Hierarchy of Gene Expression Data is Predictive of Future Breast Cancer Outcome

We calculate measures of hierarchy in gene and tissue networks of breast cancer patients. We find that the likelihood of metastasis in the future is correlated with increased values of network hierarchy for expression networks of cancer-associated genes, due to correlated expression of cancer-specific pathways. Conversely, future metastasis and quick relapse times are negatively correlated with values of network hierarchy in the expression network of all genes, due to dedifferentiation of gene pathways and circuits. These results suggest that hierarchy of gene expression may be useful as an additional biomarker for breast cancer prognosis.Comment: 14 pages, 5 figure

Network hierarchy evolution and system vulnerability in power grids

(c) 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.The seldom addressed network hierarchy property and its relationship with vulnerability analysis for power transmission grids from a complex-systems point of view are given in this paper. We analyze and compare the evolution of network hierarchy for the dynamic vulnerability evaluation of four different power transmission grids of real cases. Several meaningful results suggest that the vulnerability of power grids can be assessed by means of a network hierarchy evolution analysis. First, the network hierarchy evolution may be used as a novel measurement to quantify the robustness of power grids. Second, an antipyramidal structure appears in the most robust network when quantifying cascading failures by the proposed hierarchy metric. Furthermore, the analysis results are also validated and proved by empirical reliability data. We show that our proposed hierarchy evolution analysis methodology could be used to assess the vulnerability of power grids or even other networks from a complex-systems point of view.Peer ReviewedPostprint (author's final draft

A hierarchy of topological tensor network states

We present a hierarchy of quantum many-body states among which many examples of topological order can be identified by construction. We define these states in terms of a general, basis-independent framework of tensor networks based on the algebraic setting of finite-dimensional Hopf C*-algebras. At the top of the hierarchy we identify ground states of new topological lattice models extending Kitaev's quantum double models [26]. For these states we exhibit the mechanism responsible for their non-zero topological entanglement entropy by constructing a renormalization group flow. Furthermore it is shown that those states of the hierarchy associated with Kitaev's original quantum double models are related to each other by the condensation of topological charges. We conjecture that charge condensation is the physical mechanism underlying the hierarchy in general.Comment: 61 page

CAROLINE LEVINE. Forms: Whole, Rhythm, Hierarchy, Network

Review of English Studies 66 (2015), 1001-

Hierarchy and Polysynchrony in an adaptive network

We describe a simple adaptive network of coupled chaotic maps. The network reaches a stationary state (frozen topology) for all values of the coupling parameter, although the dynamics of the maps at the nodes of the network can be non-trivial. The structure of the network shows interesting hierarchical properties and in certain parameter regions the dynamics is polysynchronous: nodes can be divided in differently synchronized classes but contrary to cluster synchronization, nodes in the same class need not be connected to each other. These complicated synchrony patterns have been conjectured to play roles in systems biology and circuits. The adaptive system we study describes ways whereby this behaviour can evolve from undifferentiated nodes.Comment: 13 pages, 17 figure

From neural PCA to deep unsupervised learning

A network supporting deep unsupervised learning is presented. The network is an autoencoder with lateral shortcut connections from the encoder to decoder at each level of the hierarchy. The lateral shortcut connections allow the higher levels of the hierarchy to focus on abstract invariant features. While standard autoencoders are analogous to latent variable models with a single layer of stochastic variables, the proposed network is analogous to hierarchical latent variables models. Learning combines denoising autoencoder and denoising sources separation frameworks. Each layer of the network contributes to the cost function a term which measures the distance of the representations produced by the encoder and the decoder. Since training signals originate from all levels of the network, all layers can learn efficiently even in deep networks. The speedup offered by cost terms from higher levels of the hierarchy and the ability to learn invariant features are demonstrated in experiments.Comment: A revised version of an article that has been accepted for publication in Advances in Independent Component Analysis and Learning Machines (2015), edited by Ella Bingham, Samuel Kaski, Jorma Laaksonen and Jouko Lampine

Deep Virtual Networks for Memory Efficient Inference of Multiple Tasks

Deep networks consume a large amount of memory by their nature. A natural question arises can we reduce that memory requirement whilst maintaining performance. In particular, in this work we address the problem of memory efficient learning for multiple tasks. To this end, we propose a novel network architecture producing multiple networks of different configurations, termed deep virtual networks (DVNs), for different tasks. Each DVN is specialized for a single task and structured hierarchically. The hierarchical structure, which contains multiple levels of hierarchy corresponding to different numbers of parameters, enables multiple inference for different memory budgets. The building block of a deep virtual network is based on a disjoint collection of parameters of a network, which we call a unit. The lowest level of hierarchy in a deep virtual network is a unit, and higher levels of hierarchy contain lower levels' units and other additional units. Given a budget on the number of parameters, a different level of a deep virtual network can be chosen to perform the task. A unit can be shared by different DVNs, allowing multiple DVNs in a single network. In addition, shared units provide assistance to the target task with additional knowledge learned from another tasks. This cooperative configuration of DVNs makes it possible to handle different tasks in a memory-aware manner. Our experiments show that the proposed method outperforms existing approaches for multiple tasks. Notably, ours is more efficient than others as it allows memory-aware inference for all tasks.Comment: CVPR 201