Temporal Modes Research Articles

Brentano's theory of intentionality

AbstractChapters Five through Nine of Book Two of Brentano's 1874 Psychology From an Empirical Standpoint were republished in 1911 with a substantive Appendix of Brentano's remarks. In the Appendix Brentano makes a significant addition to his theory of intentionality. In particular, he introduces new modes within the mode of presentation itself. These new modes are needed to account for our thinking about anything in a relational structure (in recto and in obliquo modes) and for our thoughts about time (the temporal mode). I want to suggest that in the end Brentano simply takes relations to be different kinds of modes.

Research on Rural Population/Arable Land/Rural Settlements Association Model and Coordinated Development Path: A Case Analysis of the Yellow River Basin (Henan Section).

The countryside is a complex regional system with population and land as the core elements, and it is of great significance to study the coordination of the rural human-land relationship for promoting rural ecological protection and high-quality development. The Yellow River Basin (Henan section) is an important grain-producing area with dense population, fertile soil, and rich water resources. Based on the rate of change index and Tapio decoupling model, this study took county-level administrative region as the evaluation unit to explore the characteristics of the spatio-temporal correlation model of rural population/arable land/rural settlements in the Yellow River Basin (Henan section) from 2009 to 2018 and the optimal path of coordinated development. The results show the following: (1) The decrease of rural population, the increase of arable land in a relatively large part of non-central cities, the decrease of arable land in central cities, and the general increase in the area of rural settlements are the most important characteristics of the Yellow River Basin (Henan section) for the change of rural population/arable land/rural settlements. (2) There are spatial agglomeration characteristics of rural population changes, arable land changes, and rural settlements changes. Areas with a high degree of change in arable land have a certain degree of spatial consistency with areas with a high degree of change in rural settlements. (3) The type of T3 (rural population and arable land)/T3 (rural population and rural settlement) is the most important temporal and spatial combination mode, and rural population outflow is serious. In general, the spatio-temporal correlation model of rural population/arable land/rural settlements in the eastern and western sections of the Yellow River Basin (Henan section) is better than that in the middle section. The research results are helpful to deeply understand the relationship between rural population and land in the period of rapid urbanization and can provide reference for the classification and sub-standard policies of rural revitalization. It is urgent to establish sustainable rural development strategies for improving the human-land relationship, narrowing the rural-urban disparity, innovating rural residential land area policies, and revitalizing the rural area.

Cavity-enhanced and temporally multiplexed atom-photon entanglement interface.

Practical realization of quantum repeaters requires quantum memories with high retrieval efficiency, multi-mode storage capacities, and long lifetimes. Here, we report a high-retrieval-efficiency and temporally multiplexed atom-photon entanglement source. A train of 12 write pulses in time is applied to a cold atomic ensemble along different directions, which generates temporally multiplexed pairs of Stokes photons and spin waves via Duan-Lukin-Cirac-Zoller processes. The two arms of a polarization interferometer are used to encode photonic qubits of 12 Stokes temporal modes. The multiplexed spin-wave qubits, each of which is entangled with one Stokes qubit, are stored in a "clock" coherence. A ring cavity that resonates simultaneously with the two arms of the interferometer is used to enhance retrieval from the spin-wave qubits, with the intrinsic retrieval efficiency reaching 70.4%. The multiplexed source gives rise to a ∼12.1-fold increase in atom-photon entanglement-generation probability compared to the single-mode source. The measured Bell parameter for the multiplexed atom-photon entanglement is 2.21(2), along with a memory lifetime of up to ∼125 µs.

Synaptic self-organization of spatio-temporal pattern selectivity.

