Spektroskopik Verilerin Analizi ve Yorumlanması

Özet

Bu bölüm, spektroskopik verilerin ham halinden güvenilir bilgiye dönüştürülmesinde izlenen temel veri işleme ve analiz etme yöntemlerini sistematik olarak sunmaktadır. İlk olarak, spektral verilerin doğası (absorbans, emisyon, Raman vb.) ve bu verilerin dalga boyu-yoğunluk çiftleri şeklindeki yapısı açıklanmakta; ortalama, standart sapma, tekrarlanabilirlik ve dağılımlar gibi temel istatistiksel kavramlarla verinin güvenilirliğinin nasıl değerlendirileceği anlatılmaktadır. Ardından, veri ön işleme adımlarına odaklanılmaktadır. Elektronik ve optik kaynaklı gürültülerin tanımlanması, bu gürültünün giderilmesi için çeşitli yöntemler ile örneğin Savitzky-Golay filtresi ile düzgünleştirme ve çeşitli normalizasyon teknikleri detaylandırılmaktadır. Spektral çözünürlük ve sinyal-gürültü oranı (S/G) kavramları, bu performans metriklerinin nasıl ölçüleceği ve ortalama alma gibi yöntemlerle nasıl iyileştirilebileceği ile birlikte ele alınmaktadır. Bölümün ikinci yarısı, verilerin yorumlanmasına ayrılmıştır. Binlerce değişken (dalga boyu) içeren spektrumları analiz etmek için temel çok değişkenli tekniklere (PCA, PLS) giriş yapılmakta ve korelasyon analizi ile model doğrulama yöntemleri tanıtılmaktadır. Spektral kütüphaneler (HITRAN, RRUFF vb.) ve bunlarla basit eşleştirme/korelasyon teknikleri kullanılarak kimyasal tanımlamanın nasıl yapılacağı açıklanmaktadır. Son olarak, tüm bu süreç, gıda numunelerinde IR spektroskopisi ile kalite analizi yapan adım adım bir uygulamalı örnekle pekiştirilmektedir. Bu bölümün tamamı, okuyucunun bir spektroskopik veri setinin istatistiksel temellerini kavramasını, kalitesini değerlendirmesini, temel ön işleme ve çok değişkenli analiz tekniklerini uygulayabilmesini ve nihayetinde basit kimyasal tanımlama veya yorumlama yapabilmesi için gerekli bilgi altyapısını sunmayı hedeflemektedir.

Referanslar

Alam, M. N. U., Basava, K., Chitransh, A., Fattah, H. M. A., Garcia-Verdugo, H. D., Lo, S. H., Lohchab, T., Martinet, K. M., Román-Palacios, C., Salazar, J. C., & Van Boxel, D. (2025). Machine learning in biological research: Key algorithms, applications, and future directions. BMC Biology, 23(1), Article 324. https://doi.org/10.1186/s12915-025-02424-3

Baloglu, M., Vejselova Sezer, C., Izgördü, H., Yilmaz, I., & Kutlu, H. M. (2025). Could Fingolimod Combined with Bevacizumab Be a New Hope in Glioblastoma Treatment? Current Issues in Molecular Biology, 47(6), 394.

Barker, M., & Rayens, W. (2003). Partial least squares for discrimination. Journal of Chemometrics, 17(3), 166–173. https://doi.org/10.1002/cem.785

Bhadra, M., & Hölldobler, S. (2022). Identifying noise variables in singular decisions using counterfactual reasoning. Proceedings of the Workshop on Cognitive Aspects of Knowledge Representation (IJCAI-ECAI Workshop), CEUR Workshop Proceedings (Vol. 3251). CEUR-WS.org. https://ceur-ws.org/Vol-3251/paper3.pdf

Blocker, A. W., & Meng, X.-L. (2013). The potential and perils of preprocessing: Building new foundations. Bernoulli, 19(4), 1776–1792. https://doi.org/10.3150/13-BEJSP16

Bocklitz, T. W., Guo, S., Ryabchykov, O., Vogler, N., & Popp, J. (2016). Raman based molecular imaging and analytics: A magic bullet for biomedical applications? Analytical Chemistry, 88(1), 133–151. https://doi.org/10.1021/acs.analchem.5b04665

Bracewell, R. N. (2000). The Fourier Transform and Its Applications (3rd ed.). McGraw-Hill.

