Related papers: Delayed Pattern Formation in Two-Dimensional Domai…
State space models (SSMs) have shown remarkable empirical performance on many long sequence modeling tasks, but a theoretical understanding of these models is still lacking. In this work, we study the learning dynamics of linear SSMs to…
Enhancement of the predictive power and robustness of nonlinear population dynamics models allows ecologists to make more reliable forecasts about species' long term survival. However, the limited availability of detailed ecological data,…
This paper considers the problem of learning, from samples, the dependency structure of a system of linear stochastic differential equations, when some of the variables are latent. In particular, we observe the time evolution of some…
Capturing high-level structure in audio waveforms is challenging because a single second of audio spans tens of thousands of timesteps. While long-range dependencies are difficult to model directly in the time domain, we show that they can…
Symmetry breaking spatial patterns, referred to as chimera states, have recently been catapulted into the limelight due to their coexisting coherent and incoherent hybrid dynamics. Here, we present a method to engineer a chimera state by…
Swarms of coupled mobile agents subject to inter-agent wireless communication delays are known to exhibit multiple dynamic patterns in space that depend on the strength of the interactions and the magnitude of the communication delays. We…
The phenomenon of delay-induced resonance implies that in a nonlinear system a time-delay term may be used as an effective enhancer of the oscillations caused by an external forcing maintaining the same frequency. This is possible for the…
Dynamical systems with long delay feedback can exhibit complicated temporal phenomena, which once re-organized in a two-dimensional space are reminiscent of spatio-temporal behavior. In this framework, normal forms description have been…
Swarms of large numbers of agents appear in many biological and engineering fields. Dynamic bi-stability of co-existing spatio-temporal patterns has been observed in many models of large population swarms. However, many reduced models for…
Practically, training diffusion models typically requires explicit time conditioning to guide the network through the denoising sampling process. Especially in deterministic methods like DDIM, the absence of time conditioning leads to…
Domain adaptation on time series data is an important but challenging task. Most of the existing works in this area are based on the learning of the domain-invariant representation of the data with the help of restrictions like MMD.…
Reaction--diffusion mechanism are a robust paradigm that can be used to represent many biological and physical phenomena over multiple spatial scales. Applications include intracellular dynamics, the migration of cells and the patterns…
Genetically engineered bacteria to increase the tumbling frequency of the run-and-tumble motion for the higher local bacterial density form visible stripe pattern composed of successive high and low density regions on an agar plate. We…
This paper studies the effects of a time-delayed feedback control on the appearance and development of spatiotemporal patterns in a reaction-diffusion system. Different types of control schemes are investigated, including single-species,…
Throughout developmental biology and ecology, transport can be driven by nonlocal interactions. Examples include cells that migrate based on contact with pseudopodia extended from other cells, and animals that move based on their vision of…
Many complex structures and stochastic patterns emerge from simple kinetic rules and local interactions, and are governed by scale invariance properties in combination with effects of the global geometry. We consider systems that can be…
A model of pattern formation in living systems is presented. The pattern is achieved by the sequential interaction of two signaling pathways. The coupling of the pattern to the (thick) epithelial sheet changes is given, when the Gauss…
A nonlinear time-delay model is proposed to describe the interaction dynamics between criminal and non-criminal populations, combining social influence mechanisms, saturation effects represented by a Holling type II functional response, and…
Owing to the influence of real-world networks both in science and society, numerous mathematical models have been developed to understand the structure and evolution of these systems, particularly in a temporal context. Recent advancements…
Fourier analysis has been an instrumental tool in the development of signal processing. This leads us to wonder whether this framework could similarly benefit generative modelling. In this paper, we explore this question through the scope…