quasi-Newton Method Research Articles

Method for optical proximity correction based ona vector imaging model.

Optical proximity correction (OPC) has become an indispensable step in integrated circuit manufacturing. It requires a huge amount of calculation to obtain a sufficiently accurate OPC model and implement pattern correction. In this paper, the authors proposed an edge-based OPC method built on a vector imaging model, where the analytical correlation between the cost function and movement of each edge segment is established by the chain rule. First, the mask pattern is segmented and downsampled to get the mask image in order to reduce the total data. Second, the aerial image, various parameters on each evaluating point, and the final cost value are obtained in proper sequence. In each part of the OPC process, the procedures of solution and derivation are both recorded. After obtaining the cost value, the chain rule is applied, by which the differential relation between the cost value and movement of each segment is built. According to this differential relation, the next movement of each segment is decided under a quasi-Newton method. All results obtained by the proposed method are compared with results from commercial software. The comparison shows that the proposed OPC method has good OPC accuracy in few iterations.

Early Physiologic Numerical and Waveform Characteristics of Simulated Hemorrhagic Events With Healthy Volunteers Donating Blood.

Early signs of bleeding are often masked by the physiologic compensatory responses delaying its identification. We sought to describe early physiologic signatures of bleeding during the blood donation process. Waveform-level vital sign data including electrocardiography, photoplethysmography (PPG), continuous noninvasive arterial pressure, and respiratory waveforms were collected before, during, and after bleeding. Fifty-five healthy volunteers visited blood donation center to donate whole blood. After obtaining the informed consent, 3 minutes of resting time was given to each subject. Then 3 minutes of orthostasis was done, followed by another 3 minutes of resting before the blood donation. After the completion of donating blood, another 3 minutes of postbleeding resting time, followed by 3 minutes of orthostasis period again. From 55 subjects, waveform signals as well as numerical vital signs (heart rate [HR], respiratory rate, blood pressure) and clinical characteristics were collected, and data from 51 subjects were analyzable. Any adverse events (AEs; dizziness, lightheadedness, nausea) were documented. Statistical and physiologic features including HR variability (HRV) metrics and other waveform morphologic parameters were modeled. Feature trends for all participants across the study protocol were analyzed. No significant changes in HR, blood pressure, or estimated cardiac output were seen during bleeding. Both orthostatic challenges and bleeding significantly decreased time domain and high-frequency domain HRV, and PPG amplitude, whereas increasing PPG amplitude variation. During bleeding, time-domain HRV feature trends were most sensitive to the first 100 mL of blood loss, and incremental changes of different HRV parameters (from 300 mL of blood loss), as well as a PPG morphologic feature (from 400 mL of blood loss), were shown with statistical significance. The AE group (n = 6) showed decreased sample entropy compared with the non-AE group during postbleed orthostatic challenge (p = 0.003). No significant other trend differences were observed during bleeding between AE and non-AE groups. Various HRV-related features were changed during rapid bleeding seen within the first minute. Subjects with AE during postbleeding orthostasis showed decreased sample entropy. These findings could be leveraged toward earlier identification of donors at risk for AE, and more broadly building a data-driven hemorrhage model for the early treatment of critical bleeding.

From lab to life: Evaluating the reliability and validity of psychophysiological data from wearable devices in laboratory and ambulatory settings.

Despite the increasing popularity of ambulatory assessment, the reliability and validity of psychophysiological signals from wearable devices is unproven in daily life settings. We evaluated the reliability and validity of physiological signals (electrocardiogram, ECG; photoplethysmography, PPG; electrodermal activity, EDA) collected from two wearable devices (Movisens EcgMove4 and Empatica E4) in the lab (N = 67) and daily life (N = 20) among adults aged 18-64 with Mindware as the laboratory gold standard. Results revealed that both wearable devices' valid data rates in daily life were lower than in the laboratory (Movisens ECG 82.94 vs. 93.10%, Empatica PPG 8.79 vs. 26.14%, and Empatica EDA 41.16 vs. 42.67%, respectively). The poor valid data rates of Empatica PPG signals in the laboratory could be partially attributed to participants' hand movements (r = - .27, p = .03). In laboratory settings, heart rate (HR) derived from both wearable devices exhibited higher concurrent validity than heart rate variability (HRV) metrics (ICCs 0.98-1.00 vs. 0.75-0.97). The number of skin conductance responses (SCRs) derived from Empatica showed higher concurrent validity than skin conductance level (SCL, ICCs 0.38 vs. 0.09). Movisens EcgMove4 provided more reliable and valid HRV measurements than Empatica E4 in both laboratory (split-half reliability: 0.95-0.99 vs. 0.85-0.98; concurrent validity: 0.95-1.00 vs. 0.75-0.98; valid data rate: 93.10 vs. 26.14%) and ambulatory settings (split-half reliability: 0.99-1.00 vs. 0.89-0.98; valid data rate: 82.94 vs. 8.79%). Although the reliability and validity of wearable devices are improving, findings suggest researchers should select devices that yield consistently robust and valid data for their measures of interest.

