35,080 research outputs found
The achievable performance of convex demixing
Demixing is the problem of identifying multiple structured signals from a
superimposed, undersampled, and noisy observation. This work analyzes a general
framework, based on convex optimization, for solving demixing problems. When
the constituent signals follow a generic incoherence model, this analysis leads
to precise recovery guarantees. These results admit an attractive
interpretation: each signal possesses an intrinsic degrees-of-freedom
parameter, and demixing can succeed if and only if the dimension of the
observation exceeds the total degrees of freedom present in the observation
Effect of Zero Modes on the Bound-State Spectrum in Light-Cone Quantisation
We study the role of bosonic zero modes in light-cone quantisation on the
invariant mass spectrum for the simplified setting of two-dimensional SU(2)
Yang-Mills theory coupled to massive scalar adjoint matter. Specifically, we
use discretised light-cone quantisation where the momentum modes become
discrete. Two types of zero momentum mode appear -- constrained and dynamical
zero modes. In fact only the latter type of modes turn out to mix with the Fock
vacuum. Omission of the constrained modes leads to the dynamical zero modes
being controlled by an infinite square-well potential. We find that taking into
account the wavefunctions for these modes in the computation of the full bound
state spectrum of the two dimensional theory leads to 21% shifts in the masses
of the lowest lying states.Comment: LaTeX with 5 postscript file
Hyperspectral Unmixing Overview: Geometrical, Statistical, and Sparse Regression-Based Approaches
Imaging spectrometers measure electromagnetic energy scattered in their
instantaneous field view in hundreds or thousands of spectral channels with
higher spectral resolution than multispectral cameras. Imaging spectrometers
are therefore often referred to as hyperspectral cameras (HSCs). Higher
spectral resolution enables material identification via spectroscopic analysis,
which facilitates countless applications that require identifying materials in
scenarios unsuitable for classical spectroscopic analysis. Due to low spatial
resolution of HSCs, microscopic material mixing, and multiple scattering,
spectra measured by HSCs are mixtures of spectra of materials in a scene. Thus,
accurate estimation requires unmixing. Pixels are assumed to be mixtures of a
few materials, called endmembers. Unmixing involves estimating all or some of:
the number of endmembers, their spectral signatures, and their abundances at
each pixel. Unmixing is a challenging, ill-posed inverse problem because of
model inaccuracies, observation noise, environmental conditions, endmember
variability, and data set size. Researchers have devised and investigated many
models searching for robust, stable, tractable, and accurate unmixing
algorithms. This paper presents an overview of unmixing methods from the time
of Keshava and Mustard's unmixing tutorial [1] to the present. Mixing models
are first discussed. Signal-subspace, geometrical, statistical, sparsity-based,
and spatial-contextual unmixing algorithms are described. Mathematical problems
and potential solutions are described. Algorithm characteristics are
illustrated experimentally.Comment: This work has been accepted for publication in IEEE Journal of
Selected Topics in Applied Earth Observations and Remote Sensin
Fixed Boundary Flows
We consider the fixed boundary flow with canonical interpretability as
principal components extended on the non-linear Riemannian manifolds. We aim to
find a flow with fixed starting and ending point for multivariate datasets
lying on an embedded non-linear Riemannian manifold, differing from the
principal flow that starts from the center of the data cloud. Both points are
given in advance, using the intrinsic metric on the manifolds. From the
perspective of geometry, the fixed boundary flow is defined as an optimal curve
that moves in the data cloud. At any point on the flow, it maximizes the inner
product of the vector field, which is calculated locally, and the tangent
vector of the flow. We call the new flow the fixed boundary flow. The rigorous
definition is given by means of an Euler-Lagrange problem, and its solution is
reduced to that of a Differential Algebraic Equation (DAE). A high level
algorithm is created to numerically compute the fixed boundary. We show that
the fixed boundary flow yields a concatenate of three segments, one of which
coincides with the usual principal flow when the manifold is reduced to the
Euclidean space. We illustrate how the fixed boundary flow can be used and
interpreted, and its application in real data
Refined algebraic quantisation with the triangular subgroup of SL(2,R)
We investigate refined algebraic quantisation with group averaging in a
constrained Hamiltonian system whose gauge group is the connected component of
the lower triangular subgroup of SL(2,R). The unreduced phase space is
T^*R^{p+q} with p>0 and q>0, and the system has a distinguished classical
o(p,q) observable algebra. Group averaging with the geometric average of the
right and left invariant measures, invariant under the group inverse, yields a
Hilbert space that carries a maximally degenerate principal unitary series
representation of O(p,q). The representation is nontrivial iff (p,q) is not
(1,1), which is also the condition for the classical reduced phase space to be
a symplectic manifold up to a singular subset of measure zero. We present a
detailed comparison to an algebraic quantisation that imposes the constraints
in the sense H_a Psi = 0 and postulates self-adjointness of the o(p,q)
observables. Under certain technical assumptions that parallel those of the
group averaging theory, this algebraic quantisation gives no quantum theory
when (p,q) = (1,2) or (2,1), or when p>1, q>1 and p+q is odd.Comment: 30 pages. LaTeX with amsfonts, amsmath, amssymb. (v4: Typos
corrected. Published version.
Attitude motion planning for a spin stabilised disk sail
While solar sails are capable of providing continuous low thrust propulsion the size and flexibility of the sail structure poses difficulties to their attitude control. Rapid slewing of the sail can cause excitation of structural modes, resulting in flexing and oscillation of the sail film and a subsequent loss of performance and decrease in controllability. Disk shaped solar sails are particularly flexible as they have no supporting structure and so these spacecraft must be spun around their major axis to stiffen the sail membrane via the centrifugal force. In addition to stiffening the structure this spin stabilisation also provides gyroscopic stiffness to disturbances, aiding the spacecraft in maintaining its desired attitude. A method is applied which generates smooth reference motions between arbitrary orientations for a spin-stabilised disk sail. The method minimises the sum square of the body rates of the spacecraft, therefore ensuring that the generated attitude slews are slow and smooth, while the spin stabilisation provides gyroscopic stiffness to disturbances. An application of Pontryagin’s maximum principle yields an optimal Hamiltonian which is completely solvable in closed form. The resulting analytical expressions are a function of several free parameters enabling parametric optimisation to be used to provide reference motions which match prescribed boundary conditions on the initial and final configurations. The generated reference motions are utilised in the repointing of a 70m radius spin-stabilised disk solar sail in a heliocentric orbit, with the aim of assessing the feasibility of the motion planning method in terms of the control torques required to track the motions
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