Tootfinder

NYTimes makes a good point (giftlink ): A.I. Has a Measurement Problem
A.I. Has a Measurement Problem https://www.nytimes.com/2024/04/15/technology/ai-models-measurement.html?unlocked_article_code=1.kk0.oMBm.397…

A.I. Has a Measurement Problem
Which A.I. system writes the best computer code or generates the most realistic image? Right now, there’s no easy way to answer those questions.

#GiftLink 🎁
Takeaways From Day 2 of the Fani Willis Hearing in the Georgia Trump Case - The New York Times
https://www.

Takeaways From Day 2 of the Fani Willis Hearing in the Georgia Trump Case
In questioning a key witness, defense lawyers failed to undercut assertions by the prosecutors whom they are trying to get disqualified from the election interference case.

Every subcubic graph is packing $(1,1,2,2,3)$-colorable
Xujun Liu, Xin Zhang, Yanting Zhang
https://arxiv.org/abs/2404.09337 https://…

Every subcubic graph is packing $(1,1,2,2,3)$-colorable
For a sequence $S=(s_1, \ldots, s_k)$ of non-decreasing integers, a packing $S$-coloring of a graph $G$ is a partition of its vertex set $V(G)$ into $V_1, \ldots, V_k$ such that for every pair of distinct vertices $u,v \in V_i$, where $1 \le i \le k$, the distance between $u$ and $v$ is at least $s_i+1$. The packing chromatic number, $χ_p(G)$, of a graph $G$ is the smallest integer $k$ such that $G$ has a packing $(1,2, \ldots, k)$-coloring. Gastineau and Togni asked an open question ``Is it t…

This https://arxiv.org/abs/2403.12168 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On primitive element of finite k-algebras and applications to commuting matrices
Using the properties of the ideal of the coordinate Hermite interpolation on n-dimensional grid [4], we prove that the extension k in k[x1, x2, ..., xn] / (f1(x1), ..., fn(xn)) has a primitive element if and only if at most one of the univariate polynomials f1, ..., fn is inseparable. This result lead to some Corollaries related to the existence of primitive element of finite k-algebras. Finally, these results are further used to investigate the well known Frobenius question, whether two commut…

This https://arxiv.org/abs/2306.09852 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csRO_…

Actor-Critic Model Predictive Control
An open research question in robotics is how to combine the benefits of model-free reinforcement learning (RL) - known for its strong task performance and flexibility in optimizing general reward formulations - with the robustness and online replanning capabilities of model predictive control (MPC). This paper provides an answer by introducing a new framework called Actor-Critic Model Predictive Control. The key idea is to embed a differentiable MPC within an actor-critic RL framework. The prop…

Testing CCC TL Cosmology with Observed Baryon Acoustic Oscillation Features - IOPscience
“There are several papers that question the existence of dark matter, but mine is the first one, to my knowledge, that eliminates its cosmological existence while being consistent with key cosmological observations that we have had time to confirm.” — Rajendra P. Gupta

This https://arxiv.org/abs/2403.04643 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csCL_…

QAQ: Quality Adaptive Quantization for LLM KV Cache
The emergence of LLMs has ignited a fresh surge of breakthroughs in NLP applications, particularly in domains such as question-answering systems and text generation. As the need for longer context grows, a significant bottleneck in model deployment emerges due to the linear expansion of the Key-Value (KV) cache with the context length. Existing methods primarily rely on various hypotheses, such as sorting the KV cache based on attention scores for replacement or eviction, to compress the KV cac…

This https://arxiv.org/abs/2111.05698 has been replaced.
link: https://scholar.google.com/scholar?q=a

Mutually unbiased bases: polynomial optimization and symmetry
A set of $k$ orthonormal bases of $\mathbb C^d$ is called mutually unbiased if $|\langle e,f\rangle |^2 = 1/d$ whenever $e$ and $f$ are basis vectors in distinct bases. A natural question is for which pairs $(d,k)$ there exist~$k$ mutually unbiased bases in dimension $d$. The (well-known) upper bound $k \leq d+1$ is attained when~$d$ is a power of a prime. For all other dimensions it is an open problem whether the bound can be attained. Navascués, Pironio, and Acín showed how to ref…

Integers that are not the sum of positive powers
Brennan Benfield, Oliver Lippard
https://arxiv.org/abs/2404.08193 https://arxiv.org/…

Integers that are not the sum of positive powers
Exactly which positive integers cannot be expressed as the sum of $j$ positive $k$-th powers? This paper utilizes theoretical and computational techniques to answer this question for $k\leq9$. Results from Waring's problem are used throughout to catalogue the sets of such integers. These sets are then considered in a general setting, and several curious properties are established.

This https://arxiv.org/abs/2111.05698 has been replaced.
link: https://scholar.google.com/scholar?q=a

Mutually unbiased bases: polynomial optimization and symmetry
A set of $k$ orthonormal bases of $\mathbb C^d$ is called mutually unbiased if $|\langle e,f\rangle |^2 = 1/d$ whenever $e$ and $f$ are basis vectors in distinct bases. A natural question is for which pairs $(d,k)$ there exist~$k$ mutually unbiased bases in dimension $d$. The (well-known) upper bound $k \leq d+1$ is attained when~$d$ is a power of a prime. For all other dimensions it is an open problem whether the bound can be attained. Navascués, Pironio, and Acín showed how to ref…