Incremental Quasi-Newton Methods with Faster Superlinear Convergence Rates

We consider the finite-sum optimization problem, where each component function is strongly convex and has Lipschitz continuous gradient and Hessian. The recently proposed incremental quasi-Newton method is based on BFGS update and achieves a local superlinear convergence rate that is dependent on the condition number of the problem. This paper proposes a more efficient quasi-Newton method by incorporating the symmetric rank-1 update into the incremental framework, which results in the condition-number-free local superlinear convergence rate. Furthermore, we can boost our method by applying the block update on the Hessian approximation, which leads to an even faster local convergence rate. The numerical experiments show the proposed methods significantly outperform the baseline methods.

Dynamic fuzzy temperature control with quasi-Newtonian particle swarm optimization for precise air conditioning

Precise air conditioners are renowned for their ability to deliver accurate and stable air output. However, achieving precise temperature control can be challenging due to the complexity of the air conditioner. To address this issue, a dynamic fuzzy control method based on quasi-Newton particle swarm optimization (QNPSO) is put forward for precise air conditioning. The air conditioning dynamics is first modelled using the interconnection of the first-order delayed transfer functions. Incremental fuzzy controllers are then employed to track temperature changes and prevent steady-state errors for all internal components of the conditioner. By employing QNPSO to optimize all control parameters simultaneously, the present method effectively addresses the limitations of particle swarm optimization in poor local search capability, and the sensitivity of the quasi-Newton algorithm to initial values. Additionally, a dynamic adjustment optimization strategy is suggested to accommodate start-up dynamics and meet temperature change requirements. In this way, the precise air conditioning is achieved by regulating internal components in an integrated fashion. The superior performance of the proposed method is validated through model simulation evaluations and prototype conditioner experiments using a water-cooled precise air conditioner. The results demonstrate that the proposed method achieves faster stabilization time and higher control accuracy compared to the state-of-the-art peers.

Toward a cross-cultural understanding of intraindividual variability metrics

ABSTRACT Objective Compare the construct validity and predictive utility of cognitive intraindividual variability (IIV) in a sample of community-dwelling Hispanic and non-Hispanic white (NHW) older adults. Methods The present study included annual data from 651 older adult control participants (Hispanic = 293; NHW = 358) enrolled in the Texas Alzheimer’s Research and Care Consortium for at least 5 years. Mean composite z-scores were calculated for attention, language, memory, and executive domains. IIV was calculated as was the standard deviation both within (IIV-Within) and between (IIV-Between) these domains. Results At baseline, NHW individuals obtained significantly higher mean scores in each domain than their Hispanic counterparts. They also showed significantly greater variability within and between domains, except for IIV-Within the language domain which was significantly larger in the Hispanic group. IIV-Between domains was driven primarily by IIV-Within the executive function domain in the NHW cohort and by IIV-Within the language domain in the Hispanic cohort. In both groups, the addition of IIV-Within and IIV-Between cognitive domains at baseline significantly improved prediction of global cognitive status after 5 years above and beyond demographic characteristics, genetic and cardiovascular risk. However, IIV-Between domains was the strongest predictor in the NHW group, while IIV-Within the attention domain was the strongest predictor in the Hispanic group. Conclusions Findings suggest that, while IIV-Between domains is a promising adjunctive method for predicting future cognitive decline, its construct validity and predictive utility varies based on ethnic group.

