Mixed sums of primes and other terms

In this paper we study mixed sums of primes and linear recurrences. We show that if m=2(mod 4) and m+1 is a prime then $(m^{2^n-1}-1)/(m-1)\not=m^n+p^a$ for any n=3,4,... and prime power p^a. We also prove that if a>1 is an integer, u_0=0, u_1=1 and u_{i+1}=au_i+u_{i-1} for i=1,2,3,..., then all the sums u_m+au_n (m,n=1,2,3,...) are distinct. One of our conjectures states that any integer n>4 can be written as the sum of an odd prime, an odd Fibonacci number and a positive Fibonacci number.Comment: 11 page

Crystal structure of Zen4 in the apo state reveals a missing conformation of kinesin

© 2017 The Author(s). Kinesins hydrolyse ATP to transport intracellular cargoes along microtubules. Kinesin neck linker (NL) functions as the central mechano-chemical coupling element by changing its conformation through the ATPase cycle. Here we report the crystal structure of kinesin-6 Zen4 in a nucleotide-free, apo state, with the NL initial segment (NIS) adopting a backward-docked conformation and the preceding α6 helix partially melted. Single-molecule fluorescence resonance energy transfer (smFRET) analyses indicate the NIS of kinesin-1 undergoes similar conformational changes under tension in the two-head bound (2HB) state, whereas it is largely disordered without tension. The backward-docked structure of NIS is essential for motility of the motor. Our findings reveal a key missing conformation of kinesins, which provides the structural basis of the stable 2HB state and offers a tension-based rationale for an optimal NL length to ensure processivity of the motor

Interphase chromosome positioning in in vitro porcine cells and ex vivo porcine tissues

Copyright @ 2012 The Authors. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and 85 reproduction in any medium, provided the original author and source are credited. The article was made available through the Brunel University Open Access Publishing Fund.BACKGROUND: In interphase nuclei of a wide range of species chromosomes are organised into their own specific locations termed territories. These chromosome territories are non-randomly positioned in nuclei which is believed to be related to a spatial aspect of regulatory control over gene expression. In this study we have adopted the pig as a model in which to study interphase chromosome positioning and follows on from other studies from our group of using pig cells and tissues to study interphase genome re-positioning during differentiation. The pig is an important model organism both economically and as a closely related species to study human disease models. This is why great efforts have been made to accomplish the full genome sequence in the last decade. RESULTS: This study has positioned most of the porcine chromosomes in in vitro cultured adult and embryonic fibroblasts, early passage stromal derived mesenchymal stem cells and lymphocytes. The study is further expanded to position four chromosomes in ex vivo tissue derived from pig kidney, lung and brain. CONCLUSIONS: It was concluded that porcine chromosomes are also non-randomly positioned within interphase nuclei with few major differences in chromosome position in interphase nuclei between different cell and tissue types. There were also no differences between preferred nuclear location of chromosomes in in vitro cultured cells as compared to cells in tissue sections. Using a number of analyses to ascertain by what criteria porcine chromosomes were positioned in interphase nuclei; we found a correlation with DNA content.This study is partly supported by Sygen International PLC

Comments on: Multicriteria Decision Systems for Financial Problems

The final publication is available at Springer via http://dx.doi.org/10.1007/s11750-013-0280-1Pla Santamaría, D.; García Bernabeu, AM. (2013). Comments on: Multicriteria Decision Systems for Financial Problems. TOP. 21(2):275-278. doi:10.1007/s11750-013-0280-1S275278212Arrow KJ (1965) Aspects of the theory of risk-bearingBallestero E (2001) Stochastic goal programming: a mean-variance approach. Eur J Oper Res 131(3):476–481Copeland TE, Weston JF (1988) Financial theory and corporate policy. Addison-Wesley, ReadingDoumpos M, Zopounidis C (2010) A multicriteria decision support system for bank rating. Decis Support Syst 50(1):55–63Doumpos M, Zopounidis C (2011) A multicriteria outranking modeling approach for credit rating. Decis Sci 42(3):721–742Geanakoplos J (2001) Three brief proofs of arrow’s impossibility theorem. Yale Cowles Foundation discussion paper (1123RRR)Konno H, Yamazaki H (1991) Mean-absolute deviation portfolio optimization model and its applications to Tokyo Stock Market. Manag Sci 37(5):519–531Saaty TL, Ozdemir MS (2003) Why the magic number seven plus or minus two. Math Comput Model 38(3):233–244Sun S, Lu WM et al. (2005) A cross-efficiency profiling for increasing discrimination in data envelopment analysis. Inf Syst Oper Res 43(1):5

Controllable Synthesis of Magnesium Oxysulfate Nanowires with Different Morphologies

One-dimensional magnesium oxysulfate 5Mg(OH)2 · MgSO4 · 3H2O (abbreviated as 513MOS) with high aspect ratio has attracted much attention because of its distinctive properties from those of the conventional bulk materials. 513MOS nanowires with different morphologies were formed by varying the mixing ways of MgSO4 · 7H2O and NH4OH solutions at room temperature followed by hydrothermal treatment of the slurries at 150 °C for 12 h with or without EDTA. 513MOS nanowires with a length of 20–60 μm and a diameter of 60–300 nm were prepared in the case of double injection (adding MgSO4 · 7H2O and NH4OH solutions simultaneously into water), compared with the 513MOS with a length of 20–30 μm and a diameter of 0.3–1.7 μm in the case of the single injection (adding MgSO4 · 7H2O solution into NH4OH solution). The presence of minor amount of EDTA in the single injection method led to the formation of 513MOS nanowires with a length of 100–200 μm, a diameter of 80–200 nm, and an aspect ratio of up to 1000. The analysis of the experimental results indicated that the hydrothermal solutions with a lower supersaturation were favorable for the preferential growth of 513MOS nanowires along b axis