Spiking model neurons can be set up to respond selectively to specific spatio-temporal spike patterns by optimization of their input weights. It is unknown, however, if existing synaptic plasticity mechanisms can achieve this temporal mode of neuronal coding and computation. Here it is shown that changes of synaptic efficacies which tend to balance excitatory and inhibitory synaptic inputs can make neurons sensitive to particular input spike patterns. Simulations demonstrate that a combination of Hebbian mechanisms, hetero-synaptic plasticity and synaptic scaling is sufficient for self-organizing sensitivity for spatio-temporal spike patterns that repeat in the input. In networks inclusion of hetero-synaptic plasticity that depends on the pre-synaptic neurons leads to specialization and faithful representation of pattern sequences by a group of target neurons. Pattern detection is robust against a range of distortions and noise. The proposed combination of Hebbian mechanisms, hetero-synaptic plasticity and synaptic scaling is found to protect the memories for specific patterns from being overwritten by ongoing learning during extended periods when the patterns are not present. This suggests a novel explanation for the long term robustness of memory traces despite ongoing activity with substantial synaptic plasticity. Taken together, our results promote the plausibility of precise temporal coding in the brain.

Dual Light Temporal Coding Modes Enabled by Nanoparticle-Mediated Phototransistors via Gate Bias Modulation for Brain-Inspired Visual Perception.

The core integration and cooperation of the retina, neurons, and synapses in the visual systems enable humans to effectively sense and process visual information with low power consumption. To mimic the human visual system, an artificial sensory nerve, along with optical sensing─a paired-pulse ratio (PPR) of the light pulse stimulated currents─and neural coding has been developed. For performing the artificial visual perception functions, we consistently reveal the positive and negative correlations between the PPR index and light pulse time interval by applying two consecutive light stimuli with gate voltages of -10 and 5 V, respectively, to a phototransistor. This phototransistor contains a heterostructured channel layer composed of zinc-oxide nanoparticles (ZnO NPs) interconnected with a solution-processed zinc-tin oxide (ZTO) film. The oxygen adsorption and desorption on the ZnO NP surface under light illumination are responsible for the positive-sloped PPR; the electron trapping effect at the ZnO NP/SiO2 interface is attributed to the negative-sloped PPR. The various accountable light power densities and number of surface trap states are considered to be directly realizing these spike-timing interval-dependent characteristics. The actual benefit of these characteristics is the dual temporal coding modes based on multiplicative operation using a ZTO/ZnO NP phototransistor realized via the active gate voltage modulation. The contrary tendency of the PPR index and temporal coding─a major biological neural coding─is well demonstrated by the potential of ZTO/ZnO NP phototransistors to be implemented in sensor networks for an artificial visual perception.

Topological Fano resonance of symmetric Lamb wave induced by antisymmetric trapped mode

The rapid development of topological physics in recent years has greatly enriched the methods for manipulating classic waves. Fano resonance is a widespread phenomenon featured with asymmetric and ultrasharp transmission line shape, which is induced by the constructive and destructive interference of two resonance modes with different quality factors. The temporal coupling mode theory is introduced to theoretically describe the physical process of Fano phenomena with two topological resonance states. The mechanism of the pass band led by the coupling between local resonance and Bragg scattering is introduced to design the antisymmetric topological resonance state and suppress the interference of the antisymmetric propagation mode. The complex eigenvalue analysis shows that the antisymmetric topological resonance state can be treated as the bound state in continuum (BIC). The periods of the phononic crystal (PnC) can be largely reduced by this scheme. The mechanism of coupling between two topological resonance modes attributed to geometric parameter variation is explained by the perturbing perspective and the temporal coupled mode theory. By theoretical analysis, the antisymmetric topological resonance state can be simultaneously treated as symmetric protected BIC and Friedrich–Wintgen BIC. Then, the design method for PnC with Fano resonance is proposed. The numerical results are in good agreement with the theoretical outcomes. The research results may find potential applications and offer the theoretical directive guideline for design in the fields of non-destructive testing, radio-frequency filters, resonators, and sensors.