Enhancing quantum metrology for multiple frequencies of oscillating magnetic fields by quantum control

Abstract Quantum multi-parameter estimation has recently attracted increased attention due to its wide applications, with a primary goal of designing high-precision measurement schemes for unknown parameters. While existing research has predominantly concentrated on time-independent Hamiltonians, little has been known about quantum multi-parameter estimation for time-dependent Hamiltonians due to the complexity of quantum dynamics. This work bridges the gap by investigating the precision limit of multi-parameter quantum estimation for a qubit in an oscillating magnetic field model with multiple unknown frequencies. As the well-known quantum Cramér–Rao bound is generally unattainable due to the potential incompatibility between the optimal measurements for different parameters, we use the most informative bound instead which is always attainable and equivalent to the Holevo bound in the asymptotic limit. Moreover, we apply additional Hamiltonian to the system to engineer the dynamics of the qubit. By utilizing the quasi-Newton method, we explore the optimal schemes to attain the highest precision for the unknown frequencies of the magnetic field, including the simultaneous optimization of initial state preparation, the control Hamiltonian and the final measurement. The results indicate that the optimization can yield much higher precisions for the field frequencies than those without the optimizations. Finally, we study the robustness of the optimal control scheme with respect to the fluctuation of the interested frequencies, and the optimized scheme exhibits superior robustness to the scenario without any optimization.

A modified parameterization method for invariant Lagrangian tori for partially integrable Hamiltonian systems

In this paper we present an a-posteriori KAM theorem for the existence of an (n−d)-parameter family of d-dimensional isotropic invariant tori with Diophantine frequency vector ω∈Rd, of type (γ,τ), for n degrees of freedom Hamiltonian systems with (n−d) independent first integrals in involution. If the first integrals induce a Hamiltonian action of the (n−d)-dimensional torus, then we can produce n-dimensional Lagrangian tori with frequency vector of the form (ω,ωp), with ωp∈Rn−d. In the light of the parameterization method, we design a (modified) quasi-Newton method for the invariance equation of the parameterization of the torus, whose proof of convergence from an initial approximation, and under appropriate non-degeneracy conditions, is the object of this paper. We present the results in the analytic category, so the initial torus is real-analytic in a certain complex strip of width ρ, and the corresponding error in the functional equation is ɛ. We heavily use geometric properties and the so called automatic reducibility to deal directly with the functional equation and get convergence if γ−2ρ−2τ−1ɛ is small enough, in contrast with most of KAM results based on the parameterization method, that get convergence if γ−4ρ−4τɛ is small enough. The approach is suitable to perform computer assisted proofs.

Workflow-Induced Uncertainty in Data-Driven Mineral Prospectivity Mapping

The primary goal of mineral prospectivity mapping (MPM) is to narrow the search for mineral resources by producing spatially selective maps. However, in the data-driven domain, MPM products vary depending on the workflow implemented. Although the data science framework is popular to guide the implementation of data-driven MPM tasks, and is intended to create objective and replicable workflows, this does not necessarily mean that maps derived from data science workflows are optimal in a spatial sense. In this study, we explore interactions between key components of a geodata science-based MPM workflow on the geospatial outcome, within the modeling stage by modulating: (1) feature space dimensionality, (2) the choice of machine learning algorithms, and (3) performance metrics that guide hyperparameter tuning. We specifically relate these variations in the data science workflow to the spatial selectivity of resulting maps using uncertainty propagation. Results demonstrate that typical geodata science-based MPM workflows contain substantial local minima, as it is highly probable for an arbitrary combination of workflow choices to produce highly discriminating models. In addition, variable domain metrics, which are key to guide the iterative implementation of the data science framework, exhibit inconsistent relationships with spatial selectivity. We refer to this class of uncertainty as workflow-induced uncertainty. Consequently, we propose that the canonical concept of scientific consensus from the greater experimental science framework should be adhered to, in order to quantify and mitigate against workflow-induced uncertainty as part of data-driven experimentation. Scientific consensus stipulates that the degree of consensus of experimental outcomes is the determinant in the reliability of findings. Indeed, we demonstrate that consensus through purposeful modulations of components of a data-driven MPM workflow is an effective method to understand and quantify workflow-induced uncertainty on MPM products. In other words, enlarging the search space for workflow design and experimenting with workflow components can result in more meaningful reductions in the physical search space for mineral resources.

