Substitution Delone Sets

This paper addresses the problem of describing aperiodic discrete structures that have a self-similar or self-affine structure. Substitution Delone set families are families of Delone sets (X_1, ..., X_n) in R^d that satisfy an inflation functional equation under the action of an expanding integer matrix in R^d. This paper studies such functional equation in which each X_i is a discrete multiset (a set whose elements are counted with a finite multiplicity). It gives necessary conditions on the coefficients of the functional equation for discrete solutions to exist. It treats the case where the equation has Delone set solutions. Finally, it gives a large set of examples showing limits to the results obtained.Comment: 34 pages, latex file; some results in Sect 5 rearranged and theorems reformulate

Nanoporous silica-based protocells at multiple scales for designs of life and nanomedicine.

Various protocell models have been constructed de novo with the bottom-up approach. Here we describe a silica-based protocell composed of a nanoporous amorphous silica core encapsulated within a lipid bilayer built by self-assembly that provides for independent definition of cell interior and the surface membrane. In this review, we will first describe the essential features of this architecture and then summarize the current development of silica-based protocells at both micro- and nanoscale with diverse functionalities. As the structure of the silica is relatively static, silica-core protocells do not have the ability to change shape, but their interior structure provides a highly crowded and, in some cases, authentic scaffold upon which biomolecular components and systems could be reconstituted. In basic research, the larger protocells based on precise silica replicas of cells could be developed into geometrically realistic bioreactor platforms to enable cellular functions like coupled biochemical reactions, while in translational research smaller protocells based on mesoporous silica nanoparticles are being developed for targeted nanomedicine. Ultimately we see two different motivations for protocell research and development: (1) to emulate life in order to understand it; and (2) to use biomimicry to engineer desired cellular interactions

Evaluating proteasome modulation as a therapeutic strategy in nemaline myopathy

Nemaline myopathy is a subtype of congenital myopathy that is clinically characterized by muscle weakness and early hypotonia of variable severity. Pathologically, nemaline myopathy is characterized by the presence of nemaline rods that stain purple in modified Gӧmӧri trichrome dye in patient biopsies under a microscope. Affected individuals experience skeletal muscle weakness and feeding difficulties, but most individuals will also experience respiratory muscle weakness that is disproportional to the weakness in skeletal muscles. Currently, 6 different subtypes of nemaline myopathy have been identified, each caused by mutations in ACTA1, NEB, TPM2, TPM3, TNNT1, KBTBD13, CFL2, KLHL40, KLHL41, or LMOD3, which are genes that encode either thin filament proteins or Kelch-like proteins. Of these genes, mutations in NEB and ACTA1 account for the majority of nemaline myopathy cases. Due to the genetic heterogeneity of nemaline myopathy, it is imperative to discover therapeutic targets and treatments that can universally treat nemaline myopathy patients. Preliminary data from our lab has demonstrated that proteasome complexes are downregulated in nemaline myopathy patients. Further, proteasomal activators improved motor function in neb zebrafish models, demonstrating the potential for proteasome activators to be therapeutics for nemaline myopathy patients. To extend these studies, the effect of proteasome activators, betulinic acid and Rolipram, was evaluated on the motor function in neb zebrafish models. However, in our experimental trials with betulinic acid and Rolipram, no positive effect on motor function in neb zebrafish was observed. In order to confirm our findings for both betulinic acid and Rolipram, additional trials will need to be conducted.2019-10-31T00:00:00

Measuring and modeling optical diffraction from subwavelength features

We describe a technique for studying scattering from subwavelength features. A simple scatterometer was developed to measure the scattering from the single-submicrometer, subwavelength features generated with a focused ion beam system. A model that can describe diffraction from subwavelength features with arbitrary profiles is also presented and shown to agree quite well with the experimental measurements. The model is used to demonstrate ways in which the aspect ratios of subwavelength ridges and trenches can be obtained from scattering data and how ridges can be distinguished from trenches over a wide range of aspect ratios. We show that some earlier results of studies on distinguishing pits from particles do not extend to low-aspect-ratio features