Creation of nonclassical states of light in a chiral waveguide

Creating nonclassical states of light from simple quantum systems together with classical resources is a challenging problem. We show how chiral emitters under a coherent drive can generate nonclassical photon states. For our analysis, we select a specific temporal mode in the transmitted light field, resulting in a coupled master equation for the relevant mode and the chiral emitters. We characterize the mode's state by its Wigner function and show that the emission from the system predominantly produces mixtures of few-photon-added coherent states. We argue that these nonclassical states are experimentally accessible and show their application for quantum metrology.

Data-driven assessment of arch vortices in simplified urban flows

Understanding flow structures in urban areas is widely recognized as a challenging concern due to its effect on urban development, air quality, and pollutant dispersion. In this study, state-of-the-art data-driven methods for modal analysis of simplified urban flows are used to study the dominant flow processes in these environments. Higher order dynamic mode decomposition (HODMD), a highly-efficient method to analyze turbulent flows, is used together with traditional techniques such as proper-orthogonal decomposition (POD) to analyze high-fidelity simulation data of a simplified urban environment. Furthermore, the spatio-temporal Koopman decomposition (STKD) will be applied to the temporal modes obtained with HODMD to perform spatial analysis. The flow interaction within the canopy influences the flow structures, particularly the arch vortex. The latter is a vortical structure generally found downstream of wall-mounted obstacles, which is generated as a consequence of flow separation. Therefore, the main objective of the present study is to characterize the mechanisms that promote these phenomena in urban areas with different geometries. Remarkably, among all the vortical structures identified by the HODMD algorithm, low- and high-frequency modes are classified according to their relation with the arch vortex. They are referred to as vortex-generator and vortex-breaker modes, respectively. This classification implies that one of the processes driving the formation and destruction of major vortical structures in between the buildings is the interaction between low- and high-frequency structures. The high energy revealed by the POD for the vortex-breaker modes points to this destruction process as the mechanism driving the flow dynamics. Furthermore, the results obtained with the STKD method show how the generating- and breaking-mechanisms originated along with the streamwise and spanwise directions.

Photon number resolution without optical mode multiplication

Abstract Common methods to achieve photon number resolution rely on fast on-off single-photon detectors in conjunction with temporal or spatial mode multiplexing. Yet, these methods suffer from an inherent trade-off between the efficiency of photon number discrimination and photon detection rate. Here, we introduce a method of photon number resolving detection that overcomes these limitations by replacing mode multiplexing with coherent absorption of a single optical mode in a distributed detector array. Distributed coherent absorption ensures complete and uniform absorption of light among the constituent detectors, enabling fast and efficient photon number resolution. As a proof-of-concept, we consider the case of a distributed array of superconducting nanowire single-photon detectors with realistic parameters and show that deterministic absorption and arbitrarily high photon number discrimination efficiency can be achieved by increasing the number of detectors in the array. Photon number resolution without optical mode multiplication provides a simple yet effective method to discriminate an arbitrary number of photons in large arrays of on-off detectors or in smaller arrays of mode multiplexed detectors.

