Measure Of Irregularity Research Articles

Early detection and risk assessment for chronic disease with irregular longitudinal data analysis.

Early detection and risk assessment of complex chronic disease based on longitudinal clinical data is helpful for doctors to make early diagnosis and monitor the disease progression. Disease diagnosis with computer-aided methods has been extensively studied. However, early detection and contemporaneous risk assessment based on partially labeled irregular longitudinal measurements is relatively unexplored. In this paper, we propose a flexible mixed-kernel framework for training a contemporaneous disease risk detector to predict the onset of disease and monitor the disease progression. Moreover, we address the label insufficiency problem by identifying the pattern of disease-induced progression over time with longitudinal data. Our method is based on a Structured Output Support Vector Machine (SOSVM), extended to longitudinal data analysis. Extensive experiments are conducted on several datasets of varying complexity, including the contemporaneous risk assessment with simulated irregular longitudinal data; the identification of the onset of Type 1 Diabetes (T1D) with irregularly sampled longitudinal RNA-Seq gene expression dataset; as well as the monitoring of the drug long-term effects on patients using longitudinal RNA-Seq dataset containing missing time points, demonstrating that our method enhances the accuracy in both early diagnosis and risk estimation with partially labeled irregular longitudinal clinical data.

TISMorph: A tool to quantify texture, irregularity and spreading of single cells.

A number of recent studies have shown that cell shape and cytoskeletal texture can be used as sensitive readouts of the physiological state of the cell. However, utilization of this information requires the development of quantitative measures that can describe relevant aspects of cell shape. In this paper we develop a toolbox, TISMorph, that calculates a set of quantitative measures to address this need. Some of the measures introduced here have been used previously, while others are new and have desirable properties for shape and texture quantification of cells. These measures, broadly classifiable into the categories of textural, irregularity and spreading measures, are tested by using them to discriminate between osteosarcoma cell lines treated with different cytoskeletal drugs. We find that even though specific classification tasks often rely on a few measures, these are not the same between all classification tasks, thus requiring the use of the entire suite of measures for classification and discrimination. We provide detailed descriptions of the measures, as well as the TISMorph package to implement them. Quantitative morphological measures that capture different aspects of cell morphology will help enhance large-scale image-based quantitative analysis, which is emerging as a new field of biological data.

The Effect of Muscle Contraction Type on Neuromuscular Complexity in Trained Individuals

Physiological systems exhibit high levels of complexity characterized by non-linearity and persistent fractal correlations (low levels corresponding to states such as disease, injury, and fatigue) and has become recognized as a defining feature of healthy physiological functioning. Neuromuscular complexity is affected by fatigue and intensity of contractions, although no study has investigated the effect of contraction type on complexity. PURPOSE: The purpose of this study was to investigate the effect of contraction type on neuromuscular complexity. METHODS: Twelve collegiate-aged resistance-trained females (21 ± 1 years, 63.3 ± 7.4 kg) were recruited to visit the laboratory on two occasions, the first for familiarization purposes. In session two, participants performed three maximal knee extensor contractions on an isokinetic dynamometer for each contraction type [concentric (CON), eccentric (ECC), and isometric (ISO)] in random order. Relative knee angle was standardized to 120° during ISO contractions. Angular speed was standardized to 30°∙s-1 and range of motion to 90° (90° - 180° at full extension) during CON and ECC contractions. Each contraction lasted three seconds with three seconds rest between contractions. Electromyographic (EMG) signals were recorded from the vastus lateralis using a bipolar electrode configuration. Sample entropy (SE), a unitless measure of statistical irregularity was used as an index of physiological complexity. A one-way repeated measures ANOVA was performed to investigate differences in EMG SE among contraction types. Alpha level was set to 0.05. RESULTS: Contraction type was observed to have a significant effect on EMG SE (F(2,22) = 7.212, p = 0.004). Specifically, CON contractions (1.671 ± 0.193) displayed significantly greater EMG SE than ECC (1.497 ± 0.321, p = 0.017) and ISO (1.569 ± 0.223, p = 0.028) contractions. CONCLUSION: These findings indicated that neuromuscular complexity is contraction-type dependent, being significantly higher during CON than ECC and ISO contractions. In addition, there exists no generally accepted framework to explain the underlying factors regulating complexity and thus, further investigation may provide valuable insight into these potential mechanisms.

