Efficient time-dependent vibrational coupled cluster computations with time-dependent basis sets at the two-mode coupling level: Full and hybrid TDMVCC[2].

The computation of the nuclear quantum dynamics of molecules is challenging, requiring both accuracy and efficiency to be applicable to systems of interest. Recently, theories have been developed for employing time-dependent basis functions (denoted modals) with vibrational coupled cluster theory (TDMVCC). The TDMVCC method was introduced along with a pilot implementation, which illustrated good accuracy in benchmark computations.

The influence of exercise on clinical pain and pain mechanisms in patients with subacromial pain syndrome.

Background: Few studies have investigated the underlying mechanisms for unilateral subacromial pain syndrome (SAPS). Therefore, this study examined (1) if 8-weeks of exercise could modulate clinical pain or temporal summation of pain (TSP), conditioned pain modulation (CPM), and exercise-induced hypoalgesia (EIH) and (2) if any of these parameters could predict the effect of 8-weeks of exercise in patients with unilateral SAPS.

Methods: Thirty-seven patients completed a progressive abduction exercise program every other day for 8-weeks.

Sortilin Modulates Schwann Cell Signaling and Remak Bundle Regeneration Following Nerve Injury.

Peripheral nerve regeneration relies on the ability of Schwann cells to support the regrowth of damaged axons. Schwann cells re-differentiate when reestablishing contact with the sprouting axons, with large fibers becoming remyelinated and small nociceptive fibers ensheathed and collected into Remak bundles. We have previously described how the receptor sortilin facilitates neurotrophin signaling in peripheral neurons regulated trafficking of Trk receptors.

Calculating vibrational excitation energies using tensor-decomposed vibrational coupled-cluster response theory.

The first implementation of tensor-decomposed vibrational coupled cluster (CP-VCC) response theory for calculating vibrational excitation energies is presented. The CP-VCC algorithm, which has previously been applied to solving the vibrational coupled cluster (VCC) ground-state equations without explicitly constructing any tensors of order three or higher, has been generalized to allow transformations with the Jacobian matrix necessary for computation of response excitation energies by iterative algorithms. A new eigenvalue solver for computing CP-VCC excitation energies is introduced, and the different numerical thresholds used for controlling the accuracy of the obtained eigenvalues are discussed.

A general implementation of time-dependent vibrational coupled-cluster theory.

The first general excitation level implementation of the time-dependent vibrational coupled cluster (TDVCC) method introduced in a recent publication [J. Chem. Phys.

Time-dependent vibrational coupled cluster with variationally optimized time-dependent basis sets.

We develop time-dependent vibrational coupled cluster with time-dependent modals (TDMVCC), where an active set of one-mode basis functions (modals) is evolved in time alongside coupled-cluster wave-function parameters. A biorthogonal second quantization formulation of many-mode dynamics is introduced, allowing separate biorthogonal bases for the bra and ket states, thus ensuring complex analyticity. We employ the time-dependent bivariational principle to derive equations of motion for both the one-mode basis functions and the parameters describing the cluster (T) and linear de-excitation (L) operators.

Extended vibrational coupled cluster: Stationary states and dynamics.

For the first time, equations are derived for computing stationary vibrational states with extended vibrational coupled cluster (EVCC) and for propagating nuclear wave packets using time-dependent EVCC (TDEVCC). Expressions for energies, properties, and auto-correlation functions are given. For TDEVCC, convergence toward the ground state for imaginary-time propagation is shown, as well as separability in the case of non-interacting subsystems.

MR-MCTDH[]: Flexible Configuration Spaces and Nonadiabatic Dynamics within the MCTDH[] Framework.

Solving the time-dependent Schrödinger equation (TDSE) for large molecular systems is a complicated task due to the inherent exponential scaling of the problem. One of the most successful and versatile methods for obtaining numerically converged solutions for small to medium-sized systems is multiconfiguration time-dependent Hartree (MCTDH). In a recent publication [ , , 084101] we introduced a hierarchy of approximations to the MCTDH method which mitigate the exponential scaling by truncating the configuration space based on a maximum excitation level w.

Development of an individualized asynchronous sensor-based telerehabilitation program for patients undergoing total knee replacement: Participatory design.

Telerehabilitation programs can be employed to establish communication between patients and healthcare professionals and empower patients performing their training remotely. This study aimed to identify patients' requirements after a total knee replacement following a self-training rehabilitation program, leading to the design and development of a telerehabilitation program that can meet the stakeholders' actual needs. System design, development, and testing were conducted in five iterations based on a participatory design approach.