Brereton, R. G. (2003). Chemometrics: Data analysis for the laboratory and chemical plant. John Wiley & Sons.

Brereton, R. G. (2007). Applied chemometrics for scientists. John Wiley & Sons.

Brereton, R. G. (2015). Chemometrics for pattern recognition. John Wiley & Sons.

Bunaciu, A. A., Aboul-Enein, H. Y., & Fleschin, Ş. (2015). Recent applications of Fourier transform infrared spectrophotometry in herbal medicine analysis. Applied Spectroscopy Reviews, 50(3), 176–189. https://doi.org/10.1080/05704928.2014.882347

Bylesjö, M., Cloarec, O., & Rantalainen, M. (2009). Normalization and closure. In R. G. Brereton (Ed.), Comprehensive Chemometrics (Second Edition) Chemical and Biochemical Data Analysis (pp. 101–114). Elsevier. https://doi.org/10.1016/B978-0-444-64165-6.03004-4

Cattell, R. B. (1966). The scree test for the number of factors. Multivariate Behavioral Research, 1(2), 245–276. https://doi.org/10.1207/s15327906mbr0102_10

Cengiz, M., Gür, B., Sezer, C. V., Baytar, O., Şahin, Ö., Ayhanci, A., & Kutlu, H. M. (2024). Green biosynthesis of selenium and zinc oxide nanoparticles using whole plant extract of Rheum ribes: Characterization, anticancer, and antimicrobial activity. Journal of Molecular Liquids, 412, 125861.

Chen, H., Tan, C., & Lin, Z. (2021). Deep learning in spectroscopic analysis: A review. Analytica Chimica Acta, 1145, 59–78. https://doi.org/10.1016/j.aca.2020.10.045

Dhawas, P., Dhore, A., Bhagat, D., Pawar, R. D., Kukade, A., & Kalbande, K. (2024). Big Data Preprocessing, Techniques, Integration, Transformation, Normalisation, Cleaning, Discretization, and Binning. In D. Darwish (Ed.), Big Data Analytics Techniques for Market Intelligence (pp. 159-182). IGI Global Scientific Publishing. https://doi.org/10.4018/979-8-3693-0413-6.ch006.

Dührkop, K., Fleischauer, M., Ludwig, M., Aksenov, A. A., Melnik, A. V., Meusel, M., Dorrestein, P. C., Rousu, J., & Böcker, S. (2019). SIRIUS 4: A rapid tool for turning tandem mass spectra into metabolite structure information. Nature Methods, 16(4), 299–302. https://doi.org/10.1038/s41592-019-0344-8

Eilers, P. H. C., & Boelens, H. F. M. (2005). Baseline correction with asymmetric least squares smoothing. Leiden University Medical Centre Report.

Ernst, R. R., Bodenhausen, G., & Wokaun, A. (1990). Principles of nuclear magnetic resonance in one and two dimensions. Oxford University Press. https://doi.org/10.1093/oso/9780198556473.001.0001.

Ferguson, B., & Zhang, X.-C. (2002). Materials for terahertz science and technology. Nature Materials, 1(1), 26–33. https://doi.org/10.1038/nmat708

Food and Drug Administration (FDA). (2004). Guidance for industry: PAT — A framework for innovative pharmaceutical development, manufacturing, and quality assurance. U.S. Department of Health and Human Services.

Frankel, E. N. (2005). Lipid oxidation (2nd ed.). The Oily Press.

García, S., Luengo, J., & Herrera, F. (2015). Data Preparation Basic Models. In: Data Preprocessing in Data Mining. Intelligent Systems (Reference Library, vol 72) Springer, Cham. https://doi.org/10.1007/978-3-319-10247-4_3

Giesriegl, F., Mrazek, C., & Cadamuro, J. (2025). How laboratory medicine will change in the near future: Integrating artificial intelligence, automation, and human expertise in the era of Industry 5.0. Journal of Laboratory and Precision Medicine, 10, Article 6. https://doi.org/10.21037/jlpm-25-6

Gowen, A. A., O’Donnell, C. P., Cullen, P. J., Downey, G., & Frias, J. M. (2015). Hyperspectral imaging – An emerging process analytical tool for food quality and safety control. Trends in Food Science & Technology, 18(12), 590–598. https://doi.org/10.1016/j.tifs.2007.06.001

Griffiths, P. R., & de Haseth, J. A. (2007). Fourier transform infrared spectrometry (2nd ed.). John Wiley & Sons.

