Residue conservation is a common observation in alignments of protein families, underscoring positions important in protein structure and function. Though many methods measure the level of conservation of particular residue positions, currently we do not have a way to study spatial oscillations occurring in protein conservation patterns. It is known that hydrophobicity shows spatial oscillations in proteins, which is characterized by computing the hydrophobic moment of the protein domains. Here, we advance the study of moments of conservation of protein families to know whether there might exist spatial asymmetry in the conservation patterns of regular secondary structures. Analogous to the hydrophobic moment, the conservation moment is defined as the modulus of the Fourier transform of the conservation function of an alignment of related protein, where the conservation function is the vector of conservation values at each column of the alignment. The profile of the conservation moment is useful in ascertaining any periodicity of conservation, which might correlate with the period of the secondary structure. To demonstrate the concept, conservation in the family of potassium ion channel proteins was analyzed using moments. It was shown that the pore helix of the potassium channel showed oscillations in the moment of conservation matching the period of the α-helix. This implied that one side of the pore helix was evolutionarily conserved in contrast to its opposite side. In addition, the method of conservation moments correctly identified the disposition of the voltage sensor of voltage-gated potassium channels to form a 310 helix in the membrane.

Collagen bundle orientation (CBO) in myocardial infarct scars plays a major role in scar mechanics and complications after infarction. We aim to compare four histopathological methods for CBO measurement in myocardial scarring. Myocardial infarction was induced in 21 pigs by balloon coronary occlusion. Scar samples were obtained at 4 weeks, stained with Masson's trichrome, Picrosirius red, and Hematoxylin-Eosin (H&E), and photographed using light, polarized light microscopy, and confocal microscopy, respectively. Masson's trichrome images were also optimized to remove non-collagenous structures. Two observers measured CBO by means of a semi-automated, Fourier analysis protocol. Interrater reliability and comparability between techniques were studied by the intraclass correlation coefficient (ICC) and Bland-Altman (B&A) plots and limits of agreement. Fourier analysis showed an almost perfect interrater reliability for each technique (ICC ≥ 0.95, p < 0.001 in all cases). CBO showed more randomly oriented values in Masson's trichrome and worse comparability with other techniques (ICC vs. Picrosirius red: 0.79 [0.47-0.91], p = 0.001; vs. H&E-confocal: 0.70 [0.26-0.88], p = 0.005). However, optimized Masson's trichrome showed almost perfect agreement with Picrosirius red (ICC 0.84 [0.6-0.94], p < 0.001) and H&E-confocal (ICC 0.81 [0.54-0.92], p < 0.001), as well as these latter techniques between each other (ICC 0.84 [0.60-0.93], p < 0.001). In summary, a semi-automated, Fourier-based method can provide highly reproducible CBO measurements in four different histopathological techniques. Masson's trichrome tends to provide more randomly oriented CBO index values, probably due to non-specific visualization of non-collagenous structures. However, optimization of Masson's trichrome microphotographs to remove non-collagenous components provides an almost perfect comparability between this technique, Picrosirius red and H&E-confocal.

A novel clustering method is proposed to classify genes or genomes. This method uses a natural representation of genomic data by binary indicator sequences of each nucleotide (adenine (A), cytosine (C), guanine (G), and thymine (T)). Afterwards, the discrete Fourier transform is applied to these indicator sequences to calculate spectra of the nucleotides. Mathematical moments are calculated for each of these spectra to create a multidimensional vector in a Euclidean space for each gene or genome sequence. Thus, each gene or genome sequence is realized as a geometric point in the Euclidean space. Finally, pairwise Euclidean distances between these points (i.e. genome sequences) are calculated to cluster the gene or genome sequences. This method is applied to three sets of data. The first is 34 strains of coronavirus genomic data, the second is 118 of the known strains of Human rhinovirus (HRV), and the third is 30 bacteria genomes. The distance matrices are computed based on the three sets, showing the distances from each point to the others. We used the complete linkage clustering algorithm to build phylogenetic trees to indicate how the distances among these sequence correspond to the evolutionary relationship among these sequences. This genome representation provides a powerful and efficient method to classify genomes and is much faster than the widely acknowledged multiple sequence alignment method.

