Matrix theory is one of the most fundamental tools of mathematics and science, and a
number of classical books on matrix analysis have been written to explore this theory. As a …

The stability of ecological systems is a fundamental concept in ecology, which offers
profound insights into species coexistence, biodiversity, and community persistence. In this …

We develop new tools to study landscapes in nonconvex optimization. Given one
optimization problem, we pair it with another by smoothly parametrizing the domain. This is …

Signal processing over graphs has recently attracted significant attention for dealing with the
structured data. Normal graphs, however, only model pairwise relationships between nodes …

Conventional network data have largely focused on pairwise interactions between two
entities, yet multi-way interactions among multiple entities have been frequently observed in …

Graph signal processing (GSP) techniques are powerful tools that model complex
relationships within large datasets, being now used in a myriad of applications in different …

Field-guided parameterization methods have proven effective for quad meshing of surfaces;
these methods compute smooth cross fields to guide the meshing process and then …

We investigate the computational complexity of tensor rank, a concept that plays
fundamental role in different topics of modern applied mathematics. For tensors over any …

Inference for low-rank tensors-no need to debias Page 1 The Annals of Statistics 2022, Vol. 50,
No. 2, 1220–1245 https://doi.org/10.1214/21-AOS2146 © Institute of Mathematical Statistics …

In this paper, we study the power iteration algorithm for the asymmetric spiked tensor model,
as introduced in Richard and Montanari (2014). We give necessary and sufficient conditions …