581 research outputs found
Deep Functional Maps: Structured Prediction for Dense Shape Correspondence
We introduce a new framework for learning dense correspondence between
deformable 3D shapes. Existing learning based approaches model shape
correspondence as a labelling problem, where each point of a query shape
receives a label identifying a point on some reference domain; the
correspondence is then constructed a posteriori by composing the label
predictions of two input shapes. We propose a paradigm shift and design a
structured prediction model in the space of functional maps, linear operators
that provide a compact representation of the correspondence. We model the
learning process via a deep residual network which takes dense descriptor
fields defined on two shapes as input, and outputs a soft map between the two
given objects. The resulting correspondence is shown to be accurate on several
challenging benchmarks comprising multiple categories, synthetic models, real
scans with acquisition artifacts, topological noise, and partiality.Comment: Accepted for publication at ICCV 201
Diagonal resolutions for metacyclic groups
We show the finite metacyclic groups G(p, q) admit a class of projective resolutions which are periodic of period 2q and which in addition possess the properties that a) the differentials are 2×2 diagonal matrices; b) the Swan-Wall finiteness obstruction (cf [21], [22]) vanishes. We obtain thereby a purely algebraic proof of Petrie’s Theorem ([16])
that G(p, q) has free period 2q
Spectral and spatial shaping of Smith Purcell Radiation
The Smith Purcell effect, observed when an electron beam passes in the
vicinity of a periodic structure, is a promising platform for the generation of
electromagnetic radiation in previously-unreachable spectral ranges. However,
most of the studies of this radiation were performed on simple periodic
gratings, whose radiation spectrum exhibits a single peak and its higher
harmonics predicted by a well-established dispersion relation. Here, we propose
a method to shape the spatial and spectral far-field distribution of the
radiation using complex periodic and aperiodic gratings. We show, theoretically
and experimentally, that engineering multiple peak spectra with controlled
widths located at desired wavelengths is achievable using Smith-Purcell
radiation. Our method opens the way to free-electron driven sources with
tailored angular and spectral response, and gives rise to focusing
functionality for spectral ranges where lenses are unavailable or inefficient
Diagonal resolutions for the metacyclic groups G(pq)
We study the notion of a free resolution. In general a free resolution can be of any length depending on the group ring under investigation. We consider the metacyclic groups G(pq) which admit periodic resolutions. In such circumstances it is possible to achieve fully \emph{diagonalised resolutions}. By discussing the representation theory over integral group rings we obtain a complete list of indecomposable modules over Z[G(pq)]. Such a list aids the decomposition of the augmentation ideal (the first syzygy) into a direct sum of indecomposable modules. Therefore we are able to achieve a diagonalised map here. From this point it is possible to decompose all of the remaining syzygies in terms of indecomposable modules, leaving a diagonal resolution in principle. The existence of these diagonal resolutions significantly simplify a problem in low-dimensional topology, namely the R(2)-D(2) problem. There are two stages to verifying this problem, and we prove the first stage using cohomological properties of the syzygy decompositions. The second stage is realising the Swan map. Although we do not manage to realise it fully, we are able to realise certain terms. Finally this thesis includes an in depth exposition of the R(2)-D(2) for the non-abelian group of order 21. In this case a positive result has been achieved using an explicitly calculated diagonal resolution
Quantum theory of Bloch oscillations in a resistively shunted transmon
A transmon qubit embedded in a high-impedance environment acts in a way dual
to a conventional Josephson junction. In analogy to the AC Josephson effect,
biasing of the transmon by a direct current leads to the oscillations of
voltage across it. These oscillations are known as the Bloch oscillations. We
find the Bloch oscillations spectrum, and show that the zero-point fluctuations
of charge make it broad-band. Despite having a broad-band spectrum, Bloch
oscillations can be brought in resonance with an external microwave radiation.
The resonances lead to steps in the voltage-current relation, which are dual to
the conventional Shapiro steps. We find how the shape of the steps depends on
the environment impedance , parameters of the transmon, and the microwave
amplitude. The Bloch oscillations rely on the insulating state of the transmon
which is realized at impedances exceeding the Schmid transition point, .Comment: 8 pages, 4 figure
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