Systematic and variational truncation of the configuration space in the multiconfiguration time-dependent Hartree method: The MCTDH[n] hierarchy.

The multiconfiguration time-dependent Hartree (MCTDH) method is a powerful method for solving the time-dependent Schrödinger equation in quantum molecular dynamics. It is, however, hampered by the so-called curse of dimensionality which results in exponential scaling with respect to the number of degrees of freedom in the system and, thus, limits its applicability to small- and medium-sized molecules. To avoid this scaling, we derive equations of motion for a series of truncated MCTDH methods using a many-mode second-quantization formulation where the configuration space is restricted based on mode-combination levels as also done in the vibrational configuration interaction and vibrational coupled cluster methods for solving the time-independent Schrödinger equation.

Time-dependent vibrational coupled cluster theory: Theory and implementation at the two-mode coupling level.

Equations are derived for the time evolution of time-dependent vibrational coupled cluster (TDVCC) wave functions covering both the TDVCC ket state and the associated so-called Λ bra state. The equations are implemented in the special case of both the Hamiltonian and the cluster operator containing at most two-mode coupling terms. The nontrivial behavior of the evolution of norm, energy, and expectation values due to the nonunitary time-evolution of the nonvariational TDVCC theory is analyzed theoretically and confirmed in numerical experiments that also include time-dependent Hamiltonians.

Developing a telerehabilitation programme for postoperative recovery from knee surgery: specifications and requirements.

Introduction: Telerehabilitation programmes have been attracting increasing attention as a potential alternative to conventional rehabilitation. Video conferencing can facilitate communication between healthcare professionals and patients. However, in certain cases, video conferencing may face practical limitations.

Exponential parameterization of wave functions for quantum dynamics: Time-dependent Hartree in second quantization.

We derive equations for describing the time evolution of variational wave functions in linear and exponential parameterization with a second-quantization (SQ) formulation. The SQ formalism covers time-dependent Hartree (TDH), while exact states and approximate vibrational configuration interaction wave functions are described using state-transfer operators. We present detailed expressions for efficient evaluation of TDH in linear (L-TDH) and exponential (X-TDH) parametrization and an efficient implementation supporting linear scaling with respect to the number of degrees of freedom when the Hamiltonian operator contains a constant number of terms per mode independently of the size of the system.

Tensor-decomposed vibrational coupled-cluster theory: Enabling large-scale, highly accurate vibrational-structure calculations.

A new implementation of vibrational coupled-cluster (VCC) theory is presented, where all amplitude tensors are represented in the canonical polyadic (CP) format. The CP-VCC algorithm solves the non-linear VCC equations without ever constructing the amplitudes or error vectors in full dimension but still formally includes the full parameter space of the VCC[n] model in question resulting in the same vibrational energies as the conventional method. In a previous publication, we have described the non-linear-equation solver for CP-VCC calculations.

Atomic-batched tensor decomposed two-electron repulsion integrals.

We present a new integral format for 4-index electron repulsion integrals, in which several strategies like the Resolution-of-the-Identity (RI) approximation and other more general tensor-decomposition techniques are combined with an atomic batching scheme. The 3-index RI integral tensor is divided into sub-tensors defined by atom pairs on which we perform an accelerated decomposition to the canonical product (CP) format. In a first step, the RI integrals are decomposed to a high-rank CP-like format by repeated singular value decompositions followed by a rank reduction, which uses a Tucker decomposition as an intermediate step to lower the prefactor of the algorithm.

Efficient algorithms for solving the non-linear vibrational coupled-cluster equations using full and decomposed tensors.

Vibrational coupled-cluster (VCC) theory provides an accurate method for calculating vibrational spectra and properties of small to medium-sized molecules. Obtaining these properties requires the solution of the non-linear VCC equations which can in some cases be hard to converge depending on the molecule, the basis set, and the vibrational state in question. We present and compare a range of different algorithms for solving the VCC equations ranging from a full Newton-Raphson method to approximate quasi-Newton models using an array of different convergence-acceleration schemes.

Comparison between Mother, ActiGraph wGT3X-BT, and a hand tally for measuring steps at various walking speeds under controlled conditions.

Introduction: Walking is endorsed as health enhancing and is the most common type of physical activity among older adults. Accelerometers are superior to self-reports when measuring steps, however, if they are to be used by clinicians the validity is of great importance. The aim of this study was to investigate the criterion validity of Mother and ActiGraph wGT3X-BT in measuring steps by comparing the devices to a hand tally under controlled conditions in healthy participants.