Choose n independent random points on the boundary of a convex body K ⊂Rd . The intersection of the supporting halfspaces at these random points is a random convex polyhedron. The expectations of its volume, its surface area and its mean width are investigated. In the case that the boundary of K is sufficiently smooth, asymptotic expansions as n→∞ are derived even in the case when the curvature...

We formulate and exploit a computational inverse-design method based on topology optimization to demonstrate photonic crystal structures supporting complex spectral degeneracies. In particular, we discover photonic crystals exhibiting third-order Dirac points formed by the accidental degeneracy of monopolar, dipolar, and quadrupolar modes. We show that, under suitable conditions, these modes ca...

Collagen VI and WARP are extracellular structural macromolecules present in cartilage and associated with BM suprastructures in non-skeletal tissues. We have previously shown that in WARP-deficient mice, collagen VI is specifically reduced in regions of the peripheral nerve ECM where WARP is expressed, suggesting that both macromolecules are part of the same suprastructure. The object of this s...

This work sought to determine the crosstalk between the Notch and Wnt signaling pathways in regulating supporting cell (SC) proliferation and hair cell (HC) regeneration in mouse utricles. We cultured postnatal day (P)3 and P60 mouse utricles, damaged the HCs with gentamicin, and treated the utricles with the γ-secretase inhibitor DAPT to inhibit the Notch pathway and with the Wnt agonist QS11 ...

Osteoid osteoma (OO) usually occurs in the extremities of young adults. The tumor can arise in any part of the skeletal tissue; however, it is rarely found in the rib, with limited reports to date. In this report, we present a rare case of OO arising in the rib, which was successfully treated under computed tomography guidance with minimal invasiveness. At the final follow-up after 4 years, no ...

In an era of reduced peer-reviewed grant funding, performing academic bone oncology-related research has become increasingly challenging. Over the last 10 years we have held an annual meeting to bring together clinicians, clinician/scientists and basic biomedical researchers interested in the effects of cancer and its treatment on skeletal tissues. In the past these "Bone and the Oncologist New...

Introduction: Fabrication of hybrid skeletal tissue constructs often involves creation of a mineralized component, mimicking bone and the interface between soft tissue and bone. One of the key structural components of the interface to bone, and bone itself, is hydroxyapatite. Hydroxyapatite can be formed rapidly in vitro by controlled reaction of calcium (Ca) and phosphate (PO4) with the use of...

INTRODUCTION The purpose of this investigation was to evaluate craniofacial growth changes from late adolescence through late adulthood in participants from the University of Michigan Elementary and Secondary School Growth Study. METHODS This was a recall study with 39 subjects (19 male, 20 female). Their lateral cephalograms taken during late adolescence (T1; mean age, about 17 years), midad...

Handling data in schools has moved from recording data in repositories, to reporting data to different stakeholders, to decision making using specific types of data. There are clear arguments that decision making functions require access to data, but the research literature indicates that discussion about points and issues is an important pre-requisite. This paper looks at evidence that highlig...

We show that multi-critical points in which more than three phases coalesce are present multiply rotating Kerr-AdS black holes $d$-dimensions. explicitly a quadruple point for triply hole $d=8$ and quintuple quadruply $d=10$. The maximal number of distinct $n$ is one larger the independent rotations, we outline method obtaining associated $n$-tuple point. Situations also exist where merge at su...