Tootfinder

Adaptive Divide and Conquer with Two Rounds of Communication
Niladri Kal, Botond Szab\'o, Rajarshi Guhaniyogi, Natesh Pillai, Debdeep Pati
https://arxiv.org/abs/2508.17073 h…

Adaptive Divide and Conquer with Two Rounds of Communication
We introduce a two-round adaptive communication strategy that enables rate-optimal estimation in the white noise model without requiring prior knowledge of the underlying smoothness. In the first round, local machines send summary statistics using $(\log_2(n))^2$ bits to enable the central machine to select the tuning parameters of the procedure. In the second round, another set of statistics are transmitted using optimal number of bits, enabling the central machine to aggregate and produce a f…

Complexity Analysis of the Regular Simplicial Search Method with Reflection and Shrinking Steps for Derivative-Free Optimization
Liyuan Cao, Wei Hu, Jinxin Wang
https://arxiv.org/abs/2508.16561

Complexity Analysis of the Regular Simplicial Search Method with Reflection and Shrinking Steps for Derivative-Free Optimization
Simplex-type methods, such as the well-known Nelder-Mead algorithm, are widely used in derivative-free optimization (DFO), particularly in practice. Despite their popularity, the theoretical understanding of their convergence properties has been limited, and until very recently essentially no worst-case complexity bounds were available. Recently, Cao et al. provided a sharp error bound for linear interpolation and extrapolation and derived a worst-case complexity result for a basic simplex-type…

hBN alignment orientation controls moir\'e strength in rhombohedral graphene
Matan Uzan, Weifeng Zhi, Matan Bocarsly, Junkai Dong, Surajit Dutta, Nadav Auerbach, Niladri Sekhar Kander, Mikhail Labendik, Yuri Myasoedov, Martin E. Huber, Kenji Watanabe, Takashi Taniguchi, Daniel E. Parker, Eli Zeldov
https://arxiv.org/abs/2507.20647

hBN alignment orientation controls moiré strength in rhombohedral graphene
Rhombohedral multilayer graphene hosts a rich landscape of correlated symmetry-broken phases, driven by strong interactions from its flat band edges. Aligning to hexagonal boron nitride (hBN) creates a moiré pattern, leading to recent observations of exotic ground states such as integer and fractional quantum anomalous Hall effects. Here, we show that the moiré effects and resulting correlated phase diagrams are critically influenced by a previously underestimated structural choice: the hBN a…