Tootfinder

Complexity of Coexistence Regions in the GRHT Map
Sishu Shankar Muni
https://arxiv.org/abs/2506.13515 https://arxiv.org/pdf/2506.1351…

Complexity of Coexistence Regions in the GRHT Map
GRHT map refers to a planar map which showcases the coexistence of infinitely many stable periodic orbits via the phenomenon of Globally Resonant Homoclinic Tangencies. This paper investigates the geometric properties of coexistence regions in the case of codimension-three scenario. We introduce parameters into the non-invertible GRHT map to understand the unfolding behavior of the GRHT. Near the infinite coexistence regions, there exists series of codimension-one saddle-node and period-doublin…

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
@…

Nonlocal invariance of the multipotentialisations of the Kupershmidt equation and its higher-order hierarchies
Marianna Euler, Norbert Euler
https://arxiv.org/abs/2506.07780

Nonlocal invariance of the multipotentialisations of the Kupershmidt equation and its higher-order hierarchies
The term multipotentialisation of evolution equations in $1+1$ dimensions refers to the process of potentialising a given evolution equation, followed by at least one further potentialisation of the resulting potential equation. For certain equations this process can be applied several times to result in a finite chain of potential equations, where each equation in the chain is a potential equation of the previous equation. By a potentialisation of an equation with dependent variable $u$ to an …

Flow-Lenia: Emergent evolutionary dynamics in mass conservative continuous cellular automata
Erwan Plantec, Gautier Hamon, Mayalen Etcheverry, Bert Wang-Chak Chan, Pierre-Yves Oudeyer, Cl\'ement Moulin-Frier
https://arxiv.org/abs/2506.08569

Flow-Lenia: Emergent evolutionary dynamics in mass conservative continuous cellular automata
Central to the artificial life endeavour is the creation of artificial systems spontaneously generating properties found in the living world such as autopoiesis, self-replication, evolution and open-endedness. While numerous models and paradigms have been proposed, cellular automata (CA) have taken a very important place in the field notably as they enable the study of phenomenons like self-reproduction and autopoiesis. Continuous CA like Lenia have been showed to produce life-like patterns rem…

Elementary Cellular Automata as Non-Cryptographic Hash Functions
Daniel McKinley
https://arxiv.org/abs/2506.06551 https://arxiv.org/p…

Elementary Cellular Automata as Non-Cryptographic Hash Functions
A subset of 10 of the 256 elementary cellular automata (ECA) are implemented as a hash function using an error minimization lossy compression algorithm operating on wrapped 4x4 neighborhood cells. All 256 rules are processed and 10 rules in two subsets of 8 are found to have properties that include both error minimization and maximization, unique solutions, a lossy inverse, efficient retroactive hashing, and an application to edge detection. The algorithm parallels the nested powers-of-two stru…

The Lie -Bianchi integrability of the full symmetric Toda system
Yury B. Chernyakov, Georgy I. Sharygin, Dmitry V. Talalaev
https://arxiv.org/abs/2506.07113

The Lie -Bianchi integrability of the full symmetric Toda system
In this paper we prove that the full symmetric Toda system is integrable in the sense of the Lie-Bianchi criterion, i.e. that there exists a solvable Lie algebra of vector fields of dimension $N=\dim M$ on the phase space $M$ of this system such that the system is invariant with respect to the action of these fields. The proof is based on the use of symmetries of the full symmetric system, which we described earlier in \cite{CSS23}, and the appearance of the structure of the stochastic Lie alge…

A State of the Art on Recent Progress and Emerging Challenges on Energy Transfer Between Vibrating Modes Under an External Mechanical Force With Time-Varying Frequency From 2020 to 2025
Jose Manoel Balthazar, Jorge Luis Palacios Felix, Mauricio A. Ribeiro, Angelo Marcelo Tusset, Jeferson Jose de Lima, Vinicius Piccirillo, Julijana Simonovic, Nikola D. Nevsic, Marcos Varanis, Clivaldo de Oliveira, Raphaela C. Machado, Gabriella O M Oliveira

A State of the Art on Recent Progress and Emerging Challenges on Energy Transfer Between Vibrating Modes Under an External Mechanical Force With Time-Varying Frequency From 2020 to 2025
In this paper, we discuss an example of current importance with a future perspective in engineering, in which excitation sources always have limited power, limited inertia, and their frequencies vary according to the instantaneous state of the vibrating system. Practical examples of non-ideal systems are considered. The most common phenomenon for this kind of system is discussed. The period considered is from 2020 to 2025. The specific properties of various models are also discussed. Directions…

On novel Hamiltonian description of the nonholonomic Suslov problem
A. V. Tsiganov
https://arxiv.org/abs/2505.19594 https://arxiv.org…

On novel Hamiltonian description of the nonholonomic Suslov problem
We present some new Poisson bivectors that are invariants by the flow of the nonholonomic Suslov problem. Two rank four invariant Poisson bivectors have globally defined Casimir functions and, therefore, define cubic Poisson brackets on the five dimensional state space with standard symplectic leaves. For the Suslov gyrostat in the potential field we found rank two Poisson bivectors having only two globally defined Casimir functions and, therefore, we say about formal Hamiltonian description in…

Quantisation ideals, canonical parametrisations of the unipotent group and consistent integrable systems
M. A. Chirkov, A. V. Mikhailov, D. V. Talalaev
https://arxiv.org/abs/2505.20253

Quantisation ideals, canonical parametrisations of the unipotent group and consistent integrable systems
Using the methods of quantisation ideals, we construct a family of quantisations corresponding to Case alpha in Sergeev's classification of solutions to the tetrahedron equation. This solution describes transformations between special parametrisations of the space of unipotent matrices with noncommutative coefficients. We analyse the classical limit of this family and construct a pencil of compatible Poisson brackets that remain invariant under the re-parametrisation maps (mutations). This deco…

Symmetry breaking in time-dependent billiards
Anne K\'etri Pasquinelli da Fonseca, Edson Denis Leonel
https://arxiv.org/abs/2505.20488 https://

Symmetry breaking in time-dependent billiards
We investigate symmetry breaking in a time-dependent billiard that undergoes a continuous phase transition when dissipation is introduced. The system presents unlimited velocity, and thus energy growth for the conservative dynamics. When inelastic collisions are introduced between the particle and the boundary, the velocity reaches a plateau after the crossover iteration. The system presents the expected behavior for this type of transition, including scale invariance, critical exponents relate…