Gratings1 and holograms2 use patterned surfaces to tailor optical signals by diffraction. Despite their long history, variants with remarkable functionalities continue to be developed3,4. Further advances could exploit Fourier optics5, which specifies the surface pattern that generates a desired diffracted output through its Fourier transform. To shape the optical wavefront, the ideal surface profile should contain a precise sum of sinusoidal waves, each with a well defined amplitude, spatial frequency and phase. However, because fabrication techniques typically yield profiles with at most a few depth levels, complex 'wavy' surfaces cannot be obtained, limiting the straightforward mathematical design and implementation of sophisticated diffractive optics. Here we present a simple yet powerful approach to eliminate this design-fabrication mismatch by demonstrating optical surfaces that contain an arbitrary number of specified sinusoids. We combine thermal scanning-probe lithography6-8 and templating9 to create periodic and aperiodic surface patterns with continuous depth control and sub-wavelength spatial resolution. Multicomponent linear gratings allow precise manipulation of electromagnetic signals through Fourier-spectrum engineering10. Consequently, we overcome a previous limitation in photonics by creating an ultrathin grating that simultaneously couples red, green and blue light at the same angle of incidence. More broadly, we analytically design and accurately replicate intricate two-dimensional moiré patterns11,12, quasicrystals13,14 and holograms15,16, demonstrating a variety of previously unattainable diffractive surfaces. This approach may find application in optical devices (biosensors17, lasers18,19, metasurfaces4 and modulators20) and emerging areas in photonics (topological structures21, transformation optics22 and valleytronics23).

A rapid method for determining the carbonyl value of frying oils has been developed using Fourier-transform infrared (FTIR) spectroscopy and chemometrics. One hundred and fifty-six frying oils with different carbonyl values were collected from an actual potato frying process. FTIR spectra in the range of 4000-650 cm(-1) were scanned with a FTIR spectroscopy apparatus using the attenuated total reflectance (ATR) method. A good calibration model was obtained using the partial least-squares (PLS) regression method with full cross validation for predicting the carbonyl value of frying oils. For the model, the coefficients of determination (R(2)), standard errors of cross validation (SECV) and standard errors of prediction (SEP) were 0.99, 1.87 μmol g(-1) and 1.93 μmol g(-1), respectively. Moreover, standard deviation ratios of reference data in the validation sample set to the SEP were higher than 3. This study shows that the carbonyl value of frying oils can be successfully determined to a high accuracy using FTIR spectroscopy combined with PLS regression.

The study of the response of cancer cells to chemotherapy drugs is of high importance due to the specificity of some drugs to certain types of cancer and the resistance of some specific cancer types to chemotherapy drugs. Our aim was to develop and apply the label-free and non-destructive Fourier transform infrared (FTIR) method to determine the sensitivity of three different cancer cell-lines to a common anti-cancer drug doxorubicin at different concentrations and to demonstrate that information about the mechanism of resistance to the chemotherapy drug can be extracted from spectral data. HeLa, PC3, and Caco-2 cells were seeded and grown on an attenuated total reflection (ATR) crystal, doxorubicin was applied at the clinically significant concentration of 0.1-20 μM, and spectra of the cells were collected hourly over 20 h. Analysis of the amide bands was correlated with cell viability, which had been cross validated with MTT assays, allowing to determine that the three cell lines had significantly different resistance to doxorubicin. The difference spectra and principal component analysis (PCA) highlighted the subtle chemical changes in the living cells under treatment. Spectral regions assigned to nucleic acids (mainly 1085 cm(-1)) and carbohydrates (mainly 1024 cm(-1)) showed changes that could be related to the mode of action of the drug and the mechanism of resistance of the cell lines to doxorubicin. This is a cost-effective method that does not require bioassay reagents but allows label-free, non-destructive and in situ analysis of chemical changes in live cells, using standard FTIR equipment adapted to ATR measurements.

