Spatiotemporal Synchronization Research Articles

Continuous and explosive synchronization transition in turbulent combustors

Thermoacoustic instabilities in turbulent combustors have disastrous consequences and present notorious challenges in their modeling, prediction, and control. Such instabilities are characterized by self-excited periodic oscillations, arising from a positive feedback between the acoustic pressure and heat release rate fluctuations. We present a mean-field approach to model thermoacoustic transitions. The nonlinear flame response is modeled using an ensemble of phase oscillators constrained to collectively evolve at the rhythm of acoustic fluctuations. Starting from the acoustic wave equation coupled with the phase oscillators, we derive the evolution equations for the amplitude and phase for acoustic oscillations. The model captures abrupt and continuous transitions to thermoacoustic instability observed in disparate combustors. We also discover that continuous and abrupt transitions happen through paradigmatic continuous and explosive synchronization, respectively. Importantly, our approach explains spatiotemporal synchronization and pattern formation underlying the transition to thermoacoustic instability. The versatility of the model in capturing different types of transitions suggests promising prospects for its extension to encompass a wide range of fluid dynamics phenomena.

High-precision spatiotemporal three-dimensional ultrashort pulse synchronization with optical Kerr effect

In studying the interaction of multiple ultrashort pulses with matter, high requirements are put forward for spatiotemporal synchronization accuracy. Limited by the response time and bandwidth of existing devices, the synchronization of multiple ultrashort pulses still faces significant difficulties. By observing the transient phenomena of the optical Kerr effect, high-precision, three-dimensional (x, y, t) synchronization of ultrashort pulses at different angles was achieved. In the optical Kerr effect, the polarization state of the signal pulse changes only when it coincides with the pump pulse, at which point the signal pulse passes through the analyzer. The changes in the intensity and phase of the signal pulse is positively correlated with the degree of spatiotemporal coincidence. In this study, 10-ps pulses were used in the experiments. By observing the intensity and phase distribution of the signal pulses, a time synchronization accuracy between two pulses of less than 1 ps and spatial synchronization accuracy of ±125 µm and ±3 µm in the x and y directions, respectively, were achieved. Moreover, the synchronization of two pulses at an angle of 90 ° was measured, further proving that the method can achieve the spatiotemporal synchronization of pulses with large angles. Therefore, this method has important application prospects in the study of multi-beam interactions with matter and other ultrafast physical phenomena.

A Qualitative Study of Water Quality Using Landsat 8 and Station Water Quality-Monitoring Data to Support SDG 6.3.2 Evaluations: A Case Study of Deqing, China

Facing the challenge of the degradation of global water quality, it is urgent to realize the Sustainable Development Goal 6.3.2 (SDG 6.3.2), which focuses on improving global water quality. Currently, remote sensing technology is widely used for water quality monitoring. Existing water quality-monitoring studies have been conducted based on quantitative water quality inversion. It requires a high degree of the synchronization of the time and location of the collection of station monitoring data and remote sensing data (air–ground spatiotemporal synchronization), which can be resource intensive and time consuming. However, policymakers and the public are more interested in the quality of water (good or poor) than in the specific values of the water quality parameters, as evidenced by the emergence of SDG 6.3.2. In this study, we change the traditional idea of quantitative water quality research, focus on water quality qualitative research combined with the characteristics of water pollution, propose a remote sensing water quality sample enhancement method under the condition of “air–ground spatiotemporal asynchrony”, and construct a remote sensing water quality sample library. On the basis of this sample library, a random forest water quality classification model was constructed to classify water quality qualitatively. We obtained the distribution of good water bodies in Deqing County, China, for example, from 2013 to 2022. The results show that the model has high accuracy (Kappa = 0.6004, OA = 0.8387), and we found that the water quality in Deqing County improved in the order of “major rivers, lakes, and tributaries” during the period from 2013 to 2015. This also verifies the feasibility of using this sample enhancement method to conduct qualitative research on water quality. Based on this water quality classification model, a set of spatial-type evaluation processes of SDG 6.3.2 based on image elements was designed. The evaluation results show that the water quality situation in Deqing County can be divided into two stages: there is a trend of substantial improvement from 2013 (evaluated value of SDG 6.3.2 = 63.25) to 2015 (evaluated value of SDG 6.3.2 = 83.16); and it has remained stable and fluctuating after reaching the good environmental water quality since 2015. This study proposes a simple method for rapidly evaluating SDG 6.3.2 via utilizing easily accessible Landsat 8 and water quality-monitoring data to classify water quality. The method can directly obtain water quality category information without the need for additional sampling, thus saving costs. It is a very simple process that is easy to implement, while also providing a high level of accuracy. This significantly reduces the barriers to evaluating SDG 6.3.2, supports the realization of the sustainable management of water resources globally, and is highly generalizable.

