Two Dimensional Signal Representation Using Prolate Spheroidal Functions

The most widely used methods of signal representation are the time function and the frequency function or spectrum representations. This work is concerned with the development of a representation which is a combination of these two. Two previous attempts at defining this type of signal representation, which is referred to as two dimensional representation, have been made and a summary and evaluation of these attempts is presented. The primary objective of the work reported here was to develop a practical two dimensional representation which has the desired two dimensional conceptual properties as well as mathematical convenience. The representations defined are based on the angular prolate spheroidal functions. These functions have a number of desirable properties among which are the followings they are orthogonal over both a finite and the infinite interval, they are bandlimited, and they have certain properties concerning their maximal proximity to being timelimited. The procedure used in defining the first two dimensional representation is to make an orthogonal expansion, using the prolate spheroidal functions, of each timelimited portion of each bandlimited portion of the signal to be represented. The second two dimensional representation is defined from an orthogonal expansion of each bandlimited portion of each timelimited portion of the signal to be represented. For both of these, the summation over all time intervals and all frequency intervals results in the complete representation of the signal. It is seen from this that since it is not possible to timelimit and bandlimit simultaneously, these limiting processes have been carried out serially. Due to the peculiar properties of the prolate spheroidal functions, as the number of orthogonal function terms is increased, the representation of a timelimited function converges first in a certain bandwidth, and the representation of a band- limited function converges first in a certain time interval. It is demonstrated that both series representations will converge to either a timelimited, or a bandlimited portion of the represented signal upon inclusion of the proper terms. Following this, several applications of the representations are presented. First, it is shown that the result of the convolution of 2 two dimensionally represented functions may be determined at discrete values of time from the expansion coefficients alone. The spectrum of the product of two functions may be determined in a similar manner at discrete values of frequency. As a result, it is possible to determine the contribution made to the output of a linear system at any time due to the portion of the input in any time and frequency interval. A technique is also developed for the solution of this same problem for the more general time variable linear system with the output being determined in continuous form rather than only at discrete values. It is somewhat more difficult to calculate the coefficients in this case, however. Another application demonstrated is a method by which the value of Woodward\u27s ambiguity function may be calculated for discrete values of the time and frequency variables. The two dimensional nature of the representation is demonstrated by two numerical examples using very elementary time functions. A further numerical example is provided for the case of the determination of the output of a linear system at discrete values of time. This work is concluded by a brief listing of further problems which seem amenable to solution as a result of this type of analysis. This list includes such problems as biological system signal analysis, signal design, and random process representation

User's manual for the coupled mode version of the normal modes rotor aeroelastic analysis computer program

This User's Manual was prepared to provide the engineer with the information required to run the coupled mode version of the Normal Modes Rotor Aeroelastic Analysis Computer Program. The manual provides a full set of instructions for running the program, including calculation of blade modes, calculations of variable induced velocity distribution and the calculation of the time history of the response for either a single blade or a complete rotor with an airframe (the latter with constant inflow)

Aesthetic Worlds: Rimbaud, Williams and Baroque Form

The sense of form that provides the modern poet with a unique experience of the literary object has been crucial to various attempts to compare poetry to other cultural activities. In maintaining similar conceptions of the relationship between poetry and painting, Arthur Rimbaud and W. C. Williams establish a common basis for interpreting their creative work. And yet their poetry is more crucially concerned with the sudden emergence of visible "worlds" containing verbal objects that integrate a new kind of literary text. This paper discusses the emergence of "aesthetic worlds" in the work of both poets and then examines how a common concern with Baroque form unites them in the phenomenological task of overcoming Cartesian dualism

On the influence of spatial information for hyper-spectral satellite imaging characterization

Land-use classification for hyper-spectral satellite images requires a previous step of pixel characterization. In the easiest case, each pixel is characterized by its spectral curve. The improvementof the spectral and spatial resolution in hyper-spectral sensors has led to very large data sets. Some researches have focused on better classifiers that can handle big amounts of data. Others have faced the problem of band selection to reduce the dimensionality of the feature space. However, thanks to the improvement in the spatial resolution of the sensors, spatial information may also provide new featuresfor hyper-spectral satellite data. Here, an study on the influence of spectral-spatial features combined with an unsupervised band selection method is presented. The results show that it is possible to reduce very significantly the number of spectral bands required while having an adequate description of the spectral-spatial characteristics of the image for pixel classification tasksThis work has been partly supported by grant FPI PREDOC/2007/20 from Fundació Caixa Castelló-Bancaixa and projects CSD2007-00018 (Consolider Ingenio 2010) and AYA2008-05965-C04-04 from the Spanish Ministry of Science and Innovatio

