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papers

Publications (30)

math.FA2012

Moving finite unit tight frames for $S^{n}$

Daniel Freeman, Ryan Hotovy, Eileen Martin

Frames for $R^{n}$ can be thought of as redundant or linearly dependent coordinate systems, and have important applications in such areas as signal processing, data compression, and…

math.FA2022

Shrinking Schauder Frames and their Associated Bases

Kevin Beanland, Daniel Freeman

For a Banach space $X$ with a shrinking Schauder frame $(x_{i}, f_{i})$ we provide an explicit method for constructing a shrinking associated basis. In the case that the minimal associa…

math.FA2022

Discretizing $L_{p}$ norms and frame theory

Daniel Freeman, Dorsa Ghoreishi

Given an $N$ -dimensional subspace $X$ of $L_{p} ([0, 1])$ , we consider the problem of choosing $M$ -sampling points which may be used to discretely approximate the $L_{p}$ norm on the sub…

math.FA2024

Declipping and the recovery of vectors from saturated measurements

Wedad Alharbi, Daniel Freeman, Dorsa Ghoreishi +2

A frame $(x_{j})_{j \in J}$ for a Hilbert space $H$ allows for a linear and stable reconstruction of any vector $x \in H$ from the linear measurements $(⟨ x, x_{j} ⟩)_{j \in J}$ …

math.FA2020

The cardinality of the sublattice of closed ideals of operators between certain classical sequence spaces

Daniel Freeman, Thomas Schlumprecht, Andras Zsak

Theorem A and Theorem B of [1] state that for $1 < p < \infty$ the lattice of closed ideals of $L (ℓ_{p}, c_{0})$ , $L (ℓ_{p}, ℓ_{\infty})$ and of $\mathcal{L}(\ell_1,\…

math.FA2025

The Cahill-Casazza-Daubechies problem on HÃ¶lder stable phase retrieval

Daniel Freeman, Mitchell A. Taylor

Phase retrieval using a frame for a finite-dimensional Hilbert space is known to always be Lipschitz stable. However, phase retrieval using a frame or a continuous frame for an inf…

math.FA2014

The stabilized set of $p$ 's in Krivine's theorem can be disconnected

Kevin Beanland, Daniel Freeman, Pavlos Motakis

For any closed subset $F$ of $[1, \infty]$ which is either finite or consists of the elements of an increasing sequence and its limit, a reflexive Banach space $X$ with a 1-uncondit…

math.FA2017

The discretization problem for continuous frames

Daniel Freeman, Darrin Speegle

We characterize when a coherent state or continuous frame for a Hilbert space may be sampled to obtain a frame, which solves the discretization problem for continuous frames. In pa…

cs.IT2025

On sharp stable recovery from clipped and folded measurements

Pedro Abdalla, Daniel Freeman, JoÃ£o P. G. Ramos +1

We investigate the stability of vector recovery from random linear measurements which have been either clipped or folded. This is motivated by applications where measurement device…

math.FA2015

Weaving Schauder frames

Peter G. Casazza, Daniel Freeman, Richard G. Lynch

We extend the concept of weaving Hilbert space frames to the Banach space setting. Similar to frames in a Hilbert space, we show that for any two approximate Schauder frames for a…

math.FA2013

Uniformly factoring weakly compact operators

Kevin Beanland, Daniel Freeman

Let $X$ and $Y$ be separable Banach spaces. Suppose $Y$ either has a shrinking basis or $Y$ is isomorphic to $C (2^{N})$ and $A$ is a subset of weakly compact operators from…

math.FA2022

Stable phase retrieval for infinite dimensional subspaces of $L_{2} (R)$

Robert Calderbank, Ingrid Daubechies, Daniel Freeman +1

Phase retrieval is known to always be unstable when using a frame or continuous frame for an infinite dimensional Hilbert space. We consider a generalization of phase retrieval to…

cs.RO2022

Blocks Assemble! Learning to Assemble with Large-Scale Structured Reinforcement Learning

