3,379 research outputs found
Multiple sampling and interpolation in the classical Fock space
We study multiple sampling, interpolation and uniqueness for the classical
Fock space in the case of unbounded mul-tiplicities
Discovery of a Proto-cluster Associated with a Ly- Blob Pair at z=2.3
Bright Ly- blobs (LABs) --- extended nebulae with sizes of
100kpc and Ly- luminosities of 10erg s ---
often reside in overdensities of compact Ly- emitters (LAEs) that may
be galaxy protoclusters. The number density, variance, and internal kinematics
of LABs suggest that they themselves trace group-like halos. Here we test this
hierarchical picture, presenting deep, wide-field Ly- narrowband
imaging of a 1 0.5 region around a LAB pair at =
2.3 discovered previously by a blind survey. We find 183 Ly- emitters,
including the original LAB pair and three new LABs with Ly-
luminosities of (0.9--1.3)10erg s and isophotal areas of
16--24 arcsec. Using the LAEs as tracers and a new kernel density
estimation method, we discover a large-scale overdensity (Bo{\"o}tes
J1430+3522) with a surface density contrast of = 2.7, a
volume density contrast of 10.4, and a projected diameter of
20 comoving Mpc. Comparing with cosmological simulations, we conclude
that this LAE overdensity will evolve into a present-day Coma-like cluster with
. In this and three other wide-field LAE
surveys re-analyzed here, the extents and peak amplitudes of the largest LAE
overdensities are similar, not increasing with survey size, implying that they
were indeed the largest structures then and do evolve into rich clusters today.
Intriguingly, LABs favor the outskirts of the densest LAE concentrations, i.e.,
intermediate LAE overdensities of . We speculate that
these LABs mark infalling proto-groups being accreted by the more massive
protocluster
The Hirsch conjecture holds for normal flag complexes
Using an intuition from metric geometry, we prove that any flag and normal
simplicial complex satisfies the non-revisiting path conjecture. As a
consequence, the diameter of its facet-ridge graph is smaller than the number
of vertices minus the dimension, as in the Hirsch conjecture. This proves the
Hirsch conjecture for all flag polytopes, and more generally, for all
(connected) flag homology manifolds.Comment: 9 pages, 1 figure; to appear in Mathematics of Operations Researc
The art of finding the optimal scattering center(s)
The efficient use of a multipole expansion of the far field for rapid
numerical modeling and optimization of the optical response from ordered and
disordered arrays of various structural elements is complicated by the
ambiguity in choosing the ultimate expansion centers for individual scatterers.
Since the multipolar decomposition depends on the position of the expansion
center, the sets of multipoles are not unique. They may require constrained
optimization to get the compact and most efficient spatial spectrum for each
scatterer. We address this problem by finding {\em the optimal scattering
centers} for which the spatial multipolar spectra become unique. We separately
derive these optimal positions for the electric and magnetic parts by
minimizing the norm of the poloidal electric and magnetic quadrupoles.
Employing the long-wave approximation (LWA) ansatz, we verify the approach with
the theoretical discrete models and realistic scatterers. We show that the
optimal electric and magnetic scattering centers, in all cases, are not
co-local with the centers of mass. The optimal multipoles, including the
toroidal terms, are calculated for several structurally distinct scattering
cases, and their utility for low-cost numerical schemes, including the
generalized T-matrix approach, is discussed. Expansion of the work beyond the
LWA is possible, with a promise for faster and universal numerical schemes
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