A subalgebra of the Hardy algebra relevant in control theory and its algebraic-analytic properties

We denote by A_0+AP_+ the Banach algebra of all complex-valued functions f defined in the closed right half plane, such that f is the sum of a holomorphic function vanishing at infinity and a ``causal'' almost periodic function. We give a complete description of the maximum ideal space M(A_0+AP_+) of A_0+AP_+. Using this description, we also establish the following results: (1) The corona theorem for A_0+AP_+. (2) M(A_0+AP_+) is contractible (which implies that A_0+AP_+ is a projective free ring). (3) A_0+AP_+ is not a GCD domain. (4) A_0+AP_+ is not a pre-Bezout domain. (5) A_0+AP_+ is not a coherent ring. The study of the above algebraic-anlaytic properties is motivated by applications in the frequency domain approach to linear control theory, where they play an important role in the stabilization problem.Comment: 17 page

Stochastic modeling of discontinuous dynamic recrystallization at finite strains in hcp metals

We present a model that aims to describe the effective, macroscale material response as well as the underlying mesoscale processes during discontinuous dynamic recrystallization under severe plastic deformation. Broadly, the model brings together two well-established but distinct approaches – first, a continuum crystal plasticity and twinning approach to describe complex deformation in the various grains, and second, a discrete Monte-Carlo-Potts approach to describe grain boundary migration and nucleation. The model is implemented within a finite-strain Fast Fourier Transform-based framework that allows for efficient simulations of recrystallization at high spatial resolution, while the grid-based Fourier treatment lends itself naturally to the Monte-Carlo approach. The model is applied to pure magnesium as a representative hexagonal closed packed metal, but is sufficiently general to admit extension to other material systems. Results demonstrate the evolution of the grain architecture in representative volume elements and the associated stress–strain history during the severe simple shear deformation typical of equal channel angular extrusion. We confirm that the recrystallization kinetics converge with increasing grid resolution and that the resulting model captures the experimentally observed transition from single- to multi-peak stress–strain behavior as a function of temperature and rate

A Calibrated Method of Massage Therapy Decreases Systolic Blood Pressure Concomitant With Changes in Heart Rate Variability in Male Rats.

ObjectiveThe purpose of this study was to develop a method for applying calibrated manual massage pressures by using commonly available, inexpensive sphygmomanometer parts and validate the use of this approach as a quantitative method of applying massage therapy to rodents.MethodsMassage pressures were monitored by using a modified neonatal blood pressure (BP) cuff attached to an aneroid gauge. Lightly anesthetized rats were stroked on the ventral abdomen for 5 minutes at pressures of 20 mm Hg and 40 mm Hg. Blood pressure was monitored noninvasively for 20 minutes following massage therapy at 5-minute intervals. Interexaminer reliability was assessed by applying 20 mm Hg and 40 mm Hg pressures to a digital scale in the presence or absence of the pressure gauge.ResultsWith the use of this method, we observed good interexaminer reliability, with intraclass coefficients of 0.989 versus 0.624 in blinded controls. In Long-Evans rats, systolic BP dropped by an average of 9.86% ± 0.27% following application of 40 mm Hg massage pressure. Similar effects were seen following 20 mm Hg pressure (6.52% ± 1.7%), although latency to effect was greater than at 40 mm Hg. Sprague-Dawley rats behaved similarly to Long-Evans rats. Low-frequency/high-frequency ratio, a widely-used index of autonomic tone in cardiovascular regulation, showed a significant increase within 5 minutes after 40 mm Hg massage pressure was applied.ConclusionsThe calibrated massage method was shown to be a reproducible method for applying massage pressures in rodents and lowering BP

Extreme mechanical resilience of self-assembled nanolabyrinthine materials

Low-density materials with tailorable properties have attracted attention for decades, yet stiff materials that can resiliently tolerate extreme forces and deformation while being manufactured at large scales have remained a rare find. Designs inspired by nature, such as hierarchical composites and atomic lattice-mimicking architectures, have achieved optimal combinations of mechanical properties but suffer from limited mechanical tunability, limited long-term stability, and low-throughput volumes that stem from limitations in additive manufacturing techniques. Based on natural self-assembly of polymeric emulsions via spinodal decomposition, here we demonstrate a concept for the scalable fabrication of nonperiodic, shell-based ceramic materials with ultralow densities, possessing features on the order of tens of nanometers and sample volumes on the order of cubic centimeters. Guided by simulations of separation processes, we numerically show that the curvature of self-assembled shells can produce close to optimal stiffness scaling with density, and we experimentally demonstrate that a carefully chosen combination of topology, geometry, and base material results in superior mechanical resilience in the architected product. Our approach provides a pathway to harnessing self-assembly methods in the design and scalable fabrication of beyond-periodic and nonbeam-based nano-architected materials with simultaneous directional tunability, high stiffness, and unsurpassed recoverability with marginal deterioration