Correlation of Corneal and Scleral Topography in Cases with Ectasias and Normal Corneas

Background and Objective
 To determine the relationships between corneal and scleral elevation topography in subjects with corneal ectasias and normal corneas.
 
 Material and Methods
 This is a multi-site retrospective study. Ocular surface topography (sMap3D, Precision Ocular Metrology, US) was collected on 115 eyes with prolate cornea profile (Group A) and 227 eyes showing corneal ectasia (Group B). Sagittal height (SAG 1) was measured in the axis of the highest elevated point of the cornea (apex), defined by the meridian joining this apex to the geometrical center of the cornea at an 16 mm chord diameter (8-mm radius). Another sag value was evaluated 180° away (SAG 2) at the same diameter/radius. The difference in height between SAG 1 and SAG 2 represents a quadrant specific effect (QSE). Conjunctival toricity is estimated by comparing the best fit of the conjunctival/scleral shape data to a toric (Sin2) curve; the root- mean-squared error (RMSE) of this curve, a measure of irregularity, was also calculated.
 
 Results
 The ectasia subjects demonstrated greater QSE, (p<0.001), standard toricity (p<0.001) and RMSE (p<0.001) on the sclera compared to normal cornea cases. If the apex of the ectasia was ≥1.25mm from the corneal center, the asymmetry was greater. Within the Group A, standard toricity was significantly higher than QSE (p<0.001) suggesting a more regular conjunctival pattern. As a proof, a significantly greater proportion of cases in Group B vs. Group A (57% vs. 26%, p<0.001) were found with conjunctival irregular shape, as previously defined. In both groups, subjects graded as having spherical/toric scleral shape had significantly lower RMSE values than those graded as having irregular shapes (p<0.001).
 
 Conclusion
 Subjects with corneal ectasia have a different scleral shape compared to those with normal corneal profiles, largely presenting as a quadrant specific effect along the same axis. This difference is higher if the apex of the ectasia is ≥1.25 mm from the corneal center. RMSE seems to correlate with scleral shape classification in both groups.

An Ultrasonographic Multiparametric Carotid Plaque Risk Index Associated with Cerebrovascular Symptomatology: A Study Comparing Color Doppler Imaging and Contrast-Enhanced Ultrasonography

Various ultrasonographic features of carortid plaques have been associated with the occurence of stroke, highlighting the need for multi-parametric assessment of plaque's vulnerability. Our aim was to compare ultrasonographic multiparametric indices using color Doppler imaging and contrast-enhanced sonography between symptomatic and asymptomatic carotid plaques. This was a cross-sectional observational study recruiting 54 patients (72.2% male; median age, 61 years) undergoing sonography and contrast-enhanced sonography. Patients were included if a moderately or severely stenotic internal carotid artery plaque was detected, with the plaque being considered symptomatic if it was ipsilateral to a stroke occuring within the last 6 months. A vulnerability index, previously described by Kanber et al, combined the degree of stenosis, gray-scale median, and a quantitative measure of surface irregularities (surface irregularity index) derived from color Doppler imaging and contrast-enhanced ultrasonography, resulting in 2 vulnerability indices, depending on the surface irregularity index used. Mann-Whitney U and t tests were used to compare variables between groups, and receiver operating characteristic curves were used to compare diagnostic accuracy. Sixty-two plaques were analyzed (50% symptomatic), with a mean degree of stenosis of 68.9%. Symptomatic plaques had a significantly higher degree of stenosis (mean, 74.7% versus 63.1%; P < .001), a lower gray-scale median (13 versus 38; P = .001), and a higher Kanber vulnerability index based both on color Doppler imaging (median, 61.4 versus 16.5; P < .001) and contrast-enhanced ultrasonography (median, 88.6 versus 25.2; P < .001). The area under the curve for the detection of symptomatic plaques was 0.772 for the degree of stenosis alone, 0.783 for the vulnerability index-color Doppler imaging, and 0.802 for the vulnerability index-contrast-enhanced ultrasonography, though no statistical significance was achieved. Symptomatic plaques had a higher degree of stenosis, lower gray-scale median values, and higher values of the Kanber vulnerability index using both color Doppler imaging and contrast-enhanced ultrasonography for plaque surface delineation.

