Time-averaged Research Articles

The Statistical Mechanics of Ideal Magnetohydrodynamic Turbulence and a Solution of the Dynamo Problem

We review and extend the theory of ideal, homogeneous, incompressible, magnetohydrodynamic (MHD) turbulence. The theory contains a solution to the ‘dynamo problem’, i.e., the problem of determining how a planetary or stellar body produces a global dipole magnetic field. We extend the theory to the case of ideal MHD turbulence with a mean magnetic field that is aligned with a rotation axis. The existing theory is also extended by developing the thermodynamics of ideal MHD turbulence based on entropy. A mathematical model is created by Fourier transforming the MHD equations and dynamical variables, resulting in a dynamical system consisting of the independent Fourier coefficients of the velocity and magnetic fields. This dynamical system has a large but finite-dimensional phase space in which the phase flow is divergenceless in the ideal case. There may be several constants of the motion, in addition to energy, which depend on the presence, or lack thereof, of a mean magnetic field or system rotation or both imposed on the magnetofluid; this leads to five different cases of MHD turbulence that must be considered. The constants of the motion (ideal invariants)—the most important being energy and magnetic helicity—are used to construct canonical probability densities and partition functions that enable ensemble predictions to be made. These predictions are compared with time averages from numerical simulations to test whether or not the system is ergodic. In the cases most pertinent to planets and stars, nonergodicity is observed at the largest length-scales and occurs when the components of the dipole field become quasi-stationary and dipole energy is directly proportional to magnetic helicity. This nonergodicity is evident in the thermodynamics, while dipole alignment with a rotation axis may be seen as the result of dynamical symmetry breaking, i.e., ‘broken ergodicity’. The relevance of ideal theoretical results to real (forced, dissipative) MHD turbulence is shown through numerical simulation. Again, an important result is a statistical solution of the ‘dynamo problem’.

Transformers in High-Frequency Trading

Transformer is a deep learning model that, having an innovative performance in many tasks, has uniquely and significantly modified all the cast of mind of the AI scientific community. In this paper, we introduce a Transformer model that is applied to 1-minute timescale in the EURUSD and GBPUSD instruments of forex trading. We use the classical Transformer architecture without the Decoder since the Encoder is enough. Moreover, the Exponential Moving Average (EMA) model is applied to the input, while different values of its smoothing factor α are tested. With cross-entropy training loss less than 0.2, it is exclamatory that Transformers are a promising tool for lucrative strategies in high-frequency trading.

The electronic and electromagnetic Dirac equations

Maxwell’s equations and the Dirac equation are the first-order differential relativistic wave equation for electromagnetic waves and electronic waves respectively. Hence, there is a notable similarity between these two wave equations, which has been widely researched since the Dirac equation was proposed. In this paper, we show that the Maxwell equations can be written in an exact form of the Dirac equation by representing the four Dirac operators with 8×8 matrices. Unlike the ordinary 4×4 Dirac equation, both spin–1/2 and spin–1 operators can be derived from the 8×8 Dirac equation, manifesting that the 8×8 Dirac equation is able to describe both electrons and photons. As a result of the restrictions that the electromagnetic wave is a transverse wave, the photon is a spin–1 particle. The four–current in the Maxwell equations and the mass in the electronic Dirac equation also force the electromagnetic field to transform differently to the electronic field. We use this 8×8 representation to find that the Zitterbewegung of the photon is actually the oscillatory part of the Poynting vector, often neglected upon time averaging.

Developing and testing a custom algorithmic trading strategy using exponential moving average, relative strength index, and sentiment analysis

<p>Stock trading is a popular and important profession that requires near-to-perfect data analytical skills, mathematical and statistical knowledge, and a broad understanding of buying and selling stocks. Often, due to the number of factors to consider and the intervention of human bias, traders and investors make wrong decisions that cost them millions of dollars. Therefore, automated algorithmic trading has gained traction in the marketplace due to its ability to process huge amounts of data, perform mathematical calculations and make quick and effective decisions. Most algorithmic trading strategies rely on a single technical indicator; however, it has been found that combining two or more indicators makes a trading strategy profitable. Therefore, this paper proposes a custom algorithmic trading strategy that combines important technical indicators such as the Exponential Moving Average and Relative Strength Index and utilizes sentiment analysis of financial news as well. This combination of technical indicators and sentiment analysis is not prevalent in existing research. The performance of the strategy was tested on fifteen stocks from different sectors of the US market using Python’s VectorBt library. The results showed that most of the stocks produced a higher win rate with the custom strategy as compared to other strategies, with the highest win rate of 88% for the S&P 500 index. To carry out sentiment analysis, a NLP model using BERT was developed which achieved an accuracy of 84%. Finally, to test the strategy on real-time data, paper trading was carried out on the Alpaca API and after six months the portfolio’s ROI is 6.26%.</p>

