A Fast Binary Splitting Approach to Non-Adaptive Group Testing

In this paper, we consider the problem of noiseless non-adaptive group testing under the for-each recovery guarantee, also known as probabilistic group testing. In the case of $n$ items and $k$ defectives, we provide an algorithm attaining high-probability recovery with $O(k \log n)$ scaling in both the number of tests and runtime, improving on the best known $O(k^2 \log k \cdot \log n)$ runtime previously available for any algorithm that only uses $O(k \log n)$ tests. Our algorithm bears resemblance to Hwang's adaptive generalized binary splitting algorithm (Hwang, 1972); we recursively work with groups of items of geometrically vanishing sizes, while maintaining a list of "possibly defective" groups and circumventing the need for adaptivity. While the most basic form of our algorithm requires $\Omega(n)$ storage, we also provide a low-storage variant based on hashing, with similar recovery guarantees.Comment: Accepted to RANDOM 202

The Capacity of Adaptive Group Testing

We define capacity for group testing problems and deduce bounds for the capacity of a variety of noisy models, based on the capacity of equivalent noisy communication channels. For noiseless adaptive group testing we prove an information-theoretic lower bound which tightens a bound of Chan et al. This can be combined with a performance analysis of a version of Hwang's adaptive group testing algorithm, in order to deduce the capacity of noiseless and erasure group testing models.Comment: 5 page

Perceptually-Driven Video Coding with the Daala Video Codec

The Daala project is a royalty-free video codec that attempts to compete with the best patent-encumbered codecs. Part of our strategy is to replace core tools of traditional video codecs with alternative approaches, many of them designed to take perceptual aspects into account, rather than optimizing for simple metrics like PSNR. This paper documents some of our experiences with these tools, which ones worked and which did not. We evaluate which tools are easy to integrate into a more traditional codec design, and show results in the context of the codec being developed by the Alliance for Open Media.Comment: 19 pages, Proceedings of SPIE Workshop on Applications of Digital Image Processing (ADIP), 201

PDE-Foam - a probability-density estimation method using self-adapting phase-space binning

Probability Density Estimation (PDE) is a multivariate discrimination technique based on sampling signal and background densities defined by event samples from data or Monte-Carlo (MC) simulations in a multi-dimensional phase space. In this paper, we present a modification of the PDE method that uses a self-adapting binning method to divide the multi-dimensional phase space in a finite number of hyper-rectangles (cells). The binning algorithm adjusts the size and position of a predefined number of cells inside the multi-dimensional phase space, minimising the variance of the signal and background densities inside the cells. The implementation of the binning algorithm PDE-Foam is based on the MC event-generation package Foam. We present performance results for representative examples (toy models) and discuss the dependence of the obtained results on the choice of parameters. The new PDE-Foam shows improved classification capability for small training samples and reduced classification time compared to the original PDE method based on range searching.Comment: 19 pages, 11 figures; replaced with revised version accepted for publication in NIM A and corrected typos in description of Fig. 7 and

Reducing the complexity of a multiview H.264/AVC and HEVC hybrid architecture

With the advent of 3D displays, an efficient encoder is required to compress the video information needed by them. Moreover, for gradual market acceptance of this new technology, it is advisable to offer backward compatibility with existing devices. Thus, a multiview H.264/Advance Video Coding (AVC) and High Efficiency Video Coding (HEVC) hybrid architecture was proposed in the standardization process of HEVC. However, it requires long encoding times due to the use of HEVC. With the aim of tackling this problem, this paper presents an algorithm that reduces the complexity of this hybrid architecture by reducing the encoding complexity of the HEVC views. By using Na < ve-Bayes classifiers, the proposed technique exploits the information gathered in the encoding of the H.264/AVC view to make decisions on the splitting of coding units in HEVC side views. Given the novelty of the proposal, the only similar work found in the literature is an unoptimized version of the algorithm presented here. Experimental results show that the proposed algorithm can achieve a good tradeoff between coding efficiency and complexity

Advanced operator-splitting-based semi-implicit spectral method to solve the binary phase-field crystal equations with variable coefficients

We present an efficient method to solve numerically the equations of dissipative dynamics of the binary phase-field crystal model proposed by Elder et al. [Phys. Rev. B 75, 064107 (2007)] characterized by variable coefficients. Using the operator splitting method, the problem has been decomposed into sub-problems that can be solved more efficiently. A combination of non-trivial splitting with spectral semi-implicit solution leads to sets of algebraic equations of diagonal matrix form. Extensive testing of the method has been carried out to find the optimum balance among errors associated with time integration, spatial discretization, and splitting. We show that our method speeds up the computations by orders of magnitude relative to the conventional explicit finite difference scheme, while the costs of the pointwise implicit solution per timestep remains low. Also we show that due to its numerical dissipation, finite differencing can not compete with spectral differencing in terms of accuracy. In addition, we demonstrate that our method can efficiently be parallelized for distributed memory systems, where an excellent scalability with the number of CPUs is observed