Circulating tumor cells (CTCs) are recognized as a candidate biomarker with strong prognostic and predictive potential in metastatic disease. Filtration-based enrichment technologies have been used for CTC characterization, and our group has previously developed a membrane microfilter device that demonstrates efficacy in model systems and clinical blood samples. However, uneven filtration surfaces make the use of standard microscopic techniques a difficult task, limiting the performance of automated imaging using commercially available technologies. Here, we report the use of Fourier ptychographic microscopy (FPM) to tackle this challenge. Employing this method, we were able to obtain high-resolution color images, including amplitude and phase, of the microfilter samples over large areas. FPM's ability to perform digital refocusing on complex images is particularly useful in this setting as, in contrast to other imaging platforms, we can focus samples on multiple focal planes within the same frame despite surface unevenness. In model systems, FPM demonstrates high image quality, efficiency, and consistency in detection of tumor cells when comparing corresponding microfilter samples to standard microscopy with high correlation (R² = 0.99932). Based on these results, we believe that FPM will have important implications for improved, high throughput, filtration-based CTC analysis, and, more generally, image analysis of uneven surfaces.

The moisture content of beetroot varies during long-term cold storage. In this work, we propose a strategy to identify the moisture content and age of beetroot using principal component analysis coupled Fourier transform infrared spectroscopy (FTIR). Frequent FTIR measurements were recorded directly from the beetroot sample surface over a period of 34 days for analysing its moisture content employing attenuated total reflectance in the spectral ranges of 2614-4000 and 1465-1853 cm-1 with a spectral resolution of 8 cm-1. In order to estimate the transmittance peak height (T p ) and area under the transmittance curve [Formula: see text] over the spectral ranges of 2614-4000 and 1465-1853 cm-1, Gaussian curve fitting algorithm was performed on FTIR data. Principal component and nonlinear regression analyses were utilized for FTIR data analysis. Score plot over the ranges of 2614-4000 and 1465-1853 cm-1 allowed beetroot quality discrimination. Beetroot quality predictive models were developed by employing biphasic dose response function. Validation experiment results confirmed that the accuracy of the beetroot quality predictive model reached 97.5%. This research work proves that FTIR spectroscopy in combination with principal component analysis and beetroot quality predictive models could serve as an effective tool for discriminating moisture content in fresh, half and completely spoiled stages of beetroot samples and for providing status alerts.

Morphology is the most visible and distinct character of plant organs and is accepted as one of the most important tools for plant biologists, plant breeders and growers. A number of methods based on plant morphology are applied to discriminate in particular close cultivars. In this study, image processing analysis was used on 20 grape cultivars ("Amasya beyazı", "Antep karası", "Bahçeli karası", "Çavuş", "Cevşen", "Crimson", "Dimrit", "Erenköy beyazı", "Hafızali", "Karaşabi", "Kırmızı", "İzabella (Isabella) ", "Morşabi", "Müşgüle", "Nuniya", "Royal", "Sultani çekirdeksiz (Sultanina)", "Yalova incisi", "Yerli beyazv", "Yuvarlak çekirdeksiz") to classify them. According to image processing analysis, the longest and the greatest projected area values were observed in "Antep karası" cultivar. The "Sultani çekirdeksiz" cultivar had the least geometric mean diameter. The greatest sphericity ratios were observed in "Yerli beyaz", "Erenköy beyazı" and "Amasya beyazı" cultivars. According to principal component analysis, dimensional attributes were identified as the most significant source of variation discriminant grape cultivars from each other. Morphological differences between the cultivars were explained by sphericity and elongation variables. According to elliptic Fourier analysis (EFA) results, grape morphology largely looks like ellipse and sphere. However, there are some cultivars that look similar to a water drop. The cultivars with similar morphology were identified by a pair-wise comparison test conducted with the use of linear discriminant analysis, and they were presented in a scatter plot. According to cluster analysis, present grape cultivars were classified into seven sub-groups, which indicated great diversity.

