2,378 research outputs found
A comprehensive analysis of the geometry of TDOA maps in localisation problems
In this manuscript we consider the well-established problem of TDOA-based
source localization and propose a comprehensive analysis of its solutions for
arbitrary sensor measurements and placements. More specifically, we define the
TDOA map from the physical space of source locations to the space of range
measurements (TDOAs), in the specific case of three receivers in 2D space. We
then study the identifiability of the model, giving a complete analytical
characterization of the image of this map and its invertibility. This analysis
has been conducted in a completely mathematical fashion, using many different
tools which make it valid for every sensor configuration. These results are the
first step towards the solution of more general problems involving, for
example, a larger number of sensors, uncertainty in their placement, or lack of
synchronization.Comment: 51 pages (3 appendices of 12 pages), 12 figure
Gorenstein formats, canonical and Calabi-Yau threefolds
We extend the known classification of threefolds of general type that are
complete intersections to various classes of non-complete intersections, and
find other classes of polarised varieties, including Calabi-Yau threefolds with
canonical singularities, that are not complete intersections. Our methods apply
more generally to construct orbifolds described by equations in given
Gorenstein formats.Comment: 25 page
Multiple Collisions and Induced Gluon Bremsstrahlung in QCD
Induced soft gluon bremsstrahlung associated with multiple collisions is
calculated via perturbative QCD. We derive the non-abelian analog of the
Landau-Pomeranchuk effect that suppresses induced soft radiation with formation
times exceeding the mean free path, . The dependence of the
suppression effect on the representation of the jet parton as well as
the kinematic variables is expressed through a radiation formation factor.
Unlike in QED, the finite contribution from the small regime in QCD leads
to an approximately constant radiative energy loss per unit length,
, in the high energy limit that is sensitive to the
infrared screening scale, , of the medium. As a function of the
dimensionless parameter , we show furthermore how the
energy dependence of evolves from the above constant for
to the more familiar (Bethe-Heitler) linear dependence for .Comment: 42 pages in LaTex, LBL-32682 and CU-TP-59
Fano 3-folds in codimension 4, Tom and Jerry, Part I
This work is part of the Graded Ring Database project [GRDB], and is a sequel
to [Altinok's 1998 PhD thesis] and [Altinok, Brown and Reid, Fano 3-folds, K3
surfaces and graded rings, in SISTAG (Singapore, 2001), Contemp. Math. 314,
2002, pp. 25-53]. We introduce a strategy based on Kustin-Miller unprojection
that constructs many hundreds of Gorenstein codimension 4 ideals with 9x16
resolutions (that is, 9 equations and 16 first syzygies). Our two basic games
are called Tom and Jerry; the main application is the biregular construction of
most of the anticanonically polarised Mori Fano 3-folds of Altinok's thesis.
There are 115 cases whose numerical data (in effect, the Hilbert series) allow
a Type I projection. In every case, at least one Tom and one Jerry construction
works, providing at least two deformation families of quasismooth Fano 3-folds
having the same numerics but different topology.Comment: 34pp. This article links to the Graded Ring Database
http://grdb.lboro.ac.uk/, and more information is available from webloc. cit.
+ Downloads. Update includes several clarifications and improvements; results
essentially unchanged. To appear in Comp. Mat
Exact Algorithms for Maximum Independent Set
We show that the maximum independent set problem (MIS) on an -vertex graph
can be solved in time and polynomial space, which even is
faster than Robson's -time exponential-space algorithm
published in 1986. We also obtain improved algorithms for MIS in graphs with
maximum degree 6 and 7, which run in time of and
, respectively. Our algorithms are obtained by using fast
algorithms for MIS in low-degree graphs in a hierarchical way and making a
careful analyses on the structure of bounded-degree graphs
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