Carbohydrate–DNA Interactions at G‐Quadruplexes: Folding and Stability Changes by Attaching Sugars at the 5′‐End

Quadruplex DNA structures are attracting an enormous interest in many areas of chemistry, ranging from chemical biology, supramolecular chemistry to nanoscience. We have prepared carbohydrate–DNA conjugates containing the oligonucleotide sequences of G‐quadruplexes (thrombin binding aptamer (TBA) and human telomere (TEL)), measured their thermal stability and studied their structure in solution by using NMR and molecular dynamics. The solution structure of a fucose–TBA conjugate shows stacking interactions between the carbohydrate and the DNA G‐tetrad in addition to hydrogen bonding and hydrophobic contacts. We have also shown that attaching carbohydrates at the 5′‐end of a quadruplex telomeric sequence can alter its folding topology. These results suggest the possibility of modulating the folding of the G‐quadruplex by linking carbohydrates and have clear implications in molecular recognition and the design of new G‐quadruplex ligands.     

Learning parametrised regularisation functions via quotient minimisation

We propose a novel strategy for the computation of adaptive regularisation functions. The general strategy consists of minimising the ratio of a parametrised regularisation function; the numerator contains the regulariser with a desirable training signal as its argument, whereas the denominator contains the same regulariser but with its argument being a training signal one wants to avoid. The rationale behind this is to adapt parametric regularisations to given training data that contain both wanted and unwanted outcomes. We discuss the numerical implementation of this minimisation problem for a specific parametrisation, and present preliminary numerical results which demonstrate that this approach is able to recover total variation as well as second-order total variation regularisation from suitable training data. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The standard proof,the elegant proof,and the proof without words of tasks in geometry,and their dynamic investigation

Solution of problems in mathematics, and in particular in the field of Euclidean geometry is in many senses a form of artisanship that can be developed so that in certain cases brief and unexpected solutions may be obtained, which would bring out aesthetically pleasing mathematical traits. We present four geometric tasks for which different proofs are given under the headings: standard proof, elegant proof, and the proof without words. The solutions were obtained through a combination of mathematical tools and by dynamic investigation of the geometrical properties.     

Time-dependent and independent control rules for coordinated production and pricing under demand uncertainty and finite planning horizons

We address the effect of uncertainty on a manufacturer’s dynamic production and pricing decisions over a finite planning horizon. The demand for products, which depends on their price, is characterized by two stochastic processes: potential demand and customer price sensitivity. An optimal policy for coordinating production and pricing is a time-dependent feedback rule with respect to the state of the manufacturer’s inventories. We show that when the volatility of customer sensitivity to the product price is negligible, the optimal policy can be obtained analytically. Moreover, our simulations demonstrate that the volatility of stochastic customer price sensitivity does not have a strong effect on the manufacturer’s expected profit. Therefore, the solution derived for the case of customer price sensitivity with zero volatility can serve as a good approximation heuristic for the optimal policy if the true volatility of customer price sensitivity is within 40 % of its mean and the volatility of potential demand is within 25 % of its mean. Moreover, under these conditions, a simplified, time-independent control rule deteriorates expected profits by only 1.5 %.     

Novel thiazole and oxazole containing cyclic hexapeptides from a waterbloom of the cyanobacterium Microcystis sp.

Eight novel thiazole and oxazole containing cyclic peptides, microcyclamides GL616, GL582, GL614A, GL614B, GL614C, GL546A, GL546B, and GL628, as well as the known microcyclamide A, were isolated from the hydrophylic extract of a Microcystis sp. water-bloom collected in Gilboa reservoir, Valley of Armageddon, Israel. The planar structure of the compounds was determined by homonuclear and inverse-heteronuclear 2D NMR techniques as well as high-resolution mass spectrometry. The absolute configuration of the asymmetric centers of the amino acids was studied using Marfey's method for HPLC following ozonolysis, hydrolysis and derivatization with Marfey's reagent. This is the first example where acidic and modified amino acids are incorporated in this group of ribosomally biosynthesized metabolites.     

Assembling OX40 aptamers on a molecular scaffold to create a receptor-activating aptamer

We show that a molecular scaffold can be utilized to convert a receptor binding aptamer into a receptor agonist. Many receptors (including tumor necrosis receptor family members) are activated when they are multimerized on the cell surface. Molecular scaffolds have been utilized to assemble multiple receptor binding peptide ligands to generate activators of such receptors. We demonstrate that an RNA aptamer that recognizes OX40, a member of the tumor necrosis factor receptor superfamily, can be converted into a receptor-activating aptamer by assembling two copies on an olignucleotide-based scaffold. The OX40 receptor-activating aptamer is able to induce nuclear localization of nuclear factor-kappaB, cytokine production, and cell proliferation, as well as enhance the potency of dendritic cell-based tumor vaccines when systemically delivered to mice.     

Temporal shaping of entangled photons

We experimentally demonstrate shaping of the two-photon wave function of entangled-photon pairs, utilizing coherent pulse-shaping techniques. By performing spectral-phase manipulations we tailor the second-order correlation function of the photons exactly like a coherent ultrashort pulse. To observe the shaping we perform sum-frequency generation with an ultrahigh flux of entangled photons. At the appropriate conditions, sum-frequency generation performs as a coincidence detector with an ultrashort response time (approximately 100 fs), enabling a direct observation of the two-photon wave function. This property also enables us to demonstrate background-free, high-visibility two-photon interference oscillations.     

Simple analysis of graph tests for linearity and PCP

We give a simple analysis of the PCP with low amortized query complexity of Samorodnitsky and Trevisan [16]. The analysis also applies to the linearity testing over finite fields, giving a better estimate of the acceptance probability in terms of the distance of the tested function to the closest linear function. © 2003 Wiley Periodicals, Inc. Random Struct. Alg., 22: 139–160, 2003     

Focusing attention on auxiliary lines when introduced into geometric problems

The introduction of auxiliary elements as a method of solving problems in high-school geometry is considered here from two perspectives: first, to elicit recalling some known result or concretizing a definition and, second, as a means of shifting the focus and structure of the students’ attention. We present and compare various examples of how auxiliary elements can be introduced in various problems and proofs and characterize their auxiliary quality. Some auxiliary elements unite previously unrelated components of the original diagram; others divide a given complex entity into manageable ones. Implications for further educational research and mathematics instruction are proposed.