Interpolating estimates with applications to some quantitative symmetry results

<abstract><p>We prove interpolating estimates providing a bound for the oscillation of a function in terms of two $ L^p $ norms of its gradient. They are based on a pointwise bound of a function on cones in terms of the Riesz potential of its gradient. The estimates hold for a general class of domains, including, e.g., Lipschitz domains. All the constants involved can be explicitly computed. As an application, we show how to use these estimates to obtain stability for Alexandrov's Soap Bubble Theorem and Serrin's overdetermined boundary value problem. The new approach results in several novelties and benefits for these problems.</p></abstract>

Benign fibrous histiocytoma of the femur: A rare pediatric case report

BACKGROUND: Benign fibrous histiocytoma is known to be a frequent skin tumor but its occurrence in bone remains very rare especially in pