Tootfinder

Root Cause Analysis of Outliers in Unknown Cyclic Graphs
Daniela Schkoda, Dominik Janzing
https://arxiv.org/abs/2510.06995 https://arxiv.org/pdf/2510.06995…

Root Cause Analysis of Outliers in Unknown Cyclic Graphs
We study the propagation of outliers in cyclic causal graphs with linear structural equations, tracing them back to one or several "root cause" nodes. We show that it is possible to identify a short list of potential root causes provided that the perturbation is sufficiently strong and propagates according to the same structural equations as in the normal mode. This shortlist consists of the true root causes together with those of its parents lying on a cycle with the root cause. Notably, our m…

On Robustness of Consensus over Pseudo-Undirected Path Graphs
Abhinav Sinha, Dwaipayan Mukherjee, Shashi Ranjan Kumar
https://arxiv.org/abs/2509.20314 https://

On Robustness of Consensus over Pseudo-Undirected Path Graphs
Consensus over networked agents is typically studied using undirected or directed communication graphs. Undirected graphs enforce symmetry in information exchange, leading to convergence to the average of initial states, while directed graphs permit asymmetry but make consensus dependent on root nodes and their influence. Both paradigms impose inherent restrictions on achievable consensus values and network robustness. This paper introduces a theoretical framework for achieving consensus over a…

$TIME[t] \subseteq SPACE[O(\sqrt{t})]$ via Tree Height Compression
Logan Nye
https://arxiv.org/abs/2508.14831 https://arxiv.org/pdf/2508.14831

$TIME[t] \subseteq SPACE[O(\sqrt{t})]$ via Tree Height Compression
We prove a square-root space simulation for deterministic multitape Turing machines, showing $\TIME[t] \subseteq \SPACE[O(\sqrt{t})]$. The key step is a Height Compression Theorem that uniformly (and in logspace) reshapes the canonical left-deep succinct computation tree for a block-respecting run into a binary tree whose evaluation-stack depth along any DFS path is $O(\log T)$ for $T = \lceil t/b \rceil$, while preserving $O(b)$ work at leaves, $O(1)$ at internal nodes, and edges that are logs…

Quiver varieties and root multiplicities in rank 3
Patrick Chan, Peter Tingley
https://arxiv.org/abs/2508.04804 https://arxiv.org/pdf/2508.04804

Quiver varieties and root multiplicities in rank 3
Building on our previous work in rank two, we use quiver varieties to give a combinatorial upper bound on dimensions of certain imaginary root spaces for rank 3 symmetric Kac-Moody algebras. We describe an explicit method for extracting combinatorics when the Dynkin diagram is bipartite (i.e. two of the nodes are not connected). As in rank two we believe these bounds are quite tight and we give computational evidence to this effect, although there is more error in rank 3 than in rank 2.