Statistical methodology for the analysis of dye-switch microarray experiments

<p>Abstract</p> <p>Background</p> <p>In individually dye-balanced microarray designs, each biological sample is hybridized on two different slides, once with <it>Cy3 </it>and once with <it>Cy5</it>. While this strategy ensures an automatic correction of the gene-specific labelling bias, it also induces dependencies between log-ratio measurements that must be taken into account in the statistical analysis.</p> <p>Results</p> <p>We present two original statistical procedures for the statistical analysis of individually balanced designs. These procedures are compared with the usual ML and REML mixed model procedures proposed in most statistical toolboxes, on both simulated and real data.</p> <p>Conclusion</p> <p>The UP procedure we propose as an alternative to usual mixed model procedures is more efficient and significantly faster to compute. This result provides some useful guidelines for the analysis of complex designs.</p

Relationship between Audiometric Slope and Tinnitus Pitch in Tinnitus Patients: Insights into the Mechanisms of Tinnitus Generation

BACKGROUND: Different mechanisms have been proposed to be involved in tinnitus generation, among them reduced lateral inhibition and homeostatic plasticity. On a perceptual level these different mechanisms should be reflected by the relationship between the individual audiometric slope and the perceived tinnitus pitch. Whereas some studies found the tinnitus pitch corresponding to the maximum hearing loss, others stressed the relevance of the edge frequency. This study investigates the relationship between tinnitus pitch and audiometric slope in a large sample. METHODOLOGY: This retrospective observational study analyzed 286 patients. The matched tinnitus pitch was compared to the frequency of maximum hearing loss and the edge of the audiogram (steepest hearing loss) by t-tests and correlation coefficients. These analyses were performed for the whole group and for sub-groups (uni- vs. bilateral (117 vs. 338 ears), pure-tone vs. narrow-band (340 vs. 115 ears), and low and high audiometric slope (114 vs. 113 ears)). FINDINGS: For the right ear, tinnitus pitch was in the same range and correlated significantly with the frequency of maximum hearing loss, but differed from and did not correlate with the edge frequency. For the left ear, similar results were found but the correlation between tinnitus pitch and maximum hearing loss did not reach significance. Sub-group analyses (bi- and unilateral, tinnitus character, slope steepness) revealed identical results except for the sub-group with high audiometric slope which revealed a higher frequency of maximum hearing loss as compared to the tinnitus pitch. CONCLUSION: The study-results confirm a relationship between tinnitus pitch and maximum hearing loss but not to the edge frequency, suggesting that tinnitus is rather a fill-in-phenomenon resulting from homeostatic mechanisms, than the result of deficient lateral inhibition. Sub-group analyses suggest that audiometric steepness and the side of affected ear affect this relationship. Future studies should control for these potential confounding factors

Mining and analysis of audiology data to find significant factors associated with tinnitus masker

Objectives: The objective of this research is to find the factors associated with tinnitus masker from the literature, and by using the large amount of audiology data available from a large NHS (National Health Services, UK) hearing aid clinic. The factors evaluated were hearing impairment, age, gender, hearing aid type, mould and clinical comments. Design: The research includes literature survey for factors associated with tinnitus masker, and performs the analysis of audiology data using statistical and data mining techniques. Setting: This research uses a large audiology data but it also faced the problem of limited data for tinnitus. Participants: It uses 1,316 records for tinnitus and other diagnoses, and 10,437 records of clinical comments from a hearing aid clinic. Primary and secondary outcome measures: The research is looking for variables associated with tinnitus masker, and in future, these variables can be combined into a single model to develop a decision support system to predict about tinnitus masker for a patient. Results: The results demonstrated that tinnitus maskers are more likely to be fit to individuals with milder forms of hearing loss, and the factors age, gender, type of hearing aid and mould were all found significantly associated with tinnitus masker. In particular, those patients having Age<=55 years were more likely to wear a tinnitus masker, as well as those with milder forms of hearing loss. ITE (in the ear) hearing aids were also found associated with tinnitus masker. A feedback on the results of association of mould with tinnitus masker from a professional audiologist of a large NHS (National Health Services, UK) was also taken to better understand them. The results were obtained with different accuracy for different techniques. For example, the chi-squared test results were obtained with 95% accuracy, for Support and Confidence only those results were retained which had more than 1% Support and 80% Confidence. Conclusions: The variables audiograms, age, gender, hearing aid type and mould were found associated with the choice of tinnitus masker in the literature and by using statistical and data mining techniques. The further work in this research would lead to the development of a decision support system for tinnitus masker with an explanation that how that decision was obtained

