A general Approach to Methods with a Sparse Jacobian for Solving Nonlinear Systems of Equations

2000 Mathematics Subject Classification: 65H10.

100-Gb/s point-to-point solutions for long-reach passive optical networks in sparse rural and urban areas

Long reach-passive optical networks (LR-PON) are being proposed as a means of enabling ubiquitous fiber-to-the-home (FTTH) by massive sharing of network resources and therefore reducing per customer costs to affordable levels. In this paper, we analyze the chain solutions for LR-PON deployment in urban and rural areas at 100-Gb/s point-to-point transmission using dual polarization-quaternary phase shift-keying (DP-QPSK) modulation. The numerical analysis shows that with appropriate finite impulse response (FIR) filter designs, 100-Gb/s transmission can be achieved with at least 512 way split and up to 160 km total distance, which is sufficient for many of the optical paths in a practical situation, for point-to-point link from one LR-PON to another LR-PON through the optical switch at the metro nodes and across a core light path through the core network without regeneration.

A template model predicts detection of sparse stimul

Contemporary models of contrast integration across space assume that pooling operates uniformly over the target region. For sparse stimuli, where high contrast regions are separated by areas containing no signal, this strategy may be sub-optimal because it pools more noise than signal as area increases. Little is known about the behaviour of human observers for detecting such stimuli. We performed an experiment in which three observers detected regular textures of various areas, and six levels of sparseness. Stimuli were regular grids of horizontal grating micropatches, each 1 cycle wide. We varied the ratio of signals (marks) to gaps (spaces), with mark:space ratios ranging from 1 : 0 (a dense texture with no spaces) to 1 : 24. To compensate for the decline in sensitivity with increasing distance from fixation, we adjusted the stimulus contrast as a function of eccentricity based on previous measurements [Baldwin, Meese & Baker, 2012, J Vis, 12(11):23]. We used the resulting area summation functions and psychometric slopes to test several filter-based models of signal combination. A MAX model failed to predict the thresholds, but did a good job on the slopes. Blanket summation of stimulus energy improved the threshold fit, but did not predict an observed slope increase with mark:space ratio. Our best model used a template matched to the sparseness of the stimulus, and pooled the squared contrast signal over space. Templates for regular patterns have also recently been proposed to explain the regular appearance of slightly irregular textures (Morgan et al, 2012, Proc R Soc B, 279, 2754–2760)

Cooperative greedy pursuit strategies for sparse signal representation by partitioning

Cooperative Greedy Pursuit Strategies are considered for approximating a signal partition subjected to a global constraint on sparsity. The approach aims at producing a high quality sparse approximation of the whole signal, using highly coherent redundant dictionaries. The cooperation takes place by ranking the partition units for their sequential stepwise approximation, and is realized by means of i)forward steps for the upgrading of an approximation and/or ii) backward steps for the corresponding downgrading. The advantage of the strategy is illustrated by approximation of music signals using redundant trigonometric dictionaries. In addition to rendering stunning improvements in sparsity with respect to the concomitant trigonometric basis, these dictionaries enable a fast implementation of the approach via the Fast Fourier Transform

Grid-texture mechanisms in human vision:contrast detection of regular sparse micro-patterns requires specialist templates

Previous work has shown that human vision performs spatial integration of luminance contrast energy, where signals are squared and summed (with internal noise) over area at detection threshold. We tested that model here in an experiment using arrays of micro-pattern textures that varied in overall stimulus area and sparseness of their target elements, where the contrast of each element was normalised for sensitivity across the visual field. We found a power-law improvement in performance with stimulus area, and a decrease in sensitivity with sparseness. While the contrast integrator model performed well when target elements constituted 50–100% of the target area (replicating previous results), observers outperformed the model when texture elements were sparser than this. This result required the inclusion of further templates in our model, selective for grids of various regular texture densities. By assuming a MAX operation across these noisy mechanisms the model also accounted for the increase in the slope of the psychometric function that occurred as texture density decreased. Thus, for the first time, mechanisms that are selective for texture density have been revealed at contrast detection threshold. We suggest that these mechanisms have a role to play in the perception of visual textures.

