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Complex networks provide a powerful mathematical representation of complex systems in nature and society. To understand complex networks, it is crucial to explore their internal structures, also called structural regularities. The task of…
Discovering a suitable neural network architecture for modeling complex dynamical systems poses a formidable challenge, often involving extensive trial and error and navigation through a high-dimensional hyper-parameter space. In this…
Complex problem solving is a high level cognitive process which has been thoroughly studied over the last decade. The Tower of London (TOL) is a task that has been widely used to study problem-solving. In this study, we aim to explore the…
Recent advances demonstrate that irregularly wired neural networks from Neural Architecture Search (NAS) and Random Wiring can not only automate the design of deep neural networks but also emit models that outperform previous manual…
Uncovering latent community structure in complex networks is a field that has received an enormous amount of attention. Unfortunately, whilst potentially very powerful, unsupervised methods for uncovering labels based on topology alone has…
In this work, we developed new mathematical methods for analyzing network topology and applied these methods to the analysis of brain networks. More specifically, we rigorously developed quantitative methods based on complexes constructed…
Most complex systems can be captured by graphs or networks. Networks connect nodes (e.g.\ neurons) through edges (synapses), thus summarizing the system's structure. A popular way of interrogating graphs is community detection, which…
Deep phenotyping is an emerging conceptual paradigm and experimental approach that seeks to measure many aspects of phenotypes and link them to understand the underlying biology. Successful deep phenotyping has mostly been applied in…
Higher-order connectivity in complex systems described by simplexes of different orders provides a geometry for simplex-based dynamical variables and interactions. Simplicial complexes that constitute a functional geometry of the human…
In this study, we propose a novel deep learning-based method to predict an optimized structure for a given boundary condition and optimization setting without using any iterative scheme. For this purpose, first, using open-source topology…
Correlators of Wilson-line operators in non-abelian gauge theories are known to exponentiate, and their logarithms can be organised in terms of collections of Feynman diagrams called webs. In [1] we introduced the concept of Cweb, or…
Deep learning models are often considered black boxes due to their complex hierarchical transformations. Identifying suitable architectures is crucial for maximizing predictive performance with limited data. Understanding the geometric…
A fundamental property of complex networks is the tendency for edges to cluster. The extent of the clustering is typically quantified by the clustering coefficient, which is the probability that a length-2 path is closed, i.e., induces a…
In recent years numerous attempts to understand the human brain were undertaken from a network point of view. A network framework takes into account the relationships between the different parts of the system and enables to examine how…
Analyzing and understanding the structure of complex relational data is important in many applications including analysis of the connectivity in the human brain. Such networks can have prominent patterns on different scales, calling for a…
Network data has become widespread, larger, and more complex over the years. Traditional network data is dyadic, capturing the relations among pairs of entities. With the need to model interactions among more than two entities, significant…
The challenge of assigning importance to individual neurons in a network is of interest when interpreting deep learning models. In recent work, Dhamdhere et al. proposed Total Conductance, a "natural refinement of Integrated Gradients" for…
Synchronization plays a key role in information processing in neuronal networks. Response of specific groups of neurons are triggered by external stimuli, such as visual, tactile or olfactory inputs. Neurons, however, can be divided into…
In network science, the non-homogeneity of node degrees has been a concerned issue for study. Yet, with the modern web technologies today, the traditional social communication topologies have evolved from node-central structures to online…
In this paper, we consider the problem of exploring structural regularities of networks by dividing the nodes of a network into groups such that the members of each group have similar patterns of connections to other groups. Specifically,…