295 research outputs found
Minimizing Communication in Linear Algebra
In 1981 Hong and Kung proved a lower bound on the amount of communication
needed to perform dense, matrix-multiplication using the conventional
algorithm, where the input matrices were too large to fit in the small, fast
memory. In 2004 Irony, Toledo and Tiskin gave a new proof of this result and
extended it to the parallel case. In both cases the lower bound may be
expressed as (#arithmetic operations / ), where M is the size
of the fast memory (or local memory in the parallel case). Here we generalize
these results to a much wider variety of algorithms, including LU
factorization, Cholesky factorization, factorization, QR factorization,
algorithms for eigenvalues and singular values, i.e., essentially all direct
methods of linear algebra. The proof works for dense or sparse matrices, and
for sequential or parallel algorithms. In addition to lower bounds on the
amount of data moved (bandwidth) we get lower bounds on the number of messages
required to move it (latency). We illustrate how to extend our lower bound
technique to compositions of linear algebra operations (like computing powers
of a matrix), to decide whether it is enough to call a sequence of simpler
optimal algorithms (like matrix multiplication) to minimize communication, or
if we can do better. We give examples of both. We also show how to extend our
lower bounds to certain graph theoretic problems.
We point out recently designed algorithms for dense LU, Cholesky, QR,
eigenvalue and the SVD problems that attain these lower bounds; implementations
of LU and QR show large speedups over conventional linear algebra algorithms in
standard libraries like LAPACK and ScaLAPACK. Many open problems remain.Comment: 27 pages, 2 table
Teleoperation experiments with a Utah/MIT hand and a VPL DataGlove
A teleoperation system capable of controlling a Utah/MIT Dextrous Hand using a VPL DataGlove as a master is presented. Additionally the system is capable of running the dextrous hand in robotic (autonomous) mode as new programs are developed. The software and hardware architecture used is presented and the experiments performed are described. The communication and calibration issues involved are analyzed and applications to the analysis and development of automated dextrous manipulations are investigated
Mixed precision bisection
We discuss the implementation of the bisection algorithm for the computation of the eigenvalues of
symmetric tridiagonal matrices in a context of mixed precision arithmetic. This approach is motivated by the
emergence of processors which carry out floating-point operations much faster in single precision than they do in double precision. Perturbation theory results are used to decide when to switch from single to double precision. Numerical examples are presente
Flexible and Robust Privacy-Preserving Implicit Authentication
Implicit authentication consists of a server authenticating a user based on
the user's usage profile, instead of/in addition to relying on something the
user explicitly knows (passwords, private keys, etc.). While implicit
authentication makes identity theft by third parties more difficult, it
requires the server to learn and store the user's usage profile. Recently, the
first privacy-preserving implicit authentication system was presented, in which
the server does not learn the user's profile. It uses an ad hoc two-party
computation protocol to compare the user's fresh sampled features against an
encrypted stored user's profile. The protocol requires storing the usage
profile and comparing against it using two different cryptosystems, one of them
order-preserving; furthermore, features must be numerical. We present here a
simpler protocol based on set intersection that has the advantages of: i)
requiring only one cryptosystem; ii) not leaking the relative order of fresh
feature samples; iii) being able to deal with any type of features (numerical
or non-numerical).
Keywords: Privacy-preserving implicit authentication, privacy-preserving set
intersection, implicit authentication, active authentication, transparent
authentication, risk mitigation, data brokers.Comment: IFIP SEC 2015-Intl. Information Security and Privacy Conference, May
26-28, 2015, IFIP AICT, Springer, to appea
The bends on a quantum waveguide and cross-products of Bessel functions
A detailed analysis of the wave-mode structure in a bend and its
incorporation into a stable algorithm for calculation of the scattering matrix
of the bend is presented. The calculations are based on the modal approach. The
stability and precision of the algorithm is numerically and analytically
analysed. The algorithm enables precise numerical calculations of scattering
across the bend. The reflection is a purely quantum phenomenon and is discussed
in more detail over a larger energy interval. The behaviour of the reflection
is explained partially by a one-dimensional scattering model and heuristic
calculations of the scattering matrix for narrow bends. In the same spirit we
explain the numerical results for the Wigner-Smith delay time in the bend.Comment: 34 pages, 21 figure
Theoretical analysis of neutron scattering results for quasi-two dimensional ferromagnets
A theoretical study has been carried out to analyse the available results
from the inelastic neutron scattering experiment performed on a quasi-two
dimensional spin-1/2 ferromagnetic material . Our formalism is based
on a conventional semi-classical like treatment involving a model of an ideal
gas of vortices/anti-vortices corresponding to an anisotropic XY Heisenberg
ferromagnet on a square lattice. The results for dynamical structure functions
for our model corresponding to spin-1/2, show occurrence of negative values in
a large range of energy transfer even encompassing the experimental range, when
convoluted with a realistic spectral window function. This result indicates
failure of the conventional theoretical framework to be applicable to the
experimental situation corresponding to low spin systems. A full quantum
formalism seems essential for treating such systems.Comment: 16 pages, 6 figures, 1 Table Submitted for publicatio
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