Deep Divergence-Based Approach to Clustering

A promising direction in deep learning research consists in learning representations and simultaneously discovering cluster structure in unlabeled data by optimizing a discriminative loss function. As opposed to supervised deep learning, this line of research is in its infancy, and how to design and optimize suitable loss functions to train deep neural networks for clustering is still an open question. Our contribution to this emerging field is a new deep clustering network that leverages the discriminative power of information-theoretic divergence measures, which have been shown to be effective in traditional clustering. We propose a novel loss function that incorporates geometric regularization constraints, thus avoiding degenerate structures of the resulting clustering partition. Experiments on synthetic benchmarks and real datasets show that the proposed network achieves competitive performance with respect to other state-of-the-art methods, scales well to large datasets, and does not require pre-training steps

Block product density matrix embedding theory for strongly correlated spin systems

Density matrix embedding theory (DMET) is a relatively new technique for the calculation of strongly correlated systems. Recently, block product DMET (BPDMET) was introduced for the study of spin systems such as the antiferromagnetic $J_1 - J_2$ model on the square lattice. In this paper, we extend the variational Ansatz of BPDMET using spin-state optimization, yielding improved results. We apply the same techniques to the Kitaev-Heisenberg model on the honeycomb lattice, comparing the results when using several types of clusters. Energy profiles and correlation functions are investigated. A diagonalization in the tangent space of the variational approach yields information on the excited states and the corresponding spectral functions.Comment: 12 pages, 12 figure

Chronic infection: punctuated interpenetration and pathogen virulence

We apply an information dynamics formalism to the Levens and Lewontin vision of biological interpenetration between a 'cognitive condensation' including immune function embedded in social and cultural structure on the one hand, and an established, highly adaptive, parasite population on the other. We iterate the argument, beginning with direct interaction between cognitive condensation and pathogen, then extend the analysis to second order 'mutator' mechanisms inherent both to immune function and to certain forms of rapid pathogen antigenic variability. The methodology, based on the Large Deviations Program of applied probability, produces synergistic cognitive/adaptive 'learning plateaus' that represent stages of chronic infection, and, for human populations, is able to encompass the fundamental biological reality of culture omitted by other approaches. We conclude that, for 'evolution machine' pathogens like HIV and malaria, simplistic magic bullet 'medical' drug, vaccine, or behavior modification interventions which do not address the critical context of overall living and working conditions may constitute selection pressures triggering adaptations in life history strategy resulting in marked increase of pathogen virulenc