Stoffwechselprodukte von Mikroorganismen. 177. Mitteilung. Avilamycin C

From cultures of the Avilamycin (Avilamycin A) producing organism, Streptomyces viridochromogenes, strain ETH 23575, a second antibiotic, Avilamycin C, C₆₁H₉₀Cl₂O₃₂ could be isolated in crystalline form. Both Avilamycins belong to the group of the Orthosomycins. By IR., ¹H- and ¹³C-NMR. spectroscopy and by transformation to a common derivative it could be proven that Avilamycin A is a methyl ketone, Avilamycin C the corresponding methyl carbinol.     

A periodic isoperimetric problem related to the unique games conjecture

We prove the endpoint case of a conjecture of Khot and Moshkovitz related to the unique games conjecture, less a small error. Let n ≥ 2. Suppose a subset Ω of n‐dimensional Euclidean space satisfies ?Ω = Ω^c and Ω + v = Ω^c (up to measure zero sets) for every standard basis vector . For any and for any q ≥ 1, let and let . For any x ∈ ?Ω, let N(x) denote the exterior normal vector at x such that ‖N(x)‖₂ = 1. Let . Our main result shows that B has the smallest Gaussian surface area among all such subsets Ω, less a small error: In particular, Standard arguments extend these results to a corresponding weak inequality for noise stability. Removing the factor 6 × 10^?9 would prove the endpoint case of the Khot‐Moshkovitz conjecture. Lastly, we prove a Euclidean analogue of the Khot and Moshkovitz conjecture. The full conjecture of Khot and Moshkovitz provides strong evidence for the truth of the unique games conjecture, a central conjecture in theoretical computer science that is closely related to the P versus NP problem. So, our results also provide evidence for the truth of the unique games conjecture. Nevertheless, this paper does not prove any case of the unique games conjecture.     

Standard simplices and pluralities are not the most noise stable

The Standard Simplex Conjecture and the Plurality is Stablest Conjecture are two conjectures stating that certain partitions are optimal with respect to Gaussian and discrete noise stability respectively. These two conjectures are natural generalizations of the Gaussian noise stability result by Borell (1985) and the Majority is Stablest Theorem (2004). Here we show that the standard simplex is not the most stable partition in Gaussian space and that Plurality is not the most stable low influence partition in discrete space for every number of parts k ≥ 3, for every value ρ ≠ 0 of the noise and for every prescribed measure for the different parts as long as they are not all equal to 1/k. Our results do not contradict the original statements of the Plurality is Stablest and Standard Simplex Conjectures in their original statements concerning partitions to sets of equal measure. However, they indicate that if these conjectures are true, their veracity and their proofs will crucially rely on assuming that the sets are of equal measures, in stark contrast to Borell’s result, the Majority is Stablest Theorem and many other results in isoperimetric theory. Given our results it is natural to ask for (conjectured) partitions achieving the optimum noise stability.     

A hydrogel-based microfluidic device for the studies of directed cell migration

We have developed a hydrogel-based microfluidic device that is capable of generating a steady and long term linear chemical concentration gradient with no through flow in a microfluidic channel. Using this device, we successfully monitored the chemotactic responses of wildtype Escherichia coli (suspension cells) to alpha-methyl-DL-aspartate (attractant) and differentiated HL-60 cells (a human neutrophil-like cell line that is adherent) to formyl-Met-Leu-Phe (f-MLP, attractant). This device advances the current state of the art in microchemotaxis devices in that (1) it demonstrates the validity of using hydrogels as the building material for a microchemotaxis device; (2) it demonstrates the potential of the hydrogel based microfluidic device in biological experiments since most of the proteins and nutrients essential for cell survival are readily diffusible in hydrogel; (3) it is capable of applying chemical stimuli independently of mechanical stimuli; (4) it is straightforward to make, and requires very basic tools that are commonly available in biological labs. This device will also be useful in controlling the chemical and mechanical environment during the formation of tissue engineered constructs.     

A three-channel microfluidic device for generating static linear gradients and its application to the quantitative analysis of bacterial chemotaxis

We have developed a prototype three-channel microfluidic chip that is capable of generating a linear concentration gradient within a microfluidic channel and is useful in the study of bacterial chemotaxis. The linear chemical gradient is established by diffusing a chemical through a porous membrane located in the side wall of the channel and can be established without through-flow in the channel where cells reside. As a result, movement of the cells in the center channel is caused solely by the cells chemotactic response and not by variations in fluid flow. The advantages of this microfluidic chemical linear gradient generator are (i) its ability to produce a static chemical gradient, (ii) its rapid implementation, and (iii) its potential for highly parallel sample processing. Using this device, wildtype Escherichia coli strain RP437 was observed to move towards an attractant (e.g., l-asparate) and away from a repellent (e.g., glycerol) while derivatives of RP437 that were incapable of motility or chemotaxis showed no bias of the bacteria's distribution. Additionally, the degree of chemotaxis could be easily quantified using this assay in conjunction with fluorescence imaging techniques, allowing for estimation of the chemotactic partition coefficient (CPC) and the chemotactic migration coefficient (CMC). Finally, using this approach we demonstrate that E. coli deficient in autoinducer-2-mediated quorum sensing respond to the chemoattractant l-aspartate in a manner that is indistinguishable from wildtype cells suggesting that chemotaxis is insulated from this mode of cell-cell communication.     

Simple Zeros of the Riemann Zeta-Function

Assuming the Riemann Hypothesis, Montgomery showed by meansof his pair correlation method that at least two-thirds of thezeros of Riemann's zeta-function are simple. Later he and Taylorimproved this to 67.25 percent and, more recently, Cheer andGoldston increased the percentage to 67.2753. Here we proveby a new method that if the Riemann and Generalized LindelöofHypotheses hold, then at least 70.3704 percent of the zerosare simple and at least 84.5679 percent are distinct. Our methoduses mean value estimates for various functions defined by Dirichletseries sampled at the zeros of the Riemann zeta-function. 1991Mathematics Subject Classification: 11M26.     

Quantum Zeno and anti-Zeno paradoxes

Continuous observation of a time independent projection operator is known to prevent change of state (the quantum Zeno paradox). We discuss the recent result that generic continuous measurement of time dependent projection operators will in fact ensure change of state: an anti-Zeno paradox.