Unmanned Airborne Bistatic Interferometric Synthetic Aperture Radar Data Processing Method Using Bi-Directional Synchronization Chain Signals

The bistatic Interferometric Synthetic Aperture Radar (InSAR) system can overcome the physical limitations imposed by the baseline of monostatic dual-antenna InSAR. It provides greater flexibility and can enhance elevation measurement accuracy through a well-designed baseline configuration. Unmanned aerial vehicles (UAVs) equipped with bistatic InSAR, having relatively low cost and high flexibility, are useful for mapping and land resource exploration. However, due to challenges including spatiotemporal synchronization and motion errors, there are limited reports on UAV-borne bistatic InSAR. This paper proposes a comprehensive method for processing data from small UAV-borne bistatic InSAR by integrating two-way synchronization chain signals. The proposed method includes compensation for time and phase synchronization errors, trajectory refinement with synchronized chain and Position and Orientation System (POS) data, high-precision bistatic InSAR imaging, and interferometric processing. Height inversion results based on the proposed method are also provided, which demonstrate the effectiveness of the proposed method in improving the accuracy of interferometric measurement at calibration points from 0.66 m to 0.42 m.

Characteristics of tin droplet target system for EUV source research

Droplet-based laser-produced plasma source shows enormous significance in extreme ultraviolet lithography, which places high demands on the stability of tin droplets. This paper presents a tin droplet target system including the tin droplet generator (DG), droplet diagnosis, and spatiotemporal synchronization of tin droplets and laser. Shadowgraph technology is used to determine the stability of tin droplets. The characteristics of the DG were analyzed, and the operation parameter maps are provided. By varying operating frequencies from 18.4 kHz to 49.3 kHz, the diameter and spacing of droplets can be adjusted in the ranges of 120–200 μm and 200–1100 μm respectively. Both theoretical calculations and experimental results show that tin droplets keep high stability when the operation parameters locate at the optimal range. The long-term lateral stability is also proven under a high degree of vacuum. Additionally, the application feasibility of the DG system is verified by the experiments of laser impact tin droplets.

Pinning Spatiotemporal Sampled-Data Synchronization of Coupled Reaction-Diffusion Neural Networks Under Deception Attacks.

In this article, we investigate the pinning spatiotemporal sampled-data (SD) synchronization of coupled reaction-diffusion neural networks (CRDNNs), which are directed networks with SD in time and space communications under random deception attacks. In order to handle with the random deception attacks, we establish a directed CRDNN model, which respects the impacts of variable sampling and random deception attacks within a unified framework. Through the designed pinning spatiotemporal SD controller, sufficient conditions are obtained by linear matrix inequalities (LMIs) that guarantee the mean square exponential stability of the synchronization error system (SES) derived by utilizing inequality techniques, the stochastic analysis technique, and Lyapunov-Krasovskii functional (LKF). Finally, a numerical example is utilized to support the presented pinning spatiotemporal SD synchronization method.

Complex pattern dynamics and synchronization in a coupled spatiotemporal plankton system with zooplankton vertical migration

In aquatic environments, zooplankton often exhibits life habit of vertical migration and the phytoplankton-zooplankton predator-prey systems in different water layers are therefore coupled together. To uncover the nonlinear mechanisms of pattern dynamics in such coupled plankton system, a spatiotemporal model is developed in this research with the consideration of plankton horizontal diffusion and zooplankton vertical migration. Equation of dispersion curve for the coupled system is derived, and an extension of regular Turing instability is disclosed by determining the number of peaks on the dispersion curve. We find a mechanism named as “projection of characteristics” that local or global characteristics projecting between different subsystems causes the self-organization of complex patterns with multi-scale structures. The combination of various bifurcations with Turing instability controls the system stability and can lead to more complex pattern formation. Notably, when flip bifurcation takes place, the coupled system generates an interesting result that the phytoplankton populations in some water layers become extinct but the zooplankton populations in these layers can still be persistent due to the effect of population compensation. It is also found that the increase of zooplankton migration rate can result to spatiotemporal synchronization of pattern evolution, and that particularly, the pattern dynamics in just a part of subsystems achieve local synchronization. The methods and results presented herein may lead to a better understanding on the emergence of complex plankton patchiness in nature.

