Speed limit quasi splines and their application to interpolation with bounded first order derivative

The problem of computing spline‐like functions for ideal data, subject to two‐sided inequality constraints on the first‐order derivative, are considered, focusing primarily on constant constraints and then generalizing. Using a variational approach, in which the inequality constraints are not explicitly imposed, a special type of exponential splines we call speed limit quasi splines is introduced. A simple, non‐parametric, efficient, and robust iterative solver is suggested, which is suitable for a wide range of inequality constraints. Analysis of the convergence factor of this algorithm is provided and supported by extensive numerical tests. Copyright © 2014 John Wiley & Sons, Ltd.     

Preconditioning systems arising from the KKR Green function method using block-circulant matrices

Recently, a linearly scaling method for the calculation of the electronic structure based on the Korringa–Kohn–Rostoker Green function method has been proposed. The method uses the transpose free quasi minimal residual method (TFQMR) to solve linear systems with multiple right hand sides. These linear systems depend on the energy-level under consideration and the convergence rate deteriorates for some of these energy points. While traditional preconditioners like ILU are fairly useful for the problem, the computation of the preconditioner itself is often relatively hard to parallelize. To overcome these difficulties, we develop a new preconditioner that exploits the strong structure of the underlying systems. The resulting preconditioner is block-circulant and thus easy to compute, invert and parallelize. The resulting method yields a dramatic speedup of the computation compared to the unpreconditioned solver, especially for critical energy levels.     

Using a VOM model for reconstructing potential coding regions in EST sequences

This paper presents a method for annotating coding and noncoding DNA regions by using variable order Markov (VOM) models. A main advantage in using VOM models is that their order may vary for different sequences, depending on the sequences’ statistics. As a result, VOM models are more flexible with respect to model parameterization and can be trained on relatively short sequences and on low-quality datasets, such as expressed sequence tags (ESTs). The paper presents a modified VOM model for detecting and correcting insertion and deletion sequencing errors that are commonly found in ESTs. In a series of experiments the proposed method is found to be robust to random errors in these sequences.     

Review of Methods Inspired by Algebraic-Multigrid for Data and Image Analysis Applications

Algebraic Multigrid (AMG) methods were developed originally for numerically solving Partial Differential Equations (PDE), not necessarily on structured grids. In the last two decades solvers inspired by the AMG approach, were developed for non PDE problems, including data and image analysis problems, such as clustering, segmentation, quantization and others. These solvers share a common principle that there is a crosstalk between fine and coarse representations of the problems, with flow of information in both directions, fine-to-coarse and coarse-to-fine. This paper surveys some of these problems and the AMG-inspired algorithms for their solution.     

Detection of Static and Mobile Targets by an Autonomous Agent with Deep Q-Learning Abilities

This paper addresses the problem of detecting multiple static and mobile targets by an autonomous mobile agent acting under uncertainty. It is assumed that the agent is able to detect targets at different distances and that the detection includes errors of the first and second types. The goal of the agent is to plan and follow a trajectory that results in the detection of the targets in a minimal time. The suggested solution implements the approach of deep Q-learning applied to maximize the cumulative information gain regarding the targets’ locations and minimize the trajectory length on the map with a predefined detection probability. The Q-learning process is based on a neural network that receives the agent location and current probability map and results in the preferred move of the agent. The presented procedure is compared with the previously developed techniques of sequential decision making, and it is demonstrated that the suggested novel algorithm strongly outperforms the existing methods.