5,815 research outputs found
The M\"obius Domain Wall Fermion Algorithm
We present a review of the properties of generalized domain wall Fermions,
based on a (real) M\"obius transformation on the Wilson overlap kernel,
discussing their algorithmic efficiency, the degree of explicit chiral
violations measured by the residual mass () and the Ward-Takahashi
identities. The M\"obius class interpolates between Shamir's domain wall
operator and Bori\c{c}i's domain wall implementation of Neuberger's overlap
operator without increasing the number of Dirac applications per conjugate
gradient iteration. A new scaling parameter () reduces chiral
violations at finite fifth dimension () but yields exactly the same
overlap action in the limit . Through the use of 4d
Red/Black preconditioning and optimal tuning for the scaling , we
show that chiral symmetry violations are typically reduced by an order of
magnitude at fixed . At large we argue that the observed scaling for
for Shamir is replaced by for the
properly tuned M\"obius algorithm with Comment: 59 pages, 11 figure
Parallel Anisotropic Unstructured Grid Adaptation
Computational Fluid Dynamics (CFD) has become critical to the design and analysis of aerospace vehicles. Parallel grid adaptation that resolves multiple scales with anisotropy is identified as one of the challenges in the CFD Vision 2030 Study to increase the capacity and capability of CFD simulation. The Study also cautions that computer architectures are undergoing a radical change and dramatic increases in algorithm concurrency will be required to exploit full performance. This paper reviews four different methods to parallel anisotropic grid generation. They cover both ends of the spectrum: (i) using existing state-of-the-art software optimized for a single core and modifying it for parallel platforms and (ii) designing and implementing scalable software with incomplete, but rapidly maturating functionality. A brief overview for each grid adaptation system is presented in the context of a telescopic approach for multilevel concurrency. These methods employ different approaches to enable parallel execution, which provides a unique opportunity to illustrate the relative behavior of each approach. Qualitative and quantitative metric evaluations are used to draw lessons for future developments in this critical area for parallel CFD simulation
Hyper-Spectral Image Analysis with Partially-Latent Regression and Spatial Markov Dependencies
Hyper-spectral data can be analyzed to recover physical properties at large
planetary scales. This involves resolving inverse problems which can be
addressed within machine learning, with the advantage that, once a relationship
between physical parameters and spectra has been established in a data-driven
fashion, the learned relationship can be used to estimate physical parameters
for new hyper-spectral observations. Within this framework, we propose a
spatially-constrained and partially-latent regression method which maps
high-dimensional inputs (hyper-spectral images) onto low-dimensional responses
(physical parameters such as the local chemical composition of the soil). The
proposed regression model comprises two key features. Firstly, it combines a
Gaussian mixture of locally-linear mappings (GLLiM) with a partially-latent
response model. While the former makes high-dimensional regression tractable,
the latter enables to deal with physical parameters that cannot be observed or,
more generally, with data contaminated by experimental artifacts that cannot be
explained with noise models. Secondly, spatial constraints are introduced in
the model through a Markov random field (MRF) prior which provides a spatial
structure to the Gaussian-mixture hidden variables. Experiments conducted on a
database composed of remotely sensed observations collected from the Mars
planet by the Mars Express orbiter demonstrate the effectiveness of the
proposed model.Comment: 12 pages, 4 figures, 3 table
A Balanced Tree Approach to Construction of Length-Compatible Polar Codes
From the perspective of tree, we design a length-flexible coding scheme. For
an arbitrary code length, we first construct a balanced binary tree (BBT) where
the root node represents a transmitted codeword, the leaf nodes represent
either active bits or frozen bits, and a parent node is related to its child
nodes by a length-adaptive (U+V|V) operation. Both the encoding and the
successive cancellation (SC)-based decoding can be implemented over the
constructed coding tree. For code construction, we propose a signal-to-noise
ratio (SNR)-dependent method and two SNR-independent methods, all of which
evaluate the reliabilities of leaf nodes and then select the most reliable leaf
nodes as the active nodes. Numerical results demonstrate that our proposed
codes can have comparable performance to the 5G polar codes. To reduce the
decoding latency, we propose a partitioned successive cancellation (PSC)-based
decoding algorithm, which can be implemented over a sub-tree obtained by
pruning the coding tree. Numerical results show that the PSC-based decoding can
achieve similar performance to the conventional SC-based decoding.Comment: 30 pages, 10 figure
Biologically inspired feature extraction for rotation and scale tolerant pattern analysis
Biologically motivated information processing has been an important area of scientific research for decades. The central topic addressed in this dissertation is utilization of lateral inhibition and more generally, linear networks with recurrent connectivity along with complex-log conformal mapping in machine based implementations of information encoding, feature extraction and pattern recognition. The reasoning behind and method for spatially uniform implementation of inhibitory/excitatory network model in the framework of non-uniform log-polar transform is presented. For the space invariant connectivity model characterized by Topelitz-Block-Toeplitz matrix, the overall network response is obtained without matrix inverse operations providing the connection matrix generating function is bound by unity. It was shown that for the network with the inter-neuron connection function expandable in a Fourier series in polar angle, the overall network response is steerable. The decorrelating/whitening characteristics of networks with lateral inhibition are used in order to develop space invariant pre-whitening kernels specialized for specific category of input signals. These filters have extremely small memory footprint and are successfully utilized in order to improve performance of adaptive neural whitening algorithms. Finally, the method for feature extraction based on localized Independent Component Analysis (ICA) transform in log-polar domain and aided by previously developed pre-whitening filters is implemented. Since output codes produced by ICA are very sparse, a small number of non-zero coefficients was sufficient to encode input data and obtain reliable pattern recognition performance
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