Multiscale analysis of financial time series by Rényi distribution entropy

It is of great interests to analyze the complexity or dependence of time series of the daily stock closing price in different regions. Entropy is typically a fundamental technique to explore the complexity of time series. The well−studied irregularity measure, sample entropy (SampEn), and a more recently proposed complexity measure, distribution entropy (DistEn) are treated as classification features. In our study, based on Rényi entropy, which has been recently suggested as a measure of complexity in nonlinear systems, we propose multiscale Rényi distribution entropy (MRDE) to research the complexity of nonlinear time series over multiple time scales. Considering the validity and accuracy, Rényi entropy obtains more information than the Shannon entropy for time series mingled with much noise like financial time series, which is mainly reflected in the choice of parameters for frequent events and rare events. Both the simulated signals (logistic map and Gaussian noise) and the financial time series with three different stock markets are calculated and compared using an innovative method in different situations. For different stock markets, the entropy decreases as the scale factor increases, except when the parameter is the maximum in the special case. Meanwhile, We illustrate the necessity and advantage of Rényi distribution entropy (RDE) method by comparing RDE results with the SampEn results about stability and consistency on synthetic data and financial time series. It is applied to measure the dependence by detecting the length of the time series and special algorithm parameters.

Classifying and analysis of random composites using structural sums feature vector.

The main goal of this paper is to present the application of structural sums, mathematical objects originating from the computational materials science, in construction of a feature space vector of two-dimensional random composites simulated by distributions of non-overlapping discs on the plane. Construction of the feature vector enables the immediate application of machine learning tools and data analysis techniques to random structures. In order to present the accuracy and the potential of structural sums as geometry descriptors, we apply them to classification problems comprising composites with circular inclusions as well as composites with shapes formed by discs. As an application, we perform the analysis of different models of composites in order to formulate the irregularity measure of random structures. We also visualize the relationship between the effective conductivity of two-dimensional composites and the geometry of inclusions.

Graph irregularity and its measures

Let G be a simple graph. If all vertices of G have equal degrees, then G is said to be regular. Otherwise, G is irregular. There were various attempts to quantify the irregularity of a graph, of which the Collatz–Sinogowitz index, Bell index, Albertson index, and total irregularity are the best known. We now show that no two of these irregularity measures are mutually consistent, namely that for any two such measures, irrX and irrY there exist pairs of graphs G1, G2, such that irrX(G1) > irrX(G2) but irrY(G1) < irrY(G2). This implies that the concept of graph irregularity is not free of ambiguities.

Maximum wave heights from global model reanalysis

Very large waves populate world oceans and challenge seafarers and offshore structures, but their long-term and global assessment is uneasy because of the scarcity of observations and their narrow time-coverage. Modern model reanalysis datasets with high spatio-temporal extent and resolution represent a valuable tool for this scope. In this paper, we use for the first time reanalysis datasets to provide a long-term and global statistical assessment of the maximum wave parameters, namely crest, crest-to-trough and envelope heights. In particular, we rely on the ERA-Interim directional wave spectra that are used to estimate the parameters of the probability distributions of wave maxima. To represent the customary single-point observations we use time extreme statistical models, while to account for the three-dimensional geometry and short-crestedness of stormy ocean waves, the statistical models are extended to space-time. In order to evaluate the accuracy of the reanalysis-based wave maxima estimates we verify them against buoy and stereo-video wave observations gathered in the North Pacific Ocean. We then provide the global assessment of maximum crest, crest-to-trough and envelope heights during typical and extreme conditions, showing the regions attaining the largest values, which we show are located in the mid-latitude storm belts, in particular in the North Atlantic Ocean. With respect to previous wave climate studies that focused on the significant wave height only, in this study we quantify the maximum wave height extent, also highlighting the role of mean wave steepness and kurtosis (measures of nonlinearity) and spectral bandwidth (measure of irregularity). Beside this, we show that the contribution of the short-crestedness is significant and that taking it into account may be relevant for the safety of navigation, ship routing and marine structural design.

On Irregularity Measures of Some Dendrimers Structures

A graph is said to be a regular graph if all its vertices have the same degree, otherwise, it is irregular. Irregularity indices are usually used for quantitative characterization of the topological structure of non-regular graphs. In numerous applications and problems in material engineering and chemistry, it is useful to be aware that how irregular a molecular structure is? Furthermore, evaluations of the irregularity of underline molecular graphs could be valuable for QSAR/QSPR studies, and for the expressive determines of chemical and physical properties, such as enthalpy of vaporization, toxicity, resistance, Entropy, melting and boiling points. In this paper, we think over the following four irregularity measures: the irregularity index by Albertson, σ irregularity index, the total irregularity index and the variance of vertex degrees. By way of graph structural estimation and derivations, we determine these irregularity measures of the molecular graphs of different classes of dendrimers.

