Classical Relaxation Research Articles

Filtering the NMR Spectra of Mixtures by Coordination to Paramagnetic Cu2.

The paramagnetic spin relaxation (PSR) filter allows the selective NMR signal suppression of components in mixtures according to their complexation ability to a paramagnetic ion. It relies on the faster relaxation of nuclei in paramagnetic environments and thus is complementary to classical diffusion and relaxation filters. So far, the PSR filter has established Gd3+ as the sole PSR agent, restricting the paramagnetic filtering repertoire. Herein, we present Cu2+ as a robust PSR agent with characteristic filtering properties. While Gd3+ depends on unspecific ion-pair interactions with anionic components, Cu2+ stands out for filtering species via ordered coordination complexes. An evaluation of the paramagnetic effect of Cu2+ over more than 50 small molecules and polymers has unveiled different sensitivities to Cu2+ (especially high for pyridines, diamines, polyamines, and amino alcohols) and precise filtering conditions for mixtures (1H, COSY, and HMQC) that were challenged with a test bed of commercial drugs. The advantage of integrating Cu2+ and Gd3+ for the stepwise PSR filtering of complex mixtures is also shown.

Classical Massage and Relaxation Exercise on Symptom Status and Quality of Life in Advanced Stage Patients With Heart Failure: A Randomized Controlled Trial.

This randomized controlled study aimed to investigate the effects of classical massage (CM) and Benson relaxation exercise (BRE) on symptom status and quality of life (QoL) in patients with heart failure (HF). Seventy-two patients with HF were recruited from 4 hospitals in Ankara, Turkey. The study sample was allocated to a CM (n = 24), BRE (n = 26), or control group (n = 22) based on the New York Heart Association classification of HF (stages III and IV) through stratified randomization. The intervention groups received either CM or BRE twice daily for 7 days (total of 14 sessions). The control group received only routine care. The scores of symptom status decreased in the CM and BRE groups at the end of the intervention (first week) as compared with the control group (P < .05). Nevertheless, at the end of the monitoring period, no significant differences were detected between the 3 study groups at baseline (P = .474), week 1 (P = .936), and week 3 (P = .668) in terms of QoL scores. The CM and BRE showed beneficial effects in the management of HF symptoms in advanced stage HF patients who were hospitalized and received intensive treatment.

The application of the distributed-order time fractional Bloch model to magnetic resonance imaging

It is now well known that the magnetic resonance imaging (MRI) signal decay deviates from the classical mono-exponential relaxation. This deviation is referred to in the literature as anomalous relaxation. The modelling of this anomalous relaxation can provide a better understanding of MRI magnetization. The purpose of this work is to investigate the utility of the distributed-order time fractional Bloch equations to describe anomalous relaxation processes in human brain MRI data. Two choices of continuous distribution weight functions, which are parameterised by their mean μ and standard deviation σ, are studied to investigate their impact on the model solution behaviour. An implicit numerical method implemented on a graded mesh is proposed to solve the model and the stability and convergence analysis are presented. We also derive semi-analytical solutions of the fully coupled Bloch equations using the Laplace transform technique to assess the accuracy of the numerical scheme. Furthermore, three different voxel models of continuous distribution weight functions, namely a single continuous probability distribution (model 1), two distinct continuous probability distributions (model 2) and a mixture of two continuous probability distributions (model 3), are applied to the in vivo human brain MRI data, and a feasible and reliable parameter estimation method based on a modified hybrid Nelder-Mead simplex search and particle swarm optimization is presented to perform the voxel-level temporal fitting of the MRI data. The application of these distributed-order time fractional Bloch models highlights the validity of the proposed models, and based on the mean square error we conclude that models 2 and 3 might be more suitable than model 1 to characterize anomalous relaxation processes in human brain MRI data.

Joint Task Offloading and Caching for Massive MIMO-Aided Multi-Tier Computing Networks

In this paper, a massive multiple-input multiple-output (MIMO) relay assisted multi-tier computing (MC) system is employed to enhance the task computation. We investigate the joint design of the task scheduling, service caching and power allocation to minimize the total task scheduling delay. To this end, we formulate a robust non-convex optimization problem taking into account the impact of imperfect channel state information (CSI). In particular, multiple task nodes (TNs) offload their computational tasks either to computing and caching nodes (CCN) constituted by nearby massive MIMO-aided relay nodes (MRN) or alternatively to the cloud constituted by nearby fog access nodes (FAN). To address the non-convexity of the optimization problem, an efficient alternating optimization algorithm is developed. First, we solve the non-convex power allocation optimization problem by transforming it into a linear optimization problem for a given task offloading and service caching result. Then, we use the classic Lagrange partial relaxation for relaxing the binary task offloading as well as caching constraints and formulate the dual problem to obtain the task allocation and software caching results. Given both the power allocation, as well as the task offloading and caching result, we propose an iterative optimization algorithm for finding the jointly optimized results. The simulation results demonstrate that the proposed scheme outperforms the benchmark schemes, where the power allocation may be controlled by the asymptotic form of the effective signal-to-interference-plus-noise ratio (SINR).