The role of atmospheric rivers in the distribution of heavy precipitation events over North America

Abstract. Atmospheric rivers (ARs) are filaments of extensive water vapor transport in the lower troposphere that play a crucial role in the distribution of freshwater but can also cause natural and economic damage by facilitating heavy precipitation. Here, we investigate the large-scale spatiotemporal synchronization patterns of heavy precipitation events (HPEs) over the western coast and the continental regions of North America (NA), during the period from 1979 to 2018. In particular, we use event synchronization and a complex network approach incorporating varying delays to examine the temporal evolution of spatial patterns of HPEs in the aftermath of land-falling ARs. For that, we employ the SIO-R1 catalog of ARs that landfall on the western coast of NA, ranked in terms of intensity and persistence on an AR-strength scale which varies from level AR1 to AR5, along with daily precipitation estimates from ERA5 with a 0.25∘ spatial resolution. Our analysis reveals a cascade of synchronized HPEs, triggered by ARs of level AR3 or higher. On the first 3 d after an AR makes landfall, HPEs mostly occur and synchronize along the western coast of NA. In the subsequent days, moisture can be transported to central and eastern Canada and cause synchronized but delayed HPEs there. Furthermore, we confirm the robustness of our findings with an additional AR catalog based on a different AR detection method. Finally, analyzing the anomalies of integrated water vapor transport, geopotential height, upper-level meridional wind, and precipitation, we find atmospheric circulation patterns that are consistent with the spatiotemporal evolution of the synchronized HPEs. Revealing the role of ARs in the precipitation patterns over NA will lead to a better understanding of inland HPEs and the effects that changing climate dynamics will have on precipitation occurrence and consequent impacts in the context of a warming atmosphere.

Fluorescence-amplified nanocrystals in the second near-infrared window for in vivo real-time dynamic multiplexed imaging.

Optical imaging in the second near-infrared window (NIR-II, 1,000-1,700 nm) holds great promise for non-invasive in vivo detection. However, real-time dynamic multiplexed imaging remains challenging due to the lack of available fluorescence probes and multiplexing techniques in the ideal NIR-IIb (1,500-1,700 nm) 'deep-tissue-transparent' sub-window. Here we report on thulium-based cubic-phase downshifting nanoparticles (α-TmNPs) with 1,632 nm fluorescence amplification. This strategy was also validated for the fluorescence enhancement of nanoparticles doped with NIR-II Er3+ (α-ErNPs) or Ho3+ (α-HoNPs). In parallel, we developed a simultaneous dual-channel imaging system with high spatiotemporal synchronization and accuracy. The NIR-IIb α-TmNPs and α-ErNPs facilitated the non-invasive real-time dynamic multiplexed imaging of cerebrovascular vasomotion activity and the single-cell-level neutrophil behaviour in mouse subcutaneous tissue and ischaemic stroke model.

Mean-field model of synchronization for open-loop, swirl controlled thermoacoustic system.

Open-loop control is known to be an effective strategy for controlling self-excited periodic oscillations, known as thermoacoustic instability, in turbulent combustors. Here, we present experimental observations and a synchronization model for the suppression of thermoacoustic instability achieved by rotating the otherwise static swirler in a lab-scale turbulent combustor. Starting with the state of thermoacoustic instability in the combustor, we find that a progressive increase in the swirler rotation rate leads to a transition from the state of limit cycle oscillations to the low-amplitude aperiodic oscillations through a state of intermittency. To model such a transition while also quantifying the underlying synchronization characteristics, we extend the model of Dutta et al. [Phys. Rev. E 99, 032215 (2019)] by introducing a feedback between the ensemble of phase oscillators and the acoustic. The coupling strength in the model is determined by considering the effect of the acoustic and swirl frequencies. The link between the model and experimental results is quantitatively established by implementing an optimization algorithm for model parameter estimation. We show that the model is capable of replicating the bifurcation characteristics, nonlinear features of time series, probability density function, and amplitude spectrum of acoustic pressure and heat release rate fluctuations at various dynamical states observed during the transition to the state of suppression. Most importantly, we discuss the flame dynamics and demonstrate that the model without any spatial inputs qualitatively captures the characteristics of the spatiotemporal synchronization between the local heat release rate fluctuations and the acoustic pressure that underpins a transition to the state of suppression. As a result, the model emerges as a powerful tool for explaining and controlling instabilities in thermoacoustic and other extended fluid dynamical systems, where spatiotemporal interactions lead to rich dynamical phenomena.

