On the chromatic numbers of 3-dimensional slices

We prove that for an arbitrary $\varepsilon > 0$ holds $$\chi (\mathbb{R}^3 \times [0,\varepsilon]^6) \geq 10,$$ where $\chi(M)$ stands for the chromatic number of an (infinite) graph with the vertex set $M$ and the edge set consists of pairs of monochromatic points at the distance 1 apart

Ultrasonic field mapping through a multimode optical fibre

Miniaturising ultrasonic field mapping systems could lead to novel endoscopes capable of photoacoustic tomography and other techniques. However, developing high-resolution arrays of sensitive, sub-millimetre scale ultrasound sensors presents a challenge for traditional piezoelectric transducers. To address this challenge, we conceived an ultrasonic detection concept in which an optical ultrasonic sensor array is read out using a laser beam scanned through a 0.24 mm diameter multimode optical fibre using optical wavefront shaping. We demonstrate this system enables ultrasonic field mapping with >2500 measurement points, paving the way to developing miniaturised photoacoustic endoscopes and other ultrasonic systems based on the presented concept

The experience of radiofrequency ablation of atrial tachycardia focus with the use of high-density myocardial mapping

The article presents a case of successful treatment of focal atrial tachycardia by radiofrequency ablation using high-density myocardial mapping. The aim of the work was to evaluate the possibilities of high-resolution myocardial mapping by EnsitePrecision® navigation system in the treatment of complex arrhythmias. The analysis of clinical data and results of electrophysiological examination of a 29-year-old patient with continuous recurrent focal atrial tachycardia was carried out. The patient was admitted with complaints of heart rate disorders and frequent short attacks of palpitations. According to electrocardiography, frequent short paroxysms of focal atrial tachycardia were revealed. The patient was taken for electrophysiological examination and radiofrequency ablation of the focus of atrial tachycardia. The focus of atrial tachycardia was located in the anterior septal part of the left atrium, which is a rare localization. After radiofrequency ablation tachycardia was terminated, no complications and recurrences were registered. The patient was discharged with the sinus rhythm. Navigation system EnsitePrecision® enables conducting high-density myocardial mapping, which helps to accurately determine the localization of the source of tachycardia. The radiation load on the patient and ablation time are reduced, which reduces the frequency of complications from the procedure