To determine the spatial pattern of beta-amyloid (Abeta) deposition throughout the temporal lobe in Alzheimer's disease (AD).

Studies of plant cell and organ outline using shape analysis for taxonomic and morphological research have increased in the past decade. However, there are a limited number of available modern, intuitive, and easy software tools to conduct this work.

Copper-exchanged zeolites are a class of redox-active materials that find application in the selective catalytic reduction of exhaust gases of diesel vehicles and, more recently, the selective oxidation of methane to methanol. However, the structure of the active copper-oxo species present in zeolites under oxidative environments is still a subject of debate. Herein, we make a comprehensive study of copper species in copper-exchanged zeolites with MOR, MFI, BEA, and FAU frameworks and for different Si/Al ratios and copper loadings using X-ray absorption spectroscopy. Only obtaining high quality EXAFS data, collected at large k-values and measured under cryogenic conditions, in combination with wavelet transform analysis enables the discrimination between the copper-oxo species having different structures. The zeolite topology strongly affects the copper speciation, ranging from monomeric copper species to copper-oxo clusters, hosted in zeolites of different topologies. In contrast, the variation of the Si/Al ratio or copper loading in mordenite does not lead to significant differences in XAS spectra, suggesting that a change, if any, in the structure of copper species in these materials is not distinguishable by EXAFS.

We developed a data-driven method to spatiotemporally and spectrally characterize the dynamics of brain oscillations in resting-state magnetoencephalography (MEG) data. The method, called envelope spatial Fourier independent component analysis (eSFICA), maximizes the spatial and spectral sparseness of Fourier energies of a cortically constrained source current estimate. We compared this method using a simulated data set against 5 other variants of independent component analysis and found that eSFICA performed on par with its temporal variant, eTFICA, and better than other ICA variants, in characterizing dynamics at time scales of the order of minutes. We then applied eSFICA to real MEG data obtained from 9 subjects during rest. The method identified several networks showing within- and cross-frequency inter-areal functional connectivity profiles which resemble previously reported resting-state networks, such as the bilateral sensorimotor network at ~20Hz, the lateral and medial parieto-occipital sources at ~10Hz, a subset of the default-mode network at ~8 and ~15Hz, and lateralized temporal lobe sources at ~8Hz. Finally, we interpreted the estimated networks as spatiospectral filters and applied the filters to obtain the dynamics during a natural stimulus sequence presented to the same 9 subjects. We observed occipital alpha modulation to visual stimuli, bilateral rolandic mu modulation to tactile stimuli and video clips of hands, and the temporal lobe network modulation to speech stimuli, but no modulation of the sources in the default-mode network. We conclude that (1) the proposed method robustly detects inter-areal cross-frequency networks at long time scales, (2) the functional relevance of the resting-state networks can be probed by applying the obtained spatiospectral filters to data from measurements with controlled external stimulation.

The purpose of this study has been to describe motor activity data obtained by using wrist-worn actigraphs in patients with schizophrenia and major depression by the use of linear and non-linear methods of analysis. Different time frames were investigated, i.e., activity counts measured every minute for up to five hours and activity counts made hourly for up to two weeks. The results show that motor activity was lower in the schizophrenic patients and in patients with major depression, compared to controls. Using one minute intervals the depressed patients had a higher standard deviation (SD) compared to both the schizophrenic patients and the controls. The ratio between the root mean square successive differences (RMSSD) and SD was higher in the schizophrenic patients compared to controls. The Fourier analysis of the activity counts measured every minute showed that the relation between variance in the low and the high frequency range was lower in the schizophrenic patients compared to the controls. The sample entropy was higher in the schizophrenic patients compared to controls in the time series from the activity counts made every minute. The main conclusions of the study are that schizophrenic and depressive patients have distinctly different profiles of motor activity and that the results differ according to period length analysed.

