5,245 research outputs found
Interpolating point spread function anisotropy
Planned wide-field weak lensing surveys are expected to reduce the
statistical errors on the shear field to unprecedented levels. In contrast,
systematic errors like those induced by the convolution with the point spread
function (PSF) will not benefit from that scaling effect and will require very
accurate modeling and correction. While numerous methods have been devised to
carry out the PSF correction itself, modeling of the PSF shape and its spatial
variations across the instrument field of view has, so far, attracted much less
attention. This step is nevertheless crucial because the PSF is only known at
star positions while the correction has to be performed at any position on the
sky. A reliable interpolation scheme is therefore mandatory and a popular
approach has been to use low-order bivariate polynomials. In the present paper,
we evaluate four other classical spatial interpolation methods based on splines
(B-splines), inverse distance weighting (IDW), radial basis functions (RBF) and
ordinary Kriging (OK). These methods are tested on the Star-challenge part of
the GRavitational lEnsing Accuracy Testing 2010 (GREAT10) simulated data and
are compared with the classical polynomial fitting (Polyfit). We also test all
our interpolation methods independently of the way the PSF is modeled, by
interpolating the GREAT10 star fields themselves (i.e., the PSF parameters are
known exactly at star positions). We find in that case RBF to be the clear
winner, closely followed by the other local methods, IDW and OK. The global
methods, Polyfit and B-splines, are largely behind, especially in fields with
(ground-based) turbulent PSFs. In fields with non-turbulent PSFs, all
interpolators reach a variance on PSF systematics better than
the upper bound expected by future space-based surveys, with
the local interpolators performing better than the global ones
A Discrete Adapted Hierarchical Basis Solver For Radial Basis Function Interpolation
In this paper we develop a discrete Hierarchical Basis (HB) to efficiently
solve the Radial Basis Function (RBF) interpolation problem with variable
polynomial order. The HB forms an orthogonal set and is adapted to the kernel
seed function and the placement of the interpolation nodes. Moreover, this
basis is orthogonal to a set of polynomials up to a given order defined on the
interpolating nodes. We are thus able to decouple the RBF interpolation problem
for any order of the polynomial interpolation and solve it in two steps: (1)
The polynomial orthogonal RBF interpolation problem is efficiently solved in
the transformed HB basis with a GMRES iteration and a diagonal, or block SSOR
preconditioner. (2) The residual is then projected onto an orthonormal
polynomial basis. We apply our approach on several test cases to study its
effectiveness, including an application to the Best Linear Unbiased Estimator
regression problem
Entangled cloud storage
Entangled cloud storage (Aspnes et al., ESORICS 2004) enables a set of clients to âentangleâ their files into a single clew to be stored by a (potentially malicious) cloud provider. The entanglement makes it impossible to modify or delete significant part of the clew without affecting all files encoded in the clew. A clew keeps the files in it private but still lets each client recover his own data by interacting with the cloud provider; no cooperation from other clients is needed. At the same time, the cloud provider is discouraged from altering or overwriting any significant part of the clew as this will imply that none of the clients can recover their files. We put forward the first simulation-based security definition for entangled cloud storage, in the framework of universal composability (Canetti, 2001). We then construct a protocol satisfying our security definition, relying on an entangled encoding scheme based on privacy-preserving polynomial interpolation; entangled encodings were originally proposed by Aspnes et al. as useful tools for the purpose of data entanglement. As a contribution of independent interest we revisit the security notions for entangled encodings, putting forward stronger definitions than previous work (that for instance did not consider collusion between clients and the cloud provider). Protocols for entangled cloud storage find application in the cloud setting, where clients store their files on a remote server and need to be ensured that the cloud provider will not modify or delete their data illegitimately. Current solutions, e.g., based on Provable Data Possession and Proof of Retrievability, require the server to be challenged regularly to provide evidence that the clientsâ files are stored at a given time. Entangled cloud storage provides an alternative approach where any single client operates implicitly on behalf of all others, i.e., as long as one client's files are intact, the entire remote database continues to be safe and unblemishe
A conference key distribution system based on cross-product
AbstractExtended from the Diffie-Hellman public key distribution system (PKDS), we propose a conference key distribution system (CKDS) based on the cross-product operations on row vectors over a Galois field GF(P), where P is a prime number. In our CKDS, the chairperson computes a conference key CK and then embeds it to some public interpolating polynomials to let only the legal intended principals recover CK, while the illegal intended principals can not. From the public parameters, an intruder or any intended principal in the network does not know how many and who are the legal intended principals in the conference. Furthermore, since the construction of the CK does not interfere with the secret keys of the intended principals, any intended principals in the network has no useful information for revealing any other principals' secret keys. Besides, our CKDS can be implemented practically
Polynomial approximation of functions of matrices and its application to the solution of a general system of linear equations
During the process of solving a mathematical model numerically, there is often a need to operate on a vector v by an operator which can be expressed as f(A) while A is NxN matrix (ex: exp(A), sin(A), A sup -1). Except for very simple matrices, it is impractical to construct the matrix f(A) explicitly. Usually an approximation to it is used. In the present research, an algorithm is developed which uses a polynomial approximation to f(A). It is reduced to a problem of approximating f(z) by a polynomial in z while z belongs to the domain D in the complex plane which includes all the eigenvalues of A. This problem of approximation is approached by interpolating the function f(z) in a certain set of points which is known to have some maximal properties. The approximation thus achieved is almost best. Implementing the algorithm to some practical problem is described. Since a solution to a linear system Ax = b is x= A sup -1 b, an iterative solution to it can be regarded as a polynomial approximation to f(A) = A sup -1. Implementing the algorithm in this case is also described
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