Approximation with ergodic processes and testability

AbstractWe show that stationary time series can be uniformly approximated over all finite time intervals by mixing, non-ergodic, non-mean-ergodic, and periodic processes, and by codings of aperiodic processes. A corollary is that the ergodic hypothesis—that time averages will converge to their statistical counterparts—and several adjacent hypotheses are not testable in the non-parametric case. Further Baire category implications are also explored.

Trend-Enhanced Improved Bollinger Bands Trend-Following High-Frequency Trading Strategy for Futures Market

The application of digital scientific technologies in the global financial markets has become widespread, which has led to the prevalence of the concept of quantitative trading. Among various quantitative trading strategies, high-frequency trading has gained significant popularity. In this study, we propose an improved Bollinger Bands trend-following high-frequency trading strategy based on trend enhancement. Instead of using the simple moving average (SMA), we replace it with the exponential moving average (EMA). Furthermore, we introduce a 3-times average true range (ATR) limit price rebound exit system to achieve timely profit-taking and stop-loss. By incorporating trend measurement indicators such as the average directional index (ADX), moving average convergence divergence (MACD), and commodity channel index (CCI), we determine the futures trend. Subsequently, this study formulates suitable parameters for the high-frequency trading strategy and conduct backtesting on the 2022 CSI 300 stock index futures, resulting in a remarkably high annualized return. These results present a novel approach to high-frequency trading strategy and provide valuable insights for the market.

Statistical Relations among Solid Precipitation, Atmospheric Moisture and Cloud Parameters in the Arctic

Observations collected during cold-season precipitation periods at Utquagvik, Alaska and at the multidisciplinary drifting observatory for the study of Arctic climate (MOSAiC) are used to statistically analyze the relations among the atmospheric water cycle parameters including the columnar supercooled liquid and ice amounts (expressed as liquid-water and ice-water paths, i.e., LWP and IWP), the integrated water vapor (IWV) and the near-surface snowfall rate. Data come from radar and radiometer-based retrievals and from optical precipitation sensors. While the correlation between snowfall rate and LWP is rather weak, correlation coefficients between radar-derived snowfall rate and IWP are high (~0.8), which is explained, in part, by the generally low LWP/IWP ratios during significant precipitation. Correlation coefficients between snowfall rate and IWV are moderate (~0.45). Correlations are generally weaker if snowfall is estimated by optical sensors, which is, in part, due to blowing snow. Correlation coefficients between near-surface temperature and snowfall rates are low (r < 0.3). The results from the Alaska and MOSAiC sites are generally similar. These results are not very sensitive to the amount of time averaging (e.g., 15 min averaging versus daily averages). Observationally based relations among the water cycle parameters are informative about atmospheric moisture conversion processes and can be used for model evaluations.

Statistical analysis of coupled oscillations with a single fixed endpoint and its application to carbon nanomaterials

Squared deviations from the equilibrium positions of one-dimensional coupled harmonic oscillators with fixed and free endpoints are calculated, and the time averages are expressed as a function of the initial displacements and velocities. Furthermore, we consider the averages of squared deviations over an ensemble of initial displacements and velocities, which distribute based on a product of the same distribution functions with variances of the initial coordinates σx2 and velocities σv2 , respectively. We demonstrate that the mean squared deviation linearly increases as the oscillator separates further from the fixed endpoint because of the asymmetrical boundary conditions, and that the increase rate depends only on σv2 and not on σx2 . This simple statistical property of harmonic oscillation is similarly observed in the oscillations of a graphene sheet and carbon nanotube in molecular dynamics simulations, in which the interacting forces are nonlinear.

Kolmogorov’s dissipation number and determining wavenumber for dyadic models

We study some dyadic models for incompressible magnetohydrodynamics and Navier–Stokes equation. The existence of fixed point and stability of the fixed point are established. The scaling law of Kolmogorov’s dissipation wavenumber arises from heuristic analysis. In addition, a time-dependent determining wavenumber is shown to exist; moreover, the time average of the determining wavenumber is proved to be bounded above by Kolmogorov’s dissipation wavenumber. Additionally, based on the knowledge of the fixed point and stability of the fixed point, numerical simulations are performed to illustrate the energy spectrum in the inertial range below Kolmogorov’s dissipation wavenumber.

