Related papers: Proximal Nerve Complexes. A Computational Topology…
A main result in this paper is the proof that proximal Delaunay triangulation regions are convex polygons. In addition, it is proved that every Delaunay triangulation region has a local Leader uniform topology.
Spectral clustering is known as a powerful technique in unsupervised data analysis. The vast majority of approaches to spectral clustering are driven by a single modality, leaving the rich information in multi-modal representations…
We introduce the notion of a special complex manifold: a complex manifold (M,J) with a flat torsionfree connection \nabla such that (\nabla J) is symmetric. A special symplectic manifold is then defined as a special complex manifold…
Covering-based rough set theory is an extension to classical rough set. The main purpose of this paper is to study covering rough sets from a topological point of view. The relationship among upper approximations based on topological spaces…
Starting from the working hypothesis that both physics and the corresponding mathematics have to be described by means of discrete concepts on the Planck scale, one of the many problems one has to face in this enterprise is to find the…
Structured meshes, composed of quadrilateral elements in 2D and hexahedral elements in 3D, are widely used in industrial applications and engineering simulations due to their regularity and superior accuracy in finite element analysis.…
The article is devoted to a structure of topological spaces related with topological quasigroups. Regular and complete spaces over topological quasigroups are studied. Separations and embeddings are also investigated for them. Their…
The effective receptive field of a fully convolutional neural network is an important consideration when designing an architecture, as it defines the portion of the input visible to each convolutional kernel. We propose a neural network…
In order to choose a neural network architecture that will be effective for a particular modeling problem, one must understand the limitations imposed by each of the potential options. These limitations are typically described in terms of…
Universal approximation theory offers a foundational framework to verify neural network expressiveness, enabling principled utilization in real-world applications. However, most existing theoretical constructions are established by…
Using the notion of contiguity of simplicial maps, we adapt Farber's topological complexity to the realm of simplicial complexes. We show that, for a finite simplicial complex $K$, our discretized concept recovers the topological complexity…
The paper surveys recent progress in understanding geometric, topological and combinatorial properties of large simplicial complexes, focusing mainly on ampleness, connectivity and universality. In the first part of the paper we concentrate…
Artificial neurons with arbitrarily complex internal structure are introduced. The neurons can be described in terms of a set of internal variables, a set activation functions which describe the time evolution of these variables and a set…
Complex networks can be used to represent and model an ample diversity of abstract and real-world systems and structures. A good deal of the research on these structures has focused on specific topological properties, including node degree,…
Understanding how biological neural networks carry out learning using spike-based local plasticity mechanisms can lead to the development of powerful, energy-efficient, and adaptive neuromorphic processing systems. A large number of…
A perturbative method is developed for calculating the effects of recurrent synaptic interactions between neurons embedded in a network. A series expansion is constructed that converges for networks with noisy membrane potential and weak…
Recent advances in machine learning have created increasing interest in solving visual computing problems using a class of coordinate-based neural networks that parametrize physical properties of scenes or objects across space and time.…
The complexity of a graph is the number of its labeled spanning trees. In this work complexity is studied in settings that admit regular graphs. An exact formula is established linking complexity of the complement of a regular graph to…
In this paper, we introduce a geometric structure called top, which is a trivialized bundle of plane pencils over a Riemannian 3-manifold, defined as the set of kernels of a circle of 1-forms (e.g. of contact and integrable forms) with…
Complex networks can be used to represent complex systems which originate in the real world. Here we study a transformation of these complex networks into simplicial complexes, where cliques represent the simplices of the complex. We extend…