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Kaposzta Z, Czoch A, Stylianou O, Kim K, Mukli P, Eke A, Racz FS. Real-Time Algorithm for Detrended Cross-Correlation Analysis of Long-Range Coupled Processes. Front Physiol 2022; 13:817268. [PMID: 35360238 PMCID: PMC8963246 DOI: 10.3389/fphys.2022.817268] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/17/2021] [Accepted: 02/07/2022] [Indexed: 11/13/2022] Open
Abstract
Assessing power-law cross-correlations between a pair - or among a set - of processes is of great significance in diverse fields of analyses ranging from neuroscience to financial markets. In most cases such analyses are computationally expensive and thus carried out offline once the entire signal is obtained. However, many applications - such as mental state monitoring or financial forecasting - call for fast algorithms capable of estimating scale-free coupling in real time. Detrended cross-correlation analysis (DCCA), a generalization of the detrended fluctuation analysis (DFA) to the bivariate domain, has been introduced as a method designed to quantify power-law cross-correlations between a pair of non-stationary signals. Later, in analogy with the Pearson cross-correlation coefficient, DCCA was adapted to the detrended cross-correlation coefficient (DCCC), however as of now no online algorithms were provided for either of these analysis techniques. Here we introduce a new formula for obtaining the scaling functions in real time for DCCA. Moreover, the formula can be generalized via matrix notation to obtain the scaling relationship between not only a pair of signals, but also all possible pairs among a set of signals at the same time. This includes parallel estimation of the DFA scaling function of each individual process as well, thus allowing also for real-time acquisition of DCCC. The proposed algorithm matches its offline variants in precision, while being substantially more efficient in terms of execution time. We demonstrate that the method can be utilized for mental state monitoring on multi-channel electroencephalographic recordings obtained in eyes-closed and eyes-open resting conditions.
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Affiliation(s)
- Zalan Kaposzta
- Department of Physiology, Faculty of Medicine, Semmelweis University, Budapest, Hungary
| | - Akos Czoch
- Department of Physiology, Faculty of Medicine, Semmelweis University, Budapest, Hungary
| | - Orestis Stylianou
- Department of Physiology, Faculty of Medicine, Semmelweis University, Budapest, Hungary
- Institute of Translational Medicine, Semmelweis University, Budapest, Hungary
| | - Keumbi Kim
- Department of Physiology, Faculty of Medicine, Semmelweis University, Budapest, Hungary
| | - Peter Mukli
- Department of Physiology, Faculty of Medicine, Semmelweis University, Budapest, Hungary
- Oklahoma Center for Geroscience and Healthy Brain Aging, Department of Biochemistry and Molecular Biology, University of Oklahoma Health Sciences Center, Oklahoma City, OK, United States
| | - Andras Eke
- Department of Physiology, Faculty of Medicine, Semmelweis University, Budapest, Hungary
- Department of Radiology and Biomedical Imaging, Yale University School of Medicine, New Haven, CT, United States
| | - Frigyes Samuel Racz
- Department of Physiology, Faculty of Medicine, Semmelweis University, Budapest, Hungary
- Department of Neurology, Dell Medical School, University of Texas at Austin, Austin, TX, United States
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Sánchez-Pedregal VM, Kertesz M, Weiss RG, Navarro-Vázquez A, Cid MM. NMR spectral fingerprint patterns as diagnostics for the unambiguous configurational analysis of the classic organo-gelator 1,3:2,4-dibenzylidene-d-sorbitol (DBS) and its derivatives. Magn Reson Chem 2021; 59:608-613. [PMID: 33368599 DOI: 10.1002/mrc.5124] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/03/2020] [Revised: 12/11/2020] [Accepted: 12/17/2020] [Indexed: 06/12/2023]
Abstract
On the basis of experimental data and density functional theory (DFT) chemical shift and scalar coupling predictions, simple spectral nuclear magnetic resonance (NMR) fingerprint patterns have been established for the determination of the configuration in 1,3:2,4-dibenzylidene-d-sorbitol (DBS), a classic low molecular weight gelator, and its derivatives. The results rigorously prove the orientation of the phenyl rings in DBS that had been previously assumed in the literature on the basis of thermodynamic arguments.
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Affiliation(s)
- Víctor M Sánchez-Pedregal
- Departamento de Química Orgánica, Universidade de Santiago de Compostela, Santiago de Compostela, 15782, Spain
| | - Miklos Kertesz
- Department of Chemistry and Institute for Soft Matter Synthesis and Metrology, Georgetown University, Washington, District of Columbia, 20057-1227, USA
| | - Richard G Weiss
- Department of Chemistry and Institute for Soft Matter Synthesis and Metrology, Georgetown University, Washington, District of Columbia, 20057-1227, USA
| | - Armando Navarro-Vázquez
- Departmento de Química Fundamental, Centro de Ciências Exatas e da Natureza, Universidade Federal de Pernambuco, Recife, 50740-540, Brazil
| | - María Magdalena Cid
- Departmento de Química Orgánica and Agrupación Estratéxica CITACA, Universidade de Vigo, Vigo, 36310, Spain
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Piltz C, Sriarunothai T, Ivanov SS, Wölk S, Wunderlich C. Versatile microwave-driven trapped ion spin system for quantum information processing. Sci Adv 2016; 2:e1600093. [PMID: 27419233 PMCID: PMC4942346 DOI: 10.1126/sciadv.1600093] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/19/2016] [Accepted: 06/14/2016] [Indexed: 05/11/2023]
Abstract
Using trapped atomic ions, we demonstrate a tailored and versatile effective spin system suitable for quantum simulations and universal quantum computation. By simply applying microwave pulses, selected spins can be decoupled from the remaining system and, thus, can serve as a quantum memory, while simultaneously, other coupled spins perform conditional quantum dynamics. Also, microwave pulses can change the sign of spin-spin couplings, as well as their effective strength, even during the course of a quantum algorithm. Taking advantage of the simultaneous long-range coupling between three spins, a coherent quantum Fourier transform-an essential building block for many quantum algorithms-is efficiently realized. This approach, which is based on microwave-driven trapped ions and is complementary to laser-based methods, opens a new route to overcoming technical and physical challenges in the quest for a quantum simulator and a quantum computer.
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Affiliation(s)
- Christian Piltz
- Department Physik, Naturwissenschaftlich-Technische Fakultät, Universität Siegen, 57068 Siegen, Germany
| | - Theeraphot Sriarunothai
- Department Physik, Naturwissenschaftlich-Technische Fakultät, Universität Siegen, 57068 Siegen, Germany
| | - Svetoslav S. Ivanov
- Department of Physics, Sofia University, 5 James Bourchier Boulevard, 1164 Sofia, Bulgaria
| | - Sabine Wölk
- Department Physik, Naturwissenschaftlich-Technische Fakultät, Universität Siegen, 57068 Siegen, Germany
| | - Christof Wunderlich
- Department Physik, Naturwissenschaftlich-Technische Fakultät, Universität Siegen, 57068 Siegen, Germany
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