Technical note: Isotopic fractionation of evaporating waters: effect of sub-daily atmospheric variations and eventual depletion of heavy isotopes

Abstract. Isotopic fractionation of evaporating waters has been studied constantly in recent decades, particularly because it enables calculation of both the volume of water evaporated from a water body and the isotopic composition of its source water. We studied the stable water isotopic composition of an artificial pan filled with water and subject to total evaporation in a sub-humid environment, in order to put into practice an operational method for estimating the time since disconnection of riverine pools when these are sampled for the quality of aquatic life. Results indicate that (i) when about 70 % of pan water had evaporated and its isotopic composition had become enriched in heavy isotopes, some subsequent periods of depletion instead of enrichment happened; and (ii) the customary application of isotopic fractionation equations to determine the isotopic composition of the water in the pan using weekly averaged atmospheric conditions (temperature and relative humidity) strongly underestimated the changes observed but predicted an early depletion of heavy isotopes. The first result, rarely reported in the literature, was found to be fully consistent with the early studies of the isotopic composition of evaporating waters. The second one could be attributed to the fact that weekly averages of temperature and relative humidity strongly overestimated air relative humidity during daylight periods of active evaporation. However, when the fractionation equations were parameterized using temperature and relative humidity weighted by potential evapotranspiration at sub-hourly time steps, they adequately reproduced the observed isotopic composition of the water in the pan, including the late periods of heavy isotope depletion. We demonstrate how weekly increases in air relative humidity when the pan water was already enriched in heavy isotopes led to their depletion. We also analyse the errors that can be incurred if time averages are used instead of flux-weighted meteorological data for model parameterization and if unidentified periods of heavy isotope depletion occur. Our results should be taken into account when applying fractionation equations, particularly in conditions or areas with high air relative humidity.

On the prevalence of the periodicity of maximizing measures

For a continuous map T:X→X on a compact metric space (X,d), we say that a function f:X→R has the property PT if its time averages along forward orbits of T are maximized at a periodic orbit. In this paper, we prove that for the one-sided full shift on two symbols, the property PT is prevalent (in the sense of Hunt–Sauer–Yorke) in spaces of Lipschitz functions with respect to metrics with mildly fast decaying rate on the diameters of cylinder sets. This result is a strengthening of [3, Theorem A], confirms the prediction mentioned in the ICM proceeding contribution of J. Bochi ([1, Section 1]) suggested by experimental evidence, and is another step towards the Hunt–Ott conjectures in the area of ergodic optimization.

The ergodicity question when imaging DNA conformation using liquid cell electron microscopy.

Assessing the ergodicity of graphene liquid cell electron microscope measurements, we report that loop states of circular DNA interconvert reversibly and that loop numbers follow the Boltzmann distribution expected for this molecule in bulk solution, provided that the electron dose is low (80-keV electron energy and electron dose rate 1-20 e- Å-2 s-1). This imaging technique appears to act as a "slow motion" camera that reveals equilibrated distributions by imaging the time average of a few molecules without the need to image a spatial ensemble.

Adaptive Normalization and Feature Extraction for Electrodermal Activity Analysis

Electrodermal Activity (EDA) has shown great potential for emotion recognition and the early detection of physiological anomalies associated with stress. However, its non-stationary nature limits the capability of current analytical and detection techniques, which are highly dependent on signal stability and controlled environmental conditions. This paper proposes a framework for EDA normalization based on the exponential moving average (EMA) with outlier removal applicable to non-stationary heteroscedastic signals and a novel set of features for analysis. The normalized time series preserves the morphological and statistical properties after transformation. Meanwhile, the proposed features expand on typical time-domain EDA features and profit from the resulting normalized signal properties. Parameter selection and validation were performed using two different EDA databases on stress assessment, accomplishing trend preservation using windows between 5 and 20 s. The proposed normalization and feature extraction framework for EDA analysis showed promising results for the identification of noisy, relaxed and arousal-like patterns in data with conventional clustering approaches like K-means over the aforementioned normalized features.

