Complex wavelets and shift invariance

Recently we have developed a new form of discrete wavelet transform, which generates complex coefficients by using a dual tree of wavelet filters to obtain their real and imaginary parts. This introduces limited redundancy (2 m:1 for m-dimensional signals) and allows the transform to provide approximate shift invariance and directionally selective filters (properties lacking in the traditional wavelet transform) while preserving the usual properties of perfect reconstruction and computational efficiency with good well-balanced frequency responses. In this paper we analyse why the new transform can be designed to be shift invariant, and describe how to estimate the accuracy of this approximation and design suitable filters to achieve this.

Evaluating perceptual maps of asymmetries for gait symmetry quantification and pathology detection

Le mouvement de la marche est un processus essentiel de l'activité humaine et aussi le résultat de nombreuses interactions collaboratives entre les systèmes neurologiques, articulaires et musculo-squelettiques fonctionnant ensemble efficacement. Ceci explique pourquoi une analyse de la marche est aujourd'hui de plus en plus utilisée pour le diagnostic (et aussi la prévention) de différents types de maladies (neurologiques, musculaires, orthopédique, etc.). Ce rapport présente une nouvelle méthode pour visualiser rapidement les différentes parties du corps humain liées à une possible asymétrie (temporellement invariante par translation) existant dans la démarche d'un patient pour une possible utilisation clinique quotidienne. L'objectif est de fournir une méthode à la fois facile et peu dispendieuse permettant la mesure et l'affichage visuel, d'une manière intuitive et perceptive, des différentes parties asymétriques d'une démarche. La méthode proposée repose sur l'utilisation d'un capteur de profondeur peu dispendieux (la Kinect) qui est très bien adaptée pour un diagnostique rapide effectué dans de petites salles médicales car ce capteur est d'une part facile à installer et ne nécessitant aucun marqueur. L'algorithme que nous allons présenter est basé sur le fait que la marche saine possède des propriétés de symétrie (relativement à une invariance temporelle) dans le plan coronal.

The temporal pattern of customer satisfaction: a construal-level approach

Customer satisfaction has been traditionally studied and measured regardless of the time elapsed since the purchase. Some studies have recently reopened the debate about the temporal pattern of satisfaction. This research aims to explain why “how you evaluate a service depends on when you evaluate it” on the basis of the theoretical framework proposed by Construal-Level Theory (CLT). Although an empirical investigation is still lacking, the literature does not deny that CLT can be applied also with regard to past events. Moreover, some studies support the idea that satisfaction is a good predictor of future intentions, while others do not. On the basis of CLT, we argue that these inconsistent results are due to the different construal levels of the information pertaining to retrospective and prospective evaluations. Building on the Two-Factor Theory, we explain the persistence of certain attributes’ representations over time according to their relationship with overall performance. We present and discuss three experiments and one field study that were conducted a) to test the extensibility of CLT to past events, b) to disentangle memory and construal effects, c) to study the effect of different temporal perspective on overall satisfaction judgements, and d) to investigate the temporal shift of the determinants of customer satisfaction as a function of temporal distance.

Position, rotation, and scale invariant recognition of images using higher-order spectra

A new approach to recognition of images using invariant features based on higher-order spectra is presented. Higher-order spectra are translation invariant because translation produces linear phase shifts which cancel. Scale and amplification invariance are satisfied by the phase of the integral of a higher-order spectrum along a radial line in higher-order frequency space because the contour of integration maps onto itself and both the real and imaginary parts are affected equally by the transformation. Rotation invariance is introduced by deriving invariants from the Radon transform of the image and using the cyclic-shift invariance property of the discrete Fourier transform magnitude. Results on synthetic and actual images show isolated, compact clusters in feature space and high classification accuracies

Gigabit Pulse Position Bistability in Semiconductor Lasers

The paper briefly reviews the major forms of optical bistability in active optical devices compatible for use in gigabit optical communication systems, and reports an entirely new optical bistability for the first time. Unlike previous devices, the two bistable states of the optical device are each a series of picosecond optical pulses at 1 GHz or greater repetition rates, and are distinguished by a half period temporal shift between their temporal positions in relation to a clock pulse. The bistable device is based on a gain switched semiconductor laser. Theoretical studies suggest 100-ps switching speeds might be achieved, and experimental results are reported indicating optically triggered switching times of 500 ps. © 1987, American Medical Association. All rights reserved.

