Tootfinder

On the Spielman-Teng Conjecture
Ashwin Sah, Julian Sahasrabudhe, Mehtaab Sawhney
https://arxiv.org/abs/2405.20308 https://arxiv.org/p…

On the Spielman-Teng Conjecture
Let $M$ be an $n\times n$ matrix with iid subgaussian entries with mean $0$ and variance $1$ and let $σ_n(M)$ denote the least singular value of $M$. We prove that \[\mathbb{P}\big( σ_{n}(M) \leq \varepsilon n^{-1/2} \big) = (1+o(1)) \varepsilon + e^{-Ω(n)}\] for all $0 \leq \varepsilon \ll 1$. This resolves, up to a $1+o(1)$ factor, a seminal conjecture of Spielman and Teng.

I mentioned this on a Unix mail list, and Doug McIlroy replied.
https://mastodon.social/@mhoye/112615649865163136

@… don’t forget @…’s seminal blog post! https://

This https://arxiv.org/abs/2307.14168 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csLO_…

$\text{TT}^{\Box}_{\mathcal C}$: a Family of Extensional Type Theories with Effectful Realizers of Continuity
$\text{TT}^{\Box}_{\mathcal C}$ is a generic family of effectful, extensional type theories with a forcing interpretation parameterized by modalities. This paper identifies a subclass of $\text{TT}^{\Box}_{\mathcal C}$ theories that internally realizes continuity principles through stateful computations, such as reference cells. The principle of continuity is a seminal property that holds for a number of intuitionistic theories such as System T. Roughly speaking, it states that functions on rea…

This https://arxiv.org/abs/2311.04831 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csIT_…

Derivatives of entropy and the MMSE conjecture
We investigate the entropy $H(μ,t)$ of a probability measure $μ$ along the heat flow and more precisely we seek for closed algebraic representations of its derivatives. Provided that $μ$ admits moments of any order, it is indeed proved in [Guo et al., 2010] that $t\mapsto H(μ,t)$ is smooth, and in [Ledoux, 2016] that its derivatives at zero can be expressed into multivariate polynomials evaluated in the moments (or cumulants) of $μ$. In the seminal contribution \cite{Led}, these algebraic …

Some theoretical foundations for the design and analysis of randomized experiments
Lei Shi, Xinran Li
https://arxiv.org/abs/2406.10444 https://

Some theoretical foundations for the design and analysis of randomized experiments
Neyman[106]'s seminal work in 1923 has been a milestone in statistics over the century, which has motivated many fundamental statistical concepts and methodology. In this review, we delve into Neyman[106]'s groundbreaking contribution and offer technical insights into the design and analysis of randomized experiments. We shall review the basic setup of completely randomized experiments and the classical approaches for inferring the average treatment effects. We shall in particular review more e…

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The Sentinel of Vision and Eye Health 👀
Vitamin B2 stands as a lighthouse for eye health, proving instrumental in warding off cataracts and safeguarding against ocular diseases. A seminal study featured in the "American Journal of Clinical Nutrition" (2013) highlights how appropriate intake of Riboflavin markedly diminishes the risk of cataract formation. Serving as an antioxidant, it shields our eyes from the ravages of free radicals.

Prioritized-MVBA: A New Approach to Design an Optimal Asynchronous Byzantine Agreement Protocol
Nasit S Sony, Xianzhong Ding, Mukesh Singhal
https://arxiv.org/abs/2406.03739

Prioritized-MVBA: A New Approach to Design an Optimal Asynchronous Byzantine Agreement Protocol
The multi-valued byzantine agreement protocol (MVBA) in the authenticated setting has been widely used as a core to design atomic broadcast and fault-tolerant state machine replication protocols in asynchronous networks. Originating from the seminal work of Cachin et al. \cite{CACHIN01}, subsequent research endeavors have sought to optimize protocol efficiency in terms of communication complexity. Notable advancements following Cachin's contributions include: i) VABA \cite{BYZ17}, requiring mul…

PSMC: Provable and Scalable Algorithms for Motif Conductance Based Graph Clustering
Longlong Lin, Tao Jia, Zeli Wang, Jin Zhao, Rong-Hua Li
https://arxiv.org/abs/2406.07357

PSMC: Provable and Scalable Algorithms for Motif Conductance Based Graph Clustering
Higher-order graph clustering aims to partition the graph using frequently occurring subgraphs. Motif conductance is one of the most promising higher-order graph clustering models due to its strong interpretability. However, existing motif conductance based graph clustering algorithms are mainly limited by a seminal two-stage reweighting computing framework, needing to enumerate all motif instances to obtain an edge-weighted graph for partitioning. However, such a framework has two-fold vital d…

This https://arxiv.org/abs/2312.08077 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csGT_…

Auctions and mass transportation
In this survey paper we present classical and recent results relating the auction design and the optimal transportation theory. In particular, we discuss in details the seminal result of Daskalakis, Deckelbaum and Tzamos \cite{DDT} about duality between auction design with $1$ bidder and the weak transportation problem. Later investigations revealed the connection of multi-bidder case to the Beckmann's transportation problem. In this paper we overview a number of works on related subjects (mono…