Tootfinder

This https://arxiv.org/abs/2308.00060 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_nli…

An Invitation to Number-Conserving Cellular Automata
Number-conserving cellular automata are discrete dynamical systems that simulate interacting particles like e.g. grains of sand. In an earlier paper, I had already derived a uniform construction for all transition rules of one-dimensional number-conserving automata. Here I describe in greater detail how one can simulate the automata on a computer and how to find interesting rules. I show several rules that I have found this way and also some theorems about the space of number-conserving automat…

High-Dimensional Regularized Additive Matrix Autoregressive Model
Debika Ghosh, Samrat Roy, Nilanjana Chakraborty
https://arxiv.org/abs/2506.01403 https://…

High-Dimensional Regularized Additive Matrix Autoregressive Model
High-dimensional time series has diverse applications in econometrics and finance. Recent models for capturing temporal dependence have employed a bilinear representation for matrix time series, or the Tucker-decomposition based representation in case of tensor time series. A bilinear or Tucker-decomposition based temporal effect is difficult to interpret on many occasions, along with its computational complexity due to the non-convex nature of the underlying optimization problem. Moreover, the…

Last week, we continued our #ISE2025 lecture on distributional semantics with the introduction of neural language models (NLMs) and compared them to traditional statistical n-gram models.
Benefits of NLMs:
- Capturing Long-Range Dependencies
- Computational and Statistical Tractability
- Improved Generalisation
- Higher Accuracy
@…

This https://arxiv.org/abs/2505.20572 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_nli…

Conserved Quantities in the Lorenz System
The Lorenz system, a seminal model in chaos theory, is renowned for its complex dynamics and sensitive dependence on initial conditions. This work investigates conserved quantities within the standard Lorenz equations. The system exhibits phase space volume contraction, a characteristic of dissipative systems. Despite the common understanding suggesting an absence of conserved quantities in its typical chaotic parameter regimes, this study demonstrates that the Lorenz system possesses at least …

[2025-06-03 Tue (UTC), no new articles found for nlin.SI Exactly Solvable and Integrable Systems]
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[2025-05-02 Fri (UTC), no new articles found for nlin.CG Cellular Automata and Lattice Gases]
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[2025-05-02 Fri (UTC), no new articles found for nlin.CG Cellular Automata and Lattice Gases]
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[2025-06-02 Mon (UTC), no new articles found for nlin.CG Cellular Automata and Lattice Gases]
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This https://arxiv.org/abs/2406.15408 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_nli…

Effects of a Vanishing Noise on Elementary Cellular Automata Phase-Space Structure
We investigate elementary cellular automata (ECA) from the point of view of (discrete) dynamical systems. By studying small lattice sizes, we obtain the complete phase space of all minimal ECA, and, starting from a maximal entropy distribution (all configurations equiprobable), we show how the dynamics affects this distribution. We then investigate how a vanishing noise alters this phase space, connecting attractors and modifying the asymptotic probability distribution. What is interesting is t…

This https://arxiv.org/abs/2406.15408 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_nli…

Effects of a Vanishing Noise on Elementary Cellular Automata Phase-Space Structure
We investigate elementary cellular automata (ECA) from the point of view of (discrete) dynamical systems. By studying small lattice sizes, we obtain the complete phase space of all minimal ECA, and, starting from a maximal entropy distribution (all configurations equiprobable), we show how the dynamics affects this distribution. We then investigate how a vanishing noise alters this phase space, connecting attractors and modifying the asymptotic probability distribution. What is interesting is t…