Spatio-Temporal Connectivity of the Long-Term Dynamics of the Forest Phyllophagus Insects’ Abundance

The study was conducted regarding the conjugation of the population dynamics of different forest insects species under different landscape conditions on the territory of the Krasnoturansky pine forest (South of the Krasnoyarsk Territory). The population dynamics conjugation indicates the presence of an ecological mechanism that leads to the coordination of the temporal series of different species’ population dynamics in one habitat or one species in different habitats. This means that using the conjugation indicators of insect dynamics one can indirectly assess the influence of various factors affecting these populations. To assess the spatio-temporal synchronization of the population dynamics of insects in different landscape conditions, the data of the phyllophagous insects counts for the period from 1979 to 2016 were used. According to the phases of dynamics, although the periods of cyclic fluctuations of phyllophages’ populations in different stows are close, the characteristics of the phyllophagous insects number dynamics still differ in both the absolute values and the phases of dynamics, even when the distance between the test sites is relatively small. The “memory” of the system, expressed in the order of the autoregressive model of the population dynamics, is fairly large for the studied complexes of phyllophagous species: the current value of the phyllophagous populations density can be influenced by the population density values from as far as four years before the counts. Such values of “memory” lead to an increase in the populations’ stability margin, and a decrease in the risks of developing insect outbreaks. The determination coefficients close to 1 for the phyllophages dynamics models in the stows of the Krasnoturansky pine forest indicate a weak influence of modifying factors (such as weather) on the population dynamics.

Spatiotemporal synchronous coupling algorithm for urban rail transit timetables design under dynamic passenger demand

This paper focuses on the problem of designing the schedule of urban rail transit systems under dynamic passenger demand considering limited train capacity and congestion. From the point of view of operators, the goal of timetable optimization consists of using as few as possible service trains to transport the arriving passengers to their destinations securely and quickly. On the other hand, passengers want to spend the minimum time travelling to their destinations, including the time they wait on platforms until they board the first and successive trains in case of transferring between lines. Due to the variability of passenger flows and the difficulty in exactly solving full-day timetabling problems in short computation times, it is difficult in practice to use the approaches proposed in the literature. Moreover, when the capacity of trains is considered and oversaturation conditions emerge, the problem becomes even more complex, converting into a challenge the design of schedules from an operational point of view. By considering fixed train dwell times at stations and train running times between stations, we first propose a non-linear programming formulation to model the problem of determining the most convenient interdeparture times of services at the first station of a line, aiming at minimizing the waiting time of passengers. Since the dynamic behaviour of passenger demand and the maximum sectional passenger flow are approximately synchronous, an innovative method, the spatiotemporal synchronization coupling algorithm, based on working with the time-varying maximum sectional passenger flow instead of the demand patterns is proposed to quickly solve in an approximate way the demand-driven timetabling problem. The proposed approach is applied to a real case of Chengdu Metro Line 1 in China. The results show the effectiveness of the algorithm, both in terms of computational effort and in terms of reducing the waiting time currently experienced by passengers.

Multi-layer visualization for media planning

The paper deals with data visualization for media planning. Media planning database is a collection of heterogeneous content (image/video/graphics, text, data analytics, logical expressions, …) to be aggregated, managed, and displayed together. The main contribution is the multi-layer visualization architecture that allows any type of visualization element to be created in its most appropriate libraries. Such visualization ensures spatio-temporal synchronization of displayed content, as well as the proper evolution with the user interaction. The illustrations are provided on two real (yet anonymized) media plans and show how a complex, 7 steps interaction workflow with the media plan can be dealt with.

