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

Does Doxycycline work in synergy with cisplatin and oxaliplatin in colorectal cancer?

Background: In recent years, apart from antibacterial properties, doxycycline is reported to have cytotoxic and anti-proliferative actions in various cancers including colorectal cancer. Colorectal cancer constitutes one of the most common cancers in the western population. Apart from surgery, chemotherapy plays crucial role in the treatment of colorectal cancer. Cisplatin and oxaliplatin are most commonly used platinum compounds for the cancer chemotherapy. This study has looked for any impact of doxycycline on the cytotoxic effects of platinum compounds in colorectal cancer including its mechanisms of actions.Methods: HT 29 colorectal cancer cells were used for this study. These cells were treated with cisplatin and oxaliplatin with or without doxycycline treatment. The caspase 3 gene expression was quantitated by gel electrophoresis and qualitated by real time polymerase chain reactions. The caspase 3 activity was assessed in HT 29 cells with fluorescence kit.Results: The results revealed increased caspase 3 gene expressions and activities in HT 29 cells treated with cisplatin, oxaliplatin and doxycycline; however the combination of doxycycline with cisplatin and oxaliplatin did not report increased caspase 3 gene expressions and activity compared to cisplatin and oxaliplatin alone.Conclusion: We concluded that doxycycline has role in apoptosis induction in the colorectal cancer. However, it did not show any synergy with platinum compounds in the colorectal cancer cells. This study also pointed towards possible caspase-independent actions of doxycycline with cisplatin and oxaliplatin. However, further work is required to underpin the mechanisms of actions of doxycycline

Bioinformatics in crosslinking chemistry of collagen with selective cross linkers

<p>Abstract</p> <p>Background</p> <p>Identifying the molecular interactions using bioinformatics tools before venturing into wet lab studies saves the energy and time considerably. The present study summarizes, molecular interactions and binding energy calculations made for major structural protein, collagen of Type I and Type III with the chosen cross-linkers, namely, coenzyme Q₁₀, dopaquinone, embelin, embelin complex-1 & 2, idebenone, 5-O-methyl embelin, potassium embelate and vilangin.</p> <p>Results</p> <p>Molecular descriptive analyses suggest, dopaquinone, embelin, idebenone, 5-O-methyl embelin, and potassium embelate display nil violations. And results of docking analyses revealed, best affinity for Type I (- 4.74 kcal/mol) and type III (-4.94 kcal/mol) collagen was with dopaquinone.</p> <p>Conclusions</p> <p>Among the selected cross-linkers, dopaquinone, embelin, potassium embelate and 5-O-methyl embelin were the suitable cross-linkers for both Type I and Type III collagen and stabilizes the collagen at the expected level.</p

Reliability of Synaptic Transmission at the Synapses of Held In Vivo under Acoustic Stimulation

BACKGROUND:The giant synapses of Held play an important role in high-fidelity auditory processing and provide a model system for synaptic transmission at central synapses. Whether transmission of action potentials can fail at these synapses has been investigated in recent studies. At the endbulbs of Held in the anteroventral cochlear nucleus (AVCN) a consistent picture emerged, whereas at the calyx of Held in the medial nucleus of the trapezoid body (MNTB) results on the reliability of transmission remain inconsistent. In vivo this discrepancy could be due to the difficulty in identifying failures of transmission. METHODS/FINDINGS:We introduce a novel method for detecting unreliable transmission in vivo. Based on the temporal relationship between a cells' waveform and other potentials in the recordings, a statistical test is developed that provides a balanced decision between the presence and the absence of failures. Its performance is quantified using simulated voltage recordings and found to exhibit a high level of accuracy. The method was applied to extracellular recordings from the synapses of Held in vivo. At the calyces of Held failures of transmission were found only rarely. By contrast, at the endbulbs of Held in the AVCN failures were found under spontaneous, excited, and suppressed conditions. In accordance with previous studies, failures occurred most abundantly in the suppressed condition, suggesting a role for inhibition. CONCLUSIONS/SIGNIFICANCE:Under the investigated activity conditions/anesthesia, transmission seems to remain largely unimpeded in the MNTB, whereas in the AVCN the occurrence of failures is related to inhibition and could be the basis/result of computational mechanisms for temporal processing. More generally, our approach provides a formal tool for studying the reliability of transmission with high statistical accuracy under typical in vivo recording conditions

Selective patterning of ZnO nanorods on silicon substrates using nanoimprint lithography