Space time coding for polynomial phase modulated signals

Polynomial phase modulated (PPM) signals have been shown to provide improved error rate performance with respect to conventional modulation formats under additive white Gaussian noise and fading channels in single-input single-output (SISO) communication systems. In this dissertation, systems with two and four transmit antennas using PPM signals were presented. In both cases we employed full-rate space-time block codes in order to take advantage of the multipath channel. For two transmit antennas, we used the orthogonal space-time block code (OSTBC) proposed by Alamouti and performed symbol-wise decoding by estimating the phase coefficients of the PPM signal using three different methods: maximum-likelihood (ML), sub-optimal ML (S-ML) and the high-order ambiguity function (HAF). In the case of four transmit antennas, we used the full-rate quasi-OSTBC (QOSTBC) proposed by Jafarkhani. However, in order to ensure the best error rate performance, PPM signals were selected such as to maximize the QOSTBC’s minimum coding gain distance (CGD). Since this method does not always provide a unique solution, an additional criterion known as maximum channel interference coefficient (CIC) was proposed. Through Monte Carlo simulations it was shown that by using QOSTBCs along with the properly selected PPM constellations based on the CGD and CIC criteria, full diversity in flat fading channels and thus, low BER at high signal-to-noise ratios (SNR) can be ensured. Lastly, the performance of symbol-wise decoding for QOSTBCs was evaluated. In this case a quasi zero-forcing method was used to decouple the received signal and it was shown that although this technique reduces the decoding complexity of the system, there is a penalty to be paid in terms of error rate performance at high SNRs.

Quasi-Orthogonal Space-Time Block Coding Using Polynomial Phase Modulation

Recently, polynomial phase modulation (PPM) was shown to be a power- and bandwidth-efficient modulation format. These two characteristics are in high demand nowadays specially in mobile applications, where devices with size, weight, and power (SWaP) constraints are common. In this paper, we propose implementing a full-diversity quasiorthogonal space-time block code (QOSTBC) using polynomial phase signals as modulation format. QOSTBCs along with PPM are used in order to improve the power efficiency of communication systems with four transmit antennas. We obtain the optimal PPM constellations that ensure full diversity and maximize the QOSTBC's minimum coding gain distance. Simulation results show that by using QOSTBCs along with a properly selected PPM constellation, full diversity in flat fading channels and thus low BER at high signal-to-noise ratios (SNR) can be ensured. More importantly, it is also shown that QOSTBCs using PPM achieve a better error performance than those using conventional modulation formats.

Algorithms for super-resolution of images based on Sparse Representation and Manifolds

lmage super-resolution is defined as a class of techniques that enhance the spatial resolution of images. Super-resolution methods can be subdivided in single and multi image methods. This thesis focuses on developing algorithms based on mathematical theories for single image super­ resolution problems. lndeed, in arder to estimate an output image, we adopta mixed approach: i.e., we use both a dictionary of patches with sparsity constraints (typical of learning-based methods) and regularization terms (typical of reconstruction-based methods). Although the existing methods already per- form well, they do not take into account the geometry of the data to: regularize the solution, cluster data samples (samples are often clustered using algorithms with the Euclidean distance as a dissimilarity metric), learn dictionaries (they are often learned using PCA or K-SVD). Thus, state-of-the-art methods still suffer from shortcomings. In this work, we proposed three new methods to overcome these deficiencies. First, we developed SE-ASDS (a structure tensor based regularization term) in arder to improve the sharpness of edges. SE-ASDS achieves much better results than many state-of-the- art algorithms. Then, we proposed AGNN and GOC algorithms for determining a local subset of training samples from which a good local model can be computed for recon- structing a given input test sample, where we take into account the underlying geometry of the data. AGNN and GOC methods outperform spectral clustering, soft clustering, and geodesic distance based subset selection in most settings. Next, we proposed aSOB strategy which takes into account the geometry of the data and the dictionary size. The aSOB strategy outperforms both PCA and PGA methods. Finally, we combine all our methods in a unique algorithm, named G2SR. Our proposed G2SR algorithm shows better visual and quantitative results when compared to the results of state-of-the-art methods.

‘Genetic Coding’ Reconsidered : An Analysis of Actual Usage

I thank George Pandarakalam for research assistance; Hans-Jörg Rheinberger for hosting my stay at the Max Planck Institute for History of Science, Berlin; and Sahotra Sarkar and referees of this journal for offering detailed comments. Funded by the Wellcome Trust (WT098764MA).

‘Genetic Coding’ Reconsidered : An Analysis of Actual Usage

I thank George Pandarakalam for research assistance; Hans-Jörg Rheinberger for hosting my stay at the Max Planck Institute for History of Science, Berlin; and Sahotra Sarkar and referees of this journal for offering detailed comments. Funded by the Wellcome Trust (WT098764MA).

