Quaternion symmetry is ubiquitous in the physical sciences. As such, much work has been afforded over the years to the development of efficient schemes to exploit this symmetry using real and complex linear algebra. Recent years have also seen many advances in the formal theoretical development of explicitly quaternion linear algebra with promising applications in image processing and machine learning. Despite these advances, there do not currently exist optimized software implementations of quaternion linear algebra. The leverage of optimized linear algebra software is crucial in the achievement of high levels of performance on modern computing architectures, and thus provides a central tool in the development of high-performance scientific software. In this work, a case will be made for the efficacy of high-performance quaternion linear algebra software for appropriate problems. In this pursuit, an optimized software implementation of quaternion matrix multiplication will be presented and will be shown to outperform a vendor tuned implementation for the analogous complex matrix operation. The results of this work pave the path for further development of high-performance quaternion linear algebra software which will improve the performance of the next generation of applicable scientific applications.

BACKGROUND: As the elderly population continues to expand, it becomes increasingly important to develop treatments to improve wound healing in the elderly. One problem limiting the research is the lack of appropriate animal models for wound healing in elde

The central importance of large-scale eigenvalue problems in scientific computation necessitates the development of massively parallel algorithms for their solution. Recent advances in dense numerical linear algebra have enabled the routine treatment of eigenvalue problems with dimensions on the order of hundreds of thousands on the world's largest supercomputers. In cases where dense treatments are not feasible, Krylov subspace methods offer an attractive alternative due to the fact that they do not require storage of the problem matrices. However, demonstration of scalability of either of these classes of eigenvalue algorithms on computing architectures capable of expressing massive parallelism is non-trivial due to communication requirements and serial bottlenecks, respectively. In this work, we introduce the SISLICE method: a parallel shift-invert algorithm for the solution of the symmetric self-consistent field (SCF) eigenvalue problem. The SISLICE method drastically reduces the communication requirement of current parallel shift-invert eigenvalue algorithms through various shift selection and migration techniques based on density of states estimation and k-means clustering, respectively. This work demonstrates the robustness and parallel performance of the SISLICE method on a representative set of SCF eigenvalue problems and outlines research directions that will be explored in future work.

Gait is one of the fundamental behaviors we use to interact with the world. The functionality of the locomotor system is thus related to enriching interactions with our environment. The posterior parietal cortex (PPC) has been found to contribute to motor adaptation during both visuomotor and postural adaptation tasks. Additionally, structural or functional deficits of the PPC lead to impairments in gaits such as shortened steps and increased step width. Based on the aforementioned roles of the PPC, and the importance of gait adaptability, the current investigation sought to identify the role of the PPC in gait adaptation. To achieve this, we performed transcranial direct current stimulation (tDCS) over the bilateral PPC before performing a split-belt treadmill gait adaptation paradigm. We used three stimulation conditions in a within-subject design. tDCS was administered in a randomized and double-blinded order. Following each stimulation session, subjects first performed baseline walking with both belts running at the same speed. Then, subjects walked for 15 min on an uncoupled treadmill, with the belts being driven at a 3:1 speed ratio. Last, they returned to normal (i.e., tied-belt) walking for 5 min. Results from 15 young and healthy subjects identified that subjects required more steps to adapt to split-belt walking following the suppression of the left hemisphere PPC, contralateral to the fast belt. Furthermore, while suppression of the left hemisphere PPC did not increase the number of steps required to re-adapt to tied-belt walking, this condition did lead to increased magnitude of after-effects. Together, these findings indicate that the PPC is involved in locomotor adaptation. These results support previous literature regarding the upper body or postural adaptation and extend these findings to the realm of gait. Results highlight the PPC as a potential target for neurorehabilitation designed to improve gait adaptability.

Background

As the elderly population continues to expand, it becomes increasingly important to develop treatments to improve wound healing in the elderly. One problem limiting the research is the lack of appropriate animal models for wound healing in elderly patients. We hypothesized that the Klotho mouse of premature aging is a suitable animal model to shed light on many of the biological processes involved in aging skin.