Guillén, M. D., & Goicoechea, E. (2008). Formation of toxic alkylbenzenes in edible oils submitted to frying temperature: Influence of oil composition in main components and heating time. Food Research International, 41(7), 798–806. https://doi.org/10.1016/j.foodres.2008.07.011

Gür, B., Ayhan, M. E., Türkhan, A., Gür, F., & Kaya, E. D. (2019). A facile immobilization of polyphenol oxidase enzyme on graphene oxide and reduced graphene oxide thin films: an insight into in-vitro activity measurements and characterization. Colloids and Surfaces A: Physicochemical and Engineering Aspects, 562, 179-185.

Gür, B., Cengiz, M., Sezer, C. V., Baytar, O., Şahin, Ö., Ayhanci, A., & Kutlu, H. M. (2025). Eco-friendly biosynthesized silver, copper, and nickel nanoparticles mediated Rheum ribes: Assessment of their cytotoxicity and antimicrobial activity. Inorganic Chemistry Communications, 172, 113755.

Hoffman, J. I. E. (2015). Chapter 1 – Basic concepts. In J. I. E. Hoffman, Biostatistics for medical and biomedical practitioners (pp. 3–20). Academic Press. https://doi.org/10.1016/B978-0-12-802387-7.00001-9

Horai, H., Arita, M., Kanaya, S., Nihei, Y., Ikeda, T., Suwa, K., Ojima, Y., Tanaka, K., Tanaka, S., Aoshima, K., Oda, Y., Kakazu, Y., Kusano, M., Tohge, T., Matsuda, F., Sawada, Y., Hirai, M. Y., Nakanishi, H., Ikeda, K., ... Nishioka, T. (2010). MassBank: A public repository for sharing mass spectral data for life sciences. Journal of Mass Spectrometry, 45(7), 703–714. https://doi.org/10.1002/jms.1777

Hoult, D. I., & Richards, R. E. (1976). The signal-to-noise ratio of the nuclear magnetic resonance experiment. Journal of Magnetic Resonance, 24(1), 71–85. https://doi.org/10.1016/0022-2364(76)90233-X

Iammarino, M., Miedico, O., Sangiorgi, E., D’Amore, T., Berardi, G., Accettulli, R., Dalipi, R., Marchesani, G., & Chiaravalle, A. E. (2021). Identification of mechanically separated meat in meat products: A simplified analytical approach by ion chromatography with conductivity detection. International Journal of Food Science & Technology, 56(10), 5305–5314. https://doi.org/10.1111/ijfs.15350

Itkonen, T. H., & Selpi, E. L. (2020). Characterisation of motorway driving style using naturalistic driving data. Transportation Research Part F: Traffic Psychology and Behaviour, 69, 72–79. https://doi.org/10.1016/j.trf.2020.01.002

Jolliffe, I. T. (2002). Principal component analysis (2nd ed.). Springer.

Jolliffe, I. T., & Cadima, J. (2016). Principal component analysis: A review and recent developments. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 374(2065), Article 20150202. https://doi.org/10.1098/rsta.2015.0202

Jozanikohan, G., & Abarghooei, M. N. (2022). The Fourier transform infrared spectroscopy (FTIR) analysis for the clay mineralogy studies in a clastic reservoir. Journal of Petroleum Exploration and Production Technology, 12, 2093–2106. https://doi.org/10.1007/s13202-021-01449-y.

Kalita, J., Bhattacharyya, D. K., & Roy, S. (2024). Data preparation. In Fundamentals of data science: Theory and practice (pp. 31–46). Academic Press. https://doi.org/10.1016/B978-0-32-391778-0.00010-7

Khan, S.A., Khan, S.B., Khan, L.U., Farooq, A., Akhtar, K., Asiri, A.M. (2018). Fourier Transform Infrared Spectroscopy: Fundamentals and Application in Functional Groups and Nanomaterials Characterization. In: Sharma, S. (eds) Handbook of Materials Characterization. Springer, Cham. https://doi.org/10.1007/978-3-319-92955-2_9

Kopyrin, A.S., & Makarova, I. L. (2020). Algorithm for preprocessing and unification of time series based on machine learning for data structuring. Software systems and computational methods, 3, 40–50. https://doi.org/10.7256/2454-0714.2020.3.33958

