Operator Theory and Its Applications: In Memory of V. B. Lidskii (1924-2008)

This book is a collection of articles devoted to the theory of linear operators in Hilbert spaces and its applications. The subjects covered range from the abstract theory of Toeplitz operators to the analysis of very specific differential operators arising in quantum mechanics, electromagnetism, and the theory of elasticity; the stability of numerical methods is also discussed. Many of the articles deal with spectral problems for not necessarily selfadjoint operators. Some of the articles are surveys outlining the current state of the subject and presenting open problems.

Retrieval of global atmospheric electrical activity at a polluted urban site

The atmospheric electrical Potential Gradient (PG) arises from global thunderstorm activity, but surface measurements of the atmospheric Potential Gradient (PG) are influenced by global thunderstorms and local aerosol concentration changes. The local aerosol change can be monitored independently, and in some cases the concentration changes are closely related to PG changes. For these circumstances, a general theory to remove the local aerosol influence on PG measurements has been developed. Continuous measurements of PG and aerosol mass concentration were made during 24–31 Dec, 2005 within an urban environment at Reading, UK. The average diurnal variation of PG showed a double diurnal cycle, with maxima in the early morning and evening hours. The aerosol concentration has similar double maxima. Removing the aerosol using from the PG and aerosol correlation returns a single diurnal cycle, suggestive of the more global PG diurnal cycle.

Bayesian retrieval of complete posterior PDFs of oceanic rain rate from microwave observations

A new Bayesian algorithm for retrieving surface rain rate from Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI) over the ocean is presented, along with validations against estimates from the TRMM Precipitation Radar (PR). The Bayesian approach offers a rigorous basis for optimally combining multichannel observations with prior knowledge. While other rain-rate algorithms have been published that are based at least partly on Bayesian reasoning, this is believed to be the first self-contained algorithm that fully exploits Bayes’s theorem to yield not just a single rain rate, but rather a continuous posterior probability distribution of rain rate. To advance the understanding of theoretical benefits of the Bayesian approach, sensitivity analyses have been conducted based on two synthetic datasets for which the “true” conditional and prior distribution are known. Results demonstrate that even when the prior and conditional likelihoods are specified perfectly, biased retrievals may occur at high rain rates. This bias is not the result of a defect of the Bayesian formalism, but rather represents the expected outcome when the physical constraint imposed by the radiometric observations is weak owing to saturation effects. It is also suggested that both the choice of the estimators and the prior information are crucial to the retrieval. In addition, the performance of the Bayesian algorithm herein is found to be comparable to that of other benchmark algorithms in real-world applications, while having the additional advantage of providing a complete continuous posterior probability distribution of surface rain rate.

The relation between content and structure in language production: an analysis of speech errors in semantic dementia

In order to explore the impact of a degraded semantic system on the structure of language production, we analysed transcripts from autobiographical memory interviews to identify naturally-occurring speech errors by eight patients with semantic dementia (SD) and eight age-matched normal speakers. Relative to controls, patients were significantly more likely to (a) substitute and omit open class words, (b) substitute (but not omit) closed class words, (c) substitute incorrect complex morphological forms and (d) produce semantically and/or syntactically anomalous sentences. Phonological errors were scarce in both groups. The study confirms previous evidence of SD patients’ problems with open class content words which are replaced by higher frequency, less specific terms. It presents the first evidence that SD patients have problems with closed class items and make syntactic as well as semantic speech errors, although these grammatical abnormalities are mostly subtle rather than gross. The results can be explained by the semantic deficit which disrupts the representation of a pre-verbal message, lexical retrieval and the early stages of grammatical encoding.

Speech perception and phonological short-term memory capacity in language impairment: preliminary evidence from adolescents with specific language impairment (SLI) and autism spectrum disorders (ASD)

Background: The cognitive bases of language impairment in specific language impairment (SLI) and autism spectrum disorders (ASD) were investigated in a novel non-word comparison task which manipulated phonological short-term memory (PSTM) and speech perception, both implicated in poor non-word repetition. Aims: This study aimed to investigate the contributions of PSTM and speech perception in non-word processing and whether individuals with SLI and ASD plus language impairment (ALI) show similar or different patterns of deficit in these cognitive processes. Method & Procedures: Three groups of adolescents (aged 14–17 years), 14 with SLI, 16 with ALI, and 17 age and non-verbal IQ matched typically developing (TD) controls, made speeded discriminations between non-word pairs. Stimuli varied in PSTM load (two- or four-syllables) and speech perception load (mismatches on a word-initial or word-medial segment). Outcomes & Results: Reaction times showed effects of both non-word length and mismatch position and these factors interacted: four-syllable and word-initial mismatch stimuli resulted in the slowest decisions. Individuals with language impairment showed the same pattern of performance as those with typical development in the reaction time data. A marginal interaction between group and item length was driven by the SLI and ALI groups being less accurate with long items than short ones, a difference not found in the TD group. Conclusions & Implications: Non-word discrimination suggests that there are similarities and differences between adolescents with SLI and ALI and their TD peers. Reaction times appear to be affected by increasing PSTM and speech perception loads in a similar way. However, there was some, albeit weaker, evidence that adolescents with SLI and ALI are less accurate than TD individuals, with both showing an effect of PSTM load. This may indicate, at some level, the processing substrate supporting both PSTM and speech perception is intact in adolescents with SLI and ALI, but also in both there may be impaired access to PSTM resources.

