Higher Dimensional Lattice Chains and Delannoy Numbers

Fix nonnegative integers n1 , . . ., nd, and let L denote the lattice of points (a1 , . . ., ad) ∈ ℤd that satisfy 0 ≤ ai ≤ ni for 1 ≤ i ≤ d. Let L be partially ordered by the usual dominance ordering. In this paper we use elementary combinatorial arguments to derive new expressions for the number of chains and the number of Delannoy paths in L. Setting ni = n (for all i) in these expressions yields a new proof of a recent result of Duichi and Sulanke [9] relating the total number of chains to the central Delannoy numbers. We also give a novel derivation of the generating functions for these numbers in arbitrary dimension

Intrabodies Binding the Proline-Rich Domains of Mutant Huntingtin Increase Its Turnover and Reduce Neurotoxicity

Although expanded polyglutamine (polyQ) repeats are inherently toxic, causing at least nine neurodegenerative diseases, the protein context determines which neurons are affected. The polyQ expansion that causes Huntington's disease (HD) is in the first exon (HDx-1) of huntingtin (Htt). However, other parts of the protein, including the 17 N-terminal amino acids and two proline (polyP) repeat domains, regulate the toxicity of mutant Htt. The role of the P-rich domain that is flanked by the polyP domains has not been explored. Using highly specific intracellular antibodies (intrabodies), we tested various epitopes for their roles in HDx-1 toxicity, aggregation, localization, and turnover. Three domains in the P-rich region (PRR) of HDx-1 are defined by intrabodies: MW7 binds the two polyP domains, and Happ1 and Happ3, two new intrabodies, bind the unique, P-rich epitope located between the two polyP epitopes. We find that the PRR-binding intrabodies, as well as VL12.3, which binds the N-terminal 17 aa, decrease the toxicity and aggregation of HDx-1, but they do so by different mechanisms. The PRR-binding intrabodies have no effect on Htt localization, but they cause a significant increase in the turnover rate of mutant Htt, which VL12.3 does not change. In contrast, expression of VL12.3 increases nuclear Htt. We propose that the PRR of mutant Htt regulates its stability, and that compromising this pathogenic epitope by intrabody binding represents a novel therapeutic strategy for treating HD. We also note that intrabody binding represents a powerful tool for determining the function of protein epitopes in living cells

crisscrossing Science Episode 071: To Infinity and Beyond

In this episode, Mike Crosser (professor of physics at Linfield College) and Chad Tillberg (professor of biology at Linfield College) invite Dr. Chuck Dunn (professor of mathematics at Linfield College) into the studio to talk about infinity. Dunn uses some analogies to describe real mathematical contexts in which infinity comes up

Counting lattice chains and Delannoy paths in higher dimensions

AbstractLattice chains and Delannoy paths represent two different ways to progress through a lattice. We use elementary combinatorial arguments to derive new expressions for the number of chains and the number of Delannoy paths in a lattice of arbitrary finite dimension. Specifically, fix nonnegative integers n1,…,nd, and let L denote the lattice of points (a1,…,ad)∈Zd that satisfy 0≤ai≤ni for 1≤i≤d. We prove that the number of chains in L is given by 2nd+1∑k=1kmax′∑i=1k(−1)i+kk−1i−1nd+k−1nd∏j=1d−1nj+i−1nj, where kmax′=n1+⋯+nd−1+1. We also show that the number of Delannoy paths in L equals ∑k=1kmax′∑i=1k(−1)i+k(k−1i−1)(nd+k−1nd)∏j=1d−1(nd+i−1nj). Setting ni=n (for all i) in these expressions yields a new proof of a recent result of Duchi and Sulanke [9] relating the total number of chains to the central Delannoy numbers. We also give a novel derivation of the generating functions for these numbers in arbitrary dimension

Area, perimeter, height, and width of rectangle visibility graphs

A rectangle visibility graph (RVG) is represented by assigning to each vertex a rectangle in the plane with horizontal and vertical sides in such a way that edges in the graph correspond to unobstructed horizontal and vertical lines of sight between their corresponding rectangles. To discretize, we consider only rectangles whose corners have integer coordinates. For any given RVG, we seek a representation with smallest bounding box as measured by its area, perimeter, height, or width (height is assumed not to exceed width)

Colored Shade Nets Affect Growth but Not Flowering of Four Greenhouse-grown Potted Ornamental Species

The color of horticultural shade nets is known to influence crop growth and quality because of variations in the amount and quality of light. Four ornamental plant species (celosia, begonia, gerbera, and fountain grass) were grown under aluminet, pearl, and red shade nets plus black as the control at 50% shade intensity for 8 weeks. Black had the least transmittance (∼10% to 30% of ambient) within the red spectrum (620–750 nm), whereas red had the greatest at ∼70% to 80%. Aluminet and pearl resulted in a similar reduction in photosynthetic photon flux at ∼50% to 55% and ∼55% to 65% of ambient, respectively. Aluminet increased the shoot dry weight for begonia and celosia, whereas no differences among shade nets were seen for gerbera or fountain grass. The chlorophyll concentration was greatest under aluminet for each species except begonia. Shade net color did not affect flower number

