Investigation on the Behavior of Noise in Asynchronous Spectra in Generalized Two-Dimensional (2D) Correlation Spectroscopy and Application of Butterworth Filter in the Improvement of Signal-to-Noise Ratio of 2D Asynchronous Spectra

A new approach to recognizing the correct pattern of cross-peaks from a noisy 2D asynchronous spectrum by detecting intrinsic symmetry via the Kolmogorov-Smirnov test

The characteristic cluster pattern of cross-peaks in a 2D asynchronous spectrum provides an effective way to reveal the specific physicochemical nature of subtle spectral changes caused by intermolecular interactions. However, the inevitable presence of noise in the 1D spectra used to construct a 2D asynchronous spectrum is significantly amplified, which poses a serious challenge in identifying the correct cluster pattern of the cross-peaks. While mirror symmetry occurs in some types of cross-peaks, it does not occur in other types. The Kolmogorov-Smirnov test provides a statistical means to check whether the mirror symmetry exists or not between a pair of cross-peaks covered by heavy noise. Thus, different types of cross-peak clusters can be distinguished by excavating intrinsic spectral features from the noisy 2D asynchronous spectrum. The effectiveness of this approach in investigating the nature of intermolecular interactions was showcased in both a simulated model system and a real artemisinin/N-methyl pyrrolidone system.

Use of Filters to Smooth Out Signals Collected through Mobile Devices in the Static and Dynamic Balance Assessment: A Systematic Review

Background: When performing motion analysis using sensors, the signal often comes with noise and it is necessary to use filters to exclude unwanted frequencies. For this reason, the objective of this work was to carry out a systematic review on the filters used in data recorded from smartphone applications for static and dynamic balance assessment. Methods: A systematic literature review was performed on the PubMed, ScienceDirect, Scopus, Technology Research and Web of Science databases, using the search strategy: smartphone, “mobile technology”, evaluation, “postural stability”, and balance. Results: 427 articles were found (PubMed = 107; ScienceDirect = 67; Scopus = 106; Web of Science = 95; Technology research database = 52). After applying the inclusion criteria and removing duplicates, nine studies were eligible for this review. In these studies, the fourth-order Butterworth low-pass filter was the most applied (N = 6) and the cutoff frequency of 4 Hz (N = 2) was the most frequent. Conclusions: In general, few studies have adequately described the filter used in signal processing. This step, when hidden, negatively affects the reproducibility of studies. Understanding and describing the signal processing is important not only for the correct description of the results but also for the reproducibility of the studies.

Random swapping, an effective and efficient way to boost the intensities of cross peaks in a 2D asynchronous spectrum

Analysis of mixture via chromatographic-spectroscopic and analogous experiments is a common task in analytical chemistry. A 2D/nD asynchronous spectrum is effective in retrieving spectra of pure substances even if different components cannot be separated. However, noise in the 2D/nD asynchronous spectrum becomes a bottleneck in the analysis. Finding a suitable sequence of the 1D spectra used in constructing the 2D/nD asynchronous spectrum is helpful to improve the signal-to-noise level. A 2D/nD asynchronous spectrum is often produced via a large number of 1D spectra. The resultant colossal number of the possible sequences makes stochastic search the only possible way to find a suitable sequence. Random changing (RC) and random swapping (RS) are two ways to obtain a new sequence. We found that the possibility of finding a better sequence via an RS is significantly higher than that via an RC in the advanced stage of stochastic searching. This is the reason why the performance of RS is superior to that of RC in two model systems where 2D asynchronous spectra are used. We applied the RS approach on the analysis of water/isopropanol mixtures, and satisfactory sequences are acquired with affordable computational cost. Thus, the RS approach brings about an opportunity increase the signal-to-noise level of a 2D asynchronous spectrum in the analysis of the bilinear data from complex mixed samples.