The aim of this observational study was to examine the characteristics of anterior and posterior corneal topography in keratoconic eyes more than 30 years after penetrating keratoplasty (PK). Patients who maintained clear grafts for more than 30 years after PK were included and divided into the keratoconus (KC) group or other diseases (Others) group, based on the primary indication. Twenty-six eyes of 26 patients were included. The KC group and the Others group included 14 eyes and 12 eyes, respectively. The KC group participants were younger at the time of surgery (P = 0.03). No differences were found in best-spectacle-corrected visual acuity, keratometric power, and central-corneal-thickness. Based on corneal topography using Fourier harmonic analyses, regular astigmatism in the anterior cornea was significantly larger (P = 0.047) and the spherical component in the posterior cornea was significantly lower (P = 0.01) in the KC group. The area under the receiver operating characteristic curve of the spherical component, regular astigmatism, asymmetry component, and higher-order irregularity were 66.07%, 63.10%, 57.14%, and 59.23%, respectively, in the anterior cornea and 80.65%, 52.98%, 63.10%, and 63.99%, respectively, in the posterior cornea. Our results suggested that Fourier harmonic analysis of corneal topography could be useful for patients with KC long after PK.

The exploration of the chiral configurations of enantiomers represents a highly intriguing realm of scientific inquiry due to the distinct roles played by each enantiomer (D and L) in chemical reactions and their practical utilities. This study introduces a pioneering analytical methodology, termed fast Fourier transform capacitance voltammetry (FFT-CPV), in conjunction with principal component analysis (PCA), for the identification and quantification of the chiral forms of tartaric acid (TA), serving as a representative model system for materials exhibiting pronounced chiral characteristics. The proposed methodology relies on the principle of chirality, wherein the capacitance signal generated by the adsorption of D-TA and L-TA onto the surface of a platinum electrode (Pt-electrode) in an acidic solution is harnessed. The capacitance voltammograms were meticulously recorded under optimized experimental conditions. To compile the final dataset for the analyte, the average of the FFT capacitance voltammograms of the acidic solution (without the presence of the analyte) was subtracted from those containing the analyte. A distinct arrangement was obtained by employing PCA as a linear data transformation method, representing D-TA and L-TA in a two/three-dimensional space. The outcomes of the study reveal the successful detection of the two chiral forms of TA with a considerable degree of precision and reproducibility. Moreover, the proposed method facilitated the establishment of two linear response ranges for the concentration values of each enantiomer, spanning from 1 to 20 µM, and 50 to 500 µM. The respective detection limits were also determined to be 0.4 µM for L-TA and 1.3 µM for D-TA. These findings underscore the satisfactory sensitivity and efficiency of the proposed method in both qualitative and quantitative assessments of the chiral forms of TA.

The tortuosity of nerve fibers has been shown to be important for identifying and monitoring clinically relevant manifestations resulting from of a variety of ocular and systemic disease pathologies and disorders. However, quantifying tortuosity in dense neurite networks can prove challenging, as existing methods require manual scoring and/or complete segmentation of the neurite network.

Fourier transform infrared reflectance (FTIR) spectroscopy has been used to predict properties of forest logging residue, a very heterogeneous feedstock material. Properties studied included the chemical composition, thermal reactivity, and energy content. The ability to rapidly determine these properties is vital in the optimization of conversion technologies for the successful commercialization of biobased products. Partial least squares regression of first derivative treated FTIR spectra had good correlations with the conventionally measured properties. For the chemical composition, constructed models generally did a better job of predicting the extractives and lignin content than the carbohydrates. In predicting the thermochemical properties, models for volatile matter and fixed carbon performed very well (i.e., R2 > 0.80, RPD > 2.0). The effect of reducing the wavenumber range to the fingerprint region for PLS modeling and the relationship between the chemical composition and higher heating value of logging residue were also explored. This study is new and different in that it is the first to use FTIR spectroscopy to quantitatively analyze forest logging residue, an abundant resource that can be used as a feedstock in the emerging low carbon economy. Furthermore, it provides a complete and systematic characterization of this heterogeneous raw material.