A 509 nm pulsed laser system for Rydberg excitation of cesium atoms

<sec>Single photon source is a non-classical light field with anti-bunching effect, which has a potential applications in the research of fundamental physics problems, quantum precision measurement, quantum communication, quantum computing, etc. The strong interaction between highly excited Rydberg atoms presents an excitation blockade effect. In a dense Rydberg atomic ensemble, the excitation of more than one Rydberg atom within a blockade volume is suppressed, where the interactions of Rydberg atoms shift the atomic states out of resonance with an excitation laser.</sec><sec>We consider here the generation of single photon source by using a four-wave mixing scheme in a room-temperature atomic vapor cell. In a homemade micrometer-sized atomic vapor cell, one-dimensional size is smaller than the radius of Rydberg blockade and the other two-dimensional size is limited by the size of focused laser beam. The blockade radius is on the order of a few micrometers, depending on the Rydberg atom states. An excitation blockade effect can be used to realize single photon source in thermal cesium vapor microcells. The micron cesium-cell is used to spatially localize atomic groups, which results in the atomic decoherence time on the order of microseconds or even nanoseconds. This requires a high-power pulsed laser to prepare the Rydberg atomic state at a nanosecond scale.</sec><sec>Four-photon excitation schemes with narrow linewidth lasers are also used experimentally. The cesium-Rydberg state can usually be excited by the lasers with optical wavelengths 852 and 509 nm, respectively. The laser system is well-stabilized so that the detuning is small compared with the spontaneous linewidth of Rydberg state, while the laser power and temporal mode need to be specified for ns-time coherence in thermal cesium vapor microcells. The 852 nm laser can be achieved by modulating the continuous laser beam with the help of an electro-optic intensity modulator (EOIM). While this remains a technical challenge for 509 nm laser with ns-laser pulse. There is no EOIM to generate the ns-laser pulse with high power.</sec><sec>We demonstrate a novel generation method of 509 nm laser system. In our experiments, a 1018 nm fiber laser is used to produce a continuous laser with a typical linewidth of ～8 kHz and power of 10 mW. The nanosecond pulse is generated with the help of an electro-optic intensity modulator (EOIM) by modifying the continuous laser beam. The peak power of modulated optical pulse is amplified to 4600 W by using a homemade fiber amplifier. The output beam of 1018 nm is then injected into a periodically poled lithium-niobate (PPLN) to generate the second harmonics laser of 509 nm. The typical peak power of 509 nm reaches 173 W by optimizing PPLN phase matching parameters. The pulse repetition frequency of the 509 nm laser can be continuously tuned in a range of 300 kHz–100 MHz, and the pulse width can be continuously tuned in a range of 1–100 ns. Peak power fluctuation of the pulses is about 1.3%. The power 509 nm laser with optimized pulse parameters can be used to excite the cesium atom with GHz bandwidth. Meanwhile the two seed source lasers is well established experimentally, which allows alternating pulses with a different wavelength. This is an essential capability for realizing a single photon source through four-wave mixing.</sec>

Кино: конструирование времени

Introduction. The technical art of cinematography is traditionally regarded as a synthetic unity of scientific and technological progress and creativity. The possibility of unlimited copying of movie plots makes it possible to extend the authority of cinema to broad areas of public attention and forms a mass man. At the same time, the fact that cinema is, first of all, an experiment with time, organized by technical means, remains behind the scenes. The purpose of the study. If the core issues of humanity are centered on the problem of life and death, on the problem of mastering and overcoming time, then cinema clearly shows that humanity has a ready-made embodied model of its desire. Methods. The authors use a phenomenological method that allows one to see the temporal fabric behind the “opaque body” of cinema. The eidetic reduction to the foundations of the constructed film plot temporal reality is complemented by the structuralist method of analyzing technical devices and technological methods of the film industry. Scientific novelty of the research. The ontology of the technical art of cinema goes beyond rationality and pragmatics. By launching a special kind of experiment with time, cinema technologies allow the viewer to be present in the bifurcation moments of temporal metamorphoses that connect different temporal modes. The temporal fabric is subject to the plot logic. Results. In cinema, time is constructed by technical means. The nature of this construction allows us to see the layered structure of time, the intersections of time flows, influxes, reverse time orders and stops in time. The cinema technique clearly shows that time barriers are conditional. Conclusions. Cinema dissolves any empirical density, creating gaps in it and transitions to other worlds. The connection between the worlds is carried out by constructed time. Time is taken out of objects and, obeying the course of the narrative, expands the reality of the world.

Transcription factor TOX maintains the expression of Mst1 in controlling the early mouse NK cell development.

