Low-dimensional embeddings are a cornerstone in the modelling and analysis of complex networks. However, most existing approaches for mining network embedding spaces rely on computationally intensive machine learning systems to facilitate downstream tasks. In the field of NLP, word embedding spaces capture semantic relationships \textit{linearly}, allowing for information retrieval using \textit{simple linear operations} on word embedding vectors. Here, we demonstrate that there are structural properties of network data that yields this linearity. We show that the more homophilic the network representation, the more linearly separable the corresponding network embedding space, yielding better downstream analysis results. Hence, we introduce novel graphlet-based methods enabling embedding of networks into more linearly separable spaces, allowing for their better mining. Our fundamental insights into the structure of network data that enable their \textit{\textbf{linear}} mining and exploitation enable the ML community to build upon, towards efficiently and explainably mining of the complex network data.

The paper studies the problem of memory storage with discrete (digital) synapses. Previous work established that memory capacity can be increased by adding a cascade of (latent) states but the optimal state transition dynamics was unknown and the actual dynamics was usually hand-picked using some heuristic rules. In this paper the authors aim to derive the optimal transition dynamics for synaptic cascades. They first derive an upper bound on achievable memory capacity and show that simple models with linear chain structures can approach (achieve) this bound. The paper is clear, high quality, generally well written and has a clear contribution to the field.

Brain function is made possible by an interconnected structure of neurons, glia and microvessels relying on exchange of information with one another as well as with the extracellular compartment. This communication engenders the phenomenon of the mind, frequently referred to as the mental trilogy: cognition (thinking), emotion (assigning value to stimuli), and motivation (setting and achieving goals) (1). In order to accomplish these tasks the brain utilizes over 100 billion cells and 600 km of microvessels (2) embedded in an extracellular matrix (ECM) of proteins, polysaccharides and interstitial fluid (ISF) (3). As we are getting well into the 21st century, it has become clearer that the mind is the product of the brain, just as the body movement is the product of the musculoskeletal system. With the same token, it is clearer and clearer that psychiatric disorders are disruptions of cellular or molecular communication in brain networks.