Vancomycin-resistant Enterococci, mainly Enterococcus faecium (VREfm), are causing nosocomial infections and outbreaks. Bacterial typing methods are used to assist in outbreak investigations. Most of them, especially genotypic methods like multi-locus sequence typing (MLST), whole genome sequencing (WGS), or pulsed-field gel electrophoresis, are quite expensive and time-consuming. Fourier-transform infrared (FT-IR) spectroscopy assesses the biochemical composition of bacteria, such as carboxyl groups in polysaccharides. It is an affordable technique and has a faster turnaround time. Thus, the aim of this study was to evaluate FT-IR spectroscopy for VREfm outbreak investigations. Basic performance requirements like reproducibility and the effects of incubation time were assessed in distinct sample sets. After determining a FT-IR spectroscopy cut-off range, the clustering agreement between FT-IR and WGS within a retrospective (n: 92 isolates) and a prospective outbreak (n: 15 isolates) was investigated. For WGS an average nucleotide identity (ANI) cut-off score of 0.999 was used. Basic performance analysis showed reproducible results. Moreover, FT-IR spectroscopy readouts showed a high agreement with WGS-ANI analysis in clinical outbreak investigations (V-measure 0.772 for the retrospective and 1.000 for the prospective outbreak). FT-IR spectroscopy had a higher discriminatory power than MLST in the outbreak investigations. After determining cut-off values to achieve optimal resolution, FT-IR spectroscopy is a promising technique to assist in outbreak investigation as an affordable, easy-to-use tool with a turnaround time of less than one day. IMPORTANCE Vancomycin-resistant Enterococci, mainly Enterococcus faecium (VREfm), are a frequent cause of nosocomial outbreaks. Several bacterial typing methods are used to track transmissions and investigate outbreaks, whereby genome-based techniques are used as a gold standard. Current methods are either expensive, time-consuming, or both. Additionally, often, specifically trained staff needs to be available. This study provides insight into the use of Fourier-transform infrared (FT-IR) spectroscopy, an affordable, easy-to-use tool with a short turnaround time as a typing method for VREfm. By assessing clinical samples, this work demonstrates promising results for species discrimination and reproducibility. FT-IR spectrosopy shows a high level of agreement in the analysis of VREfm outbreaks in comparison with whole genome sequencing-based methods.

The main challenge in preparing a flexible mold stamp using roll-to-roll nanoimprint lithography is to simultaneously increase the imprintable area with a minimized perceptible seam. However, the current methods for stitching multiple small molds to fabricate large-area molds and functional surfaces typically rely on the alignment mark, which inevitably produces a clear alignment mark and stitched seam. In this study, we propose a mark-less alignment by the pattern itself method inspired by moiré technique, which uses the Fourier spectral analysis of moiré patterns formed by superposed identical patterns for alignment. This method is capable of fabricating scalable functional surfaces and imprint molds with quasi-seamless and alignment mark-free patterning. By harnessing the rotational invariance property in the Fourier transform, our approach is confirmed to be a simple and efficient method for extracting the rotational and translational offsets in overlapped periodic or nonperiodic patterns with a minimized stitched region, thereby allowing for the large-area and quasi-seamless fabrication of imprinting molds and functional surfaces, such as liquid-repellent film and micro-optical sheets, that surpass the conventional alignment and stitching limits and potentially expand their application in producing large-area metasurfaces.