Asymmetric 3D video coding based on regions of perceptual relevance

This dissertation presents a study and experimental research on asymmetric coding of stereoscopic video. A review on 3D technologies, video formats and coding is rst presented and then particular emphasis is given to asymmetric coding of 3D content and performance evaluation methods, based on subjective measures, of methods using asymmetric coding. The research objective was de ned to be an extension of the current concept of asymmetric coding for stereo video. To achieve this objective the rst step consists in de ning regions in the spatial dimension of auxiliary view with di erent perceptual relevance within the stereo pair, which are identi ed by a binary mask. Then these regions are encoded with better quality (lower quantisation) for the most relevant ones and worse quality (higher quantisation) for the those with lower perceptual relevance. The actual estimation of the relevance of a given region is based on a measure of disparity according to the absolute di erence between views. To allow encoding of a stereo sequence using this method, a reference H.264/MVC encoder (JM) has been modi ed to allow additional con guration parameters and inputs. The nal encoder is still standard compliant. In order to show the viability of the method subjective assessment tests were performed over a wide range of objective qualities of the auxiliary view. The results of these tests allow us to prove 3 main goals. First, it is shown that the proposed method can be more e cient than traditional asymmetric coding when encoding stereo video at higher qualities/rates. The method can also be used to extend the threshold at which uniform asymmetric coding methods start to have an impact on the subjective quality perceived by the observers. Finally the issue of eye dominance is addressed. Results from stereo still images displayed over a short period of time showed it has little or no impact on the proposed method.

Effective video content distribution by combining TCP with adaptive FEC coding

This paper will look at the benefits and limitations of content distribution using Forward Error Correction (FEC) in conjunction with the Transmission Control Protocol (TCP). FEC can be used to reduce the number of retransmissions which would usually result from a lost packet. The requirement for TCP to deal with any losses is then greatly reduced. There are however side-effects to using FEC as a countermeasure to packet loss: an additional requirement for bandwidth. When applications such as real-time video conferencing are needed, delay must be kept to a minimum, and retransmissions are certainly not desirable. A balance, therefore, between additional bandwidth and delay due to retransmissions must be struck. Our results show that the throughput of data can be significantly improved when packet loss occurs using a combination of FEC and TCP, compared to relying solely on TCP for retransmissions. Furthermore, a case study applies the result to demonstrate the achievable improvements in the quality of streaming video perceived by end users.

Bounds on end-to-end performance of networks employing erasure control coding

Erasure control coding has been exploited in communication networks with an aim to improve the end-to-end performance of data delivery across the network. To address the concerns over the strengths and constraints of erasure coding schemes in this application, we examine the performance limits of two erasure control coding strategies, forward erasure recovery and adaptive erasure recovery. Our investigation shows that the throughput of a network using an (n, k) forward erasure control code is capped by r =k/n when the packet loss rate p ≤ (te/n) and by k(l-p)/(n-te) when p > (t e/n), where te is the erasure control capability of the code. It also shows that the lower bound of the residual loss rate of such a network is (np-te)/(n-te) for (te/n) < p ≤ 1. Especially, if the code used is maximum distance separable, the Shannon capacity of the erasure channel, i.e. 1-p, can be achieved and the residual loss rate is lower bounded by (p+r-1)/r, for (1-r) < p ≤ 1. To address the requirements in real-time applications, we also investigate the service completion time of different schemes. It is revealed that the latency of the forward erasure recovery scheme is fractionally higher than that of the scheme without erasure control coding or retransmission mechanisms (using UDP), but much lower than that of the adaptive erasure scheme when the packet loss rate is high. Results on comparisons between the two erasure control schemes exhibit their advantages as well as disadvantages in the role of delivering end-to-end services. To show the impact of the bounds derived on the end-to-end performance of a TCP/IP network, a case study is provided to demonstrate how erasure control coding could be used to maximize the performance of practical systems. © 2010 IEEE.

Suppression of patterning effects in digital communications by an adaptive constrained coding

We quantify the error statistics and patterning effects in a 5x 40 Gbit/s WDM RZ-DBPSK SMF/DCF fibre link using hybrid Raman/EDFA amplification. We propose an adaptive constrained coding for the suppression of errors due to patterning effects. It is established, that this coding technique can greatly reduce the bit error rate (BER) value even for large BER (BER > 101). The proposed approach can be used in the combination with the forward error correction schemes (FEC) to correct the errors even when real channel BER is outside the FEC workspace.

A long non-coding RNA targets microRNA miR-34a to regulate colon cancer stem cell asymmetric division.

The roles of long non-coding RNAs (lncRNAs) in regulating cancer and stem cells are being increasingly appreciated. Its diverse mechanisms provide the regulatory network with a bigger repertoire to increase complexity. Here we report a novel LncRNA, Lnc34a, that is enriched in colon cancer stem cells (CCSCs) and initiates asymmetric division by directly targeting the microRNA miR-34a to cause its spatial imbalance. Lnc34a recruits Dnmt3a via PHB2 and HDAC1 to methylate and deacetylate the miR-34a promoter simultaneously, hence epigenetically silencing miR-34a expression independent of its upstream regulator, p53. Lnc34a levels affect CCSC self-renewal and colorectal cancer (CRC) growth in xenograft models. Lnc34a is upregulated in late-stage CRCs, contributing to epigenetic miR-34a silencing and CRC proliferation. The fact that lncRNA targets microRNA highlights the regulatory complexity of non-coding RNAs (ncRNAs), which occupy the bulk of the genome.