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Topology of the spatial coherence function is considered in details. The phase singularity (coherence vortices) structures of coherence function are classified by Hopf index and Brouwer degree in topology. The coherence flux quantization…
We introduce a simple spherical model whose structural properties are similar to the ones generated by models with directional interactions, by employing a binary mixture of large and small hard spheres, with a square-well attraction acting…
In this paper, we address a way to reduce the total computational cost of meshless approximation by reducing the required stencil size through spatially varying computational node regularity. Rather than covering the entire domain with…
Spatial classification with limited feature observations has been a challenging problem in machine learning. The problem exists in applications where only a subset of sensors are deployed at certain spots or partial responses are collected…
Spatial networks, in which nodes and edges are embedded in space, play a vital role in the study of complex systems. For example, many social networks attach geo-location information to each user, allowing the study of not only topological…
In this article, a compliance minimisation scheme for designing spatially varying orthotropic porous structures is proposed. With the utilisation of conformal mapping, the porous structures here can be generated by two controlling field…
Spatial string tension is computed in finite temperature gluodynamics on asymmetric lattices in a spherical model approximation. Conditions of scaling behavior are specified. Discrepancies with a standard renormalisation procedure are…
Contemporary accelerator designs exhibit a high degree of spatial localization, wherein two-dimensional physical distance determines communication costs between processing elements. This situation presents considerable algorithmic…
As hydrodynamic simulations increase in scale and resolution, identifying structures with non-trivial geometries or regions of general interest becomes increasingly challenging. There is a growing need for algorithms that identify a variety…
We consider the problem of approximating a two-dimensional shape contour (or curve segment) using discrete assembly systems, which allow to build geometric structures based on limited sets of node and edge types subject to edge length and…
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…
Quantifying structural stress in transaction networks requires metrics that capture structural organization beyond transaction volume alone. In this work, we introduce the Inefficiency Metric, a deterministic indicator designed to…
This paper reports on ongoing research investigating more expressive approaches to spatial-temporal trajectory clustering. Spatial-temporal data is increasingly becoming universal as a result of widespread use of GPS and mobile devices,…
The topological complexity TC(X) is a numerical homotopy invariant of a topological space X which is motivated by robotics and is similar in spirit to the classical Lusternik-Schnirelmann category of X. Given a mechanical system with…
A complex system comprises multiple interacting entities whose interdependencies form a unified whole, exhibiting emergent behaviours not present in individual components. Examples include the human brain, living cells, soft matter, Earth's…
Knots are intricate structures that cannot be unambiguously distinguished with any single topological invariant. Momentum space knots, in particular, have been elusive due to their requisite finely tuned long-ranged hoppings. Even if…
This paper presents a novel and efficient method for characteristic mode decomposition in multi-structure systems. By leveraging the translation and rotation matrices of vector spherical wavefunctions, our approach enables the synthesis of…
A method to define the complex structure and separate the conformal mode is proposed for a surface constructed by two-dimensional dynamical triangulation. Applications are made for surfaces coupled to matter fields such as $n$ scalar fields…
Accurate modeling of gravitational interactions is fundamental to the analysis, prediction, and control of space systems. While the Newtonian point-mass approximation suffices for many preliminary studies, real celestial bodies exhibit…
The structural analysis of shape boundaries leads to the characterization of objects as well as to the understanding of shape properties. The literature on graphs and networks have contributed to the structural characterization of shapes…