In this research, nanoimprint lithography (NIL) was used for patterning crystalline zinc oxide (ZnO) nanorods on the silicon substrate. To fabricate nano-patterned ZnO nanorods, patterning of an n-octadecyltrichlorosilane (OTS) self-assembled monolayers (SAMs) on SiO2 substrate was prepared by the polymer mask using NI. The ZnO seed layer was selectively coated only on the hydrophilic SiO2 surface, not on the hydrophobic OTS SAMs surface. The substrate patterned with the ZnO seed layer was treated with the oxygen plasma to oxidize the silicon surface. It was found that the nucleation and initial growth of the crystalline ZnO were proceeded only on the ZnO seed layer, not on the silicon oxide surface. ZnO photoluminescence spectra showed that ZnO nanorods grown from the seed layer treated with plasma showed lower intensity than those untreated with plasma at 378 nm, but higher intensity at 605 nm. It is indicated that the seed layer treated with plasma produced ZnO nanorods that had a more oxygen vacancy than those grown from seed layer untreated with plasma. Since the oxygen vacancies on ZnO nanorods serve as strong binding sites for absorption of various organic and inorganic molecules. Consequently, a nano-patterning of the crystalline ZnO nanorods grown from the seed layer treated with plasma may give the versatile applications for the electronics devices

Parametric Study on Dimensional Control of ZnO Nanowalls and Nanowires by Electrochemical Deposition

A simple electrochemical deposition technique is used to synthesize both two-dimensional (nanowall) and one-dimensional (nanowire) ZnO nanostructures on indium-tin-oxide-coated glass substrates at 70°C. By fine-tuning the deposition conditions, particularly the initial Zn(NO3)2·6H2O electrolyte concentration, the mean ledge thickness of the nanowalls (50–100 nm) and the average diameter of the nanowires (50–120 nm) can be easily varied. The KCl supporting electrolyte used in the electrodeposition also has a pronounced effect on the formation of the nanowalls, due to the adsorption of Cl− ions on the preferred (0001) growth plane of ZnO and thereby redirecting growth on the (100) and (20) planes. Furthermore, evolution from the formation of ZnO nanowalls to formation of nanowires is observed as the KCl concentration is reduced in the electrolyte. The crystalline properties and growth directions of the as-synthesized ZnO nanostructures are studied in details by glancing-incidence X-ray diffraction and transmission electron microscopy

Flexible and Transparent All-Graphene Circuits for Quaternary Digital Modulations

In modern communication system, modulation is a key function that embeds the baseband signal (information) into a carrier wave so that it can be successfully broadcasted through a medium such as air or cables. A flexible signal modulation scheme is hence essential to wide range of applications based on flexible electronics. Here we report a fully bendable all-graphene modulator circuit with the capability to encode a carrier signal with quaternary digital information for the first time. By exploiting the ambipolarity and the nonlinearity in a graphene transistor, we demonstrated two types of quaternary modulation schemes: 4-ary amplitude-shift keying (4-ASK) and quadrature phase-shift keying (QPSK). Remarkably, 4-ASK and QPSK can be realized with just 1 and 2 all-graphene transistors, respectively, representing a drastic reduction in circuit complexity when compared with conventional digital modulators. In addition, the circuit is not only flexible but also highly transparent (~95% transmittance) owing to their all-graphene design with every component (channel, interconnects, load resistor, and source/drain/gate electrodes) fabricated from graphene films. Taken together, these results represent a significant step toward achieving a high speed communication system that can be monolithically integrated on a flexible and transparent platform.Comment: 29 pages, 8 figures, 1 tabl

The association of two single nucleotide polymorphisms (SNPs) in growth hormone (GH) gene with litter size and superovulation response in goat-breeds

Two active mutations (A 781 G and A 1575 G) in growth hormone (GH) gene, and their associations with litter size (LS), were investigated in both a high prolificacy (Matou, n = 182) and a low prolificacy breed (Boer, n = 352) by using the PCR-RFLP method. Superovulation experiments were designed in 57 dams, in order to evaluate the effect of different genotypes of the GH gene on superovulation response. Two genotypes (AA and AB, CC and CD) in each mutation were detected in these two goat breeds. Neither BB nor DD homozygous genotypes were observed. The genotypic frequencies of AB and CC were significantly higher than those of AA and CD. In the third parity, Matou dams with AB or CC genotypes had significantly larger litter sizes than those with AA and CD (p < 0.05). On combining the two loci, both Matou and Boer dams with ABCD genotype had the largest litter sizes when compared to the other genotypes (p < 0.05). When undergoing like superovulation treatments, a significantly higher number of corpora lutea and ova, with a lower incidence of ovarian cysts, were harvested in the AB and CC genotypes than in AA and CD. These results show that the two loci of GH gene are highly associated with abundant prolificacy and superovulation response in goat breeds