Construction of saliency map and hybrid set of features for efficient segmentation and classification of skin lesion.

Skin cancer is being a most deadly type of cancers which have grown extensively worldwide from the last decade. For an accurate detection and classification of melanoma, several measures should be considered which include, contrast stretching, irregularity measurement, selection of most optimal features, and so forth. A poor contrast of lesion affects the segmentation accuracy and also increases classification error. To overcome this problem, an efficient model for accurate border detection and classification is presented. The proposed model improves the segmentation accuracy in its preprocessing phase, utilizing contrast enhancement of lesion area compared to the background. The enhanced 2D blue channel is selected for the construction of saliency map, at the end of which threshold function produces the binary image. In addition, particle swarm optimization (PSO) based segmentation is also utilized for accurate border detection and refinement. Few selected features including shape, texture, local, and global are also extracted which are later selected based on genetic algorithm with an advantage of identifying the fittest chromosome. Finally, optimized features are later fed into the support vector machine (SVM) for classification. Comprehensive experiments have been carried out on three datasets named as PH2, ISBI2016, and ISIC (i.e., ISIC MSK-1, ISIC MSK-2, and ISIC UDA). The improved accuracy of 97.9, 99.1, 98.4, and 93.8%, respectively obtained for each dataset. The SVM outperforms on the selected dataset in terms of sensitivity, precision rate, accuracy, and FNR. Furthermore, the selection method outperforms and successfully removed the redundant features.

State‐switching continuous‐time correlated random walks

Abstract Continuous‐time models have been developed to capture features of animal movement across temporal scales. In particular, one popular model is the continuous‐time correlated random walk, in which the velocity of an animal is formulated as an Ornstein–Uhlenbeck process, to capture the autocorrelation in the speed and direction of its movement. In telemetry analyses, discrete‐time state‐switching models (such as hidden Markov models) have been increasingly popular to identify behavioural phases from animal tracking data. We propose a multistate formulation of the continuous‐time correlated random walk, with an underlying Markov process used as a proxy for the animal’s behavioural state process. We present a Markov chain Monte Carlo algorithm to carry out Bayesian inference for this multistate continuous‐time model. Posterior samples of the hidden state sequence, of the state transition rates, and of the state‐dependent movement parameters can be obtained. We investigate the performance of the method in a simulation study, and we illustrate its use in a case study of grey seal (Halichoerus grypus) tracking data. The method we present makes use of the state‐space model formulation of the continuous‐time correlated random walk, and can accommodate irregular sampling frequency and measurement error. It will facilitate the use of continuous‐time models to estimate movement characteristics and infer behavioural states from animal telemetry data.

Multipoint chord reference system for track irregularity: Part I – Theory and methodology

This paper proposes a novel approach to measure track irregularity by using a multipoint chord reference (MCR) system. This paper is the first part presenting the theoretical proofs and methodology for analyzing the system performance in a spatial domain. Part II will study the performance in wavelength domain through numerical approaches. In this paper, a unified framework of the MCR system is introduced with a series of definitions. Mathematical models are established based on sensor fusion and least square optimization techniques. The error theory of the MCR system is discussed and the error amplification factor (EAF) is defined to quantify the error accumulation characteristics of the MCR system in the spatial domain. The stability of the MCR system was analyzed and propositions are put forward to reveal the basic relationship between the minimum measurable wavelength and different configurations. In particular, the MCR(n, 1) system was studied, for which propositions were put forward to describe the relationship between the EAF and stability of the MCR system. The MCR system has significant advantages over some current techniques for track irregularity measurement, such as single point chord method as well as gyroscope- and accelerometer-based techniques. The MCR system enables us to use low-cost sensors to achieve the same or even higher precision as the currently used techniques by increasing the number of sensors and sampling frequency. This system can be especially useful to measure track irregularities with short wavelengths, such as rail corrugation. Although the MCR system is mostly used in the railway engineering field, it can be applied to any field in which an irregular surface or curve is required to be measured.

