Related papers: Localized Patterns
Complex networks are frequently employed to model physical or virtual complex systems. When certain entities exist across multiple systems simultaneously, unveiling their corresponding relationships across the networks becomes crucial. This…
We propose a new method for quantitative characterization of spatial network-like patterns with loops, such as surface fracture patterns, leaf vein networks and patterns of urban streets. Such patterns are not well characterized by purely…
We study numerically interaction of spatially localized modes in strongly scattering two-dimensional media. We move eigenvalues in the complex plane by changing gradually the index of a single scatterer. When spatial and spectral overlap is…
While modern deep networks have demonstrated remarkable versatility, their training dynamics remain poorly understood--often driven more by empirical tweaks than architectural insight. This paper investigates how internal structural choices…
Since many real world networks are evolving over time, such as social networks and user-item networks, there are increasing research efforts on dynamic network embedding in recent years. They learn node representations from a sequence of…
Convolutional Neural Networks (CNN) possess many positive qualities when it comes to spatial raster data. Translation invariance enables CNNs to detect features regardless of their position in the scene. However, in some domains, like…
Chaotic evolution of structures in Coupled map lattice driven by identical noise on each site is studied (a structure is a group of neighbouring lattice-sites for whom values of dynamical variable follow certain predefined pattern). Number…
Unsupervised feature learning often finds low-dimensional embeddings that capture the structure of complex data. For tasks for which prior expert topological knowledge is available, incorporating this into the learned representation may…
Shells, when confined, can deform in a broad assortment of shapes and patterns, often quite dissimilar to what is produced by their flat counterparts (plates). In this work we discuss the morphological landscape of shells deposited on a…
Many physical systems are well described on domains which are relatively large in some directions but relatively thin in other directions. In this scenario we typically expect the system to have emergent structures that vary slowly over the…
Spatio-temporal network dynamics is an emergent property of many complex systems which remains poorly understood. We suggest a new approach to its study based on the analysis of dynamical motifs -- small subnetworks with periodic and…
Deep learning based localization and mapping approaches have recently emerged as a new research direction and receive significant attentions from both industry and academia. Instead of creating hand-designed algorithms based on physical…
The existence and stability of localized patterns of criminal activity are studied for the reaction-diffusion model of urban crime that was introduced by Short et. al. [Math. Models. Meth. Appl. Sci., 18, Suppl. (2008), pp. 1249--1267].…
Hyperuniformity, the suppression of density fluctuations at large length scales, is observed across a wide variety of domains, from cosmology to condensed matter and biological systems. Although the standard definition of hyperuniformity…
Latent variable models are used to estimate variables of interest quantities which are observable only up to some measurement error. In many studies, such variables are known but not precisely quantifiable (such as "job satisfaction" in…
Language models exhibit strong robustness to paraphrasing, suggesting that semantic information may be encoded through stable internal representations, yet the structure and origin of such invariance remain unclear. We propose a local…
The understanding of emergent collective phenomena in natural and social systems has driven the interest of scientists from different disciplines during decades. Among these phenomena, the synchronization of a set of interacting individuals…
Token prediction stability remains a challenge in autoregressive generative models, where minor variations in early inference steps often lead to significant semantic drift over extended sequences. A structured modulation mechanism was…
Pattern formation in clouds is a well-known feature, which can be observed almost every day. However, the guiding processes for structure formation are mostly unknown, and also theoretical investigations of cloud patterns are quite rare.…
Nonlinear dynamical stochastic models are ubiquitous in different areas. Excitable media models are typical examples with large state dimensions. Their statistical properties are often of great interest but are also very challenging to…