Deep Separable Hypercomplex Networks

Hypercomplex Geometry

Hypercomplex Liquid Crystals

Hypercomplex fluids are amalgamations of polymers, colloids, or amphiphilic molecules that exhibit emergent properties not observed in elemental systems alone. Especially promising buildingblocks for assembly of hypercomplex materials are molecules with anisotropic shape. Alone, these molecules form numerous liquid crystalline phases with symmetries and properties that are fundamentally differe...

Linear Algebra Approach to Separable Bayesian Networks

Separable Bayesian Networks, or the Influence Model, are dynamic Bayesian Networks in which the conditional probability distribution can be separated into a function of only the marginal distribution of a node’s parents, instead of the joint distributions. We describe the connection between an arbitrary Conditional Probability Table (CPT) and separable systems using linear algebra. We give an a...

Tail Asymptotics for Monotone-separable Networks

A network belongs to the monotone separable class if its state variables are homogeneous and monotone functions of the epochs of the arrival process. This framework contains several classical queueingnetworkmodels, includinggeneralized Jacksonnetworks,maxplus networks, polling systems, multiserver queues, and various classes of stochastic Petri nets. We use comparison relationships between netw...

Detecting Overlapping Communities in Social Networks using Deep Learning

In network analysis, a community is typically considered of as a group of nodes with a great density of edges among themselves and a low density of edges relative to other network parts. Detecting a community structure is important in any network analysis task, especially for revealing patterns between specified nodes. There is a variety of approaches presented in the literature for overlapping...