First and second moments for self‐similar couplings and Wasserstein distances

We study aspects of the Wasserstein distance in the context of self‐similar measures. Computing this distance between two measures involves minimising certain moment integrals over the space of couplings, which are measures on the product space with the original measures as prescribed marginals. We focus our attention on self‐similar measures associated to equicontractive iterated function systems consisting of two maps on the unit interval and satisfying the open set condition. We are particularly interested in understanding the restricted family of self‐similar couplings and our main achievement is the explicit computation of the 1st and 2nd moment integrals for such couplings. We show that this family is enough to yield an explicit formula for the 1st Wasserstein distance and provide non‐trivial upper and lower bounds for the 2nd Wasserstein distance for these self‐similar measures.     

Mode-locked fiber laser frequency-controlled with an intracavity electro-optic modulator

We demonstrate a mode-locked, erbium-doped fiber laser with its repetition frequency synchronized to a second fiber laser via an intracavity electro-optic modulator (EOM). With servo control from the EOM (bandwidth approximately 230 kHz) and a slower speed intracavity piezoelectric transducer (resonance at approximately 20 kHz), we demonstrate stabilization of the repetition frequency with an in-loop rms timing jitter of 10 fs, integrated over a bandwidth from 1 Hz to 100 kHz. This represents what is to our knowledge the first time an EOM has been introduced inside a mode-locked laser cavity for fast servo action and the lowest timing jitter reported for a mode-locked fiber laser.     

A Boat-Shaped Tetracationic Macrocycle with a Semiconducting Organic Framework

We report the synthesis of a tetracationic macrocycle which contains two N,N′-bis(methylene)naphthalenediimide units inserted in between the pyridinium rings of the bipyridinium units in cyclobis(paraquat-p-phenylene) (CBPQT⁴⁺ or “blue box”) and describe the investigation of its potential use in materials for organic electronics. The incorporation of the two naphthalenediimide (NDI) units into the constitution of CBPQT⁴⁺, not only changes the supramolecular properties of the tetracation in the solid state, but also has a profound influence on the electrochemical and electronic behavior of the resulting tetracationic macrocycle. In particular, the solid-state (super)structure, investigated by single-crystal X-ray diffraction, reveals the formation of a three-dimensional (3D) supramolecular framework with ca. 2.8 nm diameter one-dimensional (1D) hexagonal channels. Electrochemical studies on solid-state thin films of the macrocycle show that they exhibit semiconducting properties with a redox-conductivity of up to 7.6×10⁻⁴ S m⁻¹. Moreover, EPR and ENDOR spectroscopies show that charge is equally shared between the NDIs within the one-electron reduced state of the NDI-based macrocycle on the time scale of these techniques.     

Design and Synthesis of Imidazole and Triazole Pyrazoles as Mycobacterium Tuberculosis CYP121A1 Inhibitors

The emergence of untreatable drug-resistant strains of Mycobacterium tuberculosis is a major public health problem worldwide, and the identification of new efficient treatments is urgently needed. Mycobacterium tuberculosis cytochrome P450 CYP121A1 is a promising drug target for the treatment of tuberculosis owing to its essential role in mycobacterial growth. Using a rational approach, which includes molecular modelling studies, three series of azole pyrazole derivatives were designed through two synthetic pathways. The synthesized compounds were biologically evaluated for their inhibitory activity towards M. tuberculosis and their protein binding affinity (K_D). Series 3 biarylpyrazole imidazole derivatives were the most effective with the isobutyl ( 10 f ) and tert-butyl ( 10 g ) compounds displaying optimal activity (MIC 1.562 μg/mL, K_D 0.22 μM ( 10 f ) and 4.81 μM ( 10 g )). The spectroscopic data showed that all the synthesised compounds produced a type II red shift of the heme Soret band indicating either direct binding to heme iron or (where less extensive Soret shifts are observed) putative indirect binding via an interstitial water molecule. Evaluation of biological and physicochemical properties identified the following as requirements for activity: LogP >4, H-bond acceptors/H-bond donors 4/0, number of rotatable bonds 5–6, molecular volume >340 ų, topological polar surface area <40 Ų.     

Konzertierte nukleophile aromatische Substitutionen

Jüngste Entwicklungen in der experimentellen und theoretischen Chemie haben zur Identifizierung einer schnell wachsenden Klasse von nukleophilen aromatischen Substitutionsreaktionen geführt, die einem konzertierten Mechanismus (cS_NAr) folgen, und nicht dem klassischen, zweistufigen S_NAr‐Mechanismus. Während klassische S_NAr‐Reaktionen auf die substantielle Aktivierung des aromatischen Ringes durch elektronenziehende Substituenten angewiesen sind, ist eine solche Aktivierung für den konzertierten Reaktionsverlauf nicht zwingend nötig.     

Picosecond pulses from a cryogenically cooled, composite amplifier using Yb:YAG and Yb:GSAG

A cryogenic Yb amplifier using two laser materials, Gd3Sc2Al3O12 and Y3Al5O12 (YAG), has been used to obtain 70 W average power at 5 kHz pulse repetition frequency; the output was compressed to 1.6 ps, compared with an input compressible to 1.4 ps. The gain broadening obtained by combining two media enables shorter pulses than using Yb:YAG alone but retains the power-scaling advantages of cryogenic Yb:YAG.     

Observed effects of a changing step-edge density on thin-film growth dynamics

We grew SrTiO(3) on SrTiO(3)(001) by pulsed laser deposition, while observing x-ray diffraction at the (00(1/2)) position. The drop DeltaI in the x-ray intensity following a laser pulse contains information about plume-surface interactions. Kinematic theory predicts DeltaI/I = -4sigma(1 - sigma), so that DeltaI /I depends only on the amount of deposited material sigma. In contrast, we observed experimentally that |DeltaI /I| < 4sigma(1 - sigma) and that DeltaI /I depends on the phase of x-ray growth oscillations. The combined results suggest a fast smoothing mechanism that depends on surface step-edge density.