New testable hypothesis: This result enables the hypothesis that "low-degree polynomial threshold functions can reliably distinguish between noisy random lifts and uniform random graphs in protein-protein interaction networks (e.g., Huntington’s disease condensate graphs), with performance scaling predictably in the degree of the polynomial and noise level."

Adversarial Debate Score

40% survival rate under critique

Supporting Research Papers

• Analysis of Polynomial Threshold Functions on Random Regular Graphs: Computational Complexity of Detecting Noisy Random Lift

  In this work, we present the first analysis of low degree polynomial threshold functions for the natural hypothesis testing problem of detecting the noisy random lift of a base d-regular graph from a ...

• Universality in random graphs via optimal linking systems: trees and beyond

  We develop a framework for proving universality results in sparse random graphs. As a first application, we show that there exists an absolute constant C>1 such that, with high probability, for every ...

• Adjacency Spectral Radius Under Laplacian Sparsification: Deterministic and Probabilistic Bounds

  Spielman-Srivastava spectral sparsification preserves Laplacian quadratic forms to within (1 +/- epsilon), but does not directly control the adjacency spectral radius lambda_1, which governs the NIMFA...

• Tight Hamilton Cycles in Linearly Quasirandom 3-Graphs

  We study tight Hamilton cycles in linearly quasirandom 3-graphs. An n-vertex 3-graph H is (p,\mu)-dense if e_H(X,Y,Z)\ge p|X||Y||Z|-\mu n^3 for all X,Y,Z\subseteq V(H). Ara{\'u}jo, Piga and Schacht as...

• Binary Hypothesis Testing: A Robust Framework Against the Look Elsewhere Effect

  In particle physics, discovery claims conventionally require an observed significance exceeding 5σ. However, the interpretation of a 5σ result depends critically on the testing procedure, namely wheth...

Formal Verification

Source