361,616 research outputs found
General covariance of the non-abelian DBI-action: Checks and Balances
We perform three tests on our proposal to implement diffeomorphism invariance
in the non-abelian D0-brane DBI action as a basepoint independence constraint
between matrix Riemann normal coordinate systems. First we show that T-duality
along an isometry correctly interchanges the potential and kinetic terms in the
action. Second, we show that the method to impose basepoint independence using
an auxiliary dN^2-dimensional non-linear sigma model also works for metrics
which are curved along the brane, provided a physical gauge choice is made at
the end. Third, we show that without alteration this method is applicable to
higher order in velocities. Testing specifically to order four, we elucidate
the range of validity of the symmetrized trace approximation to the non-abelian
DBI action.Comment: LaTeX, 22 page
The Conditional Lucas & Kanade Algorithm
The Lucas & Kanade (LK) algorithm is the method of choice for efficient dense
image and object alignment. The approach is efficient as it attempts to model
the connection between appearance and geometric displacement through a linear
relationship that assumes independence across pixel coordinates. A drawback of
the approach, however, is its generative nature. Specifically, its performance
is tightly coupled with how well the linear model can synthesize appearance
from geometric displacement, even though the alignment task itself is
associated with the inverse problem. In this paper, we present a new approach,
referred to as the Conditional LK algorithm, which: (i) directly learns linear
models that predict geometric displacement as a function of appearance, and
(ii) employs a novel strategy for ensuring that the generative pixel
independence assumption can still be taken advantage of. We demonstrate that
our approach exhibits superior performance to classical generative forms of the
LK algorithm. Furthermore, we demonstrate its comparable performance to
state-of-the-art methods such as the Supervised Descent Method with
substantially less training examples, as well as the unique ability to "swap"
geometric warp functions without having to retrain from scratch. Finally, from
a theoretical perspective, our approach hints at possible redundancies that
exist in current state-of-the-art methods for alignment that could be leveraged
in vision systems of the future.Comment: 17 pages, 11 figure
No-Signalling Is Equivalent To Free Choice of Measurements
No-Signalling is a fundamental constraint on the probabilistic predictions
made by physical theories. It is usually justified in terms of the constraints
imposed by special relativity. However, this justification is not as clear-cut
as is usually supposed. We shall give a different perspective on this condition
by showing an equivalence between No-Signalling and Lambda Independence, or
"free choice of measurements", a condition on hidden-variable theories which is
needed to make no-go theorems such as Bell's theorem non-trivial. More
precisely, we shall show that a probability table describing measurement
outcomes is No-Signalling if and only if it can be realized by a
Lambda-Independent hidden-variable theory of a particular canonical form, in
which the hidden variables correspond to non-contextual deterministic
predictions of measurement outcomes. The key proviso which avoids contradiction
with Bell's theorem is that we consider hidden-variable theories with signed
probability measures over the hidden variables - i.e. negative probabilities.
Negative probabilities have often been discussed in the literature on quantum
mechanics. We use a result proved previously in "The Sheaf-theoretic Structure
of Locality and Contextuality" by Abramsky and Brandenburger, which shows that
they give rise to, and indeed characterize, the entire class of No-Signalling
behaviours. In the present paper, we put this result in a broader context,
which reveals the surprising consequence that the No-Signalling condition is
equivalent to the apparently completely different notion of free choice of
measurements.Comment: In Proceedings QPL 2013, arXiv:1412.791
New modelling technique for aperiodic-sampling linear systems
A general input-output modelling technique for aperiodic-sampling linear
systems has been developed. The procedure describes the dynamics of the system
and includes the sequence of sampling periods among the variables to be
handled. Some restrictive conditions on the sampling sequence are imposed in
order to guarantee the validity of the model. The particularization to the
periodic case represents an alternative to the classic methods of
discretization of continuous systems without using the Z-transform. This kind
of representation can be used largely for identification and control purposes.Comment: 19 pages, 0 figure
Split Cycle: A New Condorcet Consistent Voting Method Independent of Clones and Immune to Spoilers
We propose a Condorcet consistent voting method that we call Split Cycle.
Split Cycle belongs to the small family of known voting methods that
significantly narrow the choice of winners in the presence of majority cycles
while also satisfying independence of clones. In this family, only Split Cycle
satisfies a new criterion we call immunity to spoilers, which concerns adding
candidates to elections, as well as the known criteria of positive involvement
and negative involvement, which concern adding voters to elections. Thus, in
contrast to other clone-independent methods, Split Cycle mitigates both
"spoiler effects" and "strong no show paradoxes."Comment: 71 pages, 15 figures. Added a new explanation of Split Cycle in
Section 1, updated the caption to Figure 2, the discussion in Section 3.3,
and Remark 4.11, and strengthened Proposition 6.20 to Theorem 6.20 to cover
single-voter resolvability in addition to asymptotic resolvability. Thanks to
Nicolaus Tideman for helpful discussio
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