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Shoikhet, D. ; Vajiac, E. (Ed.)We consider the existence and structure properties of Parseval frames of kernel functions in vector valued de Branges spaces. We develop some sufficient conditions for Parseval sequences by identifying the main construction with Naimark dilation of frames. The dilation occurs by embedding the de Branges space of vector valued functions into a dilated de Branges space of vector valued functions. The embedding also maps the kernel functions associated with a frame sequence of the original space into a Riesz basis for the embedding space. We also develop some sufficient conditions for a dilated de Branges space to have the Kramermore »Free, publiclyaccessible full text available May 21, 2023

The Kaczmarz algorithm is an iterative method for solving systems of linear equations. We introduce a randomized Kaczmarz algorithm for solving systems of linear equations in a distributed environment, i.e., the equations within the system are distributed over multiple nodes within a network. The modification we introduce is designed for a network with a tree structure that allows for passage of solution estimates between the nodes in the network. We demonstrate that the algorithm converges to the solution, or the solution of minimal norm, when the system is consistent. We also prove convergence rates of the randomized algorithm that dependmore »Free, publiclyaccessible full text available March 1, 2023

Abstract We develop a method for calculating the persistence landscapes of affine fractals using the parameters of the corresponding transformations. Given an iterated function system of affine transformations that satisfies a certain compatibility condition, we prove that there exists an affine transformation acting on the space of persistence landscapes, which intertwines the action of the iterated function system. This latter affine transformation is a strict contraction and its unique fixed point is the persistence landscape of the affine fractal. We present several examples of the theory as well as confirm the main results through simulations.Free, publiclyaccessible full text available January 1, 2023

Free, publiclyaccessible full text available December 1, 2022

In recent years, many incidents have been reported where machine learning models exhibited discrimination among people based on race, sex, age, etc. Research has been conducted to measure and mitigate unfairness in machine learning models. For a machine learning task, it is a common practice to build a pipeline that includes an ordered set of data preprocessing stages followed by a classifier. However, most of the research on fairness has considered a single classifier based prediction task. What are the fairness impacts of the preprocessing stages in machine learning pipeline? Furthermore, studies showed that often the root cause of unfairnessmore »Free, publiclyaccessible full text available August 23, 2022

Highthroughput phenotyping enables the efficient collection of plant trait data at scale. One example involves using imaging systems over key phases of a crop growing season. Although the resulting images provide rich data for statistical analyses of plant phenotypes, image processing for trait extraction is required as a prerequisite. Current methods for trait extraction are mainly based on supervised learning with human labeled data or semisupervised learning with a mixture of human labeled data and unsupervised data. Unfortunately, preparing a sufficiently large training data is both time and laborintensive. We describe a selfsupervised pipeline (KAT4IA) that uses K means clusteringmore »

Diffusion of information in social network has been the focus of intense research in the recent past decades due to its significant impact in shaping public discourse through group/individual influence. Existing research primarily models influence as a binary property of entities: influenced or not influenced. While this is a useful abstraction, it discards the notion of degree of influence, i.e., certain individuals may be influenced ``more'' than others. We introduce the notion of \emph{attitude}, which, as described in social psychology, is the degree by which an entity is influenced by the information. Intuitively, attitude captures the number of distinct neighborsmore »

Constraint satisfaction problems (CSP's) and data stream models are two powerful abstractions to capture a wide variety of problems arising in different domains of computer science. Developments in the two communities have mostly occurred independently and with little interaction between them. In this work, we seek to investigate whether bridging the seeming communication gap between the two communities may pave the way to richer fundamental insights. To this end, we focus on two foundational problems: model counting for CSP's and computation of zeroth frequency moments $(F_0)$ for data streams. Our investigations lead us to observe striking similarity in the coremore »