A Fusion Deep Learning Model via Sequence-to-Sequence Structure for Multiple-Road-Segment Spot Speed Prediction

Forecasting the future average speed fluctuation is conducive to timely perceiving the degree of urban road congestion. Nevertheless, a new challenge has arisen in accurately predicting the spot speed on an urban road network area composed by multiple road segments. To surmount this, an intelligent method for spot speed estimation, namely, the fusion deep learning model with sequence-to-sequence structure (Seq2Seq-FDL), is proposed. It is a sequence-to-sequence learning structure that covers the encoding context vector. The unidirectional convolutional long short-term memory (ConvLSTM) and bidirectional ConvLSTM networks are used to capture traffic short-term and periodic spatiotemporal synchronization characteristics, respectively. Finally, the prediction results are computed by linear feature fusion. Furthermore, the black-box effect of the proposed model is explained by the least absolute shrinkage and selection operator regression model based on Granger causality, and the rationality of the model is verified with an example of spot speed in a road network of Guangzhou. The experimental results were shown to indicate that the traffic spatiotemporal characteristics significantly contributed to the prediction effect of the Seq2Seq-FDL model. The prediction accuracy was superior to a convolutional neural network-connected LSTM network and a ConvLSTM network with or without a bidirectional LSTM; the proposed model presented good applicability in the multiple-time-step prediction of spot speed for multiple road segments.

SPsync: Lightweight multi-terminal big spatiotemporal data synchronization solution

With the rapid increase in mobile device usage and the popularity of 5G communication technology, rich Big spatiotemporal Data has become an important research resource. How to quickly synchronize the Big spatiotemporal Data collected by various types of devices to multiple distributed data centers has become the key to further utilizing spatio-temporal data. Therefore, in this paper, a new lightweight Big Spatiotemporal Data synchronization scheme called SPsync, based on a traditional file synchronization algorithm, is proposed. The contributions of SPsync are as follows. (1) SPsync leads to the optimization of the file processing strategy, changing the algorithm from a serial algorithm to a parallel one. (2) Combined with Spark, a distributed Big Data processing framework is advanced to achieve optimization of distributed tasks and further improvement of algorithm performance. Further, we demonstrate the excellent performance of SPsync through rich experiments using multiple simulated and real datasets. Compared to the best incremental synchronization algorithms currently available, the synchronization speedup is 30% faster and CPU usage 20% lower. The algorithm itself is 20% faster and CPU usage reduced by more than 25% in a multi-node scenario.

Abstract 11304: Spectrum of Clinical Response in Atrial Tachyarrhythmias Identified by Spatiotemporal Synchronization of Electrograms

Introduction: A clinical spectrum exists for atrial tachyarrhythmias, wherein tachycardia (AT) often responds to ablation, some patients with atrial fibrillation (AF) respond well to ablation, and others do not. It is undefined if this clinical spectrum can be predicted pathophysiologically. Hypothesis: We hypothesize that the size of regions within which electrograms (EGMs) show repeating shapes also synchronized in time reveals a spectrum from AT, to AF patients who respond acutely to ablation, to AF patients without acute response. Methods: We studied N=160 patients (35% women, 65.0±10.4Y) of whom (i) N=150 were AF patients propensity-matched for those whose AF terminated by ablation (N=75; “Term”) and those which did not (N=75; “Non-term”); (ii) N=10 with AT. All patients had mapping by 64 pole baskets to identify areas of repetitive electrical activity in shape and timing (REACT, range 0 to 1), by correlating unipolar electrograms (EGMs) in 2x2 grids iteratively across the atria (Fig A&B). Results: Synchronized regions (REACT) fell from AT to AF Term to AF Non-term (0.63±0.15, 0.37±0.22, 0.22±0.18, p<0.001, Fig C&D). On ROC analysis, AUC for predicting AF termination was 0.70 ([0.61, 0.78] 95% CI). Simulations revealed a nomogram in which increasing REACT represented increasing variability in clinical EGM shape and timing. Unsupervised machine learning of REACT plus 50 variables yielded 4 clusters of increasing risk for AF termination (p<0.01, chi-sq) but clinical profiles alone were less predictive (p<0.001). Conclusions: The area of synchronized EGM shape and timing within the atrium reveals a spectrum of clinical response in atrial tachyarrhythmias. These fundamental EGM properties, which do not reflect any specific mechanism or mapping technology, predict outcome and offer a platform to compare mapping tools and mechanisms between AF patient groups.

