Related papers: Multilevel Contours on Bundles of Complex Planes
Contour detection has been a fundamental component in many image segmentation and object detection systems. Most previous work utilizes low-level features such as texture or saliency to detect contours and then use them as cues for a…
Invariants underlying shape inference are elusive: a variety of shapes can give rise to the same image, and a variety of images can be rendered from the same shape. The occluding contour is a rare exception: it has both image salience, in…
Any arrangement of hyperplanes in general position in $P^n$ can be regarded as a divisor with normal crossing. We study the bundles of logarithmic 1-forms corresponding to such divisors` from the point of view of classification of vector…
The aim of this work is to establish the existence of invariant manifolds in complex systems. Considering trajectory curves integral of multiple time scales dynamical systems of dimension two and three (predator-prey models, neuronal…
We present a novel, log-radius profile representation for convex curves and define a new operation for combining the shape features of curves. Unlike the standard, angle profile-based methods, this operation accurately combines the shape…
This paper is based on my talk at ICM on recent progress in a number of classical problems of linear algebra and representation theory, based on new approach, originated from geometry of stable bundles and geometric invariant theory.
The study of networks plays a crucial role in investigating the structure, dynamics, and function of a wide variety of complex systems in myriad disciplines. Despite the success of traditional network analysis, standard networks provide a…
Relationship between agents can be conveniently represented by graphs. When these relationships have different modalities, they are better modelled by multilayer graphs where each layer is associated with one modality. Such graphs arise…
Transports along path in fibre bundles are axiomatically introduced. Their general functional form and some their simple properties are investigated. The relationships of the transports along paths and lifting of paths are studied.
Real networks often form interacting parts of larger and more complex systems. Examples can be found in different domains, ranging from the Internet to structural and functional brain networks. Here, we show that these multiplex systems are…
Deep learning provides a versatile suite of methods for extracting structured information from complex datasets, enabling deeper understanding of underlying fluid dynamic phenomena. The field of turbulence modeling, in particular, benefits…
Multinets are certain configurations of lines and points with multiplicities in the complex projective plane $\mathbb{P}^2$. They appear in the study of resonance and characteristic varieties of complex hyperplane arrangement complements…
Complex network theory aims to model and analyze complex systems that consist of multiple and interdependent components. Among all studies on complex networks, topological structure analysis is of the most fundamental importance, as it…
Multilevel modeling and simulation (M&S) is becoming increasingly relevant due to the benefits that this methodology offers. Multilevel models allow users to describe a system at multiple levels of detail. From one side, this can make…
Multilayer networks represent systems in which there are several topological levels each one representing one kind of interaction or interdependency between the systems' elements. These networks have attracted a lot of attention recently…
As Physics did in previous centuries, there is currently a common dream of extracting generic laws of nature in economics, sociology, neuroscience, by focalising the description of phenomena to a minimal set of variables and parameters,…
Tangles, as introduced by Robertson and Seymour, were designed as an indirect way of capturing clusters in graphs and matroids. They have since been shown to capture clusters in much broader discrete structures too. But not all tangles are…
We demonstrate formation of hierarchical structures in two-dimensional systems with multiple length scales in the inter-particle interaction. These include states such as clusters of clusters, concentric rings, clusters inside a ring, and…
This paper studies a discrete dynamical system belonging to the class of the networks introduced by A.P.~Buslaev. The systems contains a finite set of contours. In any contour, there are cells and a group of particles. This group is called…
In the present note we describe geometrically the homology classes in the total space of a surface bundle over a surface in terms of the holonomy map. We treat the cases where the base surface is closed or has one boundary component. We…