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The paper uses statistical and differential geometric motivation to acquire prior information about the learning capability of an artificial neural network on a given dataset. The paper considers a broad class of neural networks with…

Genetic regulation is a key component in development, but a clear understanding of the structure and dynamics of genetic networks is not yet at hand. In this paper we investigate these properties within an artificial genome model originally…

Bayesian network models (Erdos Renyi, stochastic block models, random dot product graphs, graphons) are widely used in neuroscience, epidemiology, and the social sciences, yet real networks are sparse, heterogeneous, and exhibit…

Now that Bayesian Networks (BNs) have become widely used, an appreciation is developing of just how critical an awareness of the sensitivity and robustness of certain target variables are to changes in the model. When time resources are…

Complex numbers define the relationship between entities in many situations. A canonical example would be the off-diagonal terms in a Hamiltonian matrix in quantum physics. Recent years have seen an increasing interest to extend the tools…

The need to build a link between the structure of a complex network and the dynamical properties of the corresponding complex system (comprised of multiple low dimensional systems) has recently become apparent. Several attempts to tackle…

Residual Network (ResNet) is the state-of-the-art architecture that realizes successful training of really deep neural network. It is also known that good weight initialization of neural network avoids problem of vanishing/exploding…

The Residual Network (ResNet), proposed in He et al. (2015), utilized shortcut connections to significantly reduce the difficulty of training, which resulted in great performance boosts in terms of both training and generalization error. It…

Neural networks have been successfully used for classification tasks in a rapidly growing number of practical applications. Despite their popularity and widespread use, there are still many aspects of training and classification that are…

Upper bounds are derived on the total variation distance between the invariant distributions of two stochastic matrices differing on a subset W of rows. Such bounds depend on three parameters: the mixing time and the minimal expected…

Neural networks achieve outstanding accuracy in classification and regression tasks. However, understanding their behavior still remains an open challenge that requires questions to be addressed on the robustness, explainability and…

The evolution processes of complex systems carry key information in the systems' functional properties. Applying machine learning algorithms, we demonstrate that the historical formation process of various networked complex systems can be…

Random network models play a prominent role in modeling, analyzing and understanding complex phenomena on real-life networks. However, a key property of networks is often neglected: many real-world networks exhibit spatial structure, the…

The exponential growth in scale and relevance of social networks enable them to provide expansive insights. Predicting missing links in social networks efficiently can help in various modern-day business applications ranging from generating…

One of the most challenging and long-standing problems in computational biology is the prediction of three-dimensional protein structure from amino acid sequence. A promising approach to infer spatial proximity between residues is the study…

The accurate prediction of biological features from genomic data is paramount for precision medicine and sustainable agriculture. For decades, neural network models have been widely popular in fields like computer vision, astrophysics and…

Dynamical patterns in complex networks of coupled oscillators are both of theoretical and practical interest, yet to fully reveal and understand the interplay between pattern emergence and network structure remains to be an outstanding…

Networks are widely used to model the interaction between individual dynamical systems. In many instances, the total number of units as well as the interaction coupling are not fixed in time, but rather constantly evolve. In terms of…

Learning-based methods for inverse problems, adapting to the data's inherent structure, have become ubiquitous in the last decade. Besides empirical investigations of their often remarkable performance, an increasing number of works…

In the Fourth Industrial Revolution, wherein artificial intelligence and the automation of machines occupy a central role, the deployment of robots is indispensable. However, the manufacturing process using robots, especially in…