Research
Research
Research
Research
204+ open-access research outputs.
We design the Arboretum$.$hs package for symbolic computations with algebras of trees and more general graphs in Haskell. Thanks to the declarative nature of functional programming, the package's impl…
We introduce SignatureTensors.jl, a new package for computing signature tensors of paths in julia. We present its core functionality and demonstrate its use through illustrative examples. The package …
This paper studies how post-quantum cryptographic (PQC) security assumptions can be represented and communicated through a structured, layered framework that is useful for technical interpretation but…
StreamSampling$.$jl is a Julia library designed to provide general and efficient methods for sampling from data streams in a single pass, even when the total number of items is unknown. In this paper,…
This paper presents a symmetric stream cipher that utilizes the dynamic properties of random cubic mappings in the complex plane to generate pseudo-random key streams. The system is based on the itera…
Portable GPU frameworks such as Kokkos and RAJA reduce the burden of cross-architecture development but typically incur measurable overhead on fundamental parallel primitives relative to vendor-optimi…
LLM agents are increasingly used for code generation, but physics-based simulation poses a deeper challenge: natural-language descriptions of simulation models are inherently underspecified, and diffe…
Binary convolutional coding (BCC) has been a cornerstone of the IEEE 802.11 wireless LAN standard since its inception, and it remains relevant today across the full generational arc from the legacy 80…
The complexity quasi-metric of Schellekens is a topological framework in which the asymmetry of computational comparisons -- ``$A$ is at most as fast as $B$'' carrying different information than ``$B$…
The Weyl closure is a basic operation in algebraic analysis: it converts a system of differential operators with rational coefficients into an equivalent system with polynomial coefficients. In additi…
Multi-robot coordination often exhibits hierarchical structure, with some robots' decisions depending on the planned behaviors of others. While game theory provides a principled framework for such int…
The Fast Fourier Transform (FFT) is a fundamental numerical technique with widespread application in a range of scientific problems. As scientific simulations attempt to exploit exascale systems, ther…
Symmetric linear solves are fundamental to a wide range of scientific and engineering applications, from climate modeling and structural analysis to machine learning and optimization. These workloads …
We introduce monomial divisibility diagrams (MDDs), a data structure for monomial ideals that supports insertion of new generators and fast membership tests. MDDs stem from a canonical tree representa…
L-systems are a mathematical formalism proposed by biologist Aristid Lindenmayer with the aim of simulating organic structures such as trees, snowflakes, flowers, and other branching phenomena. They a…
With the push towards Exascale computing and data-driven methods, problem sizes have increased dramatically, increasing the computational requirements of the underlying algorithms. This has led to a p…
Complex computational problems in science often consist of smaller parts that can have largely distinct compute requirements from one another. For optimal efficiency, analyzing each subtask and schedu…
Program synthesis -- the automatic generation of code given a specification -- is one of the most fundamental tasks in artificial intelligence (AI) and the dream of many programmers. Numerous synthesi…
Symbolic computation systems suffer from memory inefficiencies due to redundant storage of structurally identical subexpressions, commonly known as expression swell, which degrades performance in both…
In 2011, einsum was introduced to NumPy as a practical and convenient notation for tensor expressions in machine learning, quantum circuit simulation, and other fields. It has since been implemented i…
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