Moment-angle complexes, monomial ideals, and Massey products

Associated to every finite simplicial complex K there is a "moment-angle" finite CW-complex, Z_K; if K is a triangulation of a sphere, Z_K is a smooth, compact manifold. Building on work of Buchstaber, Panov, and Baskakov, we study the cohomology ring, the homotopy groups, and the triple Massey products of a moment-angle complex, relating these topological invariants to the algebraic combinatorics of the underlying simplicial complex. Applications to the study of non-formal manifolds and subspace arrangements are given.Comment: 30 pages. Published versio

On the homotopy Lie algebra of an arrangement

Let A be a graded-commutative, connected k-algebra generated in degree 1. The homotopy Lie algebra g_A is defined to be the Lie algebra of primitives of the Yoneda algebra, Ext_A(k,k). Under certain homological assumptions on A and its quadratic closure, we express g_A as a semi-direct product of the well-understood holonomy Lie algebra h_A with a certain h_A-module. This allows us to compute the homotopy Lie algebra associated to the cohomology ring of the complement of a complex hyperplane arrangement, provided some combinatorial assumptions are satisfied. As an application, we give examples of hyperplane arrangements whose complements have the same Poincar\'e polynomial, the same fundamental group, and the same holonomy Lie algebra, yet different homotopy Lie algebras.Comment: 20 pages; accepted for publication by the Michigan Math. Journa

Evidence for changes in the radiative efficiency of transient black hole X-ray binaries

We have used pointed RXTE data to examine the long-term X-ray light curves of six transient black hole X-ray binaries during their decay from outburst to quiescence. In most cases there is a period of exponential decay as the source approaches the soft-to-hard state transition, and another period of exponential decay following this transition as the source decays in the hard state. The e-folding times change around the time of the state transition, from typically approx 12 days at the end of the soft state to approx 7 days at the beginning of the hard state. This factor ~2 change in the decay timescale is expected if there is a change from radiatively efficient emission in the soft state to radiatively inefficient emission in the hard state, overlying an exponential decay in the mass accretion rate. This adds support to the idea that the X-ray emitting region is governed by radiatively inefficient accretion (such as an advection-dominated or jet-dominated accretion flow) during the fading hard state.Comment: 9 pages, 18 figures, accepted for publication in MNRAS, minor changes following proo

Explaining the Unexplained: A CLass-Enhanced Attentive Response (CLEAR) Approach to Understanding Deep Neural Networks

In this work, we propose CLass-Enhanced Attentive Response (CLEAR): an approach to visualize and understand the decisions made by deep neural networks (DNNs) given a specific input. CLEAR facilitates the visualization of attentive regions and levels of interest of DNNs during the decision-making process. It also enables the visualization of the most dominant classes associated with these attentive regions of interest. As such, CLEAR can mitigate some of the shortcomings of heatmap-based methods associated with decision ambiguity, and allows for better insights into the decision-making process of DNNs. Quantitative and qualitative experiments across three different datasets demonstrate the efficacy of CLEAR for gaining a better understanding of the inner workings of DNNs during the decision-making process.Comment: Accepted at Computer Vision and Patter Recognition Workshop (CVPR-W) on Explainable Computer Vision, 201