A new approach to removing interference of moisture from FTIR spectrum

An approach is developed to remove the interference of moisture from FTIR spectra. The interference arises from two aspects: the fluctuation on the temperature of the HeNe laser and the fluctuation on the transient concentration of moisture in the light - path of an FTIR spectrometer. The temperature fluctuation on the HeNe laser produces a systematic spectral shift between single-beam sample and background spectra, which often makes spectral subtraction method invalid in removing the interference of moisture. Herein, the Carbo similarity metric (the C_AB value) is used to reflect the subtle spectral shift. A database of single-beam background spectra is established based on the concept of big-data and the pigeon-hole theory. The spectral shift is corrected by selecting suitable single-beam background spectra from the database to match with the given single-beam sample spectrum according to the C_AB value. The interference caused by the fluctuation of the transient concentration of moisture is removed using a comprehensive 2D-COS method. We apply the approach on two polymeric samples to retrieve high-quality spectra and reliable second derivative spectra without the interference of moisture. The present work provides a new opportunity of obtaining the reliable second derivative spectra in the spectral region masked by moisture.

Investigation on the luminescence behavior of terbium acetylsalicylate/bilirubin system via 2D-COS approaches

Terbium acetylsalicylate has been prepared, and the ethanol solution of the complex exhibits strong luminescence under the excitation of ultraviolet radiation. When a small amount of bilirubin solution is introduced into the solution containing a high concentration of terbium acetylsalicylate, a remarkable diminution of the luminescence of the terbium complex was observed. Investigations on the behavior and life-time of luminescence indicate that the quenching is not caused by forming a stable non-luminescent product via a reaction between terbium acetylsalicylate and bilirubin. A π-π interaction between the chromophore of bilirubin and the aromatic moiety of ligand was revealed via the pattern of cross peaks in the 2D asynchronous spectrum generated using the DAOSD (double asynchronous orthogonal sample design) approach. Such an interaction paves a route for energy transfer in the quenching process. The combination of a high concentration of the terbium complex and a long life-time of luminescence in the lanthanide complex/bilirubin system forms a special scenario: a bilirubin molecule by diffusion may visit and deactivate dozens of excited terbium complexes within the half-life period of the lanthanide complex. This is why a small amount of bilirubin can bring about the significant reduction of luminescence on the solution containing a high concentration of the terbium complex.

Intensity Enhancement of a Two-Dimensional Asynchronous Spectrum Without Noise Level Fluctuation Escalation Using a One-Dimensional Spectra Sequence Change

Previously, we demonstrated that the intensities of cross-peaks in a two-dimensional asynchronous spectrum could be enhanced using sequence change of the corresponding one-dimensional spectra. This unusual approach becomes useful when the determination of the sequential order of physicochemical events is not essential. However, it was not known whether the level of noise in the two-dimensional asynchronous spectrum was also escalated as the sequence of one-dimensional spectra changed. We first investigated the noise behavior in a two-dimensional asynchronous spectrum upon changing the sequence of the corresponding one-dimensional spectra on a model system. In the model system, bilinear data from a chromatographic-spectroscopic experiment on a mixture containing two components were analyzed using a two-dimensional asynchronous spectrum. The computer simulation results confirm that the cross-peak intensities in the resultant a two-dimensional asynchronous spectrum were indeed enhanced by more than 100 times as the sequence of one-dimensional spectra changed, whereas the fluctuation level of noise, reflected by the standard deviation of the value of a two-dimensional asynchronous spectrum at a given point, was almost invariant. Further analysis on the model system demonstrated that the special mathematical property of the Hilbert-Noda matrix (the modules of all column vectors of the Hilbert-Noda matrix being a near constant) accounts for the moderate variation of the noise level during the changes of the sequence of one-dimensional spectra. Next, a realistic example from a thermogravimetry-Fourier transform infrared spectroscopy experiment with added artificial noise in seven one-dimensional spectra was studied. As we altered the sequence of the seven FT-IR spectra, the variation of the cross-peak intensities covered four orders of magnitude in the two-dimensional asynchronous spectra. In contrast, the fluctuation of noise in the two-dimensional asynchronous spectra was within two times. The above results clearly demonstrate that a change in the sequence of one-dimensional spectra is an effective way to improve the signal-to-noise level of the two-dimensional asynchronous spectra.

