Cross Correlation

– An important part of modeling with Volterra and Wiener models is the accurate measurement of the model coefficients or kernels. The formulation of Wiener model of nonlinear systems has a major breakthrough for kernel measurement. The orthogonality of the Wiener functionals for a white Gaussian input allowed the Wiener kernels to be easily measured using cross-correlation techniques. The kernel measurement techniques are widely explored in this paper. Some properties of the third order Volterra kernel and of the input-output relation are shown. Finally original contributions have been made regarding signal reconstruction using Volterra and Wiener models.

We examine the relationship between volatility and past and future returns using high-frequency aggregate equity index data. Consistent with a prolonged “leverage” effect, we find the correlations between absolute high-frequency returns and current and past high-frequency returns to ...

We describe techniques to sonify rhythmic activity of epileptic seizures as measured by human EEG. Event- based mapping of parameters is found to be informative in terms of auto- and cross-correlations of the multivariate data. For the study, a group of patients with childhood absence seizures are selected. We find consistent intra-patient conservation of the rhythmic pattern as well as

We describe several examples where we use cross-correlation functions to quantify the similarity of 2D surface profiles or of 3D areal surface topography images. The applications have included (1) the manufacture of standard reference material (SRM) bullets and casings, (2) methods to assess whether bullets or casings have been fired by the same firearm, and (3) research to quantify similarities or differences between profiles of the same surface measured by different techniques or between a master surface and its replicas. The cross-correlation maximum is the functional parameter used to quantify similarity. A second parameter, called the relative profile (2D) difference or relative areal topography (3D) difference, may also be used to quantify differences and to recognize the ambiguous condition when two results have different vertical (z-) scales but identical shapes. Most of these examples have been applied in support of ballistics inspection methods in crime labs, but the methods are generally useful for estimating the accuracy of surface replication techniques or the ability of different surface topography instruments to measure the same surface and provide the same result. The instruments used in these studies were a stylus instrument and a Nipkow-disk type confocal microscope. Cross-correlation functions may also be used to assess differences resulting from the use of different filters to modify the same surface profile or topography image.

Motivation is one of the major aspects in sport psychology for both physical education and sport. The aim of the present study was to examine the relationship between intrinsic motivation and task and ego ori- entation in athletes of climbing to estimate the factors that affects in the configuration of level of intrinsic motivation and the objects that determine the behavior of athletes. The sample was consisted of 100 athletes of climbing (71 men and 29 women), age 18 to 32 years, (M = 25.9), which had mean of weekly training 3,55 times/week and mean of degree of difficulty "7+". Participants completed the questionnaire of intrinsic mo- tivation (McAuley, Duncan & Tammen, 1989) and the questionnaire of task and ego orientation in sport (Duda & Nicholls, 1992). The results showed that exist significant differences in intrinsic motivation, de- pending on sex, experience and level of athletes. Also was found statistically significant cross-correlation between competence, ten...

This work represents a comparative study for the methods of registration for dental panoramic X-ray images. The study tried to find the best registration technique used to register images of the jaw. Three image registration techniques are implemented and applied to dental panoramic X-ray images in both spatial domain and wavelet domain. The first technique is based on cross-correlation. The second one depends on selecting control points from both the reference and the input images. The last technique is based on maximization of mutual information between the two images. In the wavelet domain, discrete wavelet transform (DWT) has been performed to the reference image and the test image before the three techniques have been applied. Then the registration methods have been applied using approximation coefficients in the registration procedure. After finishing the registration steps, inverse discrete wavelet transform (IDWT) has been applied in order to obtain the registered image. The...

Noisy signals in many real-world systems display long-range autocorrelations and long-range cross-correlations. Due to periodic trends, these correlations are difficult to quantify. We demonstrate that one can accurately quantify power-law cross-correlations between different simultaneously recorded time series in the presence of highly non-stationary sinusoidal and polynomial overlying trends by using the new technique of detrended cross-correlation analysis with varying order ell of the polynomial. To demonstrate the utility of this new method —which we call DCCA-ell(n), where n denotes the scale— we apply it to meteorological data.

