23 citations · 52 across the 12 of their papers we have counts for
14 papers
Streaming Compression of Scientific Data via weak-SINDy
Benjamin P. Russo, M. Paul Laiu, Richard Archibald
In this paper a streaming weak-SINDy algorithm is developed specifically for compressing streaming scientific data. The production of scientific data, either via simulation or expe…
Fault Detection via Occupation Kernel Principal Component Analysis
Zachary Morrison, Benjamin P. Russo, Yingzhao Lian +1
The reliable operation of automatic systems is heavily dependent on the ability to detect faults in the underlying dynamical system. While traditional model-based methods have been…
Convergence of weak-SINDy Surrogate Models
Benjamin Russo, M. Paul Laiu
In this paper, we give an in-depth error analysis for surrogate models generated by a variant of the Sparse Identification of Nonlinear Dynamics (SINDy) method. We start with an ov…
Bayesian inversion and the Tomita-Takesaki modular group
Luca Giorgetti, Arthur J. Parzygnat, Alessio Ranallo +1
We show that conditional expectations, optimal hypotheses, disintegrations, and adjoints of unital completely positive maps, are all instances of Bayesian inverses. We study the ex…
Spectra for Toeplitz Operators Associated with a Constrained Subalgebra
Christopher Felder, Douglas T. Pfeffer, Benjamin P. Russo
A two-point algebra is a set of bounded analytic functions on the unit disk that agree at two distinct points . This algebra serves as a multiplier algebra for…
Liouville Operators over the Hardy Space
Benjamin P. Russo, Joel A. Rosenfeld
The role of Liouville operators in the study of dynamical systems through the use of occupation measures have been an active area of research in control theory over the past decade…
Motion Tomography via Occupation Kernels
Benjamin P. Russo, Rushikesh Kamalapurkar, Dongsik Chang +1
The goal of motion tomography is to recover a description of a vector flow field using information on the trajectory of a sensing unit. In this paper, we develop a predictor correc…
Occupation Kernel Hilbert Spaces for Fractional Order Liouville Operators and Dynamic Mode Decomposition
Joel A. Rosenfeld, Benjamin Russo, Xiuying Li
This manuscript gives a theoretical framework for a new Hilbert space of functions, the so called occupation kernel Hilbert space (OKHS), that operate on collections of signals rat…
Theoretical Foundations for the Dynamic Mode Decomposition of High Order Dynamical Systems
Joel A. Rosenfeld, Benjamin P. Russo, Rushikesh Kamalapurkar
Conventionally, data driven identification and control problems for higher order dynamical systems are solved by augmenting the system state by the derivatives of the output to for…
A non-commutative Bayes' theorem
Arthur J. Parzygnat, Benjamin P. Russo
Using a diagrammatic reformulation of Bayes' theorem, we provide a necessary and sufficient condition for the existence of Bayesian inference in the setting of finite-dimensional $…
The Occupation Kernel Method for Nonlinear System Identification
Joel A. Rosenfeld, Benjamin Russo, Rushikesh Kamalapurkar +1
This manuscript presents a novel approach to nonlinear system identification leveraging densely defined Liouville operators and a new "kernel" function that represents an integrati…
Non-commutative disintegrations: existence and uniqueness in finite dimensions
Arthur J. Parzygnat, Benjamin P. Russo
Motivated by advances in categorical probability, we introduce non-commutative almost everywhere (a.e.) equivalence and disintegrations in the setting of C*-algebras. We show that…
Lifting Commuting 3-Isometric Tuples
Benjamin Russo
An operator is called a 3-isometry if there exists operators and such that \[Q(n)=T^{*n}T^n=1+nB_1(T^*,T)+n^2 B_2(T^*,T)\] for all natural numbers …
A lifting theorem for 3-isometries
Scott McCullough, Benjamin Russo
An operator T on Hilbert space is a 3-isometry if there exists operators B and D such that (T*)^n T^n = I+nB +n^2 D. An operator J is a Jordan operator if it the sum of a unitary U…