The Randic index and the diameter of graphs

The {\it Randi\'c index} $R(G)$ of a graph $G$ is defined as the sum of 1/\sqrt{d_ud_v} over all edges $uv$ of $G$, where $d_u$ and $d_v$ are the degrees of vertices $u$ and $v,$ respectively. Let $D(G)$ be the diameter of $G$ when $G$ is connected. Aouchiche-Hansen-Zheng conjectured that among all connected graphs $G$ on $n$ vertices the path $P_n$ achieves the minimum values for both $R(G)/D(G)$ and $R(G)- D(G)$. We prove this conjecture completely. In fact, we prove a stronger theorem: If $G$ is a connected graph, then $R(G)-(1/2)D(G)\geq \sqrt{2}-1$, with equality if and only if $G$ is a path with at least three vertices.Comment: 17 pages, accepted by Discrete Mathematic

Characterization of shape and dimensional accuracy of incrementally formed titanium sheet parts with intermediate curvatures between two feature types

Single point incremental forming (SPIF) is a relatively new manufacturing process that has been recently used to form medical grade titanium sheets for implant devices. However, one limitation of the SPIF process may be characterized by dimensional inaccuracies of the final part as compared with the original designed part model. Elimination of these inaccuracies is critical to forming medical implants to meet required tolerances. Prior work on accuracy characterization has shown that feature behavior is important in predicting accuracy. In this study, a set of basic geometric shapes consisting of ruled and freeform features were formed using SPIF to characterize the dimensional inaccuracies of grade 1 titanium sheet parts. Response surface functions using multivariate adaptive regression splines (MARS) are then generated to model the deviations at individual vertices of the STL model of the part as a function of geometric shape parameters such as curvature, depth, distance to feature borders, wall angle, etc. The generated response functions are further used to predict dimensional deviations in a specific clinical implant case where the curvatures in the part lie between that of ruled features and freeform features. It is shown that a mixed-MARS response surface model using a weighted average of the ruled and freeform surface models can be used for such a case to improve the mean prediction accuracy within ±0.5 mm. The predicted deviations show a reasonable match with the actual formed shape for the implant case and are used to generate optimized tool paths for minimized shape and dimensional inaccuracy. Further, an implant part is then made using the accuracy characterization functions for improved accuracy. The results show an improvement in shape and dimensional accuracy of incrementally formed titanium medical implants

Hydrated electron generation by excitation of copper localized surface plasmon resonance

Hydrated electrons are important in radiation chemistry and chargetransfer reactions, with applications that include chemical damage of DNA, catalysis, and signaling. Conventionally, hydrated electrons are produced by pulsed radiolysis, sonolysis, two-ultraviolet-photon laser excitation of liquid water, or photodetachment of suitable electron donors. Here we report a method for the generation of hydrated electrons via single-visible-photon excitation of localized surface plasmon resonances (LSPRs) of supported sub-3 nm copper nanoparticles in contact with water. Only excitations at the LSPR maximum resulted in the formation of hydrated electrons, suggesting that plasmon excitation plays a crucial role in promoting electron transfer from the nanoparticle into the solution. The reactivity of the hydrated electrons was confirmed via proton reduction and concomitant H2 evolution in the presence of a Ru/ TiO2 catalyst

Midday measurements of leaf water potential and stomatal conductance are highly correlated with daily water use of Thompson Seedless grapevines

A study was conducted to determine the relationship between midday measurements of vine water status and daily water use of grapevines measured with a weighing lysimeter. Water applications to the vines were terminated on August 24th for 9 days and again on September 14th for 22 days. Daily water use of the vines in the lysimeter (ETLYS) was approximately 40 L vine−1 (5.3 mm) prior to turning the pump off, and it decreased to 22.3 L vine−1 by September 2nd. Pre-dawn leaf water potential (ΨPD) and midday Ψl on August 24th were −0.075 and −0.76 MPa, respectively, with midday Ψl decreasing to −1.28 MPa on September 2nd. Leaf g s decreased from ~500 to ~200 mmol m−2 s−1 during the two dry-down periods. Midday measurements of g s and Ψl were significantly correlated with one another (r = 0.96) and both with ETLYS/ETo (r = ~0.9). The decreases in Ψl, g s, and ETLYS/ETo in this study were also a linear function of the decrease in volumetric soil water content. The results indicate that even modest water stress can greatly reduce grapevine water use and that short-term measures of vine water status taken at midday are a reflection of daily grapevine water us

Numerical modelling of the rise of Taylor bubbles through a change in pipe diameter

The rise of Taylor bubbles through expansions in vertical pipes is modelled using Computational Fluid Dynamics. The predictions from the models are compared against existing experimental work and show good agreement, both quantitatively and qualitatively. Many workers, including the present work, find that, as the bubble passes through the expansion, it will either remain intact or split into one or more daughter bubbles. We find that the critical length of bubble, defined as the maximum length that will pass through intact, is proportional to the cosecant of the angle of the expansion. Further, we show that for an abrupt expansion, the critical bubble length became unaffected by the walls of the upper pipe as the diameter was increased

Assessing the utility of geospatial technologies to investigate environmental change within lake systems

Over 50% of the world's population live within 3. km of rivers and lakes highlighting the on-going importance of freshwater resources to human health and societal well-being. Whilst covering c. 3.5% of the Earth's non-glaciated land mass, trends in the environmental quality of the world's standing waters (natural lakes and reservoirs) are poorly understood, at least in comparison with rivers, and so evaluation of their current condition and sensitivity to change are global priorities. Here it is argued that a geospatial approach harnessing existing global datasets, along with new generation remote sensing products, offers the basis to characterise trajectories of change in lake properties e.g., water quality, physical structure, hydrological regime and ecological behaviour. This approach furthermore provides the evidence base to understand the relative importance of climatic forcing and/or changing catchment processes, e.g. land cover and soil moisture data, which coupled with climate data provide the basis to model regional water balance and runoff estimates over time. Using examples derived primarily from the Danube Basin but also other parts of the World, we demonstrate the power of the approach and its utility to assess the sensitivity of lake systems to environmental change, and hence better manage these key resources in the future

