Related papers: Localized Patterns
Complex textured surfaces occur in nature and industry, from fingerprints to lithography-based micropatterns. Wrinkling by confinement to an incompatible substrate is an attractive way of generating reconfigurable patterned topographies,…
Recent work on the behaviour of localised states in pattern forming partial differential equations has focused on the traditional model Swift-Hohenberg equation which, as a result of its simplicity, has additional structure --- it is…
The area of research called \textquotedblleft Lineability\textquotedblright% \ looks for linear structures inside exotic subsets of vector spaces. In the last decade lineability/spaceability has been investigated in rather general settings;…
This report addresses state inference for hidden Markov models. These models rely on unobserved states, which often have a meaningful interpretation. This makes it necessary to develop diagnostic tools for quantification of state…
Many natural shapes have most of their characterizing features concentrated over a few regions in space. For example, humans and animals have distinctive head shapes, while inorganic objects like chairs and airplanes are made of…
Contextual adaptation in token embeddings plays a central role in determining how well language models maintain coherence and retain semantic relationships over extended text sequences. Static embeddings often impose constraints on lexical…
We consider the design of a pattern recognition that matches templates to images, both of which are spatially sampled and encoded as temporal sequences. The image is subject to a combination of various perturbations. These include ones that…
Mechanisms of pattern formation---of which the Turing instability is an archetype---constitute an important class of dynamical processes occurring in biological, ecological and chemical systems. Recently, it has been shown that the Turing…
We report a new mechanism for the formation of localized states, which takes place without front propagation. Correspondingly, localized structures appear as solitary states, displaying a behavior of single independent cells. The phenomenon…
Solitons in the fractional space, supported by lattice potentials, have recently attracted much interest. We consider the limit of deep one- and two-dimensional (1D and 2D) lattices in this system, featuring finite bandgaps separated by…
We propose a new non-equilibrium model for spatial pattern formation on the basis of local information transfer. Unlike standard models of pattern formation it is not based on the Turing instability. Information is transmitted through the…
Long-lived flow patterns in the atmosphere such as weather fronts, mid-latitude blockings or tropical cyclones often induce extreme weather conditions. As a consequence, their description, detection, and tracking has received increasing…
Transformer models underpin many recent advances in practical machine learning applications, yet understanding their internal behavior continues to elude researchers. Given the size and complexity of these models, forming a comprehensive…
Latent space is rapidly emerging as a native substrate for language-based models. While modern systems are still commonly understood through explicit token-level generation, an increasing body of work shows that many critical internal…
Spatio-temporal pattern formation over the square and rectangular domain has received significant attention from researchers. A wide range of stationary and non-stationary patterns produced by two interacting populations is abundant in the…
Deep networks realize complex mappings that are often understood by their locally linear behavior at or around points of interest. For example, we use the derivative of the mapping with respect to its inputs for sensitivity analysis, or to…
We present a new latent model of natural images that can be learned on large-scale datasets. The learning process provides a latent embedding for every image in the training dataset, as well as a deep convolutional network that maps the…
The response of dynamical systems to varying conditions and disturbances is a fundamental aspect of their analysis. In spatially extended systems, particularly in pattern-forming systems, there are many possible responses, including…
Coherence is a fundamental notion in quantum mechanics, defined relative to a reference basis. As such, it does not necessarily reveal the locality of interactions nor takes into account the accessible operations in a composite quantum…
We develop a machine learning method for mapping data originating from both Standard Model processes and various theories beyond the Standard Model into a unified representation (latent) space while conserving information about the…