From the 1 of 6 linked papers with an AI index.
6 papers
On the Number of Real Zeros of Random Sparse Polynomial Systems
Alperen A. Ergür, Máté L. Telek, Josué Tonelli-Cueto
The paper derives an upper bound on the expected number of positive real solutions of a random sparse polynomial system, showing it depends only on the number of terms per polynomi…
Almost Orthogonal Arrays: Search Three Ways
Luis MartÃnez, MarÃa Merino, Juan Manuel Montoya +1
Orthogonal arrays play a fundamental role in many applications. However, constructing orthogonal arrays with the required parameters for an application usually is extremely difficu…
Tensor learning with orthogonal, Lorentz, and symplectic symmetries
Wilson G. Gregory, Josué Tonelli-Cueto, Nicholas F. Marshall +2
Tensors are a fundamental data structure for many scientific contexts, such as time series analysis, materials science, and physics, among many others. Improving our ability to pro…
Beyond Worst-Case Analysis for Symbolic Computation: Root Isolation Algorithms
Alperen A. Ergür, Josué Tonelli-Cueto, Elias Tsigaridas
We introduce beyond-worst-case analysis into symbolic computation. This is an extensive field which almost entirely relies on worst-case bit complexity, and we start from a basic p…
Is uniform expressivity too restrictive? Towards efficient expressivity of graph neural networks
Sammy Khalife, Josué Tonelli-Cueto
Uniform expressivity guarantees that a Graph Neural Network (GNN) can express a query without the parameters depending on the size of the input graphs. This property is desirable i…
Some Lower Bounds on the Reach of an Algebraic Variety
Chris La Valle, Josué Tonelli-Cueto
Separation bounds are a fundamental measure of the complexity of solving a zero-dimensional system as it measures how difficult it is to separate its zeroes. In the positive dimens…