206,549 research outputs found
Inductive learning spatial attention
This paper investigates the automatic induction of spatial attention
from the visual observation of objects manipulated
on a table top. In this work, space is represented in terms of
a novel observer-object relative reference system, named Local
Cardinal System, defined upon the local neighbourhood
of objects on the table. We present results of applying the
proposed methodology on five distinct scenarios involving
the construction of spatial patterns of coloured blocks
A magnetic induction introscope for flaw detection of metal objects
An apparatus for obtaining two-dimensional images of sheet-metal products that is based on a scanning matrix of spiral induction coils has been designed. It was experimentally shown that it is possible to detect flaws and objects that are hidden behind metallic barriers. The scanning area was 37 × 32 cm and the measurement step was 5 mm. Special treatment allows one to restore the distribution of induction currents in conductive objects from the remote measurement of the normal-component distribution of the magnetic induction vector on a plane
Non-commutative connections of the second kind
A connection-like objects, termed {\em hom-connections} are defined in the
realm of non-commutative geometry. The definition is based on the use of
homomorphisms rather than tensor products. It is shown that hom-connections
arise naturally from (strong) connections in non-commutative principal bundles.
The induction procedure of hom-connections via a map of differential graded
algebras or a differentiable bimodule is described. The curvature for a
hom-connection is defined, and it is shown that flat hom-connections give rise
to a chain complex.Comment: 13 pages, LaTe
Do asteroids evaporate near pulsars? Induction heating by pulsar waves revisited
We investigate the evaporation of close-by pulsar companions, such as
planets, asteroids, and white dwarfs, by induction heating. Assuming that the
outflow energy is dominated by a Poynting flux (or pulsar wave) at the location
of the companions, we calculate their evaporation timescales, by applying the
Mie theory. Depending on the size of the companion compared to the incident
electromagnetic wavelength, the heating regime varies and can lead to a total
evaporation of the companion. In particular, we find that inductive heating is
mostly inefficient for small pulsar companions, although it is generally
considered the dominant process. Small objects like asteroids can survive
induction heating for years at distances as small as from
the neutron star. For degenerate companions, induction heating cannot lead to
evaporation and another source of heating (likely by kinetic energy of the
pulsar wind) has to be considered. It was recently proposed that bodies
orbiting pulsars are the cause of fast radio bursts; the present results
explain how those bodies can survive in the pulsar's highly energetic
environment.Comment: 10 pages, 4 figures, 1 table, accepted by A&
Inductive Constructions In Logic And Graph Theory
Just as much as mathematics is about results, mathematics is about methods. This thesis focuses on one method: induction. Induction, in short, allows building complex mathemati- cal objects from simple ones. These mathematical objects include the foundational, like logical statements, and the abstract, like cell complexes. Non-mathematicians struggle to find a common thread throughout all of mathematics, but I present induction as such a common thread here. In particular, this thesis discusses everything from the very foundations of mathematics all the way to combina- torial manifolds. I intend to be casual and opinionated while still providing all necessary formal rigor. This way, the content can be as readable as possible while still being complete
Logic in the Tractatus
I present a reconstruction of the logical system of the Tractatus, which differs from classical logic in two ways. It includes an account of Wittgenstein’s “form-series” device, which suffices to express some effectively generated countably infinite disjunctions. And its attendant notion of structure is relativized to the fixed underlying universe of what is named.
There follow three results. First, the class of concepts definable in the system is closed under finitary induction. Second, if the universe of objects is countably infinite, then the property of being a tautology is \Pi^1_1-complete. But third, it is only granted the assumption of countability that the class of tautologies is \Sigma_1-definable in set theory.
Wittgenstein famously urges that logical relationships must show themselves in the structure of signs. He also urges that the size of the universe cannot be prejudged. The results of this paper indicate that there is no single way in which logical relationships could be held to make themselves manifest in signs, which does not prejudge the number of objects
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