Linear Drift Research Articles

Moderate deviations for a stochastic Schrödinger equation with linear drift

Moderate deviation principle is achieved by the weak convergence approach for a stochastic Schrödinger type equation with linear drift term and noise driven by a [Formula: see text]-Wiener process. The central limit theorem is also shown for the equation to further analyze its asymptotic behavior.

Utilizing multi-point temperature sensing to evaluate the low frequency noise of phasemeter for intersatellite laser interferometer.

High-precision phasemeters are a key technology in intersatellite laser interferometers used for detecting gravitational waves (GWs) in space. As the core of the readout system, the phasemeter must operate in the bandwidth of 5-25MHz, and its resolution needs to reach the order of μrad/Hz at mHz. It presents significant challenges to electronic signal processing technology. To investigate the primary noise source in the low-frequency band, a mathematical model of thermal drift to phase noise was established, and a multi-point temperature sensing scheme for critical electronic components was proposed. In particular, we evaluated a phasemeter based on a commercial platform and assessed the thermal drift noise according to the proposed model. This study identifies and explains the effects of temperature linear drift and overcorrection in components, demonstrating that thermal drift noise is the main noise source for the phasemeter at frequencies from 0.1 to 1 mHz. In addition, the proposed scheme is universal in its applicability and may be implemented in any circuit for the evaluation of temperature effects on the components of interest.

Memristive behaviour of Al/rGO-CdS/FTO device at different temperatures: A MATLAB-integrated study

In the present work, a comprehensive study is carried out to investigate the memristive behaviour of reduced graphene oxide (rGO) conjugated cadmium sulphide quantum dot (CdS QD) nanocomposites (rGO-CdS), offering insights into their dynamic response under varying thermal conditions. The study integrates experimental analysis with MATLAB simulation to provide a detailed understanding of the complex interplay between different operating temperature (300K, 350K, 400K, and 450K) and memristive behavior in rGO-CdS nanocomposites. Different structural and chemical characterizations were carried out which confirms the formation of rGO-CdS nanocomposites. A sandwich structured device was fabricated with the synthesized rGO-CdS nanocomposites using Aluminum (Al) as top and Fluorine doped tin oxide (FTO) as bottom electrode. The influence of operating temperature on hysteresis behaviour of the fabricated Al/rGO-CdS/FTO device was investigated using Keithley 2450 source meter by sweeping a direct current (dc) voltage (−5 V → 5 V → −5 V). Notably, we observe a positive temperature coefficient in the device current, with maximum and minimum recorded current of |1.29mA| and |0.66mA| at 450K and 300K respectively. The current-voltage (I-V) behavior observed in the device reveals that in the low resistance state (LRS), conduction is dominated by bulk-limited mechanisms. However, in the high resistance state (HRS), conduction involves contributions from both Schottky barriers and the Pool-Frenkel effect. A MATLAB based linear drift model was used to simulate the device responses at different temperatures using the experimental data. The study provides first comprehensive analysis of temperature dependent hysteresis behaviour of Al/rGO-CdS/FTO device, integrating MATLAB simulation to glean valuable insights into its operation and possible applications as memristive material across different temperature regimes.

Decision cost hypersensitivity underlies Huntington's disease apathy.

