1,203 research outputs found
The Inverse Voronoi Problem in Graphs I: Hardness
International audienceWe introduce the inverse Voronoi diagram problem in graphs: given a graph G with positive edge-lengths and a collection of subsets of vertices of V (G), decide whether is a Voronoi diagram in G with respect to the shortest-path metric. We show that the problem is NP-hard, even for planar graphs where all the edges have unit length. We also study the parameterized complexity of the problem and show that the problem is W[1]-hard when parameterized by the number of Voronoi cells or by the pathwidth of the graph
Error Patterns
In coding theory the problem of decoding focuses on error vectors. In the simplest situation code words are -vectors, as are the received messages and the error vectors. Comparison of a received word with the code words yields a set of error vectors. In deciding on the original code word, usually the one for which the error vector has minimum Hamming weight is chosen. In this note some remarks are made on the problem of the elements 1 in the error vector, that may enable unique decoding, in case two or more code words have the same Hamming distance to the received message word, thus turning error detection into error correction. The essentially new aspect is that code words, message words and error vectors are put in one-one correspondence with graphs
The Spatial Clustering of Low Luminosity AGN
We present the first multi-parameter analysis of the narrow line AGN
clustering properties. Estimates of the two-point correlation function (CF)
based on SDSS DR2 data reveal that Seyferts are clearly less clustered than
normal galaxies, while the clustering amplitude (r_0) of LINERs is consistent
with that of the parent galaxy population. The similarities in the host
properties (color and concentration index) of Seyferts and LINERs suggest that
the difference in their r_0 is not driven by the morphology-density relation.
We find that the luminosity of [O I] emission shows the strongest influence on
AGN clustering, with low L([O I]) sources having the highest r_0. This trend is
much stronger than the previously detected dependence on L([O III]), which we
confirm. There is a strong correspondence between the clustering patterns of
objects of given spectral type and their physical properties. LINERs, which
exhibit high r_0, show the lowest luminosities and obscuration levels, and
relatively low gas densities (n_e), suggesting that these objects harbor black
holes that are relatively massive yet weakly active or inefficient in their
accretion, probably due to the insufficiency of their fuel supply. Seyferts,
which have low r_0, are luminous and show large n_e, suggesting that their
black holes are less massive but accrete quickly and efficiently enough to
clearly dominate the ionization. The low r_0 of the H II galaxies can be
understood as a consequence of both the morphology-density and star formation
rate-density relations, however, their spectral properties suggest that their
centers hide amidst large amounts of obscuring material black holes of
generally low mass whose activity remains relatively feeble. Our own Milky Way
may be a typical such case.[abridged]Comment: 27 pages, color figures, some are severely degraded in resolution,
emulateapj. See http://www.physics.drexel.edu/~constant/work/agnclustering.ps
for high resolution version. Accepted to Ap
No evidence for black hole spin powering of jets in X-ray binaries
In this paper we take the reported measurements of black hole spin for black
hole X-ray binaries, and compare them against measurements of jet power and
speed across all accretion states in these systems. We find no evidence for any
correlation between the properties of the jets and the reported spin
measurements. These constraints are strongest in the hard X-ray state, which is
associated with a continuous powerful jet. We are led to conclude that one or
more of the following is correct: (i) the calculated jet power and speed
measurements are wrong, (ii) the reported spin measurements are wrong, (iii)
there is no strong dependence of the jet properties on black hole spin. In
addition to this lack of observational evidence for a relation between black
hole spin and jet properties in stellar mass black holes, we highlight the fact
that there appear to be at least three different ways in which the jet power
and/or radiative efficiency from a black hole X-ray binary may vary, two of
which are certainly independent of spin because they occur in the same source
on relatively short timescales, and the third which does not correlate with any
reported measurements of black hole spin. We briefly discuss how these findings
may impact upon interpretations of populations of active galactic nuclei in the
context of black hole spin and merger history.Comment: Accepted for publication in MNRA
Multistage s-t Path: Confronting Similarity with Dissimilarity in Temporal Graphs
Addressing a quest by Gupta et al. [ICALP\u2714], we provide a first, comprehensive study of finding a short s-t path in the multistage graph model, referred to as the Multistage s-t Path problem. Herein, given a sequence of graphs over the same vertex set but changing edge sets, the task is to find short s-t paths in each graph ("snapshot") such that in the found path sequence the consecutive s-t paths are "similar". We measure similarity by the size of the symmetric difference of either the vertex set (vertex-similarity) or the edge set (edge-similarity) of any two consecutive paths. We prove that these two variants of Multistage s-t Path are already NP-hard for an input sequence of only two graphs and maximum vertex degree four. Motivated by this fact and natural applications of this scenario e.g. in traffic route planning, we perform a parameterized complexity analysis. Among other results, for both variants, vertex- and edge-similarity, we prove parameterized hardness (W[1]-hardness) regarding the parameter path length (solution size) for both variants, vertex- and edge-similarity. As a further conceptual study, we then modify the multistage model by asking for dissimilar consecutive paths. One of our main technical results (employing so-called representative sets known from non-temporal settings) is that dissimilarity allows for fixed-parameter tractability for the parameter solution size, contrasting the W[1]-hardness of the corresponding similarity case. We also provide partially positive results concerning efficient and effective data reduction (kernelization)
Double Neutron Star Formation: Merger Times, Systemic Velocities, and Travel Distances
The formation and evolution of double neutron stars (DNS) have traditionally
been studied using binary population synthesis. In this work, we take an
alternative approach by focusing only on the second supernova (SN) forming the
DNS and the subsequent orbital decay and merger due to gravitational wave
radiation. Using analytic and numerical methods, we explore how different NS
natal kick velocity distributions, pre-SN orbital separations, and progenitor
He-star masses affect the post-SN orbital periods, eccentricities, merger
times, systemic velocities, and distances traveled by the system before
merging. Comparison with the set of 17 known DNSs in the Milky Way shows that
DNSs have pre-SN orbital separations ranging between 1 and 44 .
Those DNSs with pre-SN separations 1 have merger time
distributions that peak 10-100 Myr after formation, regardless of the
kick velocity received by the NS. These DNSs are typically formed with systemic
velocities 10 km s and may travel 1-10 kpc before
merging. Depending on progenitor mass of the second-born NS, the short merger
time can account for the -process enrichment observed in compact stellar
systems such as ultra-faint dwarf galaxies. For Milky Way-mass galaxies only
DNSs with the tightest pre-SN orbits and large kick velocities (10
km s) can escape. However, those DNSs that do escape may travel as far
as Mpc before merging, which as previous studies have pointed out has
implications for identifying the host galaxies to short gamma ray bursts and
gravitational wave events.Comment: 16 pages, 10 figures, accepted for publication in MNRA
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