Synchronization Patterns in Networks of Kuramoto Oscillators: A Geometric Approach for Analysis and Control

Synchronization is crucial for the correct functionality of many natural and man-made complex systems. In this work we characterize the formation of synchronization patterns in networks of Kuramoto oscillators. Specifically, we reveal conditions on the network weights and structure and on the oscillators' natural frequencies that allow the phases of a group of oscillators to evolve cohesively, yet independently from the phases of oscillators in different clusters. Our conditions are applicable to general directed and weighted networks of heterogeneous oscillators. Surprisingly, although the oscillators exhibit nonlinear dynamics, our approach relies entirely on tools from linear algebra and graph theory. Further, we develop a control mechanism to determine the smallest (as measured by the Frobenius norm) network perturbation to ensure the formation of a desired synchronization pattern. Our procedure allows us to constrain the set of edges that can be modified, thus enforcing the sparsity structure of the network perturbation. The results are validated through a set of numerical examples

Diagnostic pitfalls of urogenital tuberculosis

Objectives: To describe characteristics, details of diagnosis and outcomes of urogenital tuberculosis (UGTB) in a low-prevalence country. Methods: We conducted a retrospective observational study of 37 consecutive patients diagnosed with UGTB between 1st January 2014 and 31st October 2019 in an East London hospital. Results: 68% (25/37) of patients were male and the median age was 42 years (IQR 34–55). 89% (33/37) of patients were born outside the United Kingdom with 65% (24/37) born in the South Asian region. Renal (32.4%), epididymal (24.3%) and endometrial TB (21.6%) were the most prevalent forms of UGTB. Only 13.5% of UGTB patients had concurrent pulmonary TB. The median length of time from symptom onset to treatment was 163 days, while endometrial TB had an average delay to diagnosis of 564 days. Approximately half of patients with UGTB were culture positive (51.4%). However, 70% of early morning urines (EMUs) sent in urinary TB were culture positive. 11 patients (30.6%) underwent two or more invasive procedures, such as biopsy to obtain specimen samples. The mean treatment length for all UGTB cases was 7.3 months (SD 3.1). Notably, 25% of patients with endometrial TB required surgery despite antituberculous treatment. Conclusions: UGTB is challenging to diagnose as early disease is often asymptomatic. Clinicians faced with non-specific symptoms, or features suggestive of urogenital malignancy amongst patients from TB-endemic areas, should maintain a high suspicion of UGTB

An open-source robotic tool for the simulation of quasi-static finger pressing on stationary and vibrating surfaces

The Bogus Finger is a remote-controllable tool for simulating vertical pressing forces of various magnitude as exerted by a human finger. Its main application is the characterization of haptic devices under realistic active touch conditions. The device is released as an open-source hardware and software DIY project that can be easily built using off-the-shelf components. We report the characterization of the quasi-static properties of the device, and validate its dynamic response to pressing on a vibrating surface by comparison with human fingers. The present prototype configuration accurately reproduces the mechanical impedance of the human finger in the frequency range 200-400 Hz

Huygens principle based UWB microwave imaging method for skin cancer detection

In recent years, Ultra Wideband (UWB) technology has emerged as a promising alternative for use in a wide range of applications. One of the potential applications of UWB is in healthcare and imaging, motivated by its non-ionizing signals, low cost, low complexity, and its ability to penetrate through mediums. Moreover, the large bandwidth covered by UWB signals permits the very high resolution required in imaging experiments. In this paper, a recently introduced UWB microwave imaging technique based on the Huygens principle (HP), has been applied to multilayered skin model with an inclusion representing a tumor. The methodology of HP permits the capture of contrast such that different material properties within the region of interest can be discriminated in the final image, and its simplicity removes the need to solve inverse problems when forward propagating the waves. Therefore the procedure can identify and localize significant scatterers inside a multilayered volume. Validation of the technique through simulations on multilayered cylindrical model of the skin with inclusion representing the tumor has been performed

Free space operating microwave imaging device for bone lesion detection: a phantom investigation

In this letter, a phantom validation of a low complexity microwave imaging device operating in free space in the 1-6.5 GHz frequency band is presented. The device, initially constructed for breast cancer detection, measures the scattered signals in a multi-bistatic fashion and employs an imaging procedure based on Huygens principle. Detection has been achieved in both bone fracture lesion and bone marrow lesion scenarios using the superimposition of five doublet transmitting positions, after applying the rotation subtraction artefact removal method. A resolution of 5 mm and a signal to clutter ratio (3.35 in linear scale) are achieved confirming the advantage of employing multiple transmitting positions on increased detection capability