The neuropsychiatric syndrome of apathy is now recognized to be a common and disabling condition in Huntington's disease (HD). However, the mechanisms underlying it are poorly understood. One way to investigate apathy is to utilise a theoretical framework of normal motivated behaviour, to determine where breakdown has occurred in people with this behavioural disruption. A fundamental computation underlying motivated, goal-directed behaviour across species is weighing up the costs and rewards associated with actions. Here, we asked whether people with apathy are more sensitive to costs of actions (physical effort and time delay), less sensitive to rewarding outcomes, or both. Based on the unique anatomical substrates associated with HD pathology, we hypothesised that a general hypersensitivity to costs would underpin HD apathy. Genetically confirmed carriers of the expanded Huntingtin gene (premanifest to mild motor manifest disease (n=53) were compared to healthy controls (n = 38). Participants performed a physical effort-based decision-making task (Apple Gathering Task) and a delay discounting task (Money Choice Questionnaire). Choice data was analysed using linear regression and drift diffusion models that also accounted for the time taken to make decisions. Apathetic people with HD accepted fewer offers overall on the Apple Gathering Task, specifically driven by increased sensitivity to physical effort costs, and not explained by motor severity, mood, cognition, or medication. Drift diffusion modelling provided further evidence of effort hypersensitivity, with apathy associated with a faster drift rate towards rejecting offers as a function of varying effort. Increased delay sensitivity was also associated with apathy, both when analysing raw choice and also drift rate, where there was moderate evidence of HD apathy drifting faster towards the immediately available (low cost) option. Furthermore, the effort and delay sensitivity parameters from these tasks were positively correlated. The results demonstrate a clear mechanism for apathy in HD, cost hypersensitivity, which manifests in both the effort and time costs associated with actions towards rewarding goals. This suggests that HD pathology may cause a domain-general disruption of cost processing, which is distinct to apathy occurrence in other brain disorders, and may require different therapeutic approaches.

Evaluation and homogenization of a marine gravity database from shipborne and satellite altimetry-derived gravity data over the coastal region of Nigeria

Abstract Accurate geoid modelling in marine areas requires the integration of gravity data from multiple sources including shipborne gravity measurements, global geopotential models, and satellite altimetry-derived gravity data. This study aims to develop homogenized gravity data for the coastal region of Nigeria to improve geoid modelling accuracy. Residual linear drifts in the shipborne gravity dataset from the Bureau Gravimétrique International (BGI) were corrected using crossover adjustments for each survey leg. We eliminated gross errors for each survey leg by using the 2-sigma method. Outliers in the historical shipborne gravity data were identified and removed using the leave-one-out cross-validation technique, resulting in a refined shipborne gravity dataset. The refined shipborne data were compared with the gravity data predicted by DTU21GRA, SSv29.1, SGG-UGM-2, XGM2019e_2159, GECO, EIGEN-6C4, and EGM2008. Our findings show that DTU21GRA outperformed the other models in the same region when compared with shipborne gravity data. The refined shipborne gravity data were merged with the DTU21GRA data using Least-Squares Collocation (LSC) to create a combined gravity dataset. The results of comparison between the complete refined shipborne gravity data and DTU21GRA before and after the integration process, shows that both the mean offset and the SD values decreased from 0.43 to −0.02 mGal and 3.14 to 2.69 mGal, respectively, which reveal an improvement in the final combined data. The geoid model constructed using the combined gravity data before and after the integration process showed an improvement in the SD values, decreasing from 0.023 m to 0.016 m when evaluated against the CNES-CLS22 MDT.

Poisson Process with Linear Drift and Related Function Series

Poisson Process with Linear Drift and Related Function Series

Comparing Weights According to Weighing Cycles with Nonlinear Drift of the Comparator

Cycle weighing is used by metrologists around the world to eliminate drift in comparator readings when comparing the mass of reference weights. Various types of cycles and their descriptions are given in the International Recommendation on legal metrology OIML R111-1-2004 adopted in the Russian Federation as a national standard. They consider cycles under the assumption of linear drift of comparator readings. The article discusses weighing cycles that eliminate nonlinear drift of the comparator. Drift models are proposed in the form of exponential and multinomial laws, which are characterized by a fast dependence of readings at the beginning of the cycle and a slower one at the end of the cycle. The derivation of formulas for the difference between the mass of the verified and the original standard according to four comparator readings at equal time intervals is given. The formulas consist of two components: the first coincides with the formula for linear drift, and the second plays the role of a correction for the drift deviation from linearity. The formulas are also correct for linear drift, since in this case the second components become zero. Estimates of the differences in the mass of the compared weights, taking into account the nonlinearity of the comparator drift, make it possible to estimate the measurement uncertainty for linear and nonlinear drift and become relevant with a constant increase in weighing accuracy, especially when comparing high-precision mass standards.