In the meeting case scenario, audio is often recorded using Multiple Distance Microphones (MDM) in a non-intrusive manner. Typically a beamforming is performed in order to obtain a single enhanced signal out of the multiple channels. This paper investigate s the use of mutual information for selecting the channel subset that produces the lowest error in a diarization system. Conventional

Hydrological monitoring is essential for meaningful water-management policies and actions, especially where water resources are scarce and/or dwindling, as is the case in Australia. In this paper, we investigate the regional 4° × 4° mascon (mass concentration) GRACE solutions for Australia provided by GSFC (Goddard Space Flight Center, NASA) for their suitability in monitoring Australian hydrology, with a particular focus on the Murray-Darling Basin (MDB). Using principal component analysis (PCA) and multi-linear regression analysis (MLRA), the main components of spatial and temporal variability in the mascon solutions are analysed over the whole Australian continent and the MDB. The results are compared to those from global solutions provided by CSR (Center for Space Research, University of Texas at Austin, USA) and CNES/GRGS (Centre National d'Études Spatiales/Groupe de Recherche de Geodesie Spatiale, France) and validated using data from the Tropical Rainfall Measuring Mission (TRMM), water storage changes predicted by the WaterGap Global Hydrological Model (WGHM) and the Global Land Data Assimilation System (GLDAS), and ground-truth (river-gauge) observations. For the challenging Australian case with generally weak hydrological signals, the mascon solutions provide similar results to those from the global solutions, with the advantage of not requiring additional filtering (destriping and smoothing) as, for example, is necessary for the CSR solutions. A further advantage of the mascon solutions is that they offer a higher temporal resolution (i.e., 10 days) compared to approximately monthly CSR solutions. Examining equivalent water volume (EWV) time series for the MDB shows a good cross-correlation (generally > 0.7) among the GRACE solutions when considering the whole basin, although lower (generally < 0.5) when all the GRACE solutions are compared to the TRMM, WGHM and GLDAS time series. Examining smaller portions of the MDB see the correlation among the GRACE solutions and the TRMM, WGHM and GLDAS EWV time series increase slightly (> 0.6), with all time series appearing to visually follow the general behaviour of the river-gauge data, although the cross-correlations are relatively low (between 0.3 and 0.6).► Mascon provides equivalent results as global CSR & CNES/GRGS solutions. ► All examined GRACE releases reveal seasonal & tropical north signals. ► GRACE, modelled hydrology & precipitation show similar behaviour Australia wide. ► GRACE solutions generally follow river gauge data.

It is believed that there is a close correlation between the physical and mental activities of human body. These physical activities can be measured using various multimodal bio-signals employing either invasive or non-invasive sensors. In contrast, although mental activities have been modeled from various standpoints, they have been associated mostly with brain activities. We have focused on mapping physical multimodal bio-signals as time series data with mental states such as somnolence, fatigue, and concentration. We will discuss two mathematical data mining tools: (1) the interval cross-correlation coefficient; and (2) the interval cross-covariance function coefficient. Given a multimodal time series bio-signal data acquired at a given frequency using non-invasive sensors attached to a human volunteer, our methods aimed to predict the mental state of a human subject. The primary objective was to examine the feasibility of our methods in predicting the mental state of students du...

Temperature reconstructions from Europe for the past 500 years based on documentary and instrumental data are analysed. First, the basic documentary data sources, including information about climate and weather-related extremes, are described. Then, the standard palaeoclimatological reconstruction method adopted here is discussed with a particular application to temperature reconstructions from documentary-based proxy data. The focus is on two new reconstructions; January–April mean temperatures for Stockholm (1502–2008), based on a combination of data for the sailing season in the Stockholm harbour and instrumental temperature measurements, and monthly Central European temperature (CEuT) series (1500–2007) based on documentary-derived temperature indices of the Czech Republic, Germany and Switzerland combined with instrumental records from the same countries. The two series, both of which are individually discussed in greater detail in subsequent papers in this special edition, are here compared and analysed using running correlations and wavelet analysis. While the Stockholm series shows a pronounced low-frequency component, the CEuT series indicates much weaker low-frequency variations. Both series are analysed with respect to three different long-period reconstructions of the North Atlantic Oscillation (NAO) and are compared with other European temperature reconstructions based on tree-rings, wine-harvest data and various climate multiproxies. Correlation coefficients between individual proxy-based series show weaker correlations compared to the instrumental data. There are also indications of temporally varying temperature cross-correlations between different areas of Europe. The two temperature reconstructions have also been compared to geographically corresponding temperature output from simulations with global and regional climate models for the past few centuries. The findings are twofold: on the one hand, the analysis reinforces the hypothesis that the index-data based CEuT reconstruction may not appropriately reflect the centennial scale variations. On the other hand, it is possible that climate models may underestimate regional decadal variability. By way of a conclusion, the results are discussed from a broader point of view and attention is drawn to some new challenges for future investigations in the historical climatology in Europe.