Identification of systematic absence of cross-peaks (SACPs) in a two-dimensional asynchronous Spectrum using an auxiliary 2D quotient Spectrum and a statistical test

Systematic Absence of Cross Peaks (SACPs) in a two-dimensional (2D) asynchronous spectrum, a sensitive indicator of the signal purity, is very important in analyzing bilinear data. However, identification of SACPs in practice remains a challenge because of noise in the corresponding 2D asynchronous spectrum. We firstly show that SACP can be identified via a statistical test using a large amount of 2D asynchronous spectra. To meet the practical demand that SACPs must be identified based on a single 2D asynchronous spectrum in many cases, we use a 2D quotient spectrum (Q (x, y)) as an effective auxiliary tool to recognize SACPs. The expectation of Q(x, y) is zero when (x, y) is within SACP or background regions in the corresponding 2D asynchronous spectrum. When (x, y) is in a cross-peak region, the expectation of the absolute value of Q(x, y) is a constant regardless of whether the cross-peak in a 2D asynchronous spectrum is strong or weak. Thus, a unified threshold can be set up to differentiate the SACP region from cross-peak region via the auxiliary 2D quotient spectrum. We have applied this approach on two real-world examples and satisfactory results have been obtained. This result demonstrates that the statistical test with a 2D quotient spectrum is applicable in real-world systems.

Application of two-dimensional correlation fluorescence spectroscopy to detect the presence of trace amount of substances

Although fluorescence spectroscopy is a highly sensitive method, it is still rather difficult to identify a minor fluorescent component whose fluorescent peak is overlapped and masked by a dominant fluorescent component in a sample solution. Herein, we describe a two-dimensional correlation spectroscopy (2D-COS) approach based on the Kasha's rule to solve the above common problem. We initially suppose that a sample solution contains the major component only, and the spectral behavior of the major component obeys the Kasha's rule. Then, the shapes of emission spectra obtained under excitation lights of different wavelengths remain invariant. Under this condition, the introduction of a minor fluorescent component can be reflected by the changes on the shapes of emission peaks in the series of emission spectra. Moreover, subtle changes, which are difficult to be found in the original spectra, can be clearly visualized as cross peaks in 2D asynchronous spectrum constructed using a series of emission spectra. In addition, we demonstrate that the intensities of cross peaks can be enhanced by changing the sequence of the series of emission spectra. We utilize the approach on an aqueous solution containing eosin Y and a trace amount of bromocresol green. The presence of bromocresol green with the concentration as low as 400 nM can be revealed via the cross peaks in the resultant 2D asynchronous spectra. In a preliminary study, we suggest that 2D disrelation spectrum might provide an alternative chance to reveal the presence of small amount bromocresol green.

Glycerol's generalized two-dimensional correlation IR/NIR spectroscopy and its principal component analysis

In this manuscript, the fundamental vibration, the combination vibration and the first overtone vibration of the glycerol hydroxyl were studied by near-infrared and infrared spectroscopy. The composition and variation of hydrogen bond were analyzed by two-dimensional correlation spectroscopy and principal component analysis. The analysis revealed five types of hydroxyl and verified the existence of independent, intramolecular, as well as intermolecular, hydrogen bond hydroxyl. The principal component analysis showed that there were three main forms of glycerol association: the first and second principal components explained the majority of the spectral features, and the third was mainly the independent hydroxyl. The results provided insight into the structure of glycerol and illustrated the potential for using these tools in analyzing bonding in even more complex systems.