Empirical analysis of crude oil dynamics using affine vs. non-affine jump-diffusion models

This paper investigates the dynamics of the United States oil (USO) exchange traded fund (ETF). Daily USO returns are modelled using stochastic volatility (SV) frameworks derived from three different model classes: SV models with contemporaneous jumps in returns and volatility (SVCJ); SV model with jumps in returns only (SVJ); and a pure SV model class without jumps. Six affine and non-affine models are considered within each model class that depend on specification of the drift and the diffusion terms in the variance process, resulting in a total of 18 models that are estimated using particle Markov Chain Monte Carlo (PMCMC) approach. Model evaluation is conducted using the Deviance Information Criterion (DIC), Bayes factors, probability plots, and deviation measures to assess the discrepancy between the estimated volatility and key benchmarks, the crude oil ETF volatility index (OVX) and the realised volatility (RV). Our analysis indicates that models incorporating jumps, particularly the SVCJ-PLY-0.5 and SVCJ-PLY-1.0, more accurately capture USO dynamics than standard SV models. The SVCJ-PLY-0.5 model ranks highest based on DIC statistics and Bayes factors, and both models excel in aligning their estimated volatility with the OVX and RV benchmarks. Overall, the statistical criteria employed in our comparison favour models with jumps over the standard SV model class, suggesting that models incorporating jumps in both return and variance processes (SVCJ) are superior to those with jumps solely in the return process (SVJ). The affine models SVJ-LIN-0.5 and SVCJ-LIN-0.5 with linear variance drift and square root diffusion that are particularly interesting for theoretical finance applications are highly ranked among considered frameworks, outperforming several non-affine alternatives. Our analysis of the regression model for volatility forecasting reveals a significant predictive accuracy in the evaluated models, demonstrating their effectiveness in anticipating future volatility trends.

Thermal-noise-limited ultra-stable laser operated at 698 nm

Ultra-stable lasers are indispensable in high precision measurements. Here we demonstrate an ultra-stable laser system that reaches the thermal noise limit of the optical cavity for the 698 nm clock transition laser of strontium atomic optical clock. This is achieved by locking the frequency of the external-cavity diode laser (ECDL) to a full ULE optical cavity with a length of 10 cm. By suppressing noise such as temperature disturbance, vibration, residual amplitude modulation (RAM), and fiber phase noise, the measured laser linewidth is less than 0.9 Hz. After subtracting the linear drift of 60 mHz/s, the frequency instability of the beat signal reaches 1.2 × 10−15 at 1 s averaging time, which is close to the thermal noise limit of the optical cavity.

Fourier transform-based post-processing drift compensation and calibration method for scanning probe microscopy

Scanning probe microscopy (SPM) is ubiquitous in nanoscale science allowing the observation of features in real space down to the angstrom resolution. The scanning nature of SPM, wherein a sharp tip rasters the surface during which a physical setpoint is maintained via a control feedback loop, often implies that the image is subject to drift effects, leading to distortion of the resulting image. While there are in-operando methods to compensate for the drift, correcting the residual linear drift in obtained images is often neglected. In this paper, we present a reciprocal space-based technique to compensate the linear drift in atomically-resolved scanning probe microscopy images without distinction of the fast and slow scanning directions; furthermore this method does not require the set of SPM images obtained for the different scanning directions. Instead, the compensation is made possible by the a priori knowledge of the lattice parameters. The method can also be used to characterize and calibrate the SPM instrument.