Self-Affine Tiles in Rn

AbstractAself-affine tilein Rnis a setTof positive measure withA(T)=∪d∈D(T+d), whereAis an expandingn×nreal matrix with |det(A)|=man integer, and D={d, d2, ..., dm}⊆Rnis a set ofmdigits. It is known that self-affine tiles always give tilings of Rnby translation. This paper extends known characterizations of digit sets D yielding self-affine tiles. It proves several results about the structure of tilings of Rnpossible using such tiles, and gives examples showing the possible relations between self-replicating tilings and general tilings, which clarify results of Kenyon on self-replicating tilings

Graph Dynamical Networks for Unsupervised Learning of Atomic Scale Dynamics in Materials

Understanding the dynamical processes that govern the performance of functional materials is essential for the design of next generation materials to tackle global energy and environmental challenges. Many of these processes involve the dynamics of individual atoms or small molecules in condensed phases, e.g. lithium ions in electrolytes, water molecules in membranes, molten atoms at interfaces, etc., which are difficult to understand due to the complexity of local environments. In this work, we develop graph dynamical networks, an unsupervised learning approach for understanding atomic scale dynamics in arbitrary phases and environments from molecular dynamics simulations. We show that important dynamical information can be learned for various multi-component amorphous material systems, which is difficult to obtain otherwise. With the large amounts of molecular dynamics data generated everyday in nearly every aspect of materials design, this approach provides a broadly useful, automated tool to understand atomic scale dynamics in material systems.Comment: 25 + 7 pages, 5 + 3 figure

Guideline update for the performance of fusion procedures for degenerative disease of the lumbar spine. Part 8: Lumbar fusion for disc herniation and radiculopathy

pre-printPatients suffering from a lumbar herniated disc will typically present with signs and symptoms consistent with radiculopathy. They may also have low-back pain, however, and the source of this pain is less certain, as it may be from the degenerative process that led to the herniation. The surgical alternative of choice remains a lumbar discectomy, but fusions have been performed for both primary and recurrent disc herniations. In the original guidelines, the inclusion of a fusion for routine discectomies was not recommended. This recommendation continues to be supported by more recent evidence. Based on low-level evidence, the incorporation of a lumbar fusion may be considered an option when a herniation is associated with evidence of spinal instability, chronic low-back pain, and/or severe degenerative changes, or if the patient participates in heavy manual labor. For recurrent disc herniations, there is low-level evidence to support the inclusion of lumbar fusion for patients with evidence of instability or chronic low-back pain

G protein-coupled receptor kinase-2 (GRK-2) regulates serotonin metabolism through the monoamine oxidase AMX-2 in Caenorhabditis elegans.

G protein-coupled receptors (GPCRs) regulate many animal behaviors. GPCR signaling is mediated by agonist-promoted interactions of GPCRs with heterotrimeric G proteins, GPCR kinases (GRKs), and arrestins. To further elucidate the role of GRKs in regulating GPCR-mediated behaviors, we utilized the genetic model system Caenorhabditis elegans Our studies demonstrate that grk-2 loss-of-function strains are egg laying-defective and contain low levels of serotonin (5-HT) and high levels of the 5-HT metabolite 5-hydroxyindole acetic acid (5-HIAA). The egg laying defect could be rescued by the expression of wild type but not by catalytically inactive grk-2 or by the selective expression of grk-2 in hermaphrodite-specific neurons. The addition of 5-HT or inhibition of 5-HT metabolism also rescued the egg laying defect. Furthermore, we demonstrate that AMX-2 is the primary monoamine oxidase that metabolizes 5-HT in C. elegans, and we also found that grk-2 loss-of-function strains have abnormally high levels of AMX-2 compared with wild-type nematodes. Interestingly, GRK-2 was also found to interact with and promote the phosphorylation of AMX-2. Additional studies reveal that 5-HIAA functions to inhibit egg laying in a manner dependent on the 5-HT receptor SER-1 and the G protein GOA-1. These results demonstrate that GRK-2 modulates 5-HT metabolism by regulating AMX-2 function and that 5-HIAA may function in the SER-1 signaling pathway