Rationale: TOX is a DNA-binding factor required for the development of multiple immune cells and the formation of lymph nodes. However, the temporal regulation mode of TOX on NK cell development and function needs to be further explored. Methods: To investigate the role of TOX in NK cells at distinct developmental phases, we deleted TOX at the hematopoietic stem cell stage (Vav-Cre), NK cell precursor (CD122-Cre) stage and late NK cell developmental stage (Ncr1-Cre), respectively. Flow cytometry was used to detect the development and functional changes of NK cell when deletion of TOX. RNA-seq was used to assess the differences in transcriptional expression profile of WT and TOX-deficient NK cells. Published Chip-seq data was exploited to search for the proteins directly interact with TOX in NK cells. Results: The deficiency of TOX at the hematopoietic stem cell stage severely retarded NK cell development. To a less extent, TOX also played an essential role in the physiological process of NKp cells differentiation into mature NK cells. Furthermore, the deletion of TOX at NKp stage severely impaired the immune surveillance function of NK cells, accompanied by down-regulation of IFN-γ and CD107a expression. However, TOX is dispensable for mature NK cell development and function. Mechanistically, by combining RNA-seq data with published TOX ChIP-seq data, we found that the inactivation of TOX at NKp stage directly repressed the expression of Mst1, an important intermediate kinase in Hippo signaling pathway. Mst1 deficient at NKp stage gained the similar phenotype with Toxfl/flCD122Cre mice. Conclusion: In our study, we conclude that TOX coordinates the early mouse NK cell development at NKp stage by maintaining the expression of Mst1. Moreover, we clarify the different dependence of the transcription factor TOX in NK cells biology.

Features of aspectual derivation in Russian (on the Slavic background)

The article considers one of the fundamental types of system-forming and functional language relations - derivation, in the most complex area of its realization, namely, in the verbal aspectual sphere, where in the Slavic languages there is a close interaction of lexicon, word formation and morphology. The notions of modification and mutation in intraglossal word formation are analyzed in this paper. The greatest attention is paid to aspectual derivation. This issue covers not only the grammatical category of species, but also related word-formation categories, namely phasic- -temporal modes of verbal action. Slavic verbal type is considered in the article as a derivational morphological category. The role of species pairing for aspectual derivation in general is shown, and the parameters of species pairs are determined. The importance of the functional criterion in determining the species pairs and the fact of the expansion of species correlations in Russian is explained on the basis of M. V. Panov?s theory of species antinomies. The article summarizes and develops the research into the category of aspect and aspectual derivation, conducted by the author of the article on the material of the Russian and other Slavic languages during the last decade, and outlines the prospects for the development of this line of research.

Assessment of URANS and LES methods in predicting wake shed behind a vertical axis wind turbine

In order to shed light on the Vertical-Axis Wind Turbines (VAWT) wake characteristics, in this paper we present high-fidelity CFD simulations of the flow around an exemplary H-shaped VAWT turbine, and we propose to apply Proper Orthogonal Decomposition (POD) to the computed flow field in the near wake of the rotor. The turbine under consideration was widely studied in previous experimental and computational investigations. In the first part of the study, multiple Reynolds-Averaged Navier–Stokes (RANS) simulations were performed at the Tip Speed Ratio (TSR) of peak power coefficient, to select the most accurate turbulence model with respect to available data. In the following step, further RANS numerical simulations were performed at different TSRs to compare the power coefficient against experimental data. Then, Large Eddy Simulation (LES) was applied for multiple TSR conditions. The spatial and temporal POD modes along with modal energy for the RANS and LES results were extracted, and the performance of the turbulence models was assessed. Also, an interpretation of the POD modes with respect to the flow structures was given to highlight the most significant time and length scales of the predictions considering the different dynamical levels of approximations of the computational models.

An attention mechanism-based deep regression approach with a sequence decomposition-granularity reconstruction-integration model for urban daily water supply forecasting