Frequency drift characterization of a laser stabilized to an optical fiber delay line

Lasers stabilized to optical fiber delay lines have been shown to deliver a comparable short-term (<1 s) frequency noise performance to that achieved by lasers stabilized to ultra-low expansion (ULE) cavities, once the linear frequency drift has been removed. However, for continuous stable laser operations, the drift can be removed only when it can be predicted, e.g., when it is linear over very long timescales. To date, such long-term behaviour of the frequency drift in fiber delay lines has not been, to the best of our knowledge, characterised. In this work we experimentally characterise the frequency drift of a laser stabilised to a 500 m-long optical fiber delay line over the course of several days. We show that the drift still follows the temperature variations even when the spool temperature is maintained constant with fluctuations below tens of mK. Consequently, the drift is not linear over long timescales, preventing a simple feed-forward compensation. However, here we show that the drift can be reduced by exploiting the high level of correlation between laser frequency and the fiber temperature. In our demonstration, by applying a frequency correction proportional to temperature readings, a calculated frequency drift of less than 16 Hz/s over the several days of our test was obtained, corresponding to a 23-fold improvement from uncorrected values.

Generalized Yang Chizhong filtering and interpolation method without stationarity assumption

The stationarity assumption of geostatistical methods is difficult to satisfy in practice. To overcome this limitation, this study proposed a geometric and statistical coupling strategy for modeling spatial dependence structures and developed a generalized Yang Chizhong filtering and interpolation (GYangCZ) method without the assumption of stationarity. In this work, we theoretically prove the effectiveness of Yang Chizhong filtering in fitting spatial dependence structures from a geometric perspective, and develop an orientation-constrained Yang Chizhong filtering to fit the local and discontinuous spatial dependence structures. To measure nonstationary spatial dependence structure, we define a local statistical indicator (i.e., fundamental variation function) by comparing the variance of the original data and the fitted geometric surfaces obtained under different filtering radii. The fundamental variation function is used as the kernel function to obtain the approximate best linear unbiased estimators at unobserved locations. We theoretically demonstrate that when only a linear drift exists in local areas, GYangCZ does not require the stationarity assumption. GYangCZ was used to estimate the gold grade of the Xiadian gold deposit in China. The results show that GYangCZ outperformed ordinary kriging, moving window kriging, and kriging convolution networks. GYangCZ is easy to implement with wide applications in geoscience.

A Novel Position-Sensitive Linear Winding Silicon Drift Detector.

A novel position-sensitive linear winding silicon drift detector (LWSDD) was designed and simulated. On the frontside (anode side), the collecting anodes were set on both sides of the detector, and an S-shaped linear winding cathode strip was arranged in the middle, which can realize independent voltage division and reduce the complexity of external bias resistor chain compared with the traditional linear silicon drift detector. The detectors were arranged in a butterfly shape, which increased the effective area of the detectors and improved the collection efficiency. The linear winding silicon drift detector can obtain one-dimensional position information by measuring the drift time of electrons. The 2D position information of the incident particle is obtained from the anodes coordinates of the readout signal. One-dimensional analytically exact solutions of electric potential and field were obtained for the first time for the linear winding silicon drift detector. The simulation results show that the electric potential distribution inside the detector is uniform, and the "drift channel" inside the detector points to the collecting anodes on both sides, which proves the reasonable and feasible design of the linear winding silicon drift detector.

Monitoring Ongoing Clinical Trials Under Fractional Brownian Motion With Drift

The standard Brownian motion (Bm) with a linear drift is a convenient statistical structure for monitoring ongoing clinical trials in practice for more than four decades (Lan and DeMets). Under this model, the most current one-point statistic is sufficient. However, in our experience, the sponsor and the data monitoring committee often would like to make decision or recommendation based on the “trend” observed from the history of data, not just a one-point snapshot. In this article, we introduce and advance the fractional Brownian motion (fBm) with drift model to formally accommodate this need. The possible dependence and/or the nonlinear trend (e.g., piecewise linear drift with change-point) of observations in clinical trials may come from uncontrollable factors such as patient entry processes may have seasonal patterns over time, patient survival time may depend on the practices of clinical centers, physicians or censoring time (Lai et al.). The violations of the standard Bm and the need for the fBm are discussed with illustrative examples. The common methods including conditional power and sample size re-estimation used for monitoring clinical trials are derived and implemented in the Dynamic Data Monitoring (DDM) system for practitioners under the fBm.