Li, Y., Kind, T., Folz, J., Vaniya, A., Mehta, S. S., & Fiehn, O. (2017). Spectral entropy outperforms MS/MS dot product similarity for small-molecule compound identification. Nature Methods, 14(2), 195–202. https://doi.org/10.1038/nmeth.4134

Long, D. A. (2002). The Raman effect: A unified treatment of the theory of Raman scattering. Wiley. https://onlinelibrary.wiley.com/doi/book/10.1002/0470845767

Manago, M., & Kodratoff, Y. (1987). Noise and knowledge acquisition. Proceedings of the 10th International Joint Conference on Artificial Intelligence (IJCAI '87) (Vol. 2, pp. 348–354). Morgan Kaufmann. https://dl.acm.org/doi/10.5555/1625015.1625087

Massart, D. L., Vandeginste, B. G. M., Buydens, L. M. C., De Jong, S., Lewi, P. J., & Smeyers-Verbeke, J. (1997). Handbook of chemometrics and qualimetrics: Part A. Elsevier.

McClure, W. F. (2003). 204 years of near-infrared technology: 1800–2003. Journal of Near Infrared Spectroscopy, 11(6), 487–518. https://doi.org/10.1255/jnirs.399

Mildner-Szkudlarz, S., Jeleń, H. H., & Zawirska-Wojtasiak, R. (2010). The use of electronic and human nose for monitoring rapeseed oil autoxidation. European Journal of Lipid Science and Technology, 112(9), 1041–1051. https://doi.org/10.1002/ejlt.201000154

Miller, J.N. & Miller, J.C. (2018). Statistics and Chemometrics for Analytical Chemistry. 7th ed., Pearson

Mizalkoff, B. (2015). Waveguide-enhanced mid-infrared chem/bio sensors. Chemical Society Reviews, 44(22), 863–874. https://doi.org/10.1039/C5CS00031J

Moses, L. E. (1985). Statistical concepts fundamental to investigations. The New England Journal of Medicine, 312(14), 890–897. https://doi.org/10.1056/NEJM198504043121405

Mumuni, A., & Mumuni, F. (2022). Data augmentation: A comprehensive survey of modern approaches. Array, 16, Article 100258. https://doi.org/10.1016/j.array.2022.100258

Myers, O. D., & Smith, C. A. (2021). Using partial and semipartial correlations to evaluate spectral similarity measures for compound identification in untargeted metabolomics. Journal of the American Society for Mass Spectrometry, 32(8), 2099–2108. https://doi.org/10.1021/jasms.1c00152

Ozaki, Y. (2012). Near-infrared spectroscopy—Its versatility in analytical chemistry. Analytical Sciences, 28(6), 545–563. https://doi.org/10.2116/analsci.28.545

Ozaki, Y., Huck, C., Tsuchikawa, S., & Engelsen, S. B. (2021). Near-infrared spectroscopy: Theory, spectral analysis, instrumentation, and applications. Springer Nature.

Pasquini, C. (2018). Near infrared spectroscopy: A mature analytical technique with new perspectives – A review. Analytica Chimica Acta, 1026, 8–36. https://doi.org/10.1016/j.aca.2018.04.004

PCA. (2025). Principal component analysis: A visual guide. Medium. https://medium.com/@erdemerzurumlu/pca-473fe69a2680

Perkins, W. D. (1987). Fourier transform-infrared spectroscopy: Part I. Instrumentation. Journal of Chemical Education, 64(11), A269–A271. https://doi.org/10.1021/ed064pA269

Rinnan, Å., van den Berg, F., & Engelsen, S. B. (2009). Review of the most common pre-processing techniques for near-infrared spectra. TrAC Trends in Analytical Chemistry, 28(10), 1201–1222. https://doi.org/10.1016/j.trac.2009.07.007

ROC. (2025). ROC eğrisi ve AUC skoru ile sınıflandırma modellerinin performans değerlendirmesi [ROC curve and AUC score for classification model performance evaluation]. Medium. https://oguzhanyenen.medium.com/classification-modellerinin-performans%C4%B1n%C4%B1-de%C4%9Ferlendirmede-roc-auc-score-d3fc7edc42a4

Roggo, Y., Chalus, P., Maurer, L., Lema-Martinez, C., Edmond, A., & Jent, N. (2007). A review of near infrared spectroscopy and chemometrics in pharmaceutical technologies. Journal of Pharmaceutical and Biomedical Analysis, 44(3), 683–700. https://doi.org/10.1016/j.jpba.2007.03.023

Rostami, M. R., Kaya, M., Gür, B., Onganer, Y., & Meral, K. (2015). Photophysical and adsorption properties of pyronin B in natural bentonite clay dispersion. Applied Surface Science, 359, 897-904.

