Related papers: Nonlinear second-order dynamics describe labial co…
A fundamental challenge in the cognitive sciences is discovering the dynamics that govern behaviour. Take the example of spoken language, which is characterised by a highly variable and complex set of physical movements that map onto the…
In this paper, we derive an accelerated continuous-time formulation of Adam by modeling it as a second-order integro-differential dynamical system. We relate this inertial nonlocal model to an existing first-order nonlocal Adam flow through…
We consider a two-dimensional model of double-diffusive convection and its time discretisation using a second-order scheme which treat the nonlinear term explicitly (backward differentiation formula with a one-leg method). Uniform bounds on…
We study long-time dynamics of a class of abstract second order in time evolution equations in a Hilbert space with the damping term depending both on displacement and velocity. This damping represents the nonlinear strong dissipation…
We consider systems characterized by the presence of a rapidly oscillating force. A general method is presented for the construction of the effective action governing the large-scale nonlinear dynamics of such systems order by order in…
In autoregressive large language models (LLMs), temporal straightening offers an account of how the next-token prediction objective shapes representations. Models learn to progressively straighten the representational trajectory of input…
We analyze the relation between the concept of auxiliary variables and the Inverse problem of the calculus of variations to construct a Lagrangian from a given set of equations of motion. The problem of the construction of a consistent…
We study a class of nonlinear nonparametric inverse problems. Specifically, we propose a nonparametric estimator of the dynamics of a monotonically increasing trajectory defined on a finite time interval. Under suitable regularity…
Standard diffusion equation is based on Brownian motion of the dispersing species without considering persistence in the movement of the individuals. This description allows for the instantaneous spreading of the transported species over an…
This paper investigates how the dynamic articulatory model DYNARTmo accounts for articulatory tradeoffs between primary and secondary articulators, with a focus on lips-jaw and tongue-jaw coordination. While DYNARTmo does not implement full…
In the causal theory of relativistic dissipative fluid dynamics, there are conditions on the equation of state and other thermodynamic properties such as the second-order coefficients of a fluid that need to be satisfied to guarantee that…
While second language (L2) learners may acquire target syntactic word order, mapping this syntax onto appropriate prosodic structures remains a persistent challenge. This study investigates the fossilization and stability of the L2…
Nonlinear contraction theory is a comparatively recent dynamic control system design tool based on an exact differential analysis of convergence, in essence converting a nonlinear stability problem into a linear time-varying stability…
Grammatical forms are said to evolve via two main mechanisms. These are, respectively, the `descent' mechanism, where current forms can be seen to have descended (albeit with occasional modifications) from their roots in ancient languages,…
The control of speech can be modelled as a dynamical system in which articulators are driven toward target positions. These models are typically evaluated using fleshpoint data, such as electromagnetic articulography (EMA), but recent…
We investigate emergent dynamics due to non-reciprocity in the $\mathcal{O}(2)$ model. The lattice XY model, where non-reciprocity stems from vision cone like couplings, can be described by a continuum description in which non-reciprocity…
This paper considers the robustness of an uncertain nonlinear system along a finite-horizon trajectory. The uncertain system is modeled as a connection of a nonlinear system and a perturbation. The analysis relies on three ingredients.…
A non--linear diffusion equation is derived by taking into account hopping rates depending on the occupation of next neighbouring sites. There appears additonal repulsive and attractive forces leading to a changed local mobiltiy. The…
The stationary and highly non-stationary resonant dynamics of the harmonically forced pendulum are described in the framework of a semi-inverse procedure combined with the Limiting Phase Trajectory concept. This procedure, implying only…
A nonlinear nonlocal cochlear model of the transmission line type is studied in order to capture the multitone interactions and resulting tonal suppression effects. The model can serve as a module for voice signal processing, it is a one…