Related papers: A framework for the study of the qualitative dynam…
In this paper we extend previous work on IFSs without overlap. Our method involves systems of operators generalizing the more familiar Cuntz relations from operator algebra theory, and from subband filter operators in signal processing.
Normalizing flow (NF) has gained popularity over traditional maximum likelihood based methods due to its strong capability to model complex data distributions. However, the standard approach, which maps the observed data to a normal…
We study iterated function systems (IFS) with compact parameter space. We show that the space of IFS with phase space $X$ is the hyperspace of the space of self continuous maps of $X$. With this result we obtain that the Hausdorff distance…
This paper develops an incremental learning algorithm based on quadratic inference function (QIF) to analyze streaming datasets with correlated outcomes such as longitudinal data and clustered data. We propose a renewable QIF (RenewQIF)…
We develop a statistical framework for conducting inference on collections of time-varying covariance operators (covariance flows) over a general, possibly infinite dimensional, Hilbert space. We model the intrinsically non-linear structure…
This paper introduces a compositional framework for constructing finite abstractions of nonlinear interconnected impulsive systems using dissipativity-based conditions. Central to our approach is the concept of "alternating simulation…
We develop a system-theoretic framework for the structured analysis of distributed optimization algorithms with decomposable cost functions. We model such algorithms as a network of interacting dynamical systems and derive tests for…
We consider inference for a collection of partially observed, stochastic, interacting, nonlinear dynamic processes. Each process is identified with a label called its unit, and our primary motivation arises in biological metapopulation…
As we aim at alleviating the curse of high-dimensionality, subspace learning is becoming more popular. Existing approaches use either information about global or local structure of the data, and few studies simultaneously focus on global…
Dynamical systems, that are used to model power grids, the brain, and other physical systems, can exhibit coexisting stable states known as attractors. A powerful tool to understand such systems, as well as to better predict when they may…
Interactive image segmentation(IIS) plays a critical role in generating precise annotations for remote sensing imagery, where objects often exhibit scale variations, irregular boundaries and complex backgrounds. However, existing IIS…
Time-discrete dynamical systems on a finite state space have been used with great success to model natural and engineered systems such as biological networks, social networks, and engineered control systems. They have the advantage of being…
The Koopman linearization of measure-preserving systems or topological dynamical systems on compact spaces has proven to be extremely useful. In this article we look at dynamics given by continuous semiflows on completely regular spaces…
In this paper we propose a method for the construction of locally conservative flux fields from Generalized Multiscale Finite Element Method (GMsFEM) pressure solutions. The flux values are obtained from an element-based postprocessing…
In many applications, smooth processes generate data that is recorded under a variety of observation regimes, such as dense, sparse or fragmented observations that are often contaminated with error. The statistical goal of registering and…
We present a systematic derivation of the gradient flows associated to a broad class of interfacial energies, emphasizing the relation between intrinsic and extrinsic variations of the interface. We show that the intrinsic variables…
Establishing the existence of periodic orbits is one of the crucial and most intricate topics in the study of dynamical systems, and over the years, many methods have been developed to this end. On the other hand, finding closed orbits in…
Segmenting thin structures like infrastructure cracks and anatomical vessels is a task hampered by topology-sensitive geometry, high annotation costs, and poor generalization across domains. Existing methods address these challenges in…
In this paper we introduce expansive iterated function systems, ( IFS) on a compact metric space then various shadowing properties and their equivalence are considered for expansive IFS.
We introduce a new and general continuum thermodynamic framework for the mathematical analysis and computation of adsorption on dynamic interfaces. To the best of our knowledge, there is no formulation available that accounts for the…