Tootfinder

An inverse problem on a metric graph with cycle
Sergei Avdonin, Julian Edward
https://arxiv.org/abs/2508.10121 https://arxiv.org/pdf/2508.10121

An inverse problem on a metric graph with cycle
Consider a quantum graph consisting of a ring with two attached edges, and assume Kirchhoff-Neumann conditions hold at the internal vertices. Associated to this graph is a Schrödinger type operator $L=-Δ+q(x)$ with Dirichlet boundary conditions at the two boundary nodes. Let $\{ ω_n^2, \ φ_n(x)\}$ be the eigenvalues and associated normalized eigenfunctions. Let $v_1$ be a boundary vertex, and $v_2$ the adjacent internal vertex. Assume we know the following data: $\{ ω_n^2,\partial_x φ_n(v…

How to Be Accountable to Yourself and Why It Matters
#integrity #MentalHealth

How to Be Accountable to Yourself and Why It Matters
What if the promises you make to yourself mattered just as much as the ones you make to others? Self-accountability starts with knowing your line and following through.

Distinguishing Curve Types and Designer Metrics
Ara Basmajian, Sayantika Mondal
https://arxiv.org/abs/2508.08539 https://arxiv.org/pdf/2508.08539

Distinguishing Curve Types and Designer Metrics
Let $γ$ be a filling curve on a topological surface $Σ$ of genus $g \geq 2$. The inf invariant of $γ$, denoted $m_γ$, is the infimum of the length function on the space of marked hyperbolic structures on $Σ$. This infimum is realized at a unique hyperbolic structure, $X_γ$, which we call the optimal metric associated to $γ$. In this paper, we investigate properties of the inf invariant and its associated optimal metric. Starting from a filling curve and a separating curve, we construct a…

Total/dual correlation/coherence, redundancy/synergy, complexity, and O-information for real and complex valued multivariate data
Roberto D. Pascual-Marqui, Kieko Kochi, Toshihiko Kinoshita
https://arxiv.org/abs/2507.08773

Total/dual correlation/coherence, redundancy/synergy, complexity, and O-information for real and complex valued multivariate data
Firstly, assuming Gaussianity, equations for the following information theory measures are presented: total correlation/coherence (TC), dual total correlation/coherence (DTC), O-information, TSE complexity, and the redundancy-synergy index (RSI). Since these measures are functions of the covariance matrix "S" and its inverse "S^-1", the associated Wishart and inverse-Wishart distributions are of note. The DTC is shown here to be the Kullback-Leibler (KL) divergence for the inverse-Wishart pair …

Null geodesics, causal structure, and matter accretion in Lorentzian-Euclidean black holes
Salvatore Capozziello, Emmanuele Battista, Silvia De Bianchi
https://arxiv.org/abs/2507.08431

Null geodesics, causal structure, and matter accretion in Lorentzian-Euclidean black holes
Recently, we introduced the Lorentzian-Euclidean black hole, a static and spherically symmetric solution of vacuum Einstein equations that exhibits a change in metric signature across the event horizon. In this framework, the analysis of radial trajectories of freely falling bodies proves that the central singularity can be avoided via a mechanism we interpret as atemporality, which is responsible for the shift of the time variable from real to imaginary values. In this paper, we further expl…

Nice to see Michael Hansmeyer still following his dreams: The White Tower was finally revealed 2 weeks ago, currently the largest 3D printed structure in the world (30 meters [90ft] tall), located in a small village in Switzerland:
https://www.michael-hansmeyer.com/white-tower

Tor Alva | White Tower - Project Overview
Tor Alva, White Tower, Weisser Turm in Mulegns, Switzerland, Origen Foundation

OdysseyBench: Evaluating LLM Agents on Long-Horizon Complex Office Application Workflows
Weixuan Wang, Dongge Han, Daniel Madrigal Diaz, Jin Xu, Victor R\"uhle, Saravan Rajmohan
https://arxiv.org/abs/2508.09124

OdysseyBench: Evaluating LLM Agents on Long-Horizon Complex Office Application Workflows
Autonomous agents powered by large language models (LLMs) are increasingly deployed in real-world applications requiring complex, long-horizon workflows. However, existing benchmarks predominantly focus on atomic tasks that are self-contained and independent, failing to capture the long-term contextual dependencies and multi-interaction coordination required in realistic scenarios. To address this gap, we introduce OdysseyBench, a comprehensive benchmark for evaluating LLM agents on long-horizo…

Analysis: Mail Online is among major news brands most-impacted by Google's AI Overviews, with 68.8% of the top 100 keyword searches resulting in no site visits (Charlotte Tobitt/Press Gazette)
https://press…

How Google AI Overviews is fuelling zero-click searches for top publishers
New Similarweb data shows likes of Mail Online and People see high proportion of AI Overviews for their key search terms.

On Chaos in QFT
Jacob Sonnenschein, Nadav Shrayer
https://arxiv.org/abs/2506.10784 https://arxiv.org/pdf/2506.10784

On Chaos in QFT
In this note we explore the chaotic behavior of non-integrable QFTs and compare them to integrable ones. We choose as prototypes the double sine-Gordon and the sine-Gordon models. We analyze their discrete spectrum determined by a truncation method. We examine the map of the corresponding energy eigenvalues to the eigenvalues of the random matrix theory (RMT) Gaussian orthogonal ensemble (GOE). This is done by computing the following properties: (a) The distribution of the adjacent spacings and…

> Two years ago, the Flemish Roads Agency (AWV) announced the introduction of the new system: via an app on your smartphone, you can get a traffic light to turn green more quickly.
https://www.vrt.be/vrtnws/en/2025/07/24/200-000-flemish…