With the depletion of globally available water resources and the rapid development of cities, helping managers of urban water departments formulate management plans and accurately forecast urban daily water supply (UDWS) is important. In this paper, to improve the ability of the model to process complex feature information, we proposed a new UDWS forecasting model that adopts the idea of sequence decomposition, secondary granularity reconstruction, and integration forecasting. First, the UDWS sequence was decomposed into multiple intrinsic mode functions (IMFs) using time varying filtering based temporal mode decomposition (TVFEMD) method. Second, fast Fourier transform (FFT) and sample entropy (SE) approaches were utilized to reconstruct the decomposed IMFs to obtain new granularity features (the FFT for the first granularity reconstruction, and the SE for the second granularity reconstruction). Third, an attention mechanism was combined with a long short-term memory model to further mine the local features in each granularity and improve the forecasting accuracy. Finally, the simulated values of all of the granularity were integrated to obtain the UDWS forecast. We applied the proposed model to the actual case of a water plant in Nan'an District, Chongqing, China, and the results had a mean absolute error (MAE) of 2680 m3/d, a root mean square error (RMSE) of 3597 m3/d, and a mean absolute percentage error (MAPE) of 1.461 %. Compared with other models, these results showed that the proposed model had better reliability and accuracy in a practical application UDWS forecasting scenario.

The Persistence of Sung History-Making in Oceania

ABSTRACT This article explores the persistence of local, sung modes of history-making in Oceania. It examines the importance of song forms as temporal modes of history, and the implication of these practices for approaches to local histories. The article first explores song within a critical overview of past scholarship, examining work that focuses on sung histories and their temporal meaning. It then discusses an example of local history-making in a genre of rhythmic recitation called itang from the islands of Chuuk, in Micronesia. I suggest that itang recitations are not only a valued mode of positioning local history in Chuuk, but the recitation form has implications for considering the Deep Time of cultural expressions in the Pacific. This study asks how a fuller integration of sung histories within scholarship might further localize the practice of history in the Pacific.

Two-photon spectral modulation via temporal manipulation: Quantum optical synthesis of spectral modes from temporal square waves

Precise manipulation of the time–frequency modes of entangled photons is crucial for future quantum science and technologies. Recently, the frequency-domain-quantum-optical-synthesis (FD-QOS) method was demonstrated by creating a superposition of different joint temporal amplitudes: those temporal distributions can be controlled by manipulating the joint spectral amplitude in 2D frequency space via a Fourier optical relation. This FD-QOS method provides an efficient, flexible, and easy-to-control way to precisely modulate the temporal distributions of the entangled photon in an ultrafast region. However, manipulation of only the temporal modes is not sufficient for various applications in quantum information, since spectral modulations are also needed on many occasions. Here, we present a proof-of-concept experiment of two-photon spectral modulation via temporal manipulation of a biphoton wave packet. This protocol, called time-domain-quantum-optical-synthesis (TD-QOS), is achieved by adjusting the relative phases between two joint temporal distributions. In addition, the two-photon joint spectral distributions are characterized by measuring the joint spectral intensities and Hong–Ou–Mandel interferences. The combination of FD-QOS and TD-QOS enables complete control over the biphoton states. Our work would further develop quantum technologies that rely on the time–frequency modes of entangled photons.

Hydrodynamics characteristics of non-uniform inflow in reactor coolant pump based on time-resolved tomographic particle image velocimetry

Non-uniform inflow at the inlet of a reactor coolant pump generates performance variations, such as in the head, efficiency, cavitation, and vibrations. The three-dimensional velocity and pressure for non-uniform inflow are reconstructed via time-resolved tomographic particle image velocimetry to evaluate its effect on the reactor coolant pump. Five volume velocity fields were reconstructed through the multiplicative algebraic reconstruction technique, which constitutes the entire non-uniform flow field. The statistics of the velocity fields were used to study the non-uniform inflow characteristics. The non-uniform inflow contains two large-scale vortices in the form of counter-rotating vortex pairs. The influence of non-uniform inflow on the performance of the pump may be caused by the non-uniform pressure field. For power fluctuations during reactor operations, this non-uniform pressure distribution may generate a low-pressure region on the impeller, which induces cavitation. The non-uniform inflow shown by inhomogeneous vectors was evaluated statistically through the turbulent kinetic energy, which represents the velocity variance in each direction. For a constant head, the non-uniformity of the flow field increased with the flow rate, and the scale of small-scale turbulent vortices decreased. With proper orthogonal decomposition analysis, 90% of the energy region and flow structures were dominated by the previous 412 modes. Furthermore, the temporal modes 1, 2, 3, 100, 200, and 400 show that the frequency of large-scale eddy turnover was about 6.6–13.2 Hz. However, the large-scale eddy could be characterized within the first mode of the spatial distribution.

