A trace on fractal graphs and the Ihara zeta function

Starting with Ihara's work in 1968, there has been a growing interest in the study of zeta functions of finite graphs, by Sunada, Hashimoto, Bass, Stark and Terras, Mizuno and Sato, to name just a few authors. Then, Clair and Mokhtari-Sharghi have studied zeta functions for infinite graphs acted upon by a discrete group of automorphisms. The main formula in all these treatments establishes a connection between the zeta function, originally defined as an infinite product, and the Laplacian of the graph. In this article, we consider a different class of infinite graphs. They are fractal graphs, i.e. they enjoy a self-similarity property. We define a zeta function for these graphs and, using the machinery of operator algebras, we prove a determinant formula, which relates the zeta function with the Laplacian of the graph. We also prove functional equations, and a formula which allows approximation of the zeta function by the zeta functions of finite subgraphs.Comment: 30 pages, 5 figures. v3: minor corrections, to appear on Transactions AM

Ihara zeta functions for periodic simple graphs

The definition and main properties of the Ihara zeta function for graphs are reviewed, focusing mainly on the case of periodic simple graphs. Moreover, we give a new proof of the associated determinant formula, based on the treatment developed by Stark and Terras for finite graphs.Comment: 17 pages, 7 figures. V3: minor correction

Genetical stability and osteogenic ability of mesenchimal stem cells on demineralized bone matrices

Journal of Osseointegration Volume 7, Issue 1, 1 March 2015, Pages 2-7 Open Access Genetical stability and osteogenic ability of mesenchimal stem cells on demineralized bone matrices (Article) Pozzuoli, A.a, Gardin, C.b, Aldegheri, R.a, Bressan, E.c, Isola, M.d, Calvo-Guirado, J.L.e, Biz, C.a, Arrigoni, P.a, Feroni, L.b, Zavan, B.b a Department of Surgical,Oncological and Gastroenterological Sciences, University of Padua, Padua, Italy b Department of Biomedical Sciences, University of Padua, Padua, Italy c Department of Neurosciences, University of Padua, Padua, Italy d Department of Animal Medicine, Production and Health (MAPS), Italy e Department of General Dentistry, Faculty of Medicine and Dentistry, University of Murcia, Murcia, Spain Hide additional affiliations View references (44) Abstract Aim: Tissue engineering is a rapidly expanding field with regard to the use of biomaterials and stem cells in the orthopedic surgery. Many experimental studies have been done to understand the best characteristics of cells, materials and laboratory methods for safe clinical applications. The aim of this study was to compare the ability of 2 different human demineralized bone matrices (DBMs), the one enriched and the other not enriched with hyaluronic acid, to stimulate in vitro the proliferation and the osteogenic differentiation of human adipose-derived stem cells (ADSCs) seeded onto an osteoconductive scaffold. Materials and Methods: ADSCs were isolated, by enzymatic digestion, from abdominal adipose tissue of 5 patients undergoing cosmetic lipoaspiration surgery. ADSCs were then seeded onto a 3D scaffold in the presence of the two different osteoinductive matrices of human demineralized bone and evaluated for proliferation and osteogenic differentiation. The safety of the methods was verified using array-Comparative Genomic Hybridization (array-CGH). Results: ADSCs were able to differentiate in osteogenic sense. Both DBMs showed the ability to induce osteogenic differentiation of the cells. Conclusion: array-CGH showed no changes at genome level, thus confirming the safety of materials and method

Multiview 3D reconstruction in geosciences

Multiview three-dimensional (3D) reconstruction is a technology that allows the creation of 3D models of a given scenario from a series of overlapping pictures taken using consumer-grade digital cameras. This type of 3D reconstruction is facilitated by freely available software, which does not require expert-level skills. This technology provides a 3D working environment, which integrates sample/field data visualization and measurement tools. In this study, we test the potential of this method for 3D reconstruction of decimeter-scale objects of geological interest. We generated 3D models of three different outcrops exposed in a marble quarry and two solids: a volcanic bomb and a stalagmite. Comparison of the models obtained in this study using the presented method with those obtained using a precise laser scanner shows that multiview 3D reconstruction yields models that present a root mean square error/average linear dimensions between 0.11 and 0.68%. Thus this technology turns out to be an extremely promising tool, which can be fruitfully applied in geosciences

A noncommutative Sierpinski gasket

A quantized version of the Sierpinski gasket is proposed, on purely topological grounds, as a C*-algebra A infinity with a suitable form of self-similarity. Several properties of A infinity are studied, in particular its nuclearity, the structure of ideals as well as the description of irreducible representations and extremal traces. A harmonic structure is introduced, giving rise to a self-similar Dirichlet form E. A spectral triple is also constructed, extending the one already known for the classical gasket, from which E can be reconstructed. Moreover we show that A infinity is a compact quantum metric space

Facial Asymmetry Detected with 3D Methods in Orthodontics: A Systematic Review

Background: Historically, the development of two-dimensional (2D) imaging techniques forerun that of three-dimensional (3D) ones. Some 2D methods are still considered valid and effective to diagnose facial asymmetry but 3D techniques may provide more precise and accurate measurements. Objective: The aim of this work is to analyze the accuracy and reliability of the imaging techniques available for the diagnosis of facial asymmetry in orthodontics and find the most reliable. Methods: A search strategy was implemented using PubMed (National Library of Medicine, NCBI). Results: A total of 3201 papers were identified in electronic searches. 90 articles, available in full text, were included in the qualitative synthesis consisting of 8 reviews on the diagnosis of facial asymmetry, 22 in vivo and in vitro studies on 2D methods and 60 in vivo and in vitro studies on 3D methods to quantify the asymmetry. Conclusion: 2D techniques include X-ray techniques such as posterior-anterior cephalogram, which still represents the first level exam in the diagnosis of facial asymmetry. 3D techniques represent the second level exam in the diagnosis of facial asymmetry. The most current used techniques are CBCT, stereophotogrammetry, laser scanning, 3D optical sensors and contact digitization. The comparison between bilateral parameters (linear distances, angles, areas, volumes and contours) and the calculation of an asymmetry index represent the best choices for clinicians who use CBCT. The creation of a color-coded distance map seems to represent the most accurate, reliable and validated methods for clinicians who use stereophotogrammetry, laser scanning and 3D optical sensors

Analysis of the vertices DDVDDV and D∗DVD^*DV with light-cone QCD sum rules

In this article, we study the vertices $DDV$ and $D^*DV$ with the light-cone QCD sum rules. The strong coupling constants $g_{DDV}$ and $f_{D^*DV}$ play an important role in understanding the final-state re-scattering effects in the hadronic B decays. They are related to the basic parameters $\beta$ and $\lambda$ respectively in the heavy quark effective Lagrangian, our numerical values are smaller than the existing estimations.Comment: 16 pages, 6 figures, revised versio