Lamb Wave Scattering from Rivets

For structures with large surface areas, a full integrity evaluation can be a time-consuming operation. Lamb wave techniques allow this evaluation to be performed with waves propagating along one dimension of the inspection area while the probing transducers are moved in the perpendicular dimension, giving information about the presence of flaws within the entire scanned area. For riveted structures the scattering of the Lamb waves from the rivets is often the dominant feature in the measured response, masking the more subtle effects of Lamb wave interactions with the flaws of interest [1]. In this paper we consider the scattering of lowest mode symmetric and antisymmetric Lamb waves from model rivets, and derive analytic expressions for the scattered fields. With solutions of this type the disruptive effects of the rivets can be “processed out” of measured data in order to expose the signals which are due to the flaws in the structure

High Fidelity Tape Transfer Printing Based On Chemically Induced Adhesive Strength Modulation

Transfer printing, a two-step process (i.e. picking up and printing) for heterogeneous integration, has been widely exploited for the fabrication of functional electronics system. To ensure a reliable process, strong adhesion for picking up and weak or no adhesion for printing are required. However, it is challenging to meet the requirements of switchable stamp adhesion. Here we introduce a simple, high fidelity process, namely tape transfer printing(TTP), enabled by chemically induced dramatic modulation in tape adhesive strength. We describe the working mechanism of the adhesion modulation that governs this process and demonstrate the method by high fidelity tape transfer printing several types of materials and devices, including Si pellets arrays, photodetector arrays, and electromyography (EMG) sensors, from their preparation substrates to various alien substrates. High fidelity tape transfer printing of components onto curvilinear surfaces is also illustrated

Entanglement-free Heisenberg-limited phase estimation

Measurement underpins all quantitative science. A key example is the measurement of optical phase, used in length metrology and many other applications. Advances in precision measurement have consistently led to important scientific discoveries. At the fundamental level, measurement precision is limited by the number N of quantum resources (such as photons) that are used. Standard measurement schemes, using each resource independently, lead to a phase uncertainty that scales as 1/sqrt(N) - known as the standard quantum limit. However, it has long been conjectured that it should be possible to achieve a precision limited only by the Heisenberg uncertainty principle, dramatically improving the scaling to 1/N. It is commonly thought that achieving this improvement requires the use of exotic quantum entangled states, such as the NOON state. These states are extremely difficult to generate. Measurement schemes with counted photons or ions have been performed with N <= 6, but few have surpassed the standard quantum limit and none have shown Heisenberg-limited scaling. Here we demonstrate experimentally a Heisenberg-limited phase estimation procedure. We replace entangled input states with multiple applications of the phase shift on unentangled single-photon states. We generalize Kitaev's phase estimation algorithm using adaptive measurement theory to achieve a standard deviation scaling at the Heisenberg limit. For the largest number of resources used (N = 378), we estimate an unknown phase with a variance more than 10 dB below the standard quantum limit; achieving this variance would require more than 4,000 resources using standard interferometry. Our results represent a drastic reduction in the complexity of achieving quantum-enhanced measurement precision.Comment: Published in Nature. This is the final versio

Droplet-based millifluidic synthesis of a proton-conducting sulfonate metal–organic framework

Metal–organic frameworks (MOFs) have emerged as promising candidate materials for proton exchange membranes (PEMs), due to the control of proton transport enabled by functional groups and the structural order within the MOFs. In this work, we report a millifluidic approach for the synthesis of a MOF incorporating both sulfonate and amine groups, termed Cu-SAT, which exhibits a high proton conductivity. The fouling-free multiphase flow reactor synthesis was operated for more than 5 h with no reduction in yield or change in the particle size distribution, demonstrating a sustained space–time yield up to 131.7 kg m−3 day−1 with consistent particle quality. Reaction yield and particle size were controllably tuned by the adjustment of reaction parameters, such as residence/reaction time, temperature, and reagent concentration. The reaction yields from the flow reactor were 10–20% higher than those of corresponding batch syntheses, indicating improved mass and heat transfer in flow. A systematic exploration of synthetic parameters using a factorial design of experiments approach revealed the key correlations between the process parameters and yields and particle size distributions. The proton conductivity of the synthesized Cu-SAT MOF was evaluated in a mixed matrix membrane model PEM with polyvinylpyrrolidone and polyvinylidene fluoride polymers, exhibiting a promising composite conductivity of 1.34 ± 0.05 mS cm−1 at 353 K and 95% relative humidity (RH)

Cross-sectional associations between dietary fat-related behaviors and continuous metabolic syndrome score among young Australian adults

Dietary guidelines recommend removing visible fat from meat, choosing low-fat options and cooking with oil instead of butter. This study examined cross-sectional associations between fat-related eating behaviors and a continuous metabolic syndrome (cMetSyn) score among young adults. During 2004⁻2006, 2071 participants aged 26⁻36 years reported how often they trimmed fat from meat, consumed low-fat dairy products and used different types of fat for cooking. A fasting blood sample was collected. Blood pressure, weight and height were measured. To create the cMetSyn score, sex-specific principal component analysis was applied to normalized risk factors of the harmonized definition of metabolic syndrome. Higher score indicates higher risk. For each behavior, differences in mean cMetSyn score were calculated using linear regression adjusted for confounders. Analyses were stratified by weight status (Body mass index (BMI) Trend = 0.013) among participants who were healthy weight and frequency of using canola/sunflower oil for cooking (PTrend = 0.008) among participants who were overweight/obese. Trimming fat from meat, cooking with olive oil, cooking with butter, and consuming low-fat dairy products were not associated with cMetSyn score. Among young adults, following fat-related dietary recommendations tended to not be associated with metabolic risk