9,034 research outputs found
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
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