3,108 research outputs found
Optimal quantization for the pricing of swing options
In this paper, we investigate a numerical algorithm for the pricing of swing
options, relying on the so-called optimal quantization method. The numerical
procedure is described in details and numerous simulations are provided to
assert its efficiency. In particular, we carry out a comparison with the
Longstaff-Schwartz algorithm.Comment: 27
Integer Factorization with a Neuromorphic Sieve
The bound to factor large integers is dominated by the computational effort
to discover numbers that are smooth, typically performed by sieving a
polynomial sequence. On a von Neumann architecture, sieving has log-log
amortized time complexity to check each value for smoothness. This work
presents a neuromorphic sieve that achieves a constant time check for
smoothness by exploiting two characteristic properties of neuromorphic
architectures: constant time synaptic integration and massively parallel
computation. The approach is validated by modifying msieve, one of the fastest
publicly available integer factorization implementations, to use the IBM
Neurosynaptic System (NS1e) as a coprocessor for the sieving stage.Comment: Fixed typos in equation for modular roots (Section II, par. 6;
Section III, par. 2) and phase calculation (Section IV, par 2
High compression image and image sequence coding
The digital representation of an image requires a very large number of bits. This number is even larger for an image sequence. The goal of image coding is to reduce this number, as much as possible, and reconstruct a faithful duplicate of the original picture or image sequence. Early efforts in image coding, solely guided by information theory, led to a plethora of methods. The compression ratio reached a plateau around 10:1 a couple of years ago. Recent progress in the study of the brain mechanism of vision and scene analysis has opened new vistas in picture coding. Directional sensitivity of the neurones in the visual pathway combined with the separate processing of contours and textures has led to a new class of coding methods capable of achieving compression ratios as high as 100:1 for images and around 300:1 for image sequences. Recent progress on some of the main avenues of object-based methods is presented. These second generation techniques make use of contour-texture modeling, new results in neurophysiology and psychophysics and scene analysis
Meron-cluster simulation of the quantum antiferromagnetic Heisenberg model in a magnetic field in one- and two-dimensions
Motivated by the numerical simulation of systems which display quantum phase
transitions, we present a novel application of the meron-cluster algorithm to
simulate the quantum antiferromagnetic Heisenberg model coupled to an external
uniform magnetic field both in one and in two dimensions. In the infinite
volume limit and at zero temperature we found numerical evidence that supports
a quantum phase transition very close to the critical values and
for the system in one and two dimensions, respectively. For the one
dimensional system, we have compared the numerical data obtained with
analytical predictions for the magnetization density as a function of the
external field obtained by scaling-behaviour analysis and Bethe Ansatz
techniques. Since there is no analytical solution for the two dimensional case,
we have compared our results with the magnetization density obtained by scaling
relations for small lattice sizes and with the approximated thermodynamical
limit at zero temperature guessed by scaling relations. Moreover, we have
compared the numerical data with other numerical simulations performed by using
different algorithms in one and two dimensions, like the directed loop method.
The numerical data obtained are in perfect agreement with all these previous
results, which confirms that the meron-algorithm is reliable for quantum Monte
Carlo simulations and applicable both in one and two dimensions. Finally, we
have computed the integrated autocorrelation time to measure the efficiency of
the meron algorithm in one dimension.Comment: 18 pages, 11 figure
A Gradient Descent Algorithm on the Grassman Manifold for Matrix Completion
We consider the problem of reconstructing a low-rank matrix from a small
subset of its entries. In this paper, we describe the implementation of an
efficient algorithm called OptSpace, based on singular value decomposition
followed by local manifold optimization, for solving the low-rank matrix
completion problem. It has been shown that if the number of revealed entries is
large enough, the output of singular value decomposition gives a good estimate
for the original matrix, so that local optimization reconstructs the correct
matrix with high probability. We present numerical results which show that this
algorithm can reconstruct the low rank matrix exactly from a very small subset
of its entries. We further study the robustness of the algorithm with respect
to noise, and its performance on actual collaborative filtering datasets.Comment: 26 pages, 15 figure
- …