Computing and Visualizing Solution Sets of Interval Linear Systems

The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006

Analysis of the Distributions of Color Characteristics in Art Painting Images

In this paper we study some of the characteristics of the art painting image color semantics. We analyze the color features of differ- ent artists and art movements. The analysis includes exploration of hue, saturation and luminance. We also use quartile’s analysis to obtain the dis- tribution of the dispersion of defined groups of paintings and measure the degree of purity for these groups. A special software system “Art Paint- ing Image Color Semantics” (APICSS) for image analysis and retrieval was created. The obtained result can be used for automatic classification of art paintings in image retrieval systems, where the indexing is based on color characteristics.

The Interval [0,1] Admits no Functorial Embedding into a Finite-Dimensional or Metrizable Topological Group

An embedding X ⊂ G of a topological space X into a topological group G is called functorial if every homeomorphism of X extends to a continuous group homomorphism of G. It is shown that the interval [0, 1] admits no functorial embedding into a finite-dimensional or metrizable topological group.

A simulation of the surface EMG for analysis of muscle activity during whole body vibratory stimulation

Many studies have accounted for whole body vibration effects in the fields of exercise physiology, sport and rehabilitation medicine. Generally, surface EMG is utilized to assess muscular activity during the treatment; however, large motion artifacts appear superimposed to the raw signal, making sEMG recording not suitable before any artifact filtering. Sharp notch filters, centered at vibration frequency and at its superior harmonics, have been used in previous studies, to remove the artifacts. [6, 10] However, to get rid of those artifacts some true EMG signal is lost. The purpose of this study was to reproduce the effect of motor-unit synchronization on a simulated surface EMG during vibratory stimulation. In addition, authors mean to evaluate the EMG power percentage in those bands in which are also typically located motion artifact components. Model characteristics were defined to take into account two main aspect: the muscle MUs discharge behavior and the triggering effects that appear during local vibratory stimulation. [7] Inter-pulse-interval, was characterized by a polimodal distribution related to the MU discharge frequency (IPI 55-80ms, σ=12ms) and to the correlation with the vibration period within the range of ±2 ms due to vibration stimulus. [1, 7] The signals were simulated using different stimulation frequencies from 30 to 70 Hz. The percentage of the total simulated EMG power within narrow bands centered at the stimulation frequency and its superior harmonics (± 1 Hz) resulted on average about 8% (± 2.85) of the total EMG power. However, the artifact in those bands may contain more than 40% of the total power of the total signal. [6] Our preliminary results suggest that the analysis of the muscular activity of muscle based on raw sEMG recordings and RMS evaluation, if not processed during vibratory stimulation may lead to a serious overestimation of muscular response.

The Space of Differences of Convex Functions on [0, 1]

∗Participant in Workshop in Linear Analysis and Probability, Texas A & M University, College Station, Texas, 2000. Research partially supported by the Edmund Landau Center for Research in Mathematical Analysis and related areas, sponsored by Minerva Foundation (Germany).

Laser-induced breakdown spectroscopy quantitative analysis method via adaptive analytical line selection and relevance vector machine regression model

Abstract A new LIBS quantitative analysis method based on analytical line adaptive selection and Relevance Vector Machine (RVM) regression model is proposed. First, a scheme of adaptively selecting analytical line is put forward in order to overcome the drawback of high dependency on a priori knowledge. The candidate analytical lines are automatically selected based on the built-in characteristics of spectral lines, such as spectral intensity, wavelength and width at half height. The analytical lines which will be used as input variables of regression model are determined adaptively according to the samples for both training and testing. Second, an LIBS quantitative analysis method based on RVM is presented. The intensities of analytical lines and the elemental concentrations of certified standard samples are used to train the RVM regression model. The predicted elemental concentration analysis results will be given with a form of confidence interval of probabilistic distribution, which is helpful for evaluating the uncertainness contained in the measured spectra. Chromium concentration analysis experiments of 23 certified standard high-alloy steel samples have been carried out. The multiple correlation coefficient of the prediction was up to 98.85%, and the average relative error of the prediction was 4.01%. The experiment results showed that the proposed LIBS quantitative analysis method achieved better prediction accuracy and better modeling robustness compared with the methods based on partial least squares regression, artificial neural network and standard support vector machine.

Application of the Artificial Intelligence Algorithms for System Analysis of Multi Dimension Physiological Data for Developing Polyparametric Information System of Public Health Diagnostics

The polyparametric intelligence information system for diagnostics human functional state in medicine and public health is developed. The essence of the system consists in polyparametric describing of human functional state with the unified set of physiological parameters and using the polyparametric cognitive model developed as the tool for a system analysis of multitude data and diagnostics of a human functional state. The model is developed on the basis of general principles geometry and symmetry by algorithms of artificial intelligence systems. The architecture of the system is represented. The model allows analyzing traditional signs - absolute values of electrophysiological parameters and new signs generated by the model – relationships of ones. The classification of physiological multidimensional data is made with a transformer of the model. The results are presented to a physician in a form of visual graph – a pattern individual functional state. This graph allows performing clinical syndrome analysis. A level of human functional state is defined in the case of the developed standard (“ideal”) functional state. The complete formalization of results makes it possible to accumulate physiological data and to analyze them by mathematics methods.