Self-training guided disentangled adaptation for cross-domain remote sensing image semantic segmentation

Remote sensing (RS) image semantic segmentation using deep convolutional neural networks (DCNNs) has shown great success in various applications. However, the high dependence on annotated data makes it challenging for DCNNs to adapt to different RS scenes. To address this challenge, we propose a cross-domain RS image semantic segmentation task that considers ground sampling distance, remote sensing sensor variation, and different geographical landscapes as the main factors causing domain shifts between source and target images. To mitigate the negative impact of domain shift, we propose a self-training guided disentangled adaptation network (ST-DASegNet) that consists of source and target student backbones to extract source-style and target-style features. To align cross-domain single-style features, we adopt feature-level adversarial learning. We also propose a domain disentangled module (DDM) to extract universal and distinct features from single-domain cross-style features. Finally, we fuse these features and generate predictions using source and target student decoders. Moreover, we employ an exponential moving average (EMA) based cross-domain separated self-training mechanism to ease the instability and disadvantageous effect during adversarial optimization. Our experiments on several prominent RS datasets (Potsdam, Vaihingen, and LoveDA) demonstrate that ST-DASegNet outperforms previous methods and achieves new state-of-the-art results. Visualization and analysis also confirm the interpretability of ST-DASegNet. The code is publicly available at https://github.com/cv516Buaa/ST-DASegNet.

Unsupervised anomaly detection for earthquake detection on Korea high-speed trains using autoencoder-based deep learning models

We propose a method for detecting earthquakes for high-speed trains based on unsupervised anomaly-detection techniques. In particular, we utilized autoencoder-based deep learning models for unsupervised learning using only normal training vibration data. Datasets were generated from South Korean high-speed train data, and seismic data were measured using seismometers nationwide. The proposed method is compared with the conventional Short Time Average over Long Time Average (STA/LTA) model, considering earthquake detection capabilities, focusing on a Peak Ground Acceleration (PGA) threshold of 0.07, a criterion for track derailment. The results show that the proposed model exhibit improved earthquake detection capabilities than STA/LTA for PGA of 0.07 or higher. Furthermore, the proposed model reduced false earthquake detections under normal operating conditions and accurately identified normal states. In contrast, the STA/LTA method demonstrated a high rate of false earthquake detection under normal operating conditions, underscoring its propensity for inaccurate detection in many instances. The proposed approach shows promising performance even in situations with limited seismic data and offers a viable solution for earthquake detection in regions with relatively few seismic events.

Dynamic light scattering and laser speckle contrast imaging of the brain: theory of the spatial and temporal statistics of speckle pattern evolution.

Dynamic light scattering (DLS) and laser speckle contrast imaging (LSCI) are closely related techniques that exploit the statistics of speckle patterns, which can be utilized to measure cerebral blood flow (CBF). Conventionally, the temporal speckle intensity auto-correlation function is calculated in DLS, while the spatial speckle contrast Ks is calculated in LSCI measurements. Due to the rapid development of CMOS detection technology with increased camera frame rates while still maintaining a large number of pixels, the ensemble or spatial average of as well as the temporal contrast Kt can be easily calculated and utilized to quantify CBF. Although many models have been established, a proper summary is still lacking to fully characterize DLS and LSCI measurements for spatial and temporal statistics, laser coherence properties, various motion types, etc. As a result, there are many instances where theoretical models are misused. For instance, mathematical formulas derived in the diffusive regime or for ergodic systems are sometimes applied to small animal brain measurements, e.g., mice brains, where the assumptions are not valid. Therefore, we aim to provide a review of the speckle theory for both DLS and LSCI measurements with detailed derivations from first principles, taking into account non-ergodicity, spatial and temporal statistics of speckles, scatterer motion types, and laser coherence properties. From these calculations, we elaborate on the differences between spatial and temporal averaging for DLS and LSCI measurements that are typically ignored but can result in inaccurate measurements of blood flow, particularly the spatially varying nature of the static component in and Kt. We also obtained maps in in vivo mouse brain measurements using high frame rate CMOS cameras which have not been demonstrated before, and compared with and Ks,t. This work provides a useful guide for choosing the correct model to analyze spatial and temporal speckle statistics in in-vivo DLS and LSCI measurements.

