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The modelling of linear and nonlinear reaction-subdiffusion processes is more subtle than normal diffusion and causes different phenomena. The resulting equations feature a spatial Laplacian with a temporal memory term through a time…

Analysis of PDEs · Mathematics 2021-08-24 Jichen Yang , Jens D. M. Rademacher

Systems of dynamical interactions between competing species can be used to model many complex systems, and can be mathematically described by {\em random} networks. Understanding how patterns of activity arise in such systems is important…

Adaptation and Self-Organizing Systems · Physics 2016-01-21 Nick McCullen , Thomas Wagenknecht

Nonlinear instabilities are responsible for spontaneous pattern formation in a vast number of natural and engineered systems ranging from biology to galaxies build-up. We propose a new instability mechanism leading to pattern formation in…

Pattern Formation and Solitons · Physics 2016-01-20 A. M. Perego , N. Tarasov , D. V. Churkin , S. K. Turitsyn , K. Staliunas

Precise identification of parameters governing quantum processes is a critical task for quantum information and communication technologies. In this work we consider a setting where system evolution is determined by a parameterized…

Quantum Physics · Physics 2014-08-27 Jun Zhang , Mohan Sarovar

Reactive sputtering is a plasma-based technique to deposit a thin film on a substrate. This contribution presents a novel parameter-interval estimation method for a well-established model that describes the uncertain and nonlinear reactive…

Systems and Control · Electrical Eng. & Systems 2026-03-27 Fabian Schneider , Christian Wölfel

We consider the problem of learning a set from random samples. We show how relevant geometric and topological properties of a set can be studied analytically using concepts from the theory of reproducing kernel Hilbert spaces. A new kind of…

Machine Learning · Statistics 2014-11-26 Ernesto De Vito , Lorenzo Rosasco , Alessandro Toigo

This study introduces a low-complexity behavioural model to describe the dynamic response of railway turnouts due to the ballast and railpad components. The behavioural model should serve as the basis for the future development of a…

Systems and Control · Electrical Eng. & Systems 2019-10-16 Pegah Barkhordari , Roberto Galeazzi , Alejandro de Miguel Tejada , Ilmar F. Santos

Pattern separation is a computational process by which dissimilar neural patterns are generated from similar input patterns. We present an information-geometric formulation of pattern separation, where a pattern separator is modelled as a…

Neurons and Cognition · Quantitative Biology 2024-07-23 Harvey Wang , Selena Singh , Thomas Trappenberg , Abraham Nunes

Non-stationary systems are found throughout the world, from climate patterns under the influence of variation in carbon dioxide concentration, to brain dynamics driven by ascending neuromodulation. Accordingly, there is a need for methods…

Data Analysis, Statistics and Probability · Physics 2024-07-15 Kieran S. Owens , Ben D. Fulcher

In this paper, we introduce a novel concept for learning of the parameters in a neural network. Our idea is grounded on modeling a learning problem that addresses a trade-off between (i) satisfying local objectives at each node and (ii)…

Machine Learning · Computer Science 2019-02-04 Dimche Kostadinov , Behrooz Razdehi , Slava Voloshynovskiy

In their way to/from turbulence, plane wall-bounded flows display an interesting transitional regime where laminar and turbulent oblique bands alternate, the origin of which is still mysterious. In line with Barkley's recent work about the…

Fluid Dynamics · Physics 2015-06-05 Paul Manneville

Estimation of parameters in differential equation models can be achieved by applying learning algorithms to quantitative time-series data. However, sometimes it is only possible to measure qualitative changes of a system in response to a…

Machine Learning · Computer Science 2021-10-28 Gregory Szep , Neil Dalchau , Attila Csikasz-Nagy

Diffusion models generate structure by progressively transforming noise into data, yet the mechanisms underlying this transition remain poorly understood. In this work, we show that pattern formation in trained diffusion models can be…

Machine Learning · Computer Science 2026-04-29 Luca Ambrogioni

We propose a kind of reaction-diffusion equations for cell differentiation, which exhibits the Turing instability. If the diffusivity of some variables is set to be infinity, we get coupled competitive reaction-diffusion equations with a…

Cell Behavior · Quantitative Biology 2015-05-13 Hidetsugu Sakaguchi

Nature is a blossoming of regular structures, signature of self-organization of the underlying microscopic interacting agents. Turing theory of pattern formation is one of the most studied mechanisms to address such phenomena and has been…

Pattern Formation and Solitons · Physics 2025-10-22 Riccardo Muolo , Lorenzo Giambagli , Hiroya Nakao , Duccio Fanelli , Timoteo Carletti

Motivated by the prediction of cell loads in cellular networks, we formulate the following new, fundamental problem of statistical learning of geometric marks of point processes: An unknown marking function, depending on the geometry of…

Machine Learning · Computer Science 2019-06-19 Antoine Brochard , Bartłomiej Błaszczyszyn , Stéphane Mallat , Sixin Zhang

To accurately reproduce measurements from the real world, simulators need to have an adequate model of the physical system and require the parameters of the model be identified. We address the latter problem of estimating parameters through…

Robotics · Computer Science 2022-03-01 Eric Heiden , Christopher E. Denniston , David Millard , Fabio Ramos , Gaurav S. Sukhatme

The problem of Turing instabilities for a reaction-diffusion system defined on a complex Cartesian product networks is considered. To this end we operate in the linear regime and expand the time dependent perturbation on a basis formed by…

Statistical Mechanics · Physics 2014-12-23 Malbor Asllani , Daniel M. Busiello , Timoteo Carletti , Duccio Fanelli , Gwendoline Planchon

It is well known that building analytical performance models in practice is difficult because it requires a considerable degree of proficiency in the underlying mathematics. In this paper, we propose a machine-learning approach to derive…

Performance · Computer Science 2020-02-26 Giulio Garbi , Emilio Incerto , Mirco Tribastone

Consistency models, which were proposed to mitigate the high computational overhead during the sampling phase of diffusion models, facilitate single-step sampling while attaining state-of-the-art empirical performance. When integrated into…

Machine Learning · Statistics 2024-02-13 Gen Li , Zhihan Huang , Yuting Wei