Threshold Average Precision (TAP-k): a measure of retrieval designed for bioinformatics

Motivation: Since database retrieval is a fundamental operation, the measurement of retrieval efficacy is critical to progress in bioinformatics. This article points out some issues with current methods of measuring retrieval efficacy and suggests some improvements. In particular, many studies have used the pooled receiver operating characteristic for n irrelevant records (ROCn) score, the area under the ROC curve (AUC) of a ‘pooled’ ROC curve, truncated at n irrelevant records. Unfortunately, the pooled ROCn score does not faithfully reflect actual usage of retrieval algorithms. Additionally, a pooled ROCn score can be very sensitive to retrieval results from as little as a single query

Predictive gene lists for breast cancer prognosis: A topographic visualisation study

<p>Abstract</p> <p>Background</p> <p>The controversy surrounding the non-uniqueness of predictive gene lists (PGL) of small selected subsets of genes from very large potential candidates as available in DNA microarray experiments is now widely acknowledged <abbrgrp><abbr bid="B1">1</abbr></abbrgrp>. Many of these studies have focused on constructing discriminative semi-parametric models and as such are also subject to the issue of random correlations of sparse model selection in high dimensional spaces. In this work we outline a different approach based around an unsupervised patient-specific nonlinear topographic projection in predictive gene lists.</p> <p>Methods</p> <p>We construct nonlinear topographic projection maps based on inter-patient gene-list relative dissimilarities. The Neuroscale, the Stochastic Neighbor Embedding(SNE) and the Locally Linear Embedding(LLE) techniques have been used to construct two-dimensional projective visualisation plots of 70 dimensional PGLs per patient, classifiers are also constructed to identify the prognosis indicator of each patient using the resulting projections from those visualisation techniques and investigate whether <it>a-posteriori </it>two prognosis groups are separable on the evidence of the gene lists.</p> <p>A literature-proposed predictive gene list for breast cancer is benchmarked against a separate gene list using the above methods. Generalisation ability is investigated by using the mapping capability of Neuroscale to visualise the follow-up study, but based on the projections derived from the original dataset.</p> <p>Results</p> <p>The results indicate that small subsets of patient-specific PGLs have insufficient prognostic dissimilarity to permit a distinction between two prognosis patients. Uncertainty and diversity across multiple gene expressions prevents unambiguous or even confident patient grouping. Comparative projections across different PGLs provide similar results.</p> <p>Conclusion</p> <p>The random correlation effect to an arbitrary outcome induced by small subset selection from very high dimensional interrelated gene expression profiles leads to an outcome with associated uncertainty. This continuum and uncertainty precludes any attempts at constructing discriminative classifiers.</p> <p>However a patient's gene expression profile could possibly be used in treatment planning, based on knowledge of other patients' responses.</p> <p>We conclude that many of the patients involved in such medical studies are <it>intrinsically unclassifiable </it>on the basis of provided PGL evidence. This additional category of 'unclassifiable' should be accommodated within medical decision support systems if serious errors and unnecessary adjuvant therapy are to be avoided.</p

Airborne Object Detection Using Hyperspectral Imaging: Deep Learning Review

© 2019, Springer Nature Switzerland AG. Hyperspectral images have been increasingly important in object detection applications especially in remote sensing scenarios. Machine learning algorithms have become emerging tools for hyperspectral image analysis. The high dimensionality of hyperspectral images and the availability of simulated spectral sample libraries make deep learning an appealing approach. This report reviews recent data processing and object detection methods in the area including hand-crafted and automated feature extraction based on deep learning neural networks. The accuracy performances were compared according to existing reports as well as our own experiments (i.e., re-implementing and testing on new datasets). CNN models provided reliable performance of over 97% detection accuracy across a large set of HSI collections. A wide range of data were used: a rural area (Indian Pines data), an urban area (Pavia University), a wetland region (Botswana), an industrial field (Kennedy Space Center), to a farm site (Salinas). Note that, the Botswana set was not reviewed in recent works, thus high accuracy selected methods were newly compared in this work. A plain CNN model was also found to be able to perform comparably to its more complex variants in target detection applications