59,398 research outputs found
A continuous analog for 4-dimensional objects
In this paper, we follow up on the studies developed by Kovalevsky (Comput Vis Graph Image Process 46:141–161, 1989) and Kenmochi et al. (Comput Vis Image Underst 71:281–293, 1998), which defined a continuous analog for a 4-dimensional digital object. Here, we construct a cell complex that has the same topological information as the original 4-dimensional digital object
The Fundamentals of Radar with Applications to Autonomous Vehicles
Radar systems can be extremely useful for applications in autonomous vehicles. This paper seeks to show how radar systems function and how they can apply to improve autonomous vehicles. First, the basics of radar systems are presented to introduce the basic terminology involved with radar. Then, the topic of phased arrays is presented because of their application to autonomous vehicles. The topic of digital signal processing is also discussed because of its importance for all modern radar systems. Finally, examples of radar systems based on the presented knowledge are discussed to illustrate the effectiveness of radar systems in autonomous vehicles
Universe creation on a computer
The purpose of this paper is to provide an account of the epistemology and
metaphysics of universe creation on a computer
Exotic Quantum Order in Low-Dimensional Systems
Strongly correlated quantum systems in low dimensions often exhibit novel
quantum ordering. This ordering is sometimes hidden and can be revealed only by
examining new `dual' types of correlations. Such ordering leads to novel
collective modes and fractional quantum numbers. Examples will be presented
from quantum spin chains and the quantum Hall effect.Comment: To appear in Solid State Communications, Proceedings of Symposium on
the Advancing Frontiers in Condensed Matter Science. 12pages +6 PS figure
Higher-Dimensional Algebra II: 2-Hilbert Spaces
A 2-Hilbert space is a category with structures and properties analogous to
those of a Hilbert space. More precisely, we define a 2-Hilbert space to be an
abelian category enriched over Hilb with a *-structure, conjugate-linear on the
hom-sets, satisfying = = . We also define monoidal,
braided monoidal, and symmetric monoidal versions of 2-Hilbert spaces, which we
call 2-H*-algebras, braided 2-H*-algebras, and symmetric 2-H*-algebras, and we
describe the relation between these and tangles in 2, 3, and 4 dimensions,
respectively. We prove a generalized Doplicher-Roberts theorem stating that
every symmetric 2-H*-algebra is equivalent to the category Rep(G) of continuous
unitary finite-dimensional representations of some compact supergroupoid G. The
equivalence is given by a categorified version of the Gelfand transform; we
also construct a categorified version of the Fourier transform when G is a
compact abelian group. Finally, we characterize Rep(G) by its universal
properties when G is a compact classical group. For example, Rep(U(n)) is the
free connected symmetric 2-H*-algebra on one even object of dimension n.Comment: 63 pages, LaTeX, 11 figures in encapsulated Postscript, 2 stylefile
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