Semi-supervised image segmentation using a residual-driven mean teacher and an exponential Dice loss

Semi-supervised segmentation plays an important role in computer vision and medical image analysis and can alleviate the burden of acquiring abundant expert-annotated images. In this paper, we developed a residual-driven semi-supervised segmentation method (termed RDMT) based on the classical mean teacher (MT) framework by introducing a novel model-level residual perturbation and an exponential Dice (eDice) loss. The introduced perturbation was integrated into the exponential moving average (EMA) scheme to enhance the performance of the MT, while the eDice loss was used to improve the detection sensitivity of a given network to object boundaries. We validated the developed method by applying it to segment 3D Left Atrium (LA) and 2D optic cup (OC) from the public LASC and REFUGE datasets based on the V-Net and U-Net, respectively. Extensive experiments demonstrated that the developed method achieved the average Dice score of 0.8776 and 0.7751, when trained on 10% and 20% labeled images, respectively for the LA and OC regions depicted on the LASC and REFUGE datasets. It significantly outperformed the MT and can compete with several existing semi-supervised segmentation methods (i.e., HCMT, UAMT, DTC and SASS).

Reproducing the temporal averaging process of the acoustic Doppler velocimeter and assessing its impact on turbulence measurements

The temporal averaging process (TAP) in Acoustic Doppler Velocimeters (ADVs) and its impact on turbulence measurement have been extensively studied. However, few studies have successfully replicated TAP. This paper utilizes a self-developed ultrasonic velocimeter recording raw acoustic signals, achieving TAP through pulse signal concatenation. Results from open-channel flow velocity measurements demonstrate measurement accuracy. Exploring TAP's effects on turbulence measurement, three velocity sequences with varying data qualities are analyzed. Proportion of valid data increases after TAP, with similar growth rates across different sampling volumes. Turbulence intensity decreases linearly with TAP, correlating with data quality. Employing an enhanced denoising method, a comparison suggests potential gradual reduction in Doppler noise with TAP implementation. This study offers valuable insights into turbulence measurement in ADV.

Anchor Association Learning for Unsupervised Video Person Re-Identification.

Video-based person re-identification (re-id) has attracted a significant attention in recent years due to the increasing demand of video surveillance. However, existing methods are usually based on the supervised learning, which requires vast labeled identities across cameras and is not suitable for real scenes. Although some unsupervised approaches have been proposed for video re-id, their performance is far from satisfactory. In this article, we propose an unsupervised anchor association learning (UAAL) framework to address the video-based person re-id task, in which the feature representation of each sampled tracklet is regarded as an anchor. Specifically, we first propose an intracamera anchor association learning (IAAL) term that learns the discriminative anchor by utilizing the affiliation relations between an image and the anchors in each camera. Then, the exponential moving average (EMA) strategy is employed to update the anchor and the updated anchors are stored into an anchor memory module. On top of that, a cross-camera anchor association learning (CAAL) term is introduced to mine potential positive anchor pairs across cameras by presenting a cyclic ranking anchor alignment and threshold filtering method. Extensive experiments conducted on two public datasets show the superiority of the proposed method; for example, our method achieves 73.2% for rank-1 accuracy and 60.1% for mean average precision (mAP) score, respectively, on MARS, similarly 89.7% and 87.0% on DukeMTMC-VideoReID.

Boosting Pseudo-Labeling With Curriculum Self-Reflection for Attributed Graph Clustering.

Attributed graph clustering is an unsupervised learning task that aims to partition various nodes of a graph into distinct groups. Existing approaches focus on devising diverse pretext tasks to obtain suitable supervised information for representation learning, among which the predictive methods show great potential. However, these methods 1) generate auxiliary task bias toward the clustering target and 2) introduce label noise due to static thresholds. To address this issue, we propose a new self-supervised learning method, namely, pseudo-labeling with curriculum self-reflection (PLCSR), that learns reliable pseudo-labels by mining its information to achieve progressive processing of nodes in a self-reflection manner. First, a self-auxiliary encoder is constructed using the exponential moving average (EMA) of the original encoder's parameters to replace the auxiliary tasks, which provides an additional perspective of finding highly confident pseudo-labels. Second, a curriculum selection strategy using dynamic thresholds is designed to take full advantage of graph nodes more accurately. Besides simple nodes with high confidence at the initial stage, nodes that yield consistent predictions from both encoders are then assigned pseudo-labels to avoid the under-learning problem. For the rest difficult nodes that are highly uncertain, we abstain from making judgments to minimize their adverse impact on the model. Extensive experiments have shown that PLCSR significantly outperforms the state-of-the-art predictive method CDRS, achieving more than 6% improvements in terms of clustering accuracy. The code is available at: https://github.com/Jillian555/PLCSR.