Revealing the state space of turbulent pipe flow by symmetry reduction

Symmetry reduction by the method of slices is applied to pipe flow in order to quotient the stream-wise translation and azimuthal rotation symmetries of turbulent flow states. Within the symmetry-reduced state space, all travelling wave solutions reduce to equilibria, and all relative periodic orbits reduce to periodic orbits. Projections of these solutions and their unstable manifolds from their $\infty$-dimensional symmetry-reduced state space onto suitably chosen 2- or 3-dimensional subspaces reveal their interrelations and the role they play in organising turbulence in wall-bounded shear flows. Visualisations of the flow within the slice and its linearisation at equilibria enable us to trace out the unstable manifolds, determine close recurrences, identify connections between different travelling wave solutions, and find, for the first time for pipe flows, relative periodic orbits that are embedded within the chaotic attractor, which capture turbulent dynamics at transitional Reynolds numbers.Comment: 24 pages, 12 figure

Phase synchronization from noisy univariate signals

We present methods for detecting phase synchronization of two unidirectionally coupled, self-sustained noisy oscillators from a signal of the driven oscillator alone. One method detects soft, another hard phase locking. Both are applied to the problem of detecting phase synchronization in von Karman vortex flow meters.Comment: 4 pages, 4 figure

NMR implementation of Quantum Delayed-Choice Experiment

We report the first experimental demonstration of quantum delayed-choice experiment via nuclear magnetic resonance techniques. An ensemble of molecules each with two spin-1/2 nuclei are used as target and the ancilla qubits to perform the quantum circuit corresponding the delayed-choice setup. As expected in theory, our experiments clearly demonstrate the continuous morphing of the target qubit between particle-like and wave-like behaviors. The experimental visibility of the interference patterns shows good agreement with the theory.Comment: Revised text, more figures adde

Infrared spectroscopy of diatomic molecules - a fractional calculus approach

The eigenvalue spectrum of the fractional quantum harmonic oscillator is calculated numerically solving the fractional Schr\"odinger equation based on the Riemann and Caputo definition of a fractional derivative. The fractional approach allows a smooth transition between vibrational and rotational type spectra, which is shown to be an appropriate tool to analyze IR spectra of diatomic molecules.Comment: revised + extended version, 9 pages, 6 figure

The microbiome of diabetic foot ulcers : a comparison of swab and tissue biopsy wound sampling techniques using 16S rRNA gene sequencing

Background: Health-care professionals need to collect wound samples to identify potential pathogens that contribute to wound infection. Obtaining appropriate samples from diabetic foot ulcers (DFUs) where there is a suspicion of infection is of high importance. Paired swabs and tissue biopsies were collected from DFUs and both sampling techniques were compared using 16S rRNA gene sequencing. Results: Mean bacterial abundance determined using quantitative polymerase chain reaction (qPCR) was significantly lower in tissue biopsies (p = 0.03). The mean number of reads across all samples was significantly higher in wound swabs X = 32,014) compared to tissue (X = 15,256, p = 0.001). Tissue biopsies exhibited greater overall diversity of bacteria relative to swabs (Shannon’s H diversity p = 0.009). However, based on a presence/ absence analysis of all paired samples, the frequency of occurrence of bacteria from genera of known and potential pathogens was generally higher in wound swabs than tissue biopsies. Multivariate analysis identified significantly different bacterial communities in swabs compared to tissue (p = 0.001). There was minimal correlation between paired wound swabs and tissue biopsies in the number and types of microorganisms. RELATE analysis revealed low concordance between paired DFU swab and tissue biopsy samples (Rho = 0.043, p = 0.34). Conclusions: Using 16S rRNA gene sequencing this study identifies the potential for using less invasive swabs to recover high relative abundances of known and potential pathogen genera from DFUs when compared to the gold standard collection method of tissue biopsy. SOME OF THE SCIENTIC SYMBOLS CAN NOT BE REPRESENTED CORRECTLY IN THE ABSTRACT. PLEASE READ WITH CAUTION AND REFER TO THE ORIGINAL PUBLICATION

