many circumstances. However, individuals may not utilize this information efficiently, i.e., they may make decision-making errors in social interactions. In this paper,…
Interactions among people or objects are often dynamic in nature and can be represented as a sequence of networks, each providing a snapshot of the interactions over a brief period of time. An important task in analyzing such evolving…
The theory of decoherence attempts to explain the emergent classical behaviour of a quantum system interacting with its quantum environment. In order to formalize this mechanism we introduce the idea that the information preserved in an…
The fixed-point analysis refers to the study of fixed-points that arise in the context of complex systems with many interacting entities. In this expository paper, we describe four levels of fixed-points in mean-field interacting particle…
$Anomaly$ $detection$ problems (also called $change$-$point$ $detection$ problems) have been studied in data mining, statistics and computer science over the last several decades in applications such as medical condition monitoring and…
This text surveys different probabilistic aspects of a model which is used to describe the evolution of an object that falls apart randomly as time passes. Each point of view yields useful techniques to establish properties of such random…
The concept of random dynamical system is a comparatively recent development combining ideas and methods from the well developed areas of probability theory and dynamical systems. Due to our inaccurate knowledge of the particular physical…
The paper deals with disorders detection in the multivariate stochastic process. We consider the multidimensional Poisson process or the multivariate renewal process. This class of processes can be used as a description of the distributed…