A Quasi-Newton method for solving generalized equations by using a Kantorovich approach

A Quasi-Newton method for solving generalized equations by using a Kantorovich approach

Monitoring autonomic responses in Parkinson’s disease individuals: non-linear and chaotic global metrics of heart rate variability

Aim To examine and compare the autonomic responses, as assessed through the non-linear and chaotic global metrics of heart rate variability in two groups: the Parkinson’s Disease Group (PDG) and the Control Group (CG), both at rest and during an active tilt test. Methods The study encompassed 46 participants (PDG: n = 23; 73.73 ± 7.28 years old; CG: n = 23; 70.17 ± 8.20 years old). Initial data collection involved the acquisition of participant’s characteristics. The autonomic modulation was estimated both at rest and during the active tilt test. For this assessment, we computed non-linear indices derived from five entropies (Approximate, Sample, Shannon, Renyi, Tsallis), Detrended Fluctuation Analysis and the seven chaotic global metrics (hsCFP1-hsCFP7). Results At rest, the PDG exhibited lower values of hsCFP3 (0.818 ± 0.116 vs. 0.904 ± 0.065; p < 0.05) and Sample Entropy (0.720 ± 0.149 vs. 0.799 ± 0.171; p < 0.05). During the test, the PDG demonstrated lower values of ApEn, while the CG presented lower values of SampEn, hsCFP1, hsCFP3, hsCFP7, and higher values of hsCFP5. An interaction was observed, indicating that hsCFP1 and hsCFP3 exhibit differential behavior for the CG and PDG in response to the test. Conclusion subjects with PD exhibited reduced complexity of the RR interval series at rest, and a diminished autonomic response to the active tilt test when compared with the CG. The test, together with non-linear indices, may serve for assessing the Autonomic Nervous System in individuals with PD in a clinical setting. The interpretation of these data should be approached with caution, given the possible influences of pharmacotherapies and the inclusion of diabetic participants.

Correlation of fetal heart rate dynamics to inflammatory markers and brain-derived neurotrophic factor during pregnancy.

This study aims to show the relation between biomarkers in maternal and cord-blood samples and fetal heart rate variability (fHRV) metrics through a non-invasive fetal magnetocardiography (fMCG) technique. Twenty-three women were enrolled for collection of maternal serum and fMCG tracings immediately prior to their scheduled cesarean delivery. The umbilical cord blood was collected for measurement of biomarker levels. The fMCG metrics were then correlated to the biomarker levels from the maternal serum and cord blood. Brain-derived neurotrophic factor (BDNF) had a moderate correlation with fetal parasympathetic activity (0.416) and fetal sympathovagal ratios (-0.309;-0.356). Interleukin (IL)-6 also had moderate-sized correlations but with an inverse relationship as compared to BDNF. These correlations were primarily in cord-blood samples and not in the maternal blood. In this small sample-sized exploratory study, we observed a moderate correlation between fHRV and cord-blood BDNF and IL-6 immediately preceding scheduled cesarean delivery at term. These findings need to be validated in a larger population.

Large-eddy simulation-based reconstruction of turbulence in a neutral boundary layer using spectral-tensor regularization

We propose an efficient method to reconstruct the turbulent flow field in a neutrally stratified atmospheric boundary layer using large-eddy simulation (LES) and a series of lidar measurements. The reconstruction is formulated as a strong four-dimensional variational data assimilation problem, which involves optimizing two competing terms that contribute in the objective functional. The first term is a likelihood term, while the second contains the initial background distribution of turbulent velocity fluctuations and works as a regularization term. However, computing and storing the full background covariance tensor in turbulent flows is time consuming and resource intensive. In the current work, we investigate the possibility of replacing the complex background tensor by simple analytical approximations based on spectral tensors such as the Hunt–Graham–Wilson (HGW) model (Boundary-Layer Meteorol., vol. 85, 1997, pp. 35–52) or the Mann model (J. Fluid Mech., vol. 273, 1994, pp. 141–168). Afterwards, the problem is solved using a quasi-Newton algorithm and preconditioned to enhance the convergence rate. We test the method using virtual lidar measurements collected on a fine reference LES. Results show a super-linear convergence rate of the optimization algorithm to a local minimum and very good agreement between virtual lidar measurements and reconstruction in the scanning region. Furthermore, we demonstrate that incorporating the Saffman energy spectrum ( $E(k) \sim k^2$ where E is the energy spectrum and k is the magnitude of the wavenumber vector) at low wavenumbers into the Mann spectral tensor yields a longer streamwise correlation length, resulting in reduced reconstruction error when compared with the Batchelor spectrum ( $E(k) \sim k^4$ ). Finally, we observe that using the HGW model or Mann model with a Saffman spectrum yields similar results.

Limitations of 14-Day Continuous Glucose Monitoring Sampling for Assessment of Hypoglycemia and Glycemic Variability in Type 1 Diabetes.

