44 citations · 165 across the 21 of their papers we have counts for
24 papers
Global Convergence of Hessenberg Shifted QR II: Numerical Stability
Jess Banks, Jorge Garza-Vargas, Nikhil Srivastava
We develop a framework for proving rapid convergence of shifted QR algorithms which use Ritz values as shifts, in finite arithmetic. Our key contribution is a dichotomy result whic…
Global Convergence of Hessenberg Shifted QR III: Approximate Ritz Values via Shifted Inverse Iteration
Jess Banks, Jorge Garza-Vargas, Nikhil Srivastava
We give a self-contained randomized algorithm based on shifted inverse iteration which provably computes the eigenvalues of an arbitrary matrix up to b…
Point Spectrum of Periodic Operators on Universal Covering Trees
Jess Banks, Jorge Garza-Vargas, Satyaki Mukherjee
For any multi-graph with edge weights and vertex potential, and its universal covering tree , we completely characterize the point spectrum of operators $A_{\mathc…
Spectral Planting and the Hardness of Refuting Cuts, Colorability, and Communities in Random Graphs
Afonso S. Bandeira, Jess Banks, Dmitriy Kunisky +2
We study the problem of efficiently refuting the k-colorability of a graph, or equivalently certifying a lower bound on its chromatic number. We give formal evidence of average-cas…
Overlaps, Eigenvalue Gaps, and Pseudospectrum under real Ginibre and Absolutely Continuous Perturbations
Jess Banks, Jorge Garza Vargas, Archit Kulkarni +1
Let be an matrix with real i.i.d. entries, let be a real matrix with , and let . We show that with p…
Local Statistics, Semidefinite Programming, and Community Detection
Jess Banks, Sidhanth Mohanty, Prasad Raghavendra
We propose a new hierarchy of semidefinite programming relaxations for inference problems. As test cases, we consider the problem of community detection in block models. The vertic…
Vector Colorings of Random, Ramanujan, and Large-Girth Irregular Graphs
Jess Banks, Luca Trevisan
We prove that in sparse Erdős-Rényi graphs of average degree , the vector chromatic number (the relaxation of chromatic number coming from the Lovàsz theta function) is typicall…
Gaussian Regularization of the Pseudospectrum and Davies' Conjecture
Jess Banks, Archit Kulkarni, Satyaki Mukherjee +1
A matrix is diagonalizable if it has a basis of linearly independent eigenvectors. Since the set of nondiagonalizable matrices has measure zero, every…
The Lovász Theta Function for Random Regular Graphs and Community Detection in the Hard Regime
Jess Banks, Robert Kleinberg, Cristopher Moore
We derive upper and lower bounds on the degree for which the Lovász function, or equivalently sum-of-squares proofs with degree two, can refute the existence of a $…
Phase transitions and optimal algorithms in high-dimensional Gaussian mixture clustering
Thibault Lesieur, Caterina De Bacco, Jess Banks +3
We consider the problem of Gaussian mixture clustering in the high-dimensional limit where the data consists of points in dimensions, and …
Information-theoretic thresholds for community detection in sparse networks
Jess Banks, Cristopher Moore, Joe Neeman +1
We give upper and lower bounds on the information-theoretic threshold for community detection in the stochastic block model. Specifically, consider the symmetric stochastic block m…
Information-theoretic bounds and phase transitions in clustering, sparse PCA, and submatrix localization
Jess Banks, Cristopher Moore, Nicolas Verzelen +2
We study the problem of detecting a structured, low-rank signal matrix corrupted with additive Gaussian noise. This includes clustering in a Gaussian mixture model, sparse PCA, and…
The quasi-isomorphism class of the Kakimizu complex
Jessica E. Banks
It has been shown that the Kakimizu complex of a knot is quasi-isomorphic to for some . We give a lower bound on , matching the upper bound previously g…
Information-theoretic thresholds for community detection in sparse networks
Jess Banks, Cristopher Moore
We give upper and lower bounds on the information-theoretic threshold for community detection in the stochastic block model. Specifically, let be the number of groups, be t…
Genus and fibredness of certain three-bridge links
Jessica E. Banks
For each three-bridge link of a certain form, we construct a taut Seifert surface for the link and establish whether the link is fibred. Using this, we also give the genus and fibr…
The Birman exact sequence for 3-manifolds
Jessica E. Banks
We study the Birman exact sequence for compact --manifolds, obtaining a complete picture of the relationship between the mapping class group of the manifold and the mapping clas…
Monodromy action on unknotting tunnels in fiber surfaces
Jessica E. Banks, Matt Rathbun
In "Tunnel one, fibered links", the second author showed that the tunnel of a tunnel number one, fibered link can be isotoped to lie as a properly embedded arc in the fiber surface…
Point-pushing in 3-manifolds
Jessica E. Banks
We study the Birman exact sequence for compact 3-manifolds.
Knots with many minimal genus Seifert surfaces
Jessica E. Banks
Roberts proved that a family of alternating, arborescent, prime knots each have at least distinct minimal genus Seifert surfaces, where is the genus of the knot in q…
The Kakimizu complex of a split link
Jessica E. Banks
We study the Kakimizu complex of a split link. As part of this, we also study Seifert surfaces and the Kakimizu complex for a non-split link in a 3-ball. In addition, we show that…
The Kakimizu complex of a connected sum of links
Jessica E. Banks
We show that $|MS(L_1 # L_2)|=|MS(L_1)|\times|MS(L_2)|\times\mathbb{R}$ when and are any non-split and non-fibred links. Here denotes the Kakimizu complex of a…
Minimal genus Seifert surfaces for alternating links
Jessica E. Banks
We give a complete proof of results announced by Hirasawa and Sakuma describing explicitly the Kakimizu complex of a non-split, prime, special, alternating link.
Homogeneous links, Seifert surfaces, digraphs and the reduced Alexander polynomial
Jessica E. Banks
We give a geometric proof of the following result of Juhasz. \emph{Let be the leading coefficient of the Alexander polynomial of an alternating knot . If then $K…
On links with locally infinite {K}akimizu complexes
Jessica E. Banks
We show that the Kakimizu complex of a knot may be locally infinite, answering a question of Przytycki--Schultens. We then prove that if a link only has connected Seifert surfa…