Methods

Klotho mice (kl/kl), Klotho-heterozygous mice (kl/+), and wild-type mice (+/+) were wounded, and the area of the wound was measured every 3 days until the wound was healed. To compare the klotho phenotype with wild-type mice, wounds were also harvested at 4 and 7 days after wounding. For histological examination, paraffin-embedded sections were stained with hematoxylin and eosin and Masson trichrome. Collagen expression in the wound was also studied by analyzing messenger RNA using real-time polymerase chain reaction.

Results

Klotho mice showed a significantly slower rate of wound closure compared with Klotho-heterozygous mice and wild-type mice. Histology showed substantial less healing and collagen deposition in the wounds of the Klotho mice. The expression of collagen messenger RNA in Klotho mice was also less than that in heterozygous and wild-type mice. The Klotho mice exhibited significant phenotypic similarities with aged skin, such as atrophy and delayed wound healing.

Conclusion

These preliminary data suggest that the Klotho mouse may be a model to further investigate wound healing in the elderly.

When people “fail to deny” unflattering claims, it is commonly taken to imply they are true. Yet, the ‘argument from ignorance’ – arguing in favour of something due to a lack of evidence against it – is often deemed a fallacy. Why is abduction from missing evidence permissible in some cases, but not others? We present a framework of factors which disambiguate these cases, using a Bayesian Network model. We suggest that a source’s silence often reflects a latent conflict between their motives for what they want their audience to believe, and complying with external constraints on their speech, like the need to be accurate. In these cases, silence implies that the source does not believe that what they would like to say is true, which licenses a probabilistic inference that it is false. We present data from two studies suggesting people infer from silence like this.

Effective central sensory integration of visual, vestibular, and proprioceptive information is required to promote adaptability in response to changes in the environment during postural control. Patients with a lesion in the posterior parietal cortex (PPC) have an impaired ability to form an internal representation of body position, an important factor for postural control and adaptation. Suppression of PPC excitability has also been shown to decrease postural stability in some contexts. As of yet, it is unknown whether stimulation of the PPC may influence postural adaptation. This investigation aimed to identify whether transcranial direct current stimulation (tDCS) of the bilateral PPC could modulate postural adaptation in response to a bipedal incline postural adaptation task. Using young, healthy subjects, we delivered tDCS over bilateral PPC followed by bouts of inclined stance (incline-interventions). Analysis of postural after-effects identified differences between stimulation conditions for maximum lean after-effect (LAE; p = 0.005) as well as a significant interaction between condition and measurement period for the average position (p = 0.03). We identified impaired postural adaptability following both active stimulation conditions. Results reinforce the notion that the PPC is involved in motor adaptation and extend this line of research to the realm of standing posture. The results further highlight the role of the bilateral PPC in utilizing sensory feedback to update one's internal representation of verticality and demonstrates the diffuse regions of the brain that are involved in postural control and adaptation. This information improves our understanding of the role of the cortex in postural control, highlighting the potential for the PPC as a target for sensorimotor rehabilitation.

We present a method to compute the many-body real-time Green's function using an adaptive variational quantum dynamics simulation approach. The real-time Green's function involves the time evolution of a quantum state with one additional electron with respect to the ground state wave function that is first expressed as a linear-linear combination of state vectors. The real-time evolution and the Green's function are obtained by combining the dynamics of the individual state vectors in a linear combination. The use of the adaptive protocol enables us to generate compact ansatzes on-the-fly while running the simulation. In order to improve the convergence of spectral features, Padé approximants are applied to obtain the Fourier transform of the Green's function. We demonstrate the evaluation of the Green's function on an IBM Q quantum computer. As a part of our error mitigation strategy, we develop a resolution-enhancing method that we successfully apply on the noisy data from the real-quantum hardware.

With a growing demand for time-domain simulations of correlated many-body systems, the development of efficient and stable integration schemes for the time-dependent Schrödinger equation is of keen interest in modern electronic structure theory. In this work, we present two approaches for the formation of the quantum propagator for time-dependent equation-of-motion coupled cluster theory based on the Chebyshev and Arnoldi expansions of the complex, nonhermitian matrix exponential, respectively. The proposed algorithms are compared with the short-iterative Lanczos method of Cooper et al. [J. Phys. Chem. A 2021 125, 5438-5447], the fourth-order Runge-Kutta method, and exact dynamics for a set of small but challenging test problems. For each of the cases studied, both of the proposed integration schemes demonstrate superior accuracy and efficiency relative to the reference simulations.