Stability, Gain, and Robustness in Quantum Feedback Networks

This paper concerns the problem of stability for quantum feedback networks. We demonstrate in the context of quantum optics how stability of quantum feedback networks can be guaranteed using only simple gain inequalities for network components and algebraic relationships determined by the network. Quantum feedback networks are shown to be stable if the loop gain is less than one-this is an extension of the famous small gain theorem of classical control theory. We illustrate the simplicity and power of the small gain approach with applications to important problems of robust stability and robust stabilization.Comment: 16 page

Synchronization of Coupled Nonidentical Genetic Oscillators

The study on the collective dynamics of synchronization among genetic oscillators is essential for the understanding of the rhythmic phenomena of living organisms at both molecular and cellular levels. Genetic oscillators are biochemical networks, which can generally be modelled as nonlinear dynamic systems. We show in this paper that many genetic oscillators can be transformed into Lur'e form by exploiting the special structure of biological systems. By using control theory approach, we provide a theoretical method for analyzing the synchronization of coupled nonidentical genetic oscillators. Sufficient conditions for the synchronization as well as the estimation of the bound of the synchronization error are also obtained. To demonstrate the effectiveness of our theoretical results, a population of genetic oscillators based on the Goodwin model are adopted as numerical examples.Comment: 16 pages, 3 figure

Analyzing the effects of surface distribution of pores in cell electroporation for a cell membrane containing cholesterol

This paper presents a model and numerical analysis (simulations) of transmembrane potential induced in biological cell membrane under the influence of externally applied electric field (i.e., electroporation). This model differs from the established models of electroporation in two distinct ways. Firstly, it incorporates the presence of cholesterol (~20% mole-fraction) in biological membrane. Secondly, it considers the distribution of pores as a function of the variation of transmembrane potential from one region of the cell to another. Formulation is based on the role of membrane tension and electrical forces in the formation of pores in a cell membrane, which is considered as an infinitesimally thin insulator. The model has been used to explore the process of creation and evolution of pores and to determine the number and size of pores as a function of applied electric field (magnitude and duration). Results show that the presence of cholesterol enhances poration by changing the membrane tension. Analyses indicate that the number of pores and average pore radii differ significantly from one part of the cell to the other. While some regions of the cell membrane undergo rapid and dense poration, others remain unaffected. The method can be a useful tool for a more realistic prediction of pore formation in cells subjected to electroporation.Comment: 11 pages, 3 figures. v2: added new references, grammatical changes, corrected typo

Comparison of the Efficacy of Caudal, Interlaminar, and Transforaminal Epidural Injections in Managing Lumbar Disc Herniation: Is One Method Superior to the Other?

Background: Epidural injections are performed utilizing 3 approaches in the lumbar spine: caudal, interlaminar, and transforaminal. The literature on the efficacy of epidural injections has been sporadic. There are few high-quality randomized trials performed under fluoroscopy in managing disc herniation that have a long-term follow-up and appropriate outcome parameters. There is also a lack of literature comparing the efficacy of these 3 approaches. Methods: This manuscript analyzes data from 3 randomized controlled trials that assessed a total of 360 patients with lumbar disc herniation. There were 120 patients per trial either receiving local anesthetic alone (60 patients) or local anesthetic with steroids (60 patients). Results: Analysis showed similar efficacy for caudal, interlaminar, and transforaminal approaches in managing chronic pain and disability from disc herniation. The analysis of caudal epidural injections showed the potential superiority of steroids compared with local anesthetic alone a 2-year follow-up, based on the average relief per procedure. In the interlaminar group, results were somewhat superior for pain relief in the steroid group at 6 months and functional status at 12 months. Interlaminar epidurals provided improvement in a significantly higher proportion of patients. The proportion of patients nonresponsive to initial injections was also lower in the group for local anesthetic with steroid in the interlaminar trial. Conclusions: The results of this assessment show significant improvement in patients suffering from chronic lumbar disc herniation with 3 lumbar epidural approaches with local anesthetic alone, or using steroids with long-term follow-up of up to 2 years, in a contemporary interventional pain management setting