874 research outputs found
A Common Symmetrization Framework for Iterative (Linear) Maps
International audienceThis paper highlights some more examples of maps that follow a recently introduced " symmetrization " structure behind the average consensus algorithm. We review among others some generalized consensus settings and coordinate descent optimization
Convergence analysis of an Inexact Infeasible Interior Point method for Semidefinite Programming
In this paper we present an extension to SDP of the well known infeasible Interior Point method for linear programming of Kojima,Megiddo and Mizuno (A primal-dual infeasible-interior-point algorithm for Linear Programming, Math. Progr., 1993). The extension developed here allows the use of inexact search directions; i.e., the linear systems defining the search directions can be solved with an accuracy that increases as the solution is approached. A convergence analysis is carried out and the global convergence of the method is prove
On the polarizability and capacitance of the cube
An efficient integral equation based solver is constructed for the
electrostatic problem on domains with cuboidal inclusions. It can be used to
compute the polarizability of a dielectric cube in a dielectric background
medium at virtually every permittivity ratio for which it exists. For example,
polarizabilities accurate to between five and ten digits are obtained (as
complex limits) for negative permittivity ratios in minutes on a standard
workstation. In passing, the capacitance of the unit cube is determined with
unprecedented accuracy. With full rigor, we develop a natural mathematical
framework suited for the study of the polarizability of Lipschitz domains.
Several aspects of polarizabilities and their representing measures are
clarified, including limiting behavior both when approaching the support of the
measure and when deforming smooth domains into a non-smooth domain. The success
of the mathematical theory is achieved through symmetrization arguments for
layer potentials.Comment: 33 pages, 7 figure
Point-wise Map Recovery and Refinement from Functional Correspondence
Since their introduction in the shape analysis community, functional maps
have met with considerable success due to their ability to compactly represent
dense correspondences between deformable shapes, with applications ranging from
shape matching and image segmentation, to exploration of large shape
collections. Despite the numerous advantages of such representation, however,
the problem of converting a given functional map back to a point-to-point map
has received a surprisingly limited interest. In this paper we analyze the
general problem of point-wise map recovery from arbitrary functional maps. In
doing so, we rule out many of the assumptions required by the currently
established approach -- most notably, the limiting requirement of the input
shapes being nearly-isometric. We devise an efficient recovery process based on
a simple probabilistic model. Experiments confirm that this approach achieves
remarkable accuracy improvements in very challenging cases
Compatibility of quantum measurements and inclusion constants for the matrix jewel
In this work, we establish the connection between the study of free
spectrahedra and the compatibility of quantum measurements with an arbitrary
number of outcomes. This generalizes previous results by the authors for
measurements with two outcomes. Free spectrahedra arise from matricial
relaxations of linear matrix inequalities. A particular free spectrahedron
which we define in this work is the matrix jewel. We find that the
compatibility of arbitrary measurements corresponds to the inclusion of the
matrix jewel into a free spectrahedron defined by the effect operators of the
measurements under study. We subsequently use this connection to bound the set
of (asymmetric) inclusion constants for the matrix jewel using results from
quantum information theory and symmetrization. The latter translate to new
lower bounds on the compatibility of quantum measurements. Among the techniques
we employ are approximate quantum cloning and mutually unbiased bases.Comment: v5: section 3.3 has been expanded significantly to incorporate the
generalization of the Cartesian product and the direct sum to matrix convex
sets. Many other minor modifications. Closed to the published versio
Simple proof of confidentiality for private quantum channels in noisy environments
Complete security proofs for quantum communication protocols can be
notoriously involved, which convolutes their verification, and obfuscates the
key physical insights the security finally relies on. In such cases, for the
majority of the community, the utility of such proofs may be restricted. Here
we provide a simple proof of confidentiality for parallel quantum channels
established via entanglement distillation based on hashing, in the presence of
noise, and a malicious eavesdropper who is restricted only by the laws of
quantum mechanics. The direct contribution lies in improving the linear
confidentiality levels of recurrence-type entanglement distillation protocols
to exponential levels for hashing protocols. The proof directly exploits the
security relevant physical properties: measurement-based quantum computation
with resource states and the separation of Bell-pairs from an eavesdropper. The
proof also holds for situations where Eve has full control over the input
states, and obtains all information about the operations and noise applied by
the parties. The resulting state after hashing is private, i.e., disentangled
from the eavesdropper. Moreover, the noise regimes for entanglement
distillation and confidentiality do not coincide: Confidentiality can be
guaranteed even in situation where entanglement distillation fails. We extend
our results to multiparty situations which are of special interest for secure
quantum networks.Comment: 5 + 11 pages, 0 + 4 figures, A. Pirker and M. Zwerger contributed
equally to this work, replaced with accepted versio
Intermolecular correlations are necessary to explain diffuse scattering from protein crystals
Conformational changes drive protein function, including catalysis,
allostery, and signaling. X-ray diffuse scattering from protein crystals has
frequently been cited as a probe of these correlated motions, with significant
potential to advance our understanding of biological dynamics. However, recent
work challenged this prevailing view, suggesting instead that diffuse
scattering primarily originates from rigid body motions and could therefore be
applied to improve structure determination. To investigate the nature of the
disorder giving rise to diffuse scattering, and thus the potential applications
of this signal, a diverse repertoire of disorder models was assessed for its
ability to reproduce the diffuse signal reconstructed from three protein
crystals. This comparison revealed that multiple models of intramolecular
conformational dynamics, including ensemble models inferred from the Bragg
data, could not explain the signal. Models of rigid body or short-range
liquid-like motions, in which dynamics are confined to the biological unit,
showed modest agreement with the diffuse maps, but were unable to reproduce
experimental features indicative of long-range correlations. Extending a model
of liquid-like motions to include disorder across neighboring proteins in the
crystal significantly improved agreement with all three systems and highlighted
the contribution of intermolecular correlations to the observed signal. These
findings anticipate a need to account for intermolecular disorder in order to
advance the interpretation of diffuse scattering to either extract biological
motions or aid structural inference.Comment: 12 pages, 5 figures (not including Supplementary Information
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