Combinatorial necklace splitting

We give a new, combinatorial proof for the necklace splitting problem for two thieves using only Tucker's lemma (a combinatorial version of the Borsuk-Ulam theorem). We show how this method can be applied to obtain a related recent result of Simonyi and even generalize it.

Efficient Continual Finite-Sum Minimization

Volkan Cevher, Efstratios Panteleimon Skoulakis, Leello Tadesse Dadi

Given a sequence of functions

f_1,\ldots,f_n

with

f_i:\mathcal{D}\mapsto \mathbb{R}

, finite-sum minimization seeks a point

{x}^\star \in \mathcal{D}

minimizing

\sum_{j=1}^nf_j(x)/n

. In this work, we propose a key twist into the finite-sum minimizat ...

2024

Combinatorial necklace splitting

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SIMPLE HIERARCHICAL PLANNING WITH DIFFUSION

Micropreparative Gel Electrophoresis for Purification of Nanoscale Bioconjugates

Efficient Continual Finite-Sum Minimization

SIMPLE HIERARCHICAL PLANNING WITH DIFFUSION

Micropreparative Gel Electrophoresis for Purification of Nanoscale Bioconjugates

Efficient Continual Finite-Sum Minimization