Predicting streamer discharge front splitting by ionization seed profiling

There has been extensive research on the branching mechanisms of streamer discharges. A consistent link between theories and experiments, which can enable prediction or even control of streamer front splitting, is to be established. For this, a clearer knowledge of streamer seed profiles needs to be first obtained with the use of specifically designed electrodes and then correlated with the observations of streamer development. In this work, a 2D deterministic model of negative streamers in air with photo-ionization in an overvolted gap is numerically solved with the ionization seeds assumed as the superposition of Gaussians. The “indicative profile approach” developed here can reliably relate the change in a quantitative measure of geometrical irregularity of the seed profiles with specific electron densities to the emergence of front splitting of streamer discharges at various voltages, seed characteristic sizes, and preionization levels. The results could inform experiments to clarify streamer branching mechanisms.

Optimizing site-specific geostatistics to improve geotechnical spatial information in Seoul, South Korea

Subsurface soil and rock profiles are commonly interpreted from borehole log datasets. These datasets include three-dimensional spatial coordinate information, layer information, and standard penetration test results. More reliable spatial distribution of target physical properties can be obtained from additional testing at locations characterized by outlier observations and geotechnical uncertainties. At a given site, irregular measurements typically differ significantly from bulk measurements or proximal observations. In this study, a process for optimizing site-specific geostatistics, which uses geotechnical spatial information and applies optimum outlier thresholds with a multi-clustering method, is proposed to incorporate site-specific geo-layer uncertainties and identify their geotechnical value. Optimized geostatistical characteristic information for geological strata boundaries was derived and verified based on a sequential procedure applied to representative test areas in Seoul, South Korea.

The Effect of Cognitive Resource Competition Due to Dual-Tasking on the Irregularity and Control of Postural Movement Components.

Postural control research suggests a non-linear, n-shaped relationship between dual-tasking and postural stability. Nevertheless, the extent of this relationship remains unclear. Since kinematic principal component analysis has offered novel approaches to study the control of movement components (PM) and n-shapes have been found in measures of sway irregularity, we hypothesized (H1) that the irregularity of PMs and their respective control, and the control tightness will display the n-shape. Furthermore, according to the minimal intervention principle (H2) different PMs should be affected differently. Finally, (H3) we expected stronger dual-tasking effects in the older population, due to limited cognitive resources. We measured the kinematics of forty-one healthy volunteers (23 aged 26 ± 3; 18 aged 59 ± 4) performing 80 s tandem stances in five conditions (single-task and auditory n-back task; n = 1–4), and computed sample entropies on PM time-series and two novel measures of control tightness. In the PM most critical for stability, the control tightness decreased steadily, and in contrast to H3, decreased further for the younger group. Nevertheless, we found n-shapes in most variables with differing magnitudes, supporting H1 and H2. These results suggest that the control tightness might deteriorate steadily with increased cognitive load in critical movements despite the otherwise eminent n-shaped relationship.