Roy, S., Sharma, P., Nath, K., Bhattacharyya, D. K., & Kalita, J. K. (2019). Pre-processing: A data preparation step. In S. Ranganathan, M. Gribskov, K. Nakai, & C. Schönbach (Eds.), Encyclopedia of bioinformatics and computational biology (Vol. 1, pp. 463–471). Academic Press. https://doi.org/10.1016/B978-0-12-809633-8.20457-3

Runkler, T. (2012). Data Preprocessing. In: Data Analytics. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-8348-2589-6_3

Sarycheva, A., & Gogotsi, Y. (2020). Raman spectroscopy analysis of the structure and surface chemistry of Ti₃C₂Tₓ MXene. Chemistry of Materials, 32(8), 3480–3488. https://doi.org/10.1021/acs.chemmater.0c00359.

Savitzky, A., & Golay, M. J. E. (1964). Smoothing and differentiation of data by simplified least squares procedures. Analytical Chemistry, 36(8), 1627–1639. https://doi.org/10.1021/ac60214a047

Sevinç, G., Orak, İ., & Kocyigit, A. (2025). BODIPY and Aza-BODIPY based Schottky-type photodiodes for optoelectronic applications, Inorganic Chemistry Communications, 184, 115975. https://doi.org/10.1016/j.inoche.2025.115975.

Shahidi, F., & Wanasundara, U. N. (2002). Methods for measuring oxidative rancidity in fats and oils. In C. C. Akoh & D. B. Min (Eds.), Food lipids: Chemistry, nutrition, and biotechnology (2nd ed., pp. 465–487). Marcel Dekker.

Skoog, D. A., & Leary, J. J. (1992). Principles of instrumental analysis (4th ed.). Saunders College Publishing.

Skoog, D. A., Holler, F. J., & Crouch, S. R. (2014). Principles of instrumental analysis (7th ed.). Cengage Learning.

Smith, B. C. (2011). Fundamentals of Fourier transform infrared spectroscopy (2nd ed.). CRC Press.

Smith, E., & Dent, G. (2019). Modern Raman spectroscopy: A practical approach (2nd ed.). John Wiley & Sons.

Stein, S. E., & Scott, D. R. (1994). Optimization and testing of mass spectral library search algorithms for compound identification. Journal of the American Society for Mass Spectrometry, 5(9), 859–866. https://doi.org/10.1016/1044-0305(94)87009-8

Stuart, B. H. (2004). Infrared spectroscopy: Fundamentals and applications. John Wiley & Sons.

Swami, K. N. S. (2024). Emerging trends in the application of artificial intelligence and machine learning for analytical chemistry: Enhancing precision and automation. International Scientific Journal of Engineering and Management, 3(5), 1–12. https://doi.org/10.55041/isjem01725

Synovec, R. E., & Yeung, E. S. (1986). Comparison of an integration procedure to Fourier transform and data averaging procedures in chromatographic data analysis. Analytical Chemistry, 58(9), 2093–2095. https://doi.org/10.1021/ac00122a037

Thomas, O., & Burgess, C. (2017). UV-visible spectrophotometry of water and wastewater. Elsevier.

Vafaei, N., Ribeiro, R. A., & Camarinha-Matos, L. M. (2021). Assessing Normalization Techniques for TOPSIS Method. In: Camarinha-Matos, L.M., Ferreira, P., Brito, G. (eds) Technological Innovation for Applied AI Systems. DoCEIS 2021. IFIP Advances in Information and Communication Technology, vol 626 (pp. 132–141). Springer, Cham. https://doi.org/10.1007/978-3-030-78288-7_13

Vinaixa, M., Schymanski, E. L., Neumann, S., Navarro, M., Salek, R. M., & Yanes, O. (2016). Mass spectral databases for LC/MS- and GC/MS-based metabolomics: State of the field and future prospects. TrAC Trends in Analytical Chemistry, 78, 23–35. https://doi.org/10.1016/j.trac.2015.09.005

Vinther, L., Broholm, M. M., Schittich, A., Haugsted, T., McKnight, U. S., Draborg, H., Bjerg, P. L., & Wünsch, U. J. (2025). Fluorescence spectroscopy as an indicator tool for pharmaceutical contamination in groundwater and surface water. Chemosphere, 372, Article 144009.

