Weighted Tree-Numbers of Matroid Complexes

International audienceWe give a new formula for the weighted high-dimensional tree-numbers of matroid complexes. This formula is derived from our result that the spectra of the weighted combinatorial Laplacians of matroid complexes consist of polynomials in the weights. In the formula, Crapo’s $\beta$-invariant appears as the key factor relating weighted combinatorial Laplacians and weighted tree-numbers for matroid complexes.Nous présentons une nouvelle formule pour les nombres d’arbres pondérés de grande dimension des matroïdes complexes. Cette formule est dérivée du résultat que le spectre des Laplaciens combinatoires pondérés des matrides complexes sont des polynômes à plusieurs variables. Dans la formule, le $\beta$;-invariant de Crapo apparaît comme étant le facteur clé reliant les Laplaciens combinatoires pondérés et les nombres d’arbres pondérés des matroïdes complexes

A weighted cellular matrix-tree theorem, with applications to complete colorful and cubical complexes

We present a version of the weighted cellular matrix-tree theorem that is suitable for calculating explicit generating functions for spanning trees of highly structured families of simplicial and cell complexes. We apply the result to give weighted generalizations of the tree enumeration formulas of Adin for complete colorful complexes, and of Duval, Klivans and Martin for skeleta of hypercubes. We investigate the latter further via a logarithmic generating function for weighted tree enumeration, and derive another tree-counting formula using the unsigned Euler characteristics of skeleta of a hypercube and the Crapo $\beta$-invariant of uniform matroids.Comment: 22 pages, 2 figures. Sections 6 and 7 of previous version simplified and condensed. Final version to appear in J. Combin. Theory Ser.

The Injectable rhBMP-2-containing Collagen Gel for Tendon Healing in a Rabbit Extra-Articular Bone Tunnel Model

This rabbit animal study has a hypothesis that the collagen gel, which is injectable easily, can be an effective carrier for recombinant human bone morphogenetic protein 2 (rhBMP-2) for the tendon healing in a bone tunnel. The cut upper long digital extensor tendon of each rabbit was inserted into the proximal tibia bone tunnel, and rhBMP-2 conjugated collagen gel was injected into the tendon-bone tunnel interface using a syringe. Biomechanical and histological performances were analyzed at 3 and 6 weeks after surgery. The collagen sol at room temperature was transformed to a gel at 37°C. The rhBMP-2 was slowly released from the collagen gel for more than 4 weeks. The in vivo experiment showed the enhanced new fibrocartilage and bone tissue formation at 6 weeks after injecting the rhBMP-2-containing collagen gel. The calcification and enthesis-like tissue were detected radiologically in the repaired tendon-bone junction. The viscous collagen gel-containing rhBMP-2 increased the fusion rate of the repaired tendon in the bone tunnel. This study showed that viscous collagen gel can be an effective carrier for rhBMP-2 for tendon healing in the bone tunnel. The rhBMP-2-containing collagen gel will be promising for tendon-bone interface healing in the future

rhBMP-2-Coated Acellular Dermal Graft for Chronic Rotator Cuff Healing: Translational Tendon Repair Research

A rotator cuff tear is a common shoulder injury in sports medicine. However, a rotator cuff repair still has the high failure rate (57%) in large torn (>8 cm2) rotator cuff cases. One of the main reasons is failing at suture-tendon cause of continuous tensional and torsional stresses even after surgery, and thus, an ideal biologic augmentation to overcome large tears is an essential challenge. The ECM graft, the biological material can be useful for augment repair of large torn rotator cuff. Recombinant human bone morphogenetic protein 2 (rhBMP-2), which belongs to transforming growth factor-β superfamily, is well known as an osteoinductive growth factor. It plays an important role in the development of bone and cartilage. rhBMP-2 also facilitates chemotaxis in the host tissue. In this study, rhBMP-2-coated acellular dermal graft, which is isolated from human cadaveric donor, was transplanted in the rabbit with the chronic rotator cuff injury. The radiologic image, histomorphometric, histologic image analyses, and tensile test were performed to evaluate the effectiveness. The results showed the enhancement of increased host cell infiltration, new bone formation, and tensile mechanical property. The rhBMP-2-coated acellular dermal graft will be promising for chronic rotator cuff healing

Design principles for transforming making programs into online settings at public libraries

Purpose This paper aims to investigate design principles for transforming existing making communities of practice within public libraries into online knowledge-building communities to support youths, families with young children and adult members’ making and tinkering during COVID-19. Design/methodology/approach Building upon C4P and connected learning framework, the authors analyze existing literature and practitioner reports on informal learning projects related to making and STEM learning, family learning and online learning as well as emergent cases of innovative approaches in response to COVID-19 from public libraries, informal learning institutions and community groups. Findings The authors suggest 11 design principles around five areas: program design, facilitation, tools and materials, process documentation and sharing and feedback. Originality/value This work contributes to the information and learning sciences concerned with community engagement and knowledge creation by suggesting a design model to transform and sustain existing making communities of practice within public libraries into online knowledge-building communities during COVID-19

Weighted Tree-Numbers of Matroid Complexes

We give a new formula for the weighted high-dimensional tree-numbers of matroid complexes. This formula is derived from our result that the spectra of the weighted combinatorial Laplacians of matroid complexes consist of polynomials in the weights. In the formula, Crapo’s $\beta$-invariant appears as the key factor relating weighted combinatorial Laplacians and weighted tree-numbers for matroid complexes

Simplicial effective resistance and enumeration of spanning trees

A graph can be regarded as an electrical network in which each edge is a resistor. This point of view relates combinatorial quantities, such as the number of spanning trees, to electrical ones such as effective resistance. The second and third authors have extended the combinatorics/electricity analogy to higher dimension and expressed the simplicial analogue of effective resistance as a ratio of weighted tree enumerators. In this paper, we first use that ratio to prove a new enumeration formula for color-shifted complexes, confirming a conjecture by Aalipour and the first author, and generalizing a result of Ehrenborg and van Willigenburg on Ferrers graphs. We then use the same technique to recover an enumeration formula for shifted complexes, first proved by Klivans and the first and fourth authors. In each case, we add facets one at a time, and give explicit expressions for simplicial effective resistances of added facets by constructing high-dimensional analogues of currents and voltages (respectively homological cycles and cohomological cocycles).Comment: 27 pages, minor revisions from v

CIB1 protects against MPTP-induced neurotoxicity through inhibiting ASK1.

Calcium and integrin binding protein 1 (CIB1) is a calcium-binding protein that was initially identified as a binding partner of platelet integrin αIIb. Although CIB1 has been shown to interact with multiple proteins, its biological function in the brain remains unclear. Here, we show that CIB1 negatively regulates degeneration of dopaminergic neurons in a mouse model of Parkinson\u27s disease using 1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine (MPTP). Genetic deficiency of the CIB1 gene enhances MPTP-induced neurotoxicity in dopaminergic neurons in CIB1(-/-) mice. Furthermore, RNAi-mediated depletion of CIB1 in primary dopaminergic neurons potentiated 1-methyl-4-phenyl pyrinidium (MPP(+))-induced neuronal death. CIB1 physically associated with apoptosis signal-regulating kinase 1 (ASK1) and thereby inhibited the MPP(+)-induced stimulation of the ASK1-mediated signaling cascade. These findings suggest that CIB1 plays a protective role in MPTP/MPP(+)-induced neurotoxicity by blocking ASK1-mediated signaling