Opioid Withdrawal for 4 Days Prevents Synaptic Depression Induced by Low Dose of Morphine or Naloxone in Rat Hippocampal CA1 Area In Vivo

The formation of memory is believed to depend on experience- or activity-dependent synaptic plasticity, which is exquisitely sensitive to psychological stress since inescapable stress impairs long-term potentiation (LTP) but facilitates long-term depression (LTD). Our recent studies demonstrated that 4 days of opioid withdrawal enables maximal extents of both hippocampal LTP and drug-reinforced behavior; while elevated-platform stress enables these phenomena at 18 h of opioid withdrawal. Here, we examined the effects of low dose of morphine (0.5 mg kg(-1), i.p.) or the opioid receptor antagonist naloxone (1 mg kg(-1), i.p.) on synaptic efficacy in the hippocampal CA1 region of anesthetized rats. A form of synaptic depression was induced by low dose of morphine or naloxone in rats after 18 h but not 4 days of opioid withdrawal. This synaptic depression was dependent on both N-methyl-D-aspartate receptor and synaptic activity, similar to the hippocampal long-term depression induced by low frequency stimulation. Elevated-platform stress given 2 h before experiment prevented the synaptic depression at 18 h of opioid withdrawal; in contrast, the glucocorticoid receptor (GR) antagonist RU38486 treatment (20 mg kg(-1), s.c., twice per day for first 3 days of withdrawal), or a high dose of morphine reexposure (15 mg kg(-1), s.c., 12 h before experiment), enabled the synaptic depression on 4 days of opioid withdrawal. This temporal shift of synaptic depression by stress or GR blockade supplements our previous findings of potentially correlated temporal shifts of LTP induction and drug-reinforced behavior during opioid withdrawal. Our results therefore support the idea that stress experience during opioid withdrawal may modify hippocampal synaptic plasticity and play important roles in drug-associated memory. (C) 2009 Wiley-Liss, Inc.

Statistical image modelling using interscale phase relationships of complex wavelet coefficients

A novel method for modelling the statistics of 2D photographic images useful in image restoration is defined. The new method is based on the Dual Tree Complex Wavelet Transform (DT-CWT) but a phase rotation is applied to the coefficients to create complex coefficients whose phase is shift-invariant at multiscale edge and ridge features. This is in addition to the magnitude shift invariance achieved by the DT-CWT. The increased correlation between coefficients adjacent in space and scale provides an improved mechanism for signal estimation. © 2006 IEEE.

Biologically-inspired object recognition system with features from complex wavelets

In this paper, a novel cortex-inspired feed-forward hierarchical object recognition system based on complex wavelets is proposed and tested. Complex wavelets contain three key properties for object representation: shift invariance, which enables the extraction of stable local features; good directional selectivity, which simplifies the determination of image orientations; and limited redundancy, which allows for efficient signal analysis using the multi-resolution decomposition offered by complex wavelets. In this paper, we propose a complete cortex-inspired object recognition system based on complex wavelets. We find that the implementation of the HMAX model for object recognition in [1, 2] is rather over-complete and includes too much redundant information and processing. We have optimized the structure of the model to make it more efficient. Specifically, we have used the Caltech 5 standard dataset to compare with Serre's model in [2] (which employs Gabor filter bands). Results demonstrate that the complex wavelet model achieves a speed improvement of about 4 times over the Serre model and gives comparable recognition performance. © 2011 IEEE.

Time-Frequency Representations for Speech Signals

This work addresses two related questions. The first question is what joint time-frequency energy representations are most appropriate for auditory signals, in particular, for speech signals in sonorant regions. The quadratic transforms of the signal are examined, a large class that includes, for example, the spectrograms and the Wigner distribution. Quasi-stationarity is not assumed, since this would neglect dynamic regions. A set of desired properties is proposed for the representation: (1) shift-invariance, (2) positivity, (3) superposition, (4) locality, and (5) smoothness. Several relations among these properties are proved: shift-invariance and positivity imply the transform is a superposition of spectrograms; positivity and superposition are equivalent conditions when the transform is real; positivity limits the simultaneous time and frequency resolution (locality) possible for the transform, defining an uncertainty relation for joint time-frequency energy representations; and locality and smoothness tradeoff by the 2-D generalization of the classical uncertainty relation. The transform that best meets these criteria is derived, which consists of two-dimensionally smoothed Wigner distributions with (possibly oriented) 2-D guassian kernels. These transforms are then related to time-frequency filtering, a method for estimating the time-varying 'transfer function' of the vocal tract, which is somewhat analogous to ceptstral filtering generalized to the time-varying case. Natural speech examples are provided. The second question addressed is how to obtain a rich, symbolic description of the phonetically relevant features in these time-frequency energy surfaces, the so-called schematic spectrogram. Time-frequency ridges, the 2-D analog of spectral peaks, are one feature that is proposed. If non-oriented kernels are used for the energy representation, then the ridge tops can be identified, with zero-crossings in the inner product of the gradient vector and the direction of greatest downward curvature. If oriented kernels are used, the method can be generalized to give better orientation selectivity (e.g., at intersecting ridges) at the cost of poorer time-frequency locality. Many speech examples are given showing the performance for some traditionally difficult cases: semi-vowels and glides, nasalized vowels, consonant-vowel transitions, female speech, and imperfect transmission channels.