The impact of fruit flavonoids on memory and cognition

There is intense interest in the studies related to the potential of phytochemical-rich foods to prevent age-related neurodegeneration and cognitive decline. Recent evidence has indicated that a group of plant-derived compounds known as flavonoids may exert particularly powerful actions on mammalian cognition and may reverse age-related declines in memory and learning. In particular, evidence suggests that foods rich in three specific flavonoid sub-groups, the flavanols, anthocyanins and/or flavanones, possess the greatest potential to act on the cognitive processes. This review will highlight the evidence for the actions of such flavonoids, found most commonly in fruits, such as apples, berries and citrus, on cognitive behaviour and the underlying cellular architecture. Although the precise mechanisms by which these flavonoids act within the brain remain unresolved, the present review focuses on their ability to protect vulnerable neurons and enhance the function of existing neuronal structures, two processes known to be influenced by flavonoids and also known to underpin neuro-cognitive function. Most notably, we discuss their selective interactions with protein kinase and lipid kinase signalling cascades (i.e. phosphoinositide-3 kinase/Akt and mitogen-activated protein kinase pathways), which regulate transcription factors and gene expression involved in both synaptic plasticity and cerebrovascular blood flow. Overall, the review attempts to provide an initial insight into the potential impact of regular flavonoid-rich fruit consumption on normal or abnormal deteriorations in cognitive performance.

Optimising memory usage in n-tuple neural networks

The use of n-tuple or weightless neural networks as pattern recognition devices is well known (Aleksander and Stonham, 1979). They have some significant advantages over the more common and biologically plausible networks, such as multi-layer perceptrons; for example, n-tuple networks have been used for a variety of tasks, the most popular being real-time pattern recognition, and they can be implemented easily in hardware as they use standard random access memories. In operation, a series of images of an object are shown to the network, each being processed suitably and effectively stored in a memory called a discriminator. Then, when another image is shown to the system, it is processed in a similar manner and the system reports whether it recognises the image; is the image sufficiently similar to one already taught? If the system is to be able to recognise and discriminate between m-objects, then it must contain m-discriminators. This can require a great deal of memory. This paper describes various ways in which memory requirements can be reduced, including a novel method for multiple discriminator n-tuple networks used for pattern recognition. By using this method, the memory normally required to handle m-objects can be used to recognise and discriminate between 2^m — 2 objects.

Auto-associative memory using n-tuple techniques

The use of n-tuple or weightless neural networks as pattern recognition devices has been well documented. They have a significant advantages over more common networks paradigms, such as the multilayer perceptron in that they can be easily implemented in digital hardware using standard random access memories. To date, n-tuple networks have predominantly been used as fast pattern classification devices. The paper describes how n-tuple techniques can be used in the hardware implementation of a general auto-associative network.

Quantifying the response of the ORAC aerosol optical depth retrieval for MSG SEVIRI to aerosol model assumptions

We test the response of the Oxford-RAL Aerosol and Cloud (ORAC) retrieval algorithm for MSG SEVIRI to changes in the aerosol properties used in the dust aerosol model, using data from the Dust Outflow and Deposition to the Ocean (DODO) flight campaign in August 2006. We find that using the observed DODO free tropospheric aerosol size distribution and refractive index increases simulated top of the atmosphere radiance at 0.55 µm assuming a fixed erosol optical depth of 0.5 by 10–15 %, reaching a maximum difference at low solar zenith angles. We test the sensitivity of the retrieval to the vertical distribution f the aerosol and find that this is unimportant in determining simulated radiance at 0.55 µm. We also test the ability of the ORAC retrieval when used to produce the GlobAerosol dataset to correctly identify continental aerosol outflow from the African continent and we find that it poorly constrains aerosol speciation. We develop spatially and temporally resolved prior distributions of aerosols to inform the retrieval which incorporates five aerosol models: desert dust, maritime, biomass burning, urban and continental. We use a Saharan Dust Index and the GEOS-Chem chemistry transport model to describe dust and biomass burning aerosol outflow, and compare AOD using our speciation against the GlobAerosol retrieval during January and July 2006. We find AOD discrepancies of 0.2–1 over regions of intense biomass burning outflow, where AOD from our aerosol speciation and GlobAerosol speciation can differ by as much as 50 - 70 %.

A Wiener model for memory high power amplifiers using B-spline function approximation

In this paper we introduce a new Wiener system modeling approach for memory high power amplifiers in communication systems using observational input/output data. By assuming that the nonlinearity in the Wiener model is mainly dependent on the input signal amplitude, the complex valued nonlinear static function is represented by two real valued B-spline curves, one for the amplitude distortion and another for the phase shift, respectively. The Gauss-Newton algorithm is applied for the parameter estimation, which incorporates the De Boor algorithm, including both the B-spline curve and the first order derivatives recursion. An illustrative example is utilized to demonstrate the efficacy of the proposed approach.