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Causal relations among neuronal populations of the brain are studied through the so-called effective connectivity (EC) network. The latter is estimated from EEG or fMRI measurements, by inverting a generative model of the corresponding…
Contemporary neuroscience has embraced network science to study the complex and self-organized structure of the human brain; one of the main outstanding issues is that of inferring from measure data, chiefly functional Magnetic Resonance…
The degree distributions of complex networks are usually considered to be power law. However, it is not the case for a large number of them. We thus propose a new model able to build random growing networks with (almost) any wanted degree…
Detailed network models of social, biological and other complex systems are often dense, which increases their computational complexity in simulations and analysis. To address this challenge, graph sparsification is used to remove edges…
It has been experimentally observed in recent years that multi-layer artificial neural networks have a surprising ability to generalize, even when trained with far more parameters than observations. Is there a theoretical basis for this?…
The brain can be considered as a system that dynamically optimizes the structure of anatomical connections based on the efficiency requirements of functional connectivity. To illustrate the power of this principle in organizing the…
Along with the rapid development of deep learning in practice, the theoretical explanations for its success become urgent. Generalization and expressivity are two widely used measurements to quantify theoretical behaviors of deep learning.…
We consider a quasi two-dimensional network connection growth model that minimizes the wiring cost while maximizing the network connections, but at the same time edge crossings are penalized or forbidden. This model is mapped to a dilute…
Motivated by results of Henry, Pralat and Zhang (PNAS 108.21 (2011): 8605-8610), we propose a general scheme for evolving spatial networks in order to reduce their total edge lengths. We study the properties of the equilbria of two networks…
This work establishes a framework of near-field communication under different array geometries of extremely large-scale multiple-input multiple-output (XL-MIMO). We first formulate the near-field spatial non-stationary channel model which…
Querying uncertain data sets (represented as probability distributions) presents many challenges due to the large amount of data involved and the difficulties comparing uncertainty between distributions. The Earth Mover's Distance (EMD) has…
The increasing access to brain signal data using electroencephalography creates new opportunities to study electrophysiological brain activity and perform ambulatory diagnoses of neuronal diseases. This work proposes a pairwise distance…
Estimating the Generalization Error (GE) of Deep Neural Networks (DNNs) is an important task that often relies on availability of held-out data. The ability to better predict GE based on a single training set may yield overarching DNN…
Biological membranes are one of the most basic structures and regions of interest in cell biology. In the study of membranes, segment extraction is a well-known and difficult problem because of impeding noise, directional and thickness…
Networks are mathematical structures that are universally used to describe a large variety of complex systems such as the brain or the Internet. Characterizing the geometrical properties of these networks has become increasingly relevant…
Alzheimer's Disease is a progressive neurological disorder that is one of the most common forms of dementia. It leads to a decline in memory, reasoning ability, and behavior, especially in older people. The cause of Alzheimer's Disease is…
A great possible achievement for the MMS mission would be crossing electron diffusion regions (EDR). EDR are regions in proximity of reconnection sites where electrons decouple from field lines, breaking the frozen in condition. Decades of…
The Exponential-family Random Graph Model (ERGM) is a powerful model to fit networks with complex structures. However, for dynamic valued networks whose observations are matrices of counts that evolve over time, the development of the ERGM…
Detecting the dimensionality of graphs is a central topic in machine learning. While the problem has been tackled empirically as well as theoretically, existing methods have several drawbacks. On the one hand, empirical tools are…
A new modelling approach for the analysis of weighted networks with ordinal/polytomous dyadic values is introduced. Specifically, it is proposed to model the weighted network connectivity structure using a hierarchical multilayer…