Watermarking for Multimedia Security using Complex Wavelets

This paper investigates the application of complex wavelet transforms to the field of digital data hiding. Complex wavelets offer improved directional selectivity and shift invariance over their discretely sampled counterparts allowing for better adaptation of watermark distortions to the host media. Two methods of deriving visual models for the watermarking system are adapted to the complex wavelet transforms and their performances are compared. To produce improved capacity a spread transform embedding algorithm is devised, this combines the robustness of spread spectrum methods with the high capacity of quantization based methods. Using established information theoretic methods, limits of watermark capacity are derived that demonstrate the superiority of complex wavelets over discretely sampled wavelets. Finally results for the algorithm against commonly used attacks demonstrate its robustness and the improved performance offered by complex wavelet transforms.

Bioavailability of 2,4-dichlorophenol associated with soil water-soluble humic material

Interaction of organic xenobiotics with soil water-soluble humic material (WSHM) may influence their environmental fate and bioavailability. We utilized bacterial assays (lux-based toxicity and mineralization by Burkholderia sp. RASC) to assess temporal changes in the bioavailability of [¹⁴C]-2,4-dichlorophenol (2,4-DCP) in soil water extracts (29.5 μg mL^-1 2,4-DCP; 840.2 μg mL^-1 organic carbon). HPLC determined and bioavailable concentrations were compared. Gel permeation chromatography (GPC) was used to confirm the association of a fraction (>50%) of [¹⁴C]-2,4-DCP with WSHM. Subtle differences in parameters describing 2,4-DCP mineralization curves were recorded for different soil-2,4-DCP contact times. Problems regarding the interpretation of mineralization data when assessing the bioavailability of toxic compounds are discussed. The lux-bioassay revealed a time-dependent reduction in 2,4-DCP bioavailability: after 7 d, less than 20% was bioavailable. However, GPC showed no quantitative difference in the amount of WSHM-associated 2,4-DCP over this time. These data suggest qualitative changes in the nature of the 2,4-DCP-WSHM association and that associated 2,4-DCP may exert a toxic effect. Although GPC distinguished between free- and WSHM-associated 2,4-DCP, it did not resolve the temporal shift in bioavailability revealed by the lux biosensor. These results stress that assessment of risk posed by chemicals must be considered using appropriate biological assays.

The influence of the loop between residues 223-235 in beetle luciferase bioluminescence spectra: A solvent gate for the active site of pH-sensitive luciferases

Beetle luciferases emit a wide range of bioluminescence colors, ranging from green to red. Firefly luciferases can shift the spectrum to red in response to pH and temperature changes, whereas click beetle and railroadworm luciferases do not. Despite many studies on firefly luciferases, the origin of pH-sensitivity is far from being understood. Through comparative site-directed mutagenesis and modeling studies, using the pH-sensitive luciferases (Macrolampis and Cratomorphus distinctus fireflies) and the pH-insensitive luciferases (Pyrearinus termitilluminans, Phrixotrix viviani and Phrixotrix hirtus) cloned by our group, here we show that substitutions dramatically affecting bioluminescence colors in both groups of luciferases are clustered in the loop between residues 223-235 (Photinus pyralis sequence). The substitutions at positions 227, 228 and 229 (P. pyralis sequence) cause dramatic redshift and temporal shift in both groups of luciferases, indicating their involvement in labile interactions. Modeling studies showed that the residues Y227 and N229 are buried in the protein core, fixing the loop to other structural elements participating at the bottom of the luciferin binding site. Changes in pH and temperature (in firefly luciferases), as well as point mutations in this loop, may disrupt the interactions of these structural elements exposing the active site and modulating bioluminescence colors. © 2007 The Authors.

Modelling the effects of land use and climate changes on hydrology in the Ursern Valley, Switzerland

While many studies have been conducted in mountainous catchments to examine the impact of climate change on hydrology, the interactions between climate changes and land use components have largely unknown impacts on hydrology in alpine regions. They need to be given special attention in order to devise possible strategies concerning general development in these regions. Thus, the main aim was to examine the impact of land use (i.e. bushland expansion) and climate changes (i.e. increase of temperature) on hydrology by model simulations. For this purpose, the physically based WaSiM-ETH model was applied to the catchment of Ursern Valley in the central Alps (191 km2) over the period of 1983−2005. Modelling results showed that the reduction of the mean monthly discharge during the summer period is due primarily to the retreat of snow discharge in time and secondarily to the reduction in the glacier surface area together with its retreat in time, rather than the increase in the evapotranspiration due to the expansion of the “green alder” on the expense of grassland. The significant decrease in summer discharge during July, August and September shows a change in the regime from b-glacio-nival to nivo-glacial. These changes are confirmed by the modeling results that attest to a temporal shift in snowmelt and glacier discharge towards earlier in the year: March, April and May for snowmelt and May and June for glacier discharge. It is expected that the yearly total discharge due to the land use changes will be reduced by 0.6% in the near future, whereas, it will be reduced by about 5% if climate change is also taken into account. Copyright © 2013 John Wiley & Sons, Ltd.