The GLP-1 Receptor Agonist Exenatide Ameliorates Bone Composition and Tissue Material Properties in High Fat Fed Diabetic Mice

Type 2 diabetes mellitus (T2DM) has recently been recognized as a significant risk factor for bone fragility. Careful investigations of bone mechanical properties in human studies suggested possible alterations of bone composition, although this axis has poorly been investigated. The main aim of this study was to evaluate the impact of high fat diet-induced diabetes and therapy using the clinically approved GLP-1 receptor agonist, exenatide, on tissue bone mechanical properties and compositional parameters. Male mice had free access to high fat diet for 16 weeks to induce diabetes prior to commencement of the study. Exenatide was administered twice daily by i.p. injection at a dose of 25 nmol/kg for 52 days. Normal and high fat diet fed (HFD) mice injected with saline were used as controls. Bone mechanical properties was assessed at the organ level by 3-point bending and at the tissue level by nanoindentation. Bone microarchitecture was investigated by microcomputed tomography and bone composition was evaluated by Fourier transform infrared imaging. HFD mice exhibited profound alterations of bone mechanical properties at both the organ and tissue level. Collagen maturity as well as trabecular and cortical bone microarchitectures were abnormal. Administration of exenatide, led to clear ameliorations in bone mechanical properties at the organ and tissue levels by modifications of both cortical microarchitecture and bone compositional parameters (collagen maturity, mineral crystallinity, carbonate/phosphate ratio, acid phosphate content). These results bring new light on the mode of action of exenatide in bone physiology and demonstrate the value of GLP-1 mimetics in the treatment of fragility fractures in diabetes

Mechanistic Basis of Branch-Site Selection in Filamentous Bacteria

Many filamentous organisms, such as fungi, grow by tip-extension and by forming new branches behind the tips. A similar growth mode occurs in filamentous bacteria, including the genus Streptomyces, although here our mechanistic understanding has been very limited. The Streptomyces protein DivIVA is a critical determinant of hyphal growth and localizes in foci at hyphal tips and sites of future branch development. However, how such foci form was previously unknown. Here, we show experimentally that DivIVA focus-formation involves a novel mechanism in which new DivIVA foci break off from existing tip-foci, bypassing the need for initial nucleation or de novo branch-site selection. We develop a mathematical model for DivIVA-dependent growth and branching, involving DivIVA focus-formation by tip-focus splitting, focus growth, and the initiation of new branches at a critical focus size. We quantitatively fit our model to the experimentally-measured tip-to-branch and branch-to-branch length distributions. The model predicts a particular bimodal tip-to-branch distribution results from tip-focus splitting, a prediction we confirm experimentally. Our work provides mechanistic understanding of a novel mode of hyphal growth regulation that may be widely employed

Risk of colorectal cancer in men on long-term androgen deprivation therapy for prostate cancer

Background Androgen deprivation with gonadotropin-releasing hormone (GnRH) agonists or orchiectomy is a common but controversial treatment for prostate cancer. Uncertainties remain about its use, particularly with increasing recognition of serious side effects. In animal studies, androgens protect against colonic carcinogenesis, suggesting that androgen deprivation may increase the risk of colorectal cancer. Methods We identified 107 859 men in the linked Surveillance, Epidemiology, and End Results (SEER)-Medicare database who were diagnosed with prostate cancer in 1993 through 2002, with follow-up available through 2004. The primary outcome was development of colorectal cancer, determined from SEER files on second primary cancers. Cox proportional hazards regression was used to assess the influence of androgen deprivation on the outcome, adjusted for patient and prostate cancer characteristics. All statistical tests were two-sided. Results Men who had orchiectomies had the highest unadjusted incidence rate of colorectal cancer (6.3 per 1000 person-years; 95% confidence interval [CI] = 5.3 to 7.5), followed by men who had GnRH agonist therapy (4.4 per 1000 person-years; 95% CI = 4.0 to 4.9), and men who had no androgen deprivation (3.7 per 1000 person-years; 95% CI = 3.5 to 3.9). After adjustment for patient and prostate cancer characteristics, there was a statistically significant dose-response effect (P(trend) = .010) with an increasing risk of colorectal cancer associated with increasing duration of androgen deprivation. Compared with the absence of these treatments, there was an increased risk of colorectal cancer associated with use of GnRH agonist therapy for 25 months or longer (hazard ratio [HR] = 1.31, 95% CI = 1.12 to 1.53) or with orchiectomy (HR = 1.37, 95% CI = 1.14 to 1.66). Conclusion Long-term androgen deprivation therapy for prostate cancer is associated with an increased risk of colorectal cancer

Defending the genome from the enemy within:mechanisms of retrotransposon suppression in the mouse germline

The viability of any species requires that the genome is kept stable as it is transmitted from generation to generation by the germ cells. One of the challenges to transgenerational genome stability is the potential mutagenic activity of transposable genetic elements, particularly retrotransposons. There are many different types of retrotransposon in mammalian genomes, and these target different points in germline development to amplify and integrate into new genomic locations. Germ cells, and their pluripotent developmental precursors, have evolved a variety of genome defence mechanisms that suppress retrotransposon activity and maintain genome stability across the generations. Here, we review recent advances in understanding how retrotransposon activity is suppressed in the mammalian germline, how genes involved in germline genome defence mechanisms are regulated, and the consequences of mutating these genome defence genes for the developing germline