Hyperbolic approximation of the BBM equation

It is well known that the Benjamin–Bona–Mahony (BBM) equation can be seen as the Euler–Lagrange equation for a Lagrangian expressed in terms of the solution potential. We approximate the Lagrangian by a two-parameter family of Lagrangians depending on three potentials. The corresponding Euler–Lagrange equations can be then written as a hyperbolic system of conservations laws. The hyperbolic BBM system has two genuinely nonlinear eigenfields and one linear degenerate eigenfield. Moreover, it can be written in terms of Riemann invariants. Such an approach conserves the variational structure of the BBM equation and does not introduce the dissipation into the governing equations as it usually happens for the classical relaxation methods. The state-of-the-art numerical methods for hyperbolic conservation laws such as the Godunov-type methods are used for solving the ‘hyperbolized’ dispersive equations. We find good agreement between the corresponding solutions for the BBM equation and for its hyperbolic counterpart.

Convexification of Permutation-Invariant Sets and an Application to Sparse Principal Component Analysis

We develop techniques to convexify a set that is invariant under permutation and/or change of sign of variables and discuss applications of these results. First, we convexify the intersection of the unit ball of a permutation and sign-invariant norm with a cardinality constraint. This gives a nonlinear formulation for the feasible set of sparse principal component analysis (PCA) and an alternative proof of the K-support norm. Second, we characterize the convex hull of sets of matrices defined by constraining their singular values. As a consequence, we generalize an earlier result that characterizes the convex hull of rank-constrained matrices whose spectral norm is below a given threshold. Third, we derive convex and concave envelopes of various permutation-invariant nonlinear functions and their level sets over hypercubes, with congruent bounds on all variables. Finally, we develop new relaxations for the exterior product of sparse vectors. Using these relaxations for sparse PCA, we show that our relaxation closes 98% of the gap left by a classical semidefinite programming relaxation for instances where the covariance matrices are of dimension up to 50 × 50.

A Global Optimization Algorithm for Solving Linearly Constrained Quadratic Fractional Problems

This paper first proposes a new and enhanced second order cone programming relaxation using the simultaneous matrix diagonalization technique for the linearly constrained quadratic fractional programming problem. The problem has wide applications in statics, economics and signal processing. Thus, fast and effective algorithm is required. The enhanced second order cone programming relaxation improves the relaxation effect and computational efficiency compared to the classical second order cone programming relaxation. Moreover, although the bound quality of the enhanced second order cone programming relaxation is worse than that of the copositive relaxation, the computational efficiency is significantly enhanced. Then we present a global algorithm based on the branch and bound framework. Extensive numerical experiments show that the enhanced second order cone programming relaxation-based branch and bound algorithm globally solves the problem in less computing time than the copositive relaxation approach.

Radiomics Feature Analysis of Cartilage and Subchondral Bone in Differentiating Knees Predisposed to Posttraumatic Osteoarthritis after Anterior Cruciate Ligament Reconstruction from Healthy Knees.

Objectives To introduce a new implementation of radiomics analysis for cartilage and subchondral bone of the knee and to compare the performance of the proposed models to classic T2 relaxation time in distinguishing knees predisposed to posttraumatic osteoarthritis (PTOA) after anterior cruciate ligament reconstruction (ACLR) and healthy controls. Methods 114 patients following ACLR after at least 2 years and 43 healthy controls were reviewed and allocated to training (n = 110) and testing (n = 47) cohorts. Radiomics models are built for cartilage and subchondral bone regions of different compartments: lateral femur (LF), lateral tibia (LT), medial femur (MF), and medial tibia (MT) and combined models of four compartments on T2 mapping images. The model performance of discrimination between patients and controls was illustrated with the receiver operating characteristic curve and compared with a classic T2 value-based model. Results The T2 value model of cartilage yielded moderate predictive performance in discerning patients and controls, with an AUC of 0.731 (95% confidence interval, 0.556–0.875) in the testing cohort, while the radiomics signature of cartilage and subchondral bone of different compartments demonstrated excellent performance, with AUCs of 0.864–0.979. Furthermore, the combined model reported an even better performance, with AUCs of 0.977 (95% confidence interval, 0.919–1.000) for the cartilage and 0.934 (95% confidence interval, 0.865–0.994) for the subchondral bone in the testing cohort. Conclusion The radiomics features of the cartilage and subchondral bone may be able to provide powerful tools with more sensitive detection than T2 values in differentiating knees at risk for PTOA after ACLR from healthy knees.