A Novel Spatio-Temporal Synchronization Method of Roadside Asynchronous MMW Radar-Camera for Sensor Fusion

Roadside sensors, such as camera and millimeter-wave (MMW) radar, provide traffic information beyond the visual range of intelligent vehicles in cooperative vehicle-infrastructure systems. Unlike onboard equipment, roadside sensors are affiliated with different systems and lack synchronization in both space and time. In this paper, we propose a novel spatio-temporal synchronization method of asynchronous roadside MMW radar–camera for sensor fusion, which utilizes features of the scenario to extract lane line corner points to pre-calibrate the camera. Based on the consistent time flow rate of the separate sensors, multiple virtual detection lines are set up to match the time headway of successive vehicles and conduct objective matching to track data. Finally, a synchronization optimization model is formulated and a constrained nonlinear minimization solver is applied to tune the parameters. Measure data from Donghai Bridge in Shanghai is applied to verify the feasibility and effectiveness of the method. The results determine that there are 33 frames (33*40 ms) of temporal deviation between the camera and the radar in this case. After the synchronization, the average spatial deviation is reduced from 2.47 m to 0.42 m in the X-direction and 64.06 m to 2.34 m in the Y-direction, respectively. This study provides an economical and effective way to solve the problem of spatio-temporal synchronization of roadside sensors.

Discrete spatiotemporal network synchronization based on adaptive control

This paper first introduces the basic concept of network synchronization and several common synchronization types. Secondly, aiming at the synchronization control problem of a class of discrete spatiotemporal networks, a standard synchronization control strategy and a synchronization controller are proposed based on Lyapunov stability theory. In order to further verify the effectiveness of the synchronization theory, the spatiotemporal network model is selected, the coupling matrix and the identification rate of unknown parameters are designed for numerical simulation. Finally, the simulation results show the feasibility of the theory.

Optical synchronization technique for all-optical Compton scattering.

In all-optical Compton scattering driven by a multi-petawatt laser, it is critical to have accurate spatiotemporal synchronization between the ultrarelativistic electron bunch and the ultrahigh-intensity laser beam. Such a synchronization was realized by using two complementary optical setups. The first setup, used for the initial synchronization, recorded the spatial interferogram between the two femtosecond lasers used for a GeV electron beam production and an ultrahigh scattering laser beam. The second one, consisting of spatial and spectral interferometers, measured the time delay between the two laser beams in the range of 0-200fs in real time. These monitoring systems played an essential role in conducting Compton scattering experiments.

Variability in the Statistical Properties of Continuous Seismic Records on a Network of Stations and Strong Earthquakes: A Case Study from the Kamchatka Peninsula, 2011–2021

A study of spatiotemporal variability and synchronization effects in continuous seismic records (seismic noise) on a network of 21 broadband seismic stations on the Kamchatka Peninsula was carried out in connection with the occurrence of strong earthquakes, M = 7.2–8.3. Data of 1-min registrations of the vertical movements velocity Earth’s surface were used for constructing time series of daily values of the generalized Hurst exponent α*, singularity spectrum support width ∆α, wavelet-based spectral exponent β, and minimum normalized entropy of squared orthogonal wavelet coefficients En for all stations during the observation period 2011–2021. Averaged maps and time-frequency diagrams of the spectral measure of four noise parameters’ coherent behavior were constructed using data from the entire network of stations and by groups of stations taking into account network configuration, volcanic activity and coastal sea waves. Based on the distribution maps of noise parameters, it was found that strong earthquakes arose near extensive areas of the minimum values of α*, ∆α, β, and the En maximum values advance manifestation during several years. The time-frequency diagrams revealed increased amplitudes of the spectral measure of the coherent behavior of the 4-dimensional time series (synchronization effects) before three earthquakes with Mw = 7.5–8.3 over months to about one year according to observations from the entire network of stations, as well as according to data obtained at groups of continental and non-volcanic stations. A less-pronounced manifestation of coherence effects diagrams plotted from data obtained at coastal and volcanic groups of stations and is apparently associated with the noisiness in seismic records caused by coastal waves and signals of modern volcanic activity. The considered synchronization effects correspond to the author’s conceptual model of seismic noise behavior in preparation of strong earthquakes and data from other regions and can also be useful for medium-term estimates of the place and time of seismic events with Mw ≥ 7.5 in the Kamchatka.