Height Control of Greenhouse-grown Pansy Using Colored Shade Nets

Pansy (Viola ×wittrockiana) is a greenhouse crop commonly grown under black shade net; it often requires the use of chemical plant growth regulators to maintain a compact growth habit. Nonchemical efforts to alter plant morphology, such as height, would provide a more sustainable solution than chemical application. The objective of these studies was to evaluate the effects of different colors of shade nets on controlling growth and flowering of pansy. In Expt. 1, ‘Clear Yellow’, ‘Buttered Popcorn’, and ‘Deep Orange’ pansy plugs were placed under 30% blue or black shade net or, as a control group, where grown with no shade net. In Expt. 2, the same three cultivars of pansy were grown under 50% black, red, pearl, or aluminized shade net. Data were collected on plant height, plant width, flower number, plant survival, soil plant analysis development chlorophyll meter (SPAD) readings, and light quality. In Expt. 1, the blue shade net reduced height to flower and height to leaves, but also decreased flower number and plant survival as compared with black shade net. All plants under no shade died. In Expt. 2, SPAD, an indicator of plant quality by estimating leaf greenness, was found to be lower under black shade net, whereas pearl shade net led to a decrease in plant height and no effect on the number of flowers. Light quality, including red-to-far-red ratio, varied among shade treatments, whereas light intensity was reduced under aluminized, black (50%), and red shade nets compared with other shade treatments. Blue and pearl shade nets both reduced plant height, but blue shade net also reduced plant survival and flowering

Use of contingency management incentives to improve completion of hepatitis B vaccination in people undergoing treatment for heroin dependence: a cluster randomised trial

Background: Poor adherence to treatment diminishes its individual and public health benefit. Financial incentives, provided on the condition of treatment attendance, could address this problem. Injecting drug users are a high-risk group for hepatitis B virus (HBV) infection and transmission, but adherence to vaccination programmes is poor. We aimed to assess whether contingency management delivered in routine clinical practice increased the completion of HBV vaccination in individuals receiving opioid substitution therapy. Methods: In our cluster randomised controlled trial, we enrolled participants at 12 National Health Service drug treatment services in the UK that provided opioid substitution therapy and nurse-led HBV vaccination with a super-accelerated schedule (vaccination days 0, 7, and 21). Clusters were randomly allocated 1:1:1 to provide vaccination without incentive (treatment as usual), with fixed value contingency management (three £10 vouchers), or escalating value contingency management (£5, £10, and £15 vouchers). Both contingency management schedules rewarded on-time attendance at appointments. The primary outcome was completion of clinically appropriate HBV vaccination within 28 days. We also did sensitivity analyses that examined vaccination completion with full adherence to appointment times and within a 3 month window. The trial is registered with Current Controlled Trials, number ISRCTN72794493. Findings: Between March 16, 2011, and April 26, 2012, we enrolled 210 eligible participants. Compared with six (9%) of 67 participants treated as usual, 35 (45%) of 78 participants in the fixed value contingency management group met the primary outcome measure (odds ratio 12·1, 95% CI 3·7–39·9; p<0·0001), as did 32 (49%) of 65 participants in the escalating value contingency management group (14·0, 4·2–46·2; p<0·0001). These differences remained significant with sensitivity analyses. Interpretation: Modest financial incentives delivered in routine clinical practice significantly improve adherence to, and completion of, HBV vaccination programmes in patients receiving opioid substitution therapy. Achievement of this improvement in routine clinical practice should now prompt actual implementation. Drug treatment providers should employ contingency management to promote adherence to vaccination programmes. The effectiveness of routine use of contingency management to achieve long-term behaviour change remains unknown

Neurocognitive function in HIV infected patients on antiretroviral therapy

OBJECTIVE To describe factors associated with neurocognitive (NC) function in HIV-positive patients on stable combination antiretroviral therapy. DESIGN We undertook a cross-sectional analysis assessing NC data obtained at baseline in patients entering the Protease-Inhibitor-Monotherapy-Versus-Ongoing-Triple therapy (PIVOT) trial. MAIN OUTCOME MEASURE NC testing comprised of 5 domains. Raw results were z-transformed using standard and demographically adjusted normative datasets (ND). Global z-scores (NPZ-5) were derived from averaging the 5 domains and percentage of subjects with test scores >1 standard deviation (SD) below population means in at least two domains (abnormal Frascati score) calculated. Patient characteristics associated with NC results were assessed using multivariable linear regression. RESULTS Of the 587 patients in PIVOT, 557 had full NC results and were included. 77% were male, 68% Caucasian and 28% of Black ethnicity. Mean (SD) baseline and nadir CD4+ lymphocyte counts were 553(217) and 177(117) cells/µL, respectively, and HIV RNA was <50 copies/mL in all. Median (IQR) NPZ-5 score was -0.5 (-1.2/-0) overall, and -0.3 (-0.7/0.1) and -1.4 (-2/-0.8) in subjects of Caucasian and Black ethnicity, respectively. Abnormal Frascati scores using the standard-ND were observed in 51%, 38%, and 81%, respectively, of subjects overall, Caucasian and Black ethnicity (p<0.001), but in 62% and 69% of Caucasian and Black subjects using demographically adjusted-ND (p = 0.20). In the multivariate analysis, only Black ethnicity was associated with poorer NPZ-5 scores (P<0.001). CONCLUSIONS In this large group of HIV-infected subjects with viral load suppression, ethnicity but not HIV-disease factors is closely associated with NC results. The prevalence of abnormal results is highly dependent on control datasets utilised. TRIAL REGISTRY ClinicalTrials.gov, NCT01230580