The Lindbladian form and the reincarnation of Felix Bloch's generalized theory of relaxation.

The relationship between the classic magnetic resonance density matrix relaxation theories of Bloch and Hubbard and the modern Lindbladian master equation methods are explored. These classic theories are in full agreement with the latest results obtained by the modern methods. A careful scrutiny shows that this also holds true for Redfield's later treatment, offered in 1965. The early contributions of Bloch and Hubbard to rotating-frame relaxation theory are also highlighted. Taken together, these seminal efforts of Bloch and Hubbard can enjoy a new birth of contemporary relevance in magnetic resonance.

Co-ferrite nanostructures prepared by solvothermal route; new ultra-low k dielectrics

Co spinel ferrite nanoparticles were successfully prepared using a solvothermal route. Their structure, morphology and cationic distribution were studied by X-ray diffraction, Transmission Electron Microscopy and 57Fe Mössbauer Spectrometry. Though, their electric conductivity and dielectric relaxation were studied on nanostructured pellets resulting from the compaction of nanoparticles, by complex impedance spectroscopy in the frequency range 1–106 Hz from 25 up to 250 °C. The dielectric properties are investigated in detail. The presence of two thermally activated relaxation peaks in the modulus loss spectra confirms the contribution of grains and grain boundaries to the electrical behavior of the material. The main dielectric relaxation comportment and the conduction process are governed by the grain boundaries. Ac-conductivity, which deviates from the usual Universal Dielectric Response, can be described by a double power-law evidenced by a Nearly Constant Loss trend followed by a Super-Linear Power Law that decreases with increasing temperature. The change in the cationic distribution in CoFe2O4, deduced from the 57Fe Mössbauer spectra, may explain the observed trend in conductivity. The classical dielectric relaxation behavior is observed and very low values of permittivity are estimated. This compound can therefore be classified as an ultra-low-k dielectric.

High-order Absorbing Boundary Condition, Domain Decomposition Method and Stratified Dispersive Wave Model

The high-order Absorbing Boundary Condition proposed by Hagstrom and Warburton was applied to various models as the wave equation, dispersive, convected with stratified materials. We propose an other way to expand the use of this condition with Domain Decomposition Method. We apply it here to a Stratified Dispersive Wave Model not just to limit the real unbounded domain but to use a non-overlapping domain decomposition method with the classical Schwarz Waveform Relaxation method using the Absorbing Boundary Condition taken as an approximation of the Transparent Operator for the interface condition. We must add terms to enrich the equations associated to the Absorbing Boundary Condition and compute them with a cumulative process. Numerical examples are used to show the performance of this Domain Decomposition Method.

Low-Depth Mechanisms for Quantum Optimization

One of the major application areas of interest for both near-term and fault-tolerant quantum computers is the optimization of classical objective functions. In this work, we develop intuitive constructions for a large class of these algorithms based on connections to simple dynamics of quantum systems, quantum walks, and classical continuous relaxations. We focus on developing a language and tools connected with kinetic energy on a graph for understanding the physical mechanisms of success and failure to guide algorithmic improvement. This physical language, in combination with uniqueness results related to unitarity, allow us to identify some potential pitfalls from kinetic energy fundamentally opposing the goal of optimization. This is connected to effects from wavefunction confinement, phase randomization, and shadow defects lurking in the objective far away from the ideal solution. As an example, we explore the surprising deficiency of many quantum methods in solving uncoupled spin problems and how this is both predictive of performance on some more complex systems while immediately suggesting simple resolutions. Further examination of canonical problems like the Hamming ramp or bush of implications show that entanglement can be strictly detrimental to performance results from the underlying mechanism of solution in approaches like QAOA. Kinetic energy and graph Laplacian perspectives provide new insights to common initialization and optimal solutions in QAOA as well as new methods for more effective layerwise training. Connections to classical methods of continuous extensions, homotopy methods, and iterated rounding suggest new directions for research in quantum optimization. Throughout, we unveil many pitfalls and mechanisms in quantum optimization using a physical perspective, which aim to spur the development of novel quantum optimization algorithms and refinements.