Vogrin, M., & Koten, J. W. (2024). RUM leads to noise: The significance of finding the sources of variability between experimental runs. Synthese, 204, Article 147. https://doi.org/10.1007/s11229-024-04798-3

Wang, M., Carver, J. J., Phelan, V. V., Sanchez, L. M., Garg, N., Peng, Y., Nguyen, D. D., Watrous, J., Kapono, C. A., Luzzatto-Knaan, T., Porto, C., Bouslimani, A., Melnik, A. V., Meehan, M. J., Liu, W.-T., Crüsemann, M., Boudreau, P. D., Esquenazi, E., Sandoval-Calderón, M., ... Bandeira, N. (2016). Sharing and community curation of mass spectrometry data with Global Natural Products Social Molecular Networking. Nature Biotechnology, 34(8), 828–837. https://doi.org/10.1038/nbt.3597

Wang, S. X., & de la Zerda, A. (2022). Imaging controls and concepts. In S. X. Wang & A. de la Zerda (Eds.), Biochips and medical imaging (pp. 45–78). Wiley. https://doi.org/10.1002/9781118910573.ch18

Westermayr, J., & Marquetand, P. (2025). Machine learning spectroscopy to advance computation and analysis. Chemical Science, 16, 21660–21676. https://doi.org/10.1039/D5SC05628D

Wilkinson, M. D., Dumontier, M., Aalbersberg, Ij. J., Appleton, G., Axton, M., Baak, A., Blomberg, N., Boiten, J.-W., da Silva Santos, L. B., Bourne, P. E., Bouwman, J., Brookes, A. J., Clark, T., Crosas, M., Dillo, I., Dumon, O., Edmunds, S., Evelo, C. T., Finkers, R., ... Mons, B. (2016). The FAIR Guiding Principles for scientific data management and stewardship. Scientific Data, 3, Article 160018. https://doi.org/10.1038/sdata.2016.18

Wilson, E. B., Decius, J. C., & Cross, P. C. (1980). Molecular vibrations: The theory of infrared and Raman vibrational spectra. Dover Publications. https://store.doverpublications.com/products/9780486639413

Wold, S., Sjöström, M., & Eriksson, L. (2001). PLS-regression: A basic tool of chemometrics. Chemometrics and Intelligent Laboratory Systems, 58(2), 109–130. https://doi.org/10.1016/S0169-7439(01)00155-1

Wu, S., Liu, S., & Li, M. (2006). The method of data pre-processing in grey information systems. Proceedings of the 9th International Conference on Control, Automation, Robotics and Vision (ICARCV) (pp. 1–4). IEEE. https://doi.org/10.1109/ICARCV.2006.345360

Xie, H., Jia, Y., & Liu, S. (2024). Integration of artificial intelligence in clinical laboratory medicine: Advancements and challenges. Interdisciplinary Medicine, 2, Article e20230056. https://doi.org/10.1002/INMD.20230056

Yang, H., & Irudayaraj, J. (2001). Comparison of near-infrared, Fourier transform-infrared, and Fourier transform-Raman methods for determining olive pomace oil adulteration in extra virgin olive oil. Journal of the American Oil Chemists' Society, 78(9), 889–895. https://doi.org/10.1007/s11746-001-0359-z

Yang, Q., Fullagar, W., Paziresh, M., Myers, G., Latham, S., Sheppard, A., & Kingston, A. (2022). Spectral information from photon statistics in x-ray radiography and computed tomography. Physical Review A, 106(1), 013511. https://doi.org/10.1103/PhysRevA.106.013511

Zamlynskyi, V., Shchurovska, A., & Trishin, F. A. (2025). Analysis of data collection problems in integrated structures and their impact on the accuracy of predictive analytics in building business processes. Economy of Ukraine, 68(6 (763), 39–57. https://doi.org/10.15407/economyukr.2025.06.039

Zhu, Y., Pei, Z., Wu, X., Chen, M., & Wang, M. (2018). Learning spectral embedding for tandem mass spectrum similarity scoring. Bioinformatics, 34(13), i751–i760. https://doi.org/10.1093/bioinformatics/bty586

Yayınlanan

10 Şubat 2026

Lisans

Lisans