Objective analysis of contact lens fit

Purpose: To assess the validity and repeatability of objective compared to subjective contact lens fit analysis. Methods: Thirty-five subjects (aged 22.0. ±. 3.0 years) wore two different soft contact lens designs. Four lens fit variables: centration, horizontal lag, post-blink movement in up-gaze and push-up recovery speed were assessed subjectively (four observers) and objectively from slit-lamp biomicroscopy captured images and video. The analysis was repeated a week later. Results: The average of the four experienced observers was compared to objective measures, but centration, movement on blink, lag and push-up recovery speed all varied significantly between them (p <. 0.001). Horizontal lens centration was on average close to central as assessed both objectively and subjectively (p > 0.05). The 95% confidence interval of subjective repeatability was better than objective assessment (±0.128. mm versus ±0.168. mm, p = 0.417), but utilised only 78% of the objective range. Vertical centration assessed objectively showed a slight inferior decentration (0.371. ±. 0.381. mm) with good inter- and intrasession repeatability (p > 0.05). Movement-on-blink was lower estimated subjectively than measured objectively (0.269. ±. 0.179. mm versus 0.352. ±. 0.355. mm; p = 0.035), but had better repeatability (±0.124. mm versus ±0.314. mm 95% confidence interval) unless correcting for the smaller range (47%). Horizontal lag was lower estimated subjectively (0.562. ±. 0.259. mm) than measured objectively (0.708. ±. 0.374. mm, p <. 0.001), had poorer repeatability (±0.132. mm versus ±0.089. mm 95% confidence interval) and had a smaller range (63%). Subjective categorisation of push-up speed of recovery showed reasonable differentiation relative to objective measurement (p <. 0.001). Conclusions: The objective image analysis allows an accurate, reliable and repeatable assessment of soft contact lens fit characteristics, being a useful tool for research and optimisation of lens fit in clinical practice.

Frontal Solutions: an Information Technology Transfer to Abstract Mathematics

The paper introduces a method for dependencies discovery during human-machine interaction. It is based on an analysis of numerical data sets in knowledge-poor environments. The driven procedures are independent and they interact on a competitive principle. The research focuses on seven of them. The application is in Number Theory.

On Multidimensional Analogue of Marchaud Formula for Fractional Riesz-Type Derivatives in Domains in R^n

2000 Mathematics Subject Classification: 26A33, 42B20

Comparative Analysis of Viscoelastic Models Involving Fractional Derivatives of Different Orders

Mathematics Subject Classification: 74D05, 26A33

Application of Fractional Calculus in the Dynamical Analysis and Control of Mechanical Manipulators

Mathematics Subject Classification: 26A33, 93C83, 93C85, 68T40

Existence and Asymptotic Stability of Solutions of a Perturbed Quadratic Fractional Integral Equation

Mathematics Subject Classification: 45G10, 45M99, 47H09

Evaluation of hemifield sector analysis protocol in multifocal visual evoked potential objective perimetry for the diagnosis and early detection of glaucomatous field defects

CONCLUSIONS: The new HSA protocol used in the mfVEP testing can be applied to detect glaucomatous visual field defects in both glaucoma and glaucoma suspect patients. Using this protocol can provide information about focal visual field differences across the horizontal midline, which can be utilized to differentiate between glaucoma and normal subjects. Sensitivity and specificity of the mfVEP test showed very promising results and correlated with other anatomical changes in glaucoma field loss. PURPOSE: Multifocal visual evoked potential (mfVEP) is a newly introduced method used for objective visual field assessment. Several analysis protocols have been tested to identify early visual field losses in glaucoma patients using the mfVEP technique, some were successful in detection of field defects, which were comparable to the standard automated perimetry (SAP) visual field assessment, and others were not very informative and needed more adjustment and research work. In this study we implemented a novel analysis approach and evaluated its validity and whether it could be used effectively for early detection of visual field defects in glaucoma. METHODS: Three groups were tested in this study; normal controls (38 eyes), glaucoma patients (36 eyes) and glaucoma suspect patients (38 eyes). All subjects had a two standard Humphrey field analyzer (HFA) test 24-2 and a single mfVEP test undertaken in one session. Analysis of the mfVEP results was done using the new analysis protocol; the hemifield sector analysis (HSA) protocol. Analysis of the HFA was done using the standard grading system. RESULTS: Analysis of mfVEP results showed that there was a statistically significant difference between the three groups in the mean signal to noise ratio (ANOVA test, p < 0.001 with a 95% confidence interval). The difference between superior and inferior hemispheres in all subjects were statistically significant in the glaucoma patient group in all 11 sectors (t-test, p < 0.001), partially significant in 5 / 11 (t-test, p < 0.01), and no statistical difference in most sectors of the normal group (1 / 11 sectors was significant, t-test, p < 0.9). Sensitivity and specificity of the HSA protocol in detecting glaucoma was 97% and 86%, respectively, and for glaucoma suspect patients the values were 89% and 79%, respectively.

Teaching University-Level Mathematics Using Mathematica

This paper considers the use of the computer algebra system Mathematica for teaching university-level mathematics subjects. Outlined are basic Mathematica concepts, connected with different mathematics areas: algebra, linear algebra, geometry, calculus and analysis, complex functions, numerical analysis and scientific computing, probability and statistics. The course “Information technologies in mathematics”, which involves the use of Mathematica, is also presented - discussed are the syllabus, aims, approaches and outcomes.