Functional connectivity between mesial temporal and default mode structures may help lateralize surgical temporal lobe epilepsy.

The most common surgically treatable epilepsy syndrome is mesial temporal lobe epilepsy (mTLE). Preoperative noninvasive lateralization of mTLE is challenging in part due to rapid contralateral seizure spread. Abnormal connections in both the mesial temporal lobe and resting-state networks have been described in mTLE, but it is unclear if connectivity between these networks may aid in lateralization. In 52 patients with left mTLE (LmTLE) or right mTLE (RmTLE) and 52 matched control subjects, the authors acquired 20 minutes of resting-state functional MRI (fMRI) and evaluated functional connectivity of bilateral hippocampi and amygdalae with selected resting-state networks. They used Pearson correlation, network-based statistic, and dynamic causal modeling. Also, to evaluate the clinical utility of a resting-state connectivity model in lateralizing unilateral presurgical mTLE patients, they used receiver operating characteristic curve analysis. RmTLE patients demonstrated decreased nondirected connectivity between the right hippocampus and default mode network compared with LmTLE patients and control subjects. Network-based statistic analysis revealed that the network with most decreased connectivity that distinguished LmTLE from RmTLE patients included the right hippocampus and amygdala, right lateral orbitofrontal cortices, and bilateral inferior parietal lobules, precuneus, and medial orbitofrontal cortices. Dynamic causal modeling analysis revealed that cross-hemispheric connectivity between hippocampi and amygdalae was predominantly inward toward the epileptogenic side. A regression model incorporating these connectivity patterns was used to accurately lateralize mTLE patients with an area under the receiver operating characteristic curve of 0.87. Evaluating fMRI connectivity between mesial temporal structures and default mode network may aid in mTLE lateralization, reduce need for intracranial monitoring, and guide surgical planning.

Phase Analysis of Event-Related Potentials Based on Dynamic Mode Decomposition

Real-time detection of event-related potentials (ERPs) and exploration of ERPs generation mechanisms are vital to practical application of brain–computer interfaces (BCI). Traditional methods for ERPs analysis often fall into time domain, time–frequency domain, or spatial domain. Methods which can reveal spatiotemporal interactions by simultaneously analyzing multi-channel EEG signals may provide new insights into ERP research and is highly desired. Additionally, although phase information has been investigated to describe the phase consistency of a certain frequency component across different ERP trials, it is of research significance to analyze the phase reorganization across different frequency components that constitute a single-trial ERP signal. To address these problems, dynamic mode decomposition (DMD) was applied to decompose multi-channel EEG into a series of spatial–temporal coherent DMD modes, and a new metric, called phase variance distribution (PVD) is proposed as an index of the phase reorganization of DMD modes during the ERP in a single trial. Based on the PVD, a new error-related potential (ErrP) detection method based on symmetric positive defined in Riemann manifold is proposed to demonstrate the significant PVD differences between correct and error trials. By including the phase reorganization index, the 10-fold cross-validation results of an ErrP detection task showed that the proposed method is 4.98%, 27.99% and 7.98% higher than the counterpart waveform-based ErrP detection method in the terms of weighted accuracy rate, precision and recall of the ErrP class, respectively. The resulting PVD curve shows that with the occurrence of ERP peaks, the phases of different frequency rhythms are getting to aligned and yields a significant smaller PVD. Since the DMD modes of different frequencies characterize spatiotemporal coherence of multi-channel EEG at different functional regions, the new phase reorganization index, PVD, may indicate the instantaneous phase alignment of different functional networks and sheds light on a new interpretation of ERP generation mechanism.