Continuous-Time Quantum Walks on Windmill Graphs

Let $A$ be the adjacency matrix of a graph. We will associate this graph with a continuous-time quantum walk by using a transition matrix $U(t) = e^{itA}$. This allows us to create another matrix $\hat{M}$ which is time-independent. $\hat{M}$ gives us some measure of average probability values and long-term behavior of a continuous time quantum walk and is called the average mixing matrix. This has been studied extensively on trees and other graphs with distinct eigenvalues.Our work focuses on graphs which have repeated eigenvalues. We give our own proof for why Star graphs have full rank, and we present an entry-wise recursive way to express the eigenvectors of Path graphs. We utilize this result to prove that the rank of Dutch Windmills with 3 or more $P_m$ blades is $\left\lceil\frac{m}{2}\right\rceil b + 1$. We go on to prove that French Windmills (appending $K_m$ instead) have full rank and that Kulli Cycle Windmills (appending $C_m$ alternate between full rank when $m$ is odd and $\frac{m}{2}b+1$ when $m$ is even.Lastly we present some experimental results for Kulli Path Windmills which appear to mirror the behavior of Dutch Windmills. Separately, we demonstrate that when adding blades of different lengths onto an initially regular Dutch Windmill, it does not always add the rank of the blade sub-matrix as might be expected

Serum and synovial fluid lipidomic profiles predict obesity-associated osteoarthritis, synovitis, and wound repair

High-fat diet-induced obesity is a major risk factor for osteoarthritis (OA) and diminished wound healing. The objective of this study was to determine the associations among serum and synovial fluid lipid levels with OA, synovitis, adipokine levels, and wound healing in a pre-clinical obese mouse model of OA. Male C57BL/6 J mice were fed either a low-fat (10% kcal) or one of three high-fat (HF, 60% kcal) diets rich in saturated fatty acids (SFAs), ω-6 or ω-3 polyunsaturated FAs (PUFAs). OA was induced by destabilization of the medial meniscus. Mice also received an ear punch for evaluating wound healing. Serum and synovial fluid were collected for lipidomic and adipokine analyses. We demonstrated that the serum levels of ω-3 PUFAs were negatively correlated with OA and wound size, but positively correlated with adiponectin levels. In contrast, most ω-6 PUFAs exhibited positive correlations with OA, impaired healing, and inflammatory adipokines. Interestingly, levels of pentadecylic acid (C15:0, an odd-chain SFA) and palmitoleic acid were inversely correlated with joint degradation. This study extends our understanding of the links of FAs with OA, synovitis and wound healing, and reports newly identified serum and synovial fluid FAs as predictive biomarkers of OA in obesity

Determining therapeutic susceptibility in multiple myeloma by single-cell mass accumulation

Multiple myeloma (MM) has benefited from significant advancements in treatment that have improved outcomes and reduced morbidity. However, the disease remains incurable and is characterized by high rates of drug resistance and relapse. Consequently, methods to select the most efficacious therapy are of great interest. Here we utilize a functional assay to assess the ex vivo drug sensitivity of single multiple myeloma cells based on measuring their mass accumulation rate (MAR). We show that MAR accurately and rapidly defines therapeutic susceptibility across human multiple myeloma cell lines to a gamut of standard-of-care therapies. Finally, we demonstrate that our MAR assay, without the need for extended culture ex vivo, correctly defines the response of nine patients to standard-of-care drugs according to their clinical diagnoses. This data highlights the MAR assay in both research and clinical applications as a promising tool for predicting therapeutic response using clinical samples

Fermi surface and quasiparticle dynamics of Na(x)CoO2 {x=0.7} investigated by Angle-Resolved Photoemission Spectroscopy

We present an angle-resolved photoemission study of Na0.7CoO2, the host cobaltate of the NaxCoO2.yH2O series. Our results show a large hexagonal-like hole-type Fermi surface, an extremely narrow strongly renormalized quasiparticle band and a small Fermi velocity. Along the Gamma to M high symmetry line, the quasiparticle band crosses the Fermi level from M toward Gamma consistent with a negative sign of effective single-particle hopping (t ): t is estimated to be about 8 meV which is on the order of exchange coupling J in this system. This suggests that t ~ J ~ 10 meV is an important energy scale in the system. Quasiparticles are well defined only in the T-linear resistivity regime. Small single particle hopping and unconventional quasiparticle dynamics may have implications for understanding the unusual behavior of this new class of compounds.Comment: Revised text, Added Figs, Submitted to PR

Silk‐Based antimicrobial polymers as a new platform to design drug‐free materials to impede microbial infections

Surgical site infections (SSI) represent a serious health problem that occur after invasive surgery, thus new antimicrobial biomaterials able to prevent SSI are needed. Silks are natural biopolymers with excellent biocompatibility, low immunogenicity and controllable biodegradability. Spider silkbased materials can be bioengineered and functionalized with specific peptides, such as antimicrobial peptides, creating innovative polymers. Herein, we explored new drugfree multifunctional silk films with antimicrobial properties, specifically tailored to hamper microbial infections. Different spider silk domains derived from the dragline sequence of the spider Nephila clavipes (6mer and 15mer, 27 and 41 kDa proteins, respectively) were fused with the two antimicrobial peptides, Hepcidin (Hep) and Human Neutrophil peptide 1 (HNP1). The selfassembly features of the spider silk domains (sheets) were maintained after functionalization. The bioengineered 6merHNP1 protein demonstrated inhibitory effects against microbial pathogens. Silkbased films with 6merHNP1 and different contents of silk fibroin (SF) significantly reduced bacterial adhesion and biofilm formation, whereas higher bacterial counts were found on the films prepared with 6mer or SF alone. The silkbased films showed no cytotoxic effects on human foreskin fibroblasts. The positive cellular response, together with structural and antimicrobial properties, highlight the potential of these multifunctional silkbased films as new materials for preventing SSI.The Portuguese Foundation for Science and Technology (FCT) under the project PTDC/BBB-BIO/0827/2012 and by the European Regional Development Fund (FEDER) through the "COMPETE" - Operational Programme for Competitiveness factors (FCOMP-01-0124-FEDER-028120) supported this work. The authors would like to thank Prof. Celia Manaia from the Escola Superior de Biotecnologia (Porto, Portugal) for providing the Pseudomonas sp. bacteria; and Dr. Alberta Faustino from the Hospital de S. Marcos (Braga, Portugal) for providing the other bacterial strains. A. R. Franco thanks FCT through the PostDoctoral scholarship SFRH/BPD/100760/2014.info:eu-repo/semantics/publishedVersio