A novel systematic absence of cross peaks-based 2D-COS approach for bilinear data

A novel approach to use two-dimensional correlation spectroscopy (2D-COS) to analyze bilinear data is proposed. A phenomenon called Systematic Absence of Cross Peaks (SACPs) is observed in a 2D asynchronous spectrum. Two theorems relevant to SACPs have been derived. The SACP-based 2D-COS method has been successfully applied on analyzing bilinear data from mixed samples (including one model system and two real systems). Implicit isolated peaks can be identified and assigned to different components based on characteristic pattern of SACPs even if the time-related profiles of different components are severely overlapped. Based on the results of SACPs, spectra of pure components can be retrieved. Identification of SACPs can still be achieved in the presence of artifacts. Thus, neither noise nor baseline drift can produce significant influence on the results obtained from the approach described in this paper. We have used several well-established chemometric methods, including N-Findr, VCA, and MCR with various initial settings, on two systems that can be successfully solved using the 2D-COS method. The chemometric methods mentioned above cannot provide correct spectra of pure components because of severe problem of rotational ambiguity derived from severe overlapping of the time-related profiles. Only when the information from SACPs in 2D-COS is used as additional constraints in MCR calculation, correct spectra can be obtained. That is to say, the SACP-based 2D-COS method provides intrinsic information which is crucial in the analysis of chromatographic-spectroscopic and analogous data even if the time-related profiles of different components overlap severely.

A Novel Approach Based on Two-Dimensional Correlation Spectroscopy to Determine the Stoichiometric Ratio of Two Substances Involved in Intermolecular Interactions

A novel technique called AOSD@Job's, combining asynchronous orthogonal sample design scheme (AOSD) with Job's method, is proposed to estimate the stoichiometric ratio of two substances that form a supramolecular aggregate under intermolecular interactions. First, a mathematical analysis was performed along with the procedure of the AOSD@Job's method. Then, the validity of the AOSD@Job's method was manifested by computer simulation on two model systems. Finally, the AOSD@Job's method was applied on two real chemical systems. The stoichiometric ratio between the coordination complex of Ni²⁺ and ethylenediaminetetraacetic acid disodium salt (EDTA) was estimated to be 1.0. Benzyl alcohol (BA) and β-cyclodextrin (β-CD) were determined to form a 1 : 1 host-guest complex. These values were consistent with the values reported in the literature. Compared with the traditional Job's method, the AOSD@Job's method has an evident advantage since it is still valid even if all the peaks of the supramolecular aggregate severely overlap with the peaks of the substances that form the aggregate.

Two-dimensional correlation spectroscopic studies on coordination between organic ligands and Ni2+ ions

³A_2g→³T_1g(P) transition band of Ni²⁺ is used to probe the coordination of Ni²⁺. Two-dimensional asynchronous spectra (2DCOS) are generated using the Double Asynchronous Orthogonal Sample Design (DAOSD), Asynchronous Spectrum with Auxiliary Peaks (ASAP) and Two-Trace Two-Dimensional (2T2D) approaches. Cross peaks relevant to the ³A_2g→³T_1g(P) transition band of Ni²⁺ are utilized to probe coordination between Ni²⁺ and various ligands. We studied the spectral behavior of the ³A_2g→³T_1g(P) transition band when Ni²⁺ is coordinated with ethylenediaminetetraacetic acid disodium salt (EDTA). The pattern of cross peaks in 2D asynchronous spectrum demonstrates that coordination brings about significant blue shift of the band. In addition, the absorptivity of the band increases remarkably. The interaction between Ni²⁺ and galactitol is also investigated. Although no clearly observable change is found on the ³A_2g→³T_1g(P) transition band when galactitol is introduced, the appearance of cross peak in 2D asynchronous spectrum demonstrates that coordination indeed occurs between Ni²⁺ and galactitol. Furthermore, the pattern of cross peak indicates that peak position, bandwidth and absorptivity of the ³A_2g→³T_1g(P) transition band of Ni(galactitol)_x²⁺ is considerably different from those of Ni(H₂O)₆²⁺. Thus, 2DCOS is helpful to reveal subtle spectral variation, which might be helpful in shedding light on the physical-chemical nature of coordination.