Continuous glucose monitoring (CGM) has become the standard of care in diabetes management with the recent advances in technology and accessibility in the last decade. An International Consensus was established to define CGM metrics and its goals in diabetes care. The 2019 International Consensus suggested 14 days of CGM sampling for the assessment of CGM metrics stating the limitations that may occur for hypoglycemia and glycemic variability metrics. Since then, several studies assessed the correlation between CGM metrics and duration of the sampling period. This review summarized the studies that investigated the relationship between 14-day CGM sampling to 90-day CGM data in >70% CGM users for all CGM metrics and highlighted possible solutions for more accurate CGM sampling durations in type 1 diabetes (T1D). Accumulating evidence showed that 14-day CGM sampling correlates well with 90-day CGM data for mean glucose, time in 70-180 mg/dL, and hyperglycemia metrics; however, it correlates weakly for hypoglycemia and glycemic variability metrics. In the studies included in this review, in adults with T1D, minimum sampling duration was 14 days for mean glucose, time in 70-180 mg/dL, and time in hyperglycemia (>180 and >250 mg/dL); however, minimum sampling duration varied between 21 to 30 days for time <70 mg/dL, 30 to 35 days for time <54 mg/dL, and 28 to 35 days for coefficient of variation. Longer than 14 days of CGM, sampling was required to properly assess hypoglycemia and glycemic variability in T1D.

The Comparison of the Multi-Layer Artificial Neural Network Training Methods in Terms of the Predictive Quality of the Coefficient of Friction of 1.0338 (DC04) Steel Sheet.

Friction is one of the main phenomena accompanying sheet metal forming methods, affecting the surface quality of products and the formability of the sheet metal. The most basic and cheapest way to reduce friction is to use lubricants, which should ensure the highest lubrication efficiency and at the same time be environmentally friendly. Due to the trend towards sustainable production, vegetable oils have been used in research as an alternative to petroleum-based lubricants. The analysis of friction in sheet metal forming requires an appropriate tribotester simulating the friction conditions in a specific area of the sheet metal being formed. Research has used a special strip drawing tribometer, enabling the determination the value of the coefficient of friction in the blankholder zone in the deep drawing process. Quantitative analysis of the friction phenomenon is necessary at the stage of designing the technological process and selecting technological parameters, including blankholder pressure. This article presents the results of friction testing of 1.0338 (DC04) steel sheets using a strip drawing test. The experimental tests involved pulling a strip of sheet metal between two countersamples with a rounded surface. The tests were carried out on countersamples with different levels of roughness for the range of contact pressures occurring in the blankholder zone in the deep drawing process (1.7-5 MPa). The values of the coefficient of friction determined under dry friction conditions were compared with the results for edible (corn, sunflower and rapeseed) and non-edible (Moringa, Karanja) vegetable lubricants. The tested oils are the most commonly used vegetable-based biolubricants in metal forming operations. Multi-layer artificial neural networks were used to determine the relationship between the value of the contact pressure, the roughness of the countersamples, the oil viscosity and density, and the value of the coefficient of friction. Rapeseed oil provided the best lubrication efficiency during friction testing for all of the tested samples, with an average surface roughness of Sa 0.44-1.34 μm. At the same time, as the roughness of the countersamples increased, a decrease in lubrication efficiency was observed. The lowest root mean squared error value was observed for the MLP-4-8-1 network trained with the quasi-Newton algorithm. Most of the analysed networks with different architectures trained using the various algorithms showed that the kinematic viscosity of the oil was the most important aspect in assessing the friction of the sheets tested. The influence of kinematic viscosity on the value of the coefficient of friction is strongly dependent on the surface roughness of the countersamples.

Two new limited-memory preconditioned conjugate gradient algorithms for nonlinear optimization problems

The conjugate gradient (CG) techniques are a class of unconstrained optimization algorithms with strong local and global convergence qualities and minimal memory needs. While the quasi-Newton methods are reliable and efficient on a wide range of problems and these methods are converge faster than the conjugate gradient methods and require fewer function evaluations, however, they are request substantially more storage, and if the problem is ill-conditioned, they may require several iterations. There is another class, termed preconditioned conjugate gradient method, it is a technique that combines two methods conjugate gradient with quasi-Newton. In this work, we proposed a new two limited memory preconditioned conjugate gradient methods (New1 and New2), to solve nonlinear unconstrained minimization problems, by using new modified symmetric rank one (NMSR1) and new modified Davidon, Fletcher, Powell (NMDFP), and also using projected vectors. We proved that these modifications fulfill some conditions. Also, the descent condition of the new technique has been proved. The numerical results showed the efficiency of the proposed new algorithms compared with some standard nonlinear, unconstrained problems.

