2,087 research outputs found
The orbifold cohomology of moduli of genus 3 curves
In this work we study the additive orbifold cohomology of the moduli stack of
smooth genus g curves. We show that this problem reduces to investigating the
rational cohomology of moduli spaces of cyclic covers of curves where the genus
of the covering curve is g. Then we work out the case of genus g=3.
Furthermore, we determine the part of the orbifold cohomology of the
Deligne-Mumford compactification of the moduli space of genus 3 curves that
comes from the Zariski closure of the inertia stack of M_3.Comment: 29 pages, 2 figures. Minor changes, to appear in Manuscripta Mat
Neural Network Approximation of Graph Fourier Transform for Sparse Sampling of Networked Dynamics
Infrastructure monitoring is critical for safe operations and sustainability. Like many networked systems, water distribution networks (WDNs) exhibit both graph topological structure and complex embedded flow dynamics. The resulting networked cascade dynamics are difficult to predict without extensive sensor data. However, ubiquitous sensor monitoring in underground situations is expensive, and a key challenge is to infer the contaminant dynamics from partial sparse monitoring data. Existing approaches use multi-objective optimization to find the minimum set of essential monitoring points but lack performance guarantees and a theoretical framework. Here, we first develop a novel Graph Fourier Transform (GFT) operator to compress networked contamination dynamics to identify the essential principal data collection points with inference performance guarantees. As such, the GFT approach provides the theoretical sampling bound. We then achieve under-sampling performance by building auto-encoder (AE) neural networks (NN) to generalize the GFT sampling process and under-sample further from the initial sampling set, allowing a very small set of data points to largely reconstruct the contamination dynamics over real and artificial WDNs. Various sources of the contamination are tested, and we obtain high accuracy reconstruction using around 5%â10% of the network nodes for known contaminant sources, and 50%â75% for unknown source cases, which although larger than that of the schemes for contaminant detection and source identifications, is smaller than the current sampling schemes for contaminant data recovery. This general approach of compression and under-sampled recovery via NN can be applied to a wide range of networked infrastructures to enable efficient data sampling for digital twins
Advanced Heart Failure: A Call to Action
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73182/1/j.1751-7133.2008.00022.x.pd
Service Orientation and the Smart Grid state and trends
The energy market is undergoing major changes, the most notable of which is the transition from a hierarchical closed system toward a more open one highly based on a âsmartâ information-rich infrastructure. This transition calls for new information and communication technologies infrastructures and standards to support it. In this paper, we review the current state of affairs and the actual technologies with respect to such transition. Additionally, we highlight the contact points between the needs of the future grid and the advantages brought by service-oriented architectures.
Grain size limits derived from 3.6 {\mu}m and 4.5 {\mu}m coreshine
Recently discovered scattered light from molecular cloud cores in the
wavelength range 3-5 {\mu}m (called "coreshine") seems to indicate the presence
of grains with sizes above 0.5 {\mu}m. We aim to analyze 3.6 and 4.5 {\mu}m
coreshine from molecular cloud cores to probe the largest grains in the size
distribution. We analyzed dedicated deep Cycle 9 Spitzer IRAC observations in
the 3.6 and 4.5 {\mu}m bands for a sample of 10 low-mass cores. We used a new
modeling approach based on a combination of ratios of the two background- and
foreground-subtracted surface brightnesses and observed limits of the optical
depth. The dust grains were modeled as ice-coated silicate and carbonaceous
spheres. We discuss the impact of local radiation fields with a spectral slope
differing from what is seen in the DIRBE allsky maps. For the cores L260,
ecc806, L1262, L1517A, L1512, and L1544, the model reproduces the data with
maximum grain sizes around 0.9, 0.5, 0.65, 1.5, 0.6, and > 1.5 {\mu}m,
respectively. The maximum coreshine intensities of L1506C, L1439, and L1498 in
the individual bands require smaller maximum grain sizes than derived from the
observed distribution of band ratios. Additional isotropic local radiation
fields with a spectral shape differing from the DIRBE map shape do not remove
this discrepancy. In the case of Rho Oph 9, we were unable to reliably
disentangle the coreshine emission from background variations and the strong
local PAH emission. Considering surface brightness ratios in the 3.6 and 4.5
{\mu}m bands across a molecular cloud core is an effective method of
disentangling the complex interplay of structure and opacities when used in
combination with observed limits of the optical depth.Comment: 23 pages, 18 figures, accepted for publication in A&
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