Related papers: Dimensionalities and multiplicities determination …
We introduce appropriate definitions of dimensions in order to characterize the fractal properties of complex networks. We compute these dimensions in a hierarchically structured network of particular interest. In spite of the nontrivial…
Dimensionality reduction is a common method for analyzing and visualizing high-dimensional data across domains. Dimensionality-reduction algorithms involve complex optimizations and the reduced dimensions computed by these algorithms…
Crystal structure prediction algorithms have become powerful tools for materials discovery in recent years, however, they are usually limited to relatively small systems. The main challenge is that the number of local minima grows…
We introduce the Computational 2D Materials Database (C2DB), which organises a variety of structural, thermodynamic, elastic, electronic, magnetic, and optical properties of around 1500 two-dimensional materials distributed over more than…
The fractal and self-similarity properties are revealed in many real complex networks. However, the classical information dimension of complex networks is not practical for real complex networks. In this paper, a new information dimension…
Many problems in science and engineering can be formulated in terms of geometric patterns in high-dimensional spaces. We present high-dimensional convolutional networks (ConvNets) for pattern recognition problems that arise in the context…
Representing various networked data as multiplex networks, networks of networks and other multilayer networks can reveal completely new types of structures in these system. We introduce a general and principled graphlet framework for…
For many graph-related problems, it can be essential to have a set of structurally diverse graphs. For instance, such graphs can be used for testing graph algorithms or their neural approximations. However, to the best of our knowledge, the…
This paper is part of a study whose goal is to show the effciency of using Bayes networks to carry out model based vision calculations. [Binford et al. 1987] Recognition proceeds by drawing up a network model from the object's geometric and…
It is difficult to quantify structure-property relationships and to identify structural features of complex materials. The characterization of amorphous materials is especially challenging because their lack of long-range order makes it…
The importance of structured, complex connectivity patterns found in several real-world systems is to a great extent related to their respective effects in constraining and even defining the respective dynamics. Yet, while complex networks…
Complex forms of quantum entanglement can arise in two qualitatively different ways; either between many qubits or between two particles with higher-than-qubit dimension. While the many-qubit frontier and the high-dimension frontier both…
Autonomous materials discovery with desired properties is one of the ultimate goals for materials science, and the current studies have been focusing mostly on high-throughput screening based on density functional theory calculations and…
Crystals arise as the result of the breaking of a spatial translation symmetry. Similarly, translation symmetries can also be broken in time so that discrete time crystals appear. Here, we introduce a method to describe, characterize, and…
The identification of materials with exceptional properties is an essential objective to enable technological progress. We propose the application of \textit{Quality-Diversity} algorithms to the field of crystal structure prediction. The…
Real-world datasets are often of high dimension and effected by the curse of dimensionality. This hinders their comprehensibility and interpretability. To reduce the complexity feature selection aims to identify features that are crucial to…
Private data analysis faces a significant challenge known as the curse of dimensionality, leading to increased costs. However, many datasets possess an inherent low-dimensional structure. For instance, during optimization via gradient…
Crystal structures can be viewed as assemblies of space-filling polyhedra, which play a critical role in determining material properties such as ionic conductivity and dielectric constant. However, most conventional crystal structure…
The ability to collect and analyze large amounts of data is a growing problem within the scientific community. The growing gap between data and users calls for innovative tools that address the challenges faced by big data volume, velocity…
Flat band systems are currently under intense investigation in quantum materials, optical lattices, and metamaterials. These efforts are motivated by potential realization of strongly correlated phenomena enabled by frustration-induced flat…