Acoustic, thermal and optical properties of organic based disodium tartrate salt

In this work, acoustic, thermal, and optical properties were tested on the different concentrations of the Disodium Tartrate solutions. First, the viscosity studies were analyzed for the Disodium tartrate in the concentration range from 2% to 20% with different temperatures 303K, 308K, 313K, and 318K. It was noted that the relative viscosity and the activation energy of the prepared compound increase with increases in concentration and decreases with temperature increases. The properties like density and ultrasonic velocity are varied when increases the concentration of the aqueous solutions of Disodium Tartrate. In this study, the values of adiabatic compressibility show an inverse behavior when compared with ultrasonic velocity due to the interaction between solute and solvent molecules. Also observed that the inter-molecular free length is maximum for a lower percentage. The free volume for the compound is maximum at 2% and a minimum of 20%, since it reduces when the internal pressure increases. It was revealed that the classical absorption coefficient and relaxation time for Disodium Tartrate is minimum for lower percentage and minimum for a higher percentage. The interactions between the solute and solvent are confirmed through the property like specific Acoustical impedance. It was noted that the increase in internal pressure increases the concentration of the compound. The ion-solvent interaction was discussed by the relative association study, thus the values of relative association increases with an increase in concentration. The Rao’s and Wada’s constant increases linearly in aqueous solutions of Disodium Tartrate for the entire system.

Node-based Lagrangian relaxations for multicommodity capacitated fixed-charge network design

Classical Lagrangian relaxations for the multicommodity capacitated fixed-charge network design problem are the so-called flow and knapsack relaxations, where the resulting Lagrangian subproblems decompose by commodities and by arcs, respectively. We introduce node-based Lagrangian relaxations, where the resulting Lagrangian subproblem decomposes by nodes. We show that the Lagrangian dual bounds of these relaxations improve upon the linear programming relaxation bound, known to be equal to the Lagrangian dual bounds for the flow and knapsack relaxations. We also develop a Lagrangian matheuristic to compute upper bounds. The computational results on a set of benchmark instances show that the Lagrangian matheuristic is competitive with the state-of-the-art heuristics from the literature.

Production scheduling problem and solver improvement via integration of the grey wolf optimizer into the augmented Lagrangian relaxation method

In open-pit mines, the long-term production scheduling problem is a mixed-integer programming optimization problem. Usually, it is tricky to reach the true optimal solution to the long-term production scheduling problem due to its complexity and dimensions. However, owing to its high-dimensional and combinatorial nature, the long-term production scheduling problem hinders the development of a precise mathematical optimization technique that can solve the whole problem for any real-size block model. In this paper, a hybrid model is introduced to solve the long-term production scheduling problem, taking into account grade uncertainty assisted by the augmented Lagrangian relaxation and the grey wolf optimizer methods. The hybrid augmented Lagrangian relaxation–the grey wolf optimizer technique is recommended to solve the long-term production scheduling problem to improve its performance and, consequently, speed up the convergence. The proposed model has been compared with the results of the hybrid methods gained from the classic Lagrangian relaxation and augmented Lagrangian relaxation methods integrated with the bat algorithm, particle swarm optimization, genetic algorithm, the traditional subgradient method, and conventional method without using the Lagrangian approach. The fallouts point out that better presentation is gained by the augmented Lagrangian relaxation–the grey wolf optimizer method in terms of net present value, average ore grade, and CPU time. Moreover, the cumulative net present value by the proposed model is 13.39% more than the conventional method.

NMR Intermolecular Dipolar Cross-Relaxation in Nanoconfined Fluids.

Spin relaxation, a defining mechanism of nuclear magnetic resonance (NMR), has been a prime method for determining three-dimensional molecular structures and their dynamics in solution. It also plays key roles for contrast enhancement in magnetic resonance imaging (MRI). In bulk solutions, rapid Brownian molecular diffusion modulates dipolar interactions between a spin pair from different molecules, resulting in very weak intermolecular relaxations. We show that in fluids confined in nanospace or nanopores (nanoconfined fluids) the correlation of dipolar coupling between spin pairs of different molecules is greatly enhanced by the nanopore constraint boundaries on the molecular diffusion, giving rise to an enhanced correlation for the spin pair. As a result, the intermolecular dipolar interaction behaves cooperatively, which leads to a large intermolecular dipolar relaxation rate and opposite in sign to the bulk solution. We found that the classical NMR relaxation theory fails to capture these observations in a nanoconfined fluid environment. Hence, we developed a formal theory and experimentally confirmed that enhanced correlation and cooperated relaxation are ubiquitous in nanoconfined fluids. The newly discovered phenomenon and the developed NMR method reveal new applications in a broad range of synthesized and naturally occurring materials in the field of nanofluidics to study molecular dynamics and structure as well as for MRI image enhancement.