Survival rate of two orthodontic bonded retainer wires

We read the article “Clinical effectiveness of two orthodontic retainer wires on mandibular arch retention” (Gunay F, Oz A. Am J Orthod Dentofacial Orthop 2018; 153:232-8) with great interest. We congratulate the authors for conducting a robust study with an effective study design on this important topic. However, we would seek certain clarifications from the authors on several points:1.In paragraph 1 of the statistical analysis section, the authors mention that lingual retainer survival rates over 12 months were evaluated by means of the Kaplan-Meier test and that differences in retainer survival curves by retainer wire type were evaluated by means of the log-rank test. In Fig 3, the authors draw a Kaplan-Meier curve depicting the cumulative survival rates of group 1 (0.0175-inch 6-stranded stainless steel retainer wire) and group 2 0.0195-inch dead-soft coaxial retainer wire), but the graph touches zero percent in both groups over a 12-month follow-up period. This means that survival or success of the bonded retainer is 0% at the end of 12 months in both groups, although it is 86.8% in group 1 and 81.1% in group 2 according to Table II (log-rank test: χ2 = 0.661; P = 0.416). Figure 3 and Table II completely contradict each other. We think that the graph should be drawn as shown in Figure (Corrected).1Egli F. Bovali E. Kiliaridis S. Cornelis M.A. Indirect vs direct bonding of mandibular fixed retainers in orthodontic patients: comparison of retainer failures and posttreatment stability. A 2-year follow-up of a single-center randomized controlled trial.Am J Orthod Dentofacial Orthop. 2017; 151: 15-27Abstract Full Text Full Text PDF PubMed Scopus (27) Google Scholar, 2Dawson B. Trapp R.G. Research question about means in three or more groups.in: Dawson B. Trapp R.G. Basic and clinical biostatistics. 4th ed. McGraw Hill, New York2004: 163-189Google Scholar2.The authors applied repeated-measures analysis of variance (ANOVA) for irregularity measurements and intercanine distance. Intragroup comparison at different time points is mentioned, but what is the intergroup difference at different time points of the above parameters? In Tables IV and V, 2 different F-values are mentioned, and it seems that the authors have applied 1-way repeated-measures ANOVA separately for each treatment group and not repeated-measures ANOVA for both groups together. Our question is why intergroup repeated-measures ANOVA2Dawson B. Trapp R.G. Research question about means in three or more groups.in: Dawson B. Trapp R.G. Basic and clinical biostatistics. 4th ed. McGraw Hill, New York2004: 163-189Google Scholar was not applied.3.Intergroup comparison (Table VI) of mean irregularity measurement (mm) difference between post-treatment and 12-month retention period (T5-T1) via Mann-Whitney test gives us vital information that mandibular arch irregularity is significantly higher in group 2 than in group I. Similarly, it would also be pertinent to know the results of a Mann-Whitney test for the difference in mean intercanine distance between the 2 groups. This result may help us in localizing the irregularity site so that adequate stress can be given to the areas requiring maximum retention. The authors should comment on why this relevant information was not shared. We emphasize that by no means are we disregarding the efforts of the authors in conducting this trial, but our intention is that correct and relevant information should reach the readers of this journal. Clinical effectiveness of 2 orthodontic retainer wires on mandibular arch retentionAmerican Journal of Orthodontics and Dentofacial OrthopedicsVol. 153Issue 2PreviewThe aim of this study was to evaluate and compare the clinical success of 2 lingual retainer wires. Full-Text PDF Author's responseAmerican Journal of Orthodontics and Dentofacial OrthopedicsVol. 155Issue 1PreviewThank you so much for your interest and the valuable contributions you have made to our work. Full-Text PDF

Algorithms and Instrument for Rapid Detection of Rail Surface Defects and Vertical Short-Wave Irregularities Based on FOG and Odometer

Defects and vertical short-wave irregularities significantly influence the maintenance of the railway tracks and the train safety, and hence, they need to be detected and eliminated in the early stages of formation. We studied the principles and algorithms to detect the defects and to measure the vertical short-wave irregularities by using a fiber optical gyroscope and an odometer, and the associated software was also developed. The principles of deformation index, namely, the ratio of angular rate to velocity and the method to determine the threshold of defects detection, are expatiated. The influence of the transfer function in measuring the vertical irregularities has long been a tough issue. The relation between the characteristics of deformation index and the wavelength of irregularities is studied by converting the deformation index from the time domain to the spatial domain. The post-processing module utilizes the results of the spectrum analysis of the deformation index to determine the wavelength of the track irregularities and eliminate the influence of the transfer function. To improve the accuracy of the calculation results, we analyzed the characteristics of the output of the gyroscope and the odometer and designed a series of targeted error-elimination methods. The forward and reverse dead-reckoning method is utilized to reduce the error accumulation, especially a high frequency noise when calculating the magnitude of the vertical short-wave irregularities. The experimental results show that the repeatability is 0.038 mm when the chord length is 1 m and 0.65 mm when the chord length is 10 m. The accuracy is 0.05 mm when compared with the results obtained using a ruler of 1 m. The moving speed of the instrument was approximately 0.6–1.2 m/s during the experiment. Both the accuracy and the efficiency can fulfill the requirements for the measurement of the short-wave irregularities.

Application of Wavelets for Evaluation of Soft Sensors under Irregular Sampling of Output Measurements

Abstract The problem of evaluating soft sensors for plants with irregular output measurement time is considered. In order to find the relationship between inputs and output, the wavelet-transformed inputs are integrated into the regression model framework. A suitable procedure for wavelet type selection is discussed. An example is provided to illustrate successful application of the proposed approach and an industrial case study is given for soft sensor evaluation of a reactive distillation process.

On Alberson irregularity measure of graphs

Let G = (V,E), V = {1,2,...,n} be a simple connected graph with n vertices, m edges and a sequence of vertex degrees d1 ≥ d2 ≥ ··· ≥ dn > 0, di = d(i). The irregularity measure of graph is defined asirr(G) = ∑i~j di -dj , where i ~ j denotes adjacency of vertices i and j. New upper bounds for irr(G) are obtained.