A likelihood-based adaptive CUSUM for monitoring linear drift of Poisson rate with time-varying sample sizes

Several weighted cumulative sum (CUSUM) and adaptive CUSUM (ACUSUM) control charts have been developed to address the challenge of time-varying sample sizes in detecting the incidence rates of Poisson count data. However, the known post-drift parameters in the CUSUM chart make it less realistic. Additionally, the adaptive component in the ACUSUM chart cannot integrate with time-varying sample sizes naturally. Furthermore, the existing charts predominantly address step drift, neglecting linear drift. Hence, this study introduces a Poisson ACUSUM chart that considers both linear drift and integration issues. Detailed comparisons are made among the proposed control chart, CUSUM control charts, and other ACUSUM control charts. Results demonstrate the proposed method's superior robustness and ability to effectively detect small drifts. Finally, the empirical results of the mortality data are employed to further validate the effectiveness of the proposed method.

Distribution of Functionals of Brownian Motion with Linear Drift and Elastically Killed at Zero

Distribution of Functionals of Brownian Motion with Linear Drift and Elastically Killed at Zero

Recurrence Times of Large Earthquakes: Assimilating the Effect of Seismic Coupling into a Renewal Model

ABSTRACT A renewal model for estimating recurrence times of large earthquakes is presented, which allows one to assimilate data from paleo, historic, and instrumental earthquake data as well as geodetic information in a simple and efficient way using three parameters: the Richter b-value, the mean recurrence time μT of paleo and historic earthquakes, and the seismic coupling coefficient χ. The core of the model is a state variable with linear drift in time reflecting Reid’s elastic rebound theory, decorated with random fluctuations modeling small and intermediate earthquakes. Furthermore, it is assumed that a fraction between 0% and 100% of the average seismic moment is released seismically, and the remaining part corresponds to aseismic processes such as creep. The model extends former renewal models of Matthews et al. (2002) and Zöller et al. (2008). Results for different regions indicate overall good performance and thus suggest that the model provides physically motivated constraints for recurrence time estimations in contrast to the standard fitting of a few data points to an assumed distribution.

The long time behavior of the fractional Ornstein-Uhlenbeck process with linear self-repelling drift

The long time behavior of the fractional Ornstein-Uhlenbeck process with linear self-repelling drift

What can entropy metrics tell us about the characteristics of ocular fixation trajectories?

In this study, we provide a detailed analysis of entropy measures calculated for fixation eye movement trajectories from the three different datasets. We employed six key metrics (Fuzzy, Increment, Sample, Gridded Distribution, Phase, and Spectral Entropies). We calculate these six metrics on three sets of fixations: (1) fixations from the GazeCom dataset, (2) fixations from what we refer to as the "Lund" dataset, and (3) fixations from our own research laboratory ("OK Lab" dataset). For each entropy measure, for each dataset, we closely examined the 36 fixations with the highest entropy and the 36 fixations with the lowest entropy. From this, it was clear that the nature of the information from our entropy metrics depended on which dataset was evaluated. These entropy metrics found various types of misclassified fixations in the GazeCom dataset. Two entropy metrics also detected fixation with substantial linear drift. For the Lund dataset, the only finding was that low spectral entropy was associated with what we call "bumpy" fixations. These are fixations with low-frequency oscillations. For the OK Lab dataset, three entropies found fixations with high-frequency noise which probably represent ocular microtremor. In this dataset, one entropy found fixations with linear drift. The between-dataset results are discussed in terms of the number of fixations in each dataset, the different eye movement stimuli employed, and the method of eye movement classification.

Joint distribution of the supremum and the time of its attaining for a trajectory of the Poisson process with linear drift

Joint distribution of the supremum and the time of its attaining for a trajectory of the Poisson process with linear drift