Fast Initial Model Design for Electrical Resistivity Inversion by Using Broad Learning Framework

The electrical resistivity method is widely used in near-surface mineral exploration. At present, the deterministic algorithm is commonly employed in three-dimensional (3-D) electrical resistivity inversion to obtain subsurface electrical structures. However, the accuracy and efficiency of deterministic inversion rely on the initial model. In practice, obtaining an initial model that approximates the true subsurface electrical structures remains challenging. To address this issue, we introduce a broad learning (BL) network to determine the initial model and utilize the limited memory quasi-Newton (L-BFGS) algorithm to conduct the 3-D electrical resistivity inversion task. The powerful mapping capability of the BL network enables one to find the model that elucidates the actual observed data. The single-layer BL network makes it efficient and easy to realize, leading to much faster network training compared to that using the deep learning network. Both the synthetic and field experiments suggest that the BL framework could effectively obtain the initial model based on observed data. Furthermore, in comparison to using a homogeneous medium as the initial model, the L-BFGS inversion with the BL framework-designed initial model improves the inversion accuracy of subsurface electrical structures and expedites the convergence speed of the iteration. This study provides an effective approach for fast initial model design in a data-driven manner when the prior information is unavailable. The proposed method can be useful in high-precision imaging of near-surface mineral electrical structures.

Novel iterative cubature Kalman filters under maximum correntropy criterion for the robust state estimation

AbstractThe cubature Kalman filter (CKF) based on maximum correntropy criterion (MCC) is robust under non‐Gaussian noises, but it may encounter numerical problems when there are large outliers. First, based on the MCC and weighted least square (WLS) methods, a new cost function is introduced to calculate the state and covariance updates, which can better solve numerical problems caused by large outliers. Then, a nonlinear measurement function is used, and the measurement information is updated through the latest iterative values, which can obtain more accurate results under various non‐Gaussian noises. In addition, the Gauss–Newton, Levenberg–Marquardt, and Quasi–Newton methods are used, and three iterative algorithms named GN‐IMCC‐CKF, LM‐IMCC‐CKF, and QN‐IMCC‐CKF are respectively derived for the updating steps. Compared with the existing algorithms, the simulation results of two classical models show that the proposed algorithms have better numerical stability and estimation accuracy under non‐Gaussian systems.

Increased Pain Variability in Patients With Chronic Pain: A Role for Pain Catastrophizing

Pain is an inherently negative perceptual and affective experience that acts as a warning system to protect the body from injury and illness. Pain unfolds over time and is influenced by myriad factors, making it highly dynamic. Despite this, statistical measures often treat any intraindividual variability in pain ratings as noise or error. This is consequential, especially for research on chronic pain, because pain variability is associated with greater pain severity and depression. Yet, differences in pain variability between patients with chronic pain and controls in response to acute pain has not been fully examined—and it is unknown if dispositional factors such as pain catastrophizing (negative cognitive-affective response to potential or actual pain in which attention cannot be diverted away from pain) relate to pain variability. In the current study, we recruited chronic-pain patients (N = 30) and pain-free controls (N = 22) to complete a 30-second thermal pain task where they continually rated a painful thermal stimulus. To quantify pain variability and capture potential dynamics, we used both a traditional intraindividual standard deviation (iSD) metric of variability and a novel derivatives approach. For both metrics, patients with chronic pain had higher variability in their pain ratings over time, and pain catastrophizing significantly mediated this relationship. This suggests patients with chronic pain experience pain stimuli differently over time, and pain catastrophizing may account for this differential experience. PerspectiveThe present study demonstrates (using multiple variability metrics) that chronic pain patients show more variability when rating experimental pain stimuli, and that pain catastrophizing helps explain this differential experience. These results provide preliminary evidence that short-term pain variability could have utility as a clinical marker in pain assessment and treatment.

Modification of Quasi-Newton Successive Substitution Method for Calculating Phase Equilibria of Hydrocarbon Mixtures Taking into Account the Capillary Pressure Jump

Modification of Quasi-Newton Successive Substitution Method for Calculating Phase Equilibria of Hydrocarbon Mixtures Taking into Account the Capillary Pressure Jump