Quantum dynamics and relaxation in comb turbulent diffusion

Continuous time quantum walks in the form of quantum counterparts of turbulent diffusion in comb geometry are considered. The interplay between the backbone inhomogeneous advection $\delta(y)x\partial_x$ along the $x$ axis, which takes place only at the $y=0$, and normal diffusion inside fingers $\partial_y^2$ along the $y$ axis leads to turbulent diffusion. This geometrical constraint of transport coefficients due to comb geometry and properties of a dilatation operator lead to consideration of two possible scenarios of quantum mechanics. These two variants of continuous time quantum walks are described by non-Hermitian operators of the form $\hat{\cal H}=\hat{A}+i\hat{B}$. Operator $\hat{A}$ is responsible for the unitary transformation, while operator $i\hat{B}$ is responsible for quantum/classical relaxation. At the first quantum scenario, the initial wave packet can move against the classical streaming. This quantum swimming upstream is due to the dilatation operator, which is responsible for the quantum (not unitary) dynamics along the backbone, while the classical relaxation takes place in fingers. In the second scenario, the dilatation operator is responsible for the quantum relaxation in the form of an imaginary optical potential, while the quantum unitary dynamics takes place in fingers. Rigorous analytical analysis is performed for both wave and Green's functions.

Anelastic and viscoplastic deformation in a Fe-based metallic glass

The micro-creep behavior of the Fe66Tb5B23Nb6 metallic glass and its anelastic and viscoplastic deformation mechanism were investigated by using nanoindentation. The Maxwell-Voigt model with one or two Kelvin units were utilized to describe three stages of creep deformations at different loading rates and temperatures during the constant load holding process. The creep displacement of the indenter into the Fe66Tb5B23Nb6 sample at a constant load obeys the classic relaxation kinetics at loading rates ranging from 5 to 100 mN s−1. The activation energy for the relaxation process increases with increasing loading rate, which leads to the pronounced relaxation with longer characteristic times under a low-velocity impact mode observed at room temperature. On the other hand, the relaxation process with a short characteristic time plays a dominant role in determining viscoplastic flow and softening behavior at the temperature approaching the glass transition temperature. This work reveals the important role of the anelasticity on the plastic flow of metallic glasses under dynamic loading conditions.

Resistance training as an acute stressor in healthy young men: associations with heart rate variability, alpha-amylase, and cortisol levels

Regular resistance training has been shown to have many physiological and psychological health benefits. However, the underlying physiological processes are not yet fully understood. One explanation is that resistance training acts like an acute stressor and modulates physiological pathways that are associated with the stress response such as the sympathetic nervous system (SNS), the parasympathetic nervous system (PNS), and the hypothalamic-pituitary-adrenal (HPA) axis. This was systematically investigated in our study. Participants were 45 healthy men who had been doing resistance training regularly for at least nine months. Salivary α-amylase and heart rate that were used as markers for SNS activity increased during the training and decreased afterwards. PNS activity that was assessed by means of heart rate variability parameters decreased during the training and increased after it. Salivary cortisol that was used as marker for HPA axis activity decreased throughout the session. Furthermore, an improvement of positive affect was found after the training. However, additional analyses indicated that the physiological response patterns were found for participants who chose upper-body exercises (in contrast to lower-body exercises) only. Therefore, we were able to show that an upper-body resistance training acts partially like an acute stressor which leads to the typical SNS and PNS – but not HPA axis – stress responses. We conclude that resistance trainings might be an alternative to classical relaxation programs which would have the additional advantage that it is a physical training at the same time. However, more research is needed to develop specific trainings which entirely fulfill this goal.

Architecture of a Distributed Process Co‐simulation Framework

AbstractAs part of the Carbon2Chem® joint research project, mathematical models are involved to simulate operating scenarios for cross‐industrial networks. An optimal model‐based system integration approach requires a scalable co‐simulation framework that enables the distributed development of constituent subsystems. By using a classic waveform relaxation algorithm, model suppliers and integrators can exchange co‐simulation units without having to disclose sensitive information and intellectual property. Here, the underlying IT architecture and the basic principles of the introduced “model as a service” approach are described.