Estimating the Prognostic Value of the NTRK Fusion Biomarker for Comparative Effectiveness Research in The Netherlands

Objectives: We evaluated the prognostic value of the neurotrophic tyrosine receptor kinase (NTRK) gene fusions by comparing the survival of patients with NTRK+ tumours with patients without NTRK+ tumours. Methods: We used genomic and clinical registry data from the Center for Personalized Cancer Treatment (CPCT-02) study containing a cohort of cancer patients who were treated in Dutch clinical practice between 2012 and 2020. We performed a propensity score matching analysis, where NTRK+ patients were matched to NTRK− patients in a 1:4 ratio. We subsequently analysed the survival of the matched sample of NTRK+ and NTRK− patients using the Kaplan–Meier method and Cox regression, and performed an analysis of credibility to evaluate the plausibility of our result. Results:Among 3556 patients from the CPCT-02 study with known tumour location, 24 NTRK+ patients were identified. NTRK+ patients were distributed across nine different tumour types: bone/soft tissue, breast, colorectal, head and neck, lung, pancreas, prostate, skin and urinary tract. NTRK fusions involving the NTRK3 gene (46%) and NTRK1 gene (33%) were most common. The survival analysis rendered a hazard ratio (HR) of 1.44 (95% CI 0.81–2.55) for NTRK+ patients. Using the point estimates of three prior studies on the prognostic value of NTRK fusions, our finding that the HR is &gt; 1 was deemed plausible. Conclusions: NTRK+ patients may have an increased risk of death compared with NTRK− patients. When using historic control data to assess the comparative effectiveness of TRK inhibitors, the prognostic value of the NTRK fusion biomarker should therefore be accounted for.</p

Estimating the Prognostic Value of the NTRK Fusion Biomarker for Comparative Effectiveness Research in The Netherlands

Objectives: We evaluated the prognostic value of the neurotrophic tyrosine receptor kinase (NTRK) gene fusions by comparing the survival of patients with NTRK+ tumours with patients without NTRK+ tumours. Methods: We used genomic and clinical registry data from the Center for Personalized Cancer Treatment (CPCT-02) study containing a cohort of cancer patients who were treated in Dutch clinical practice between 2012 and 2020. We performed a propensity score matching analysis, where NTRK+ patients were matched to NTRK− patients in a 1:4 ratio. We subsequently analysed the survival of the matched sample of NTRK+ and NTRK− patients using the Kaplan–Meier method and Cox regression, and performed an analysis of credibility to evaluate the plausibility of our result. Results:Among 3556 patients from the CPCT-02 study with known tumour location, 24 NTRK+ patients were identified. NTRK+ patients were distributed across nine different tumour types: bone/soft tissue, breast, colorectal, head and neck, lung, pancreas, prostate, skin and urinary tract. NTRK fusions involving the NTRK3 gene (46%) and NTRK1 gene (33%) were most common. The survival analysis rendered a hazard ratio (HR) of 1.44 (95% CI 0.81–2.55) for NTRK+ patients. Using the point estimates of three prior studies on the prognostic value of NTRK fusions, our finding that the HR is &gt; 1 was deemed plausible. Conclusions: NTRK+ patients may have an increased risk of death compared with NTRK− patients. When using historic control data to assess the comparative effectiveness of TRK inhibitors, the prognostic value of the NTRK fusion biomarker should therefore be accounted for.</p

The time resolution of the St. Petersburg paradox

A resolution of the St. Petersburg paradox is presented. In contrast to the standard resolution, utility is not required. Instead, the time-average performance of the lottery is computed. The final result can be phrased mathematically identically to Daniel Bernoulli's resolution, which uses logarithmic utility, but is derived using a conceptually different argument. The advantage of the time resolution is the elimination of arbitrary utility functions.Comment: 20 pages, 1 figur