Seyed Kamyar Seyed Ghasemipour, Daniel Freeman, Byron David +3

Assembly of multi-part physical structures is both a valuable end product for autonomous robotics, as well as a valuable diagnostic task for open-ended training of embodied intelli…

math.FA2018

Continuous Schauder frames for Banach spaces

Joseph Eisner, Daniel Freeman

We introduce the notion of a continuous Schauder frame for a Banach space. This is both a generalization of continuous frames and coherent states for Hilbert spaces and a generaliz…

math.FA2015

Classes of operators determined by ordinal indices

Kevin Beanland, Ryan Causey, Daniel Freeman +1

We introduce and study the Bourgain index of an operator between two Banach spaces. In particular, we study the Bourgain $ℓ_{p}$ and $c_{0}$ indices of an operator. Several estimate…

math.FA2020

A Schauder basis for $L_{2}$ consisting of non-negative functions

Daniel Freeman, Alexander M. Powell, Mitchell A. Taylor

We prove that $L_{2} (R)$ contains a Schauder basis of non-negative functions. Similarly, $L_{p} (R)$ contains a Schauder basic sequence of non-negative functions such…

math.FA2022

Locality and stability for phase retrieval

Wedad Alharbi, Salah Alshabhi, Daniel Freeman +1

A frame $(x_{j})_{j \in J}$ for a Hilbert space $H$ is said to do phase retrieval if for all distinct vectors $x, y \in H$ the magnitude of the frame coefficients $(|\langle x, x_j\rang…

cs.AI2022

Multi-Game Decision Transformers

Kuang-Huei Lee, Ofir Nachum, Mengjiao Yang +8

A longstanding goal of the field of AI is a method for learning a highly capable, generalist agent from diverse experience. In the subfields of vision and language, this was largel…

cs.RO2023

Barkour: Benchmarking Animal-level Agility with Quadruped Robots

Ken Caluwaerts, Atil Iscen, J. Chase Kew +41

Animals have evolved various agile locomotion strategies, such as sprinting, leaping, and jumping. There is a growing interest in developing legged robots that move like their biol…

cs.RO2022

Bi-Manual Manipulation and Attachment via Sim-to-Real Reinforcement Learning

Satoshi Kataoka, Seyed Kamyar Seyed Ghasemipour, Daniel Freeman +1

Most successes in robotic manipulation have been restricted to single-arm robots, which limits the range of solvable tasks to pick-and-place, insertion, and objects rearrangement.…

math.FA2010

The universality of $ℓ_{1}$ as a dual space

Daniel Freeman, Edward Odell, Thomas Schlumprecht

Let $X$ be a Banach space with a separable dual. We prove that $X$ embeds isomorphically into a $\cL_\infty$ space $Z$ whose dual is isomorphic to $ℓ_{1}$ . If, moreover, $U$ is a…

math.FA2022

Quantitative bounds for unconditional pairs of frames

Peter Balazs, Daniel Freeman, Roxana Popescu +1

We formulate a quantitative finite-dimensional conjecture about frame multipliers and prove that it is equivalent to Conjecture 1 in [SB2]. We then present solutions to the conject…

math.FA2022

Stable phase retrieval and perturbations of frames

Wedad Alharbi, Daniel Freeman, Dorsa Ghoreishi +2

A frame $(x_{j})_{j \in J}$ for a Hilbert space $H$ is said to do phase retrieval if for all distinct vectors $x, y \in H$ the magnitude of the frame coefficients $(|\langle x, x_j\rang…

math.FA2007

Weakly null sequences with upper estimates

Daniel Freeman

We prove that if $(v_{i})$ is a normalized basic sequence and X is a Banach space such that every normalized weakly null sequence in X has a subsequence that is dominated by $(v_{i})$ ,…

math.FA2026

Maximal inequalities, frames and greedy algorithms

Pablo BernÃ¡, Daniel Freeman, Timur Oikhberg +1

The aim of this article is to use Banach lattice techniques to study coordinate systems in function spaces. We begin by proving that the greedy algorithm of a basis is order conver…

cs.CL2023

Beyond the Imitation Game: Quantifying and extrapolating the capabilities of language models

Aarohi Srivastava, Abhinav Rastogi, Abhishek Rao +448

Language models demonstrate both quantitative improvement and new qualitative capabilities with increasing scale. Despite their potentially transformative impact, these new capabil…

math.FA2020

Banach spaces for which the space of operators has $2^{c}$ closed ideals

Daniel Freeman, Thomas Schlumprecht, Andras Zsak

We formulate general conditions which imply that $L (X, Y)$ , the space of operators from a Banach space $X$ to a Banach space $Y$ , has $2^{c}$ closed ideals where $\mathfra…

math.FA2012

Upper and lower estimates for schauder frames and atomic decompositions

Kevin Beanland, Daniel Freeman, Rui Liu

We prove that a Schauder frame for any separable Banach space is shrinking if and only if it has an associated space with a shrinking basis, and that a Schauder frame for any separ…

cs.LG2025

Optimal lower Lipschitz bounds for ReLU layers, saturation, and phase retrieval

Daniel Freeman, Daniel Haider

The injectivity of ReLU layers in neural networks, the recovery of vectors from clipped or saturated measurements, and (real) phase retrieval in $R^{n}$ allow for a similar…

cs.SE2017

Intelligent Perioperative System: Towards Real-time Big Data Analytics in Surgery Risk Assessment

Zheng Feng, Rajendra Rana Bhat, Xiaoyong Yuan +4

Surgery risk assessment is an effective tool for physicians to manage the treatment of patients, but most current research projects fall short in providing a comprehensive platform…

Publications (30)

Moving finite unit tight frames for Sn

Shrinking Schauder Frames and their Associated Bases

Discretizing Lp​ norms and frame theory

Declipping and the recovery of vectors from saturated measurements

The cardinality of the sublattice of closed ideals of operators between certain classical sequence spaces

The Cahill-Casazza-Daubechies problem on HÃ¶lder stable phase retrieval

The stabilized set of p's in Krivine's theorem can be disconnected

The discretization problem for continuous frames

On sharp stable recovery from clipped and folded measurements

Weaving Schauder frames

Uniformly factoring weakly compact operators

Stable phase retrieval for infinite dimensional subspaces of L2​(R)

Blocks Assemble! Learning to Assemble with Large-Scale Structured Reinforcement Learning

Continuous Schauder frames for Banach spaces

Classes of operators determined by ordinal indices

A Schauder basis for L2​ consisting of non-negative functions

Locality and stability for phase retrieval

Multi-Game Decision Transformers

Barkour: Benchmarking Animal-level Agility with Quadruped Robots

Bi-Manual Manipulation and Attachment via Sim-to-Real Reinforcement Learning

The universality of ℓ1​ as a dual space

Quantitative bounds for unconditional pairs of frames

Stable phase retrieval and perturbations of frames

Weakly null sequences with upper estimates

Maximal inequalities, frames and greedy algorithms

Beyond the Imitation Game: Quantifying and extrapolating the capabilities of language models

Banach spaces for which the space of operators has 2c closed ideals

Upper and lower estimates for schauder frames and atomic decompositions

Optimal lower Lipschitz bounds for ReLU layers, saturation, and phase retrieval

Intelligent Perioperative System: Towards Real-time Big Data Analytics in Surgery Risk Assessment

Moving finite unit tight frames for $S^{n}$

Discretizing $L_{p}$ norms and frame theory

The stabilized set of $p$ 's in Krivine's theorem can be disconnected

Stable phase retrieval for infinite dimensional subspaces of $L_{2} (R)$

A Schauder basis for $L_{2}$ consisting of non-negative functions

The universality of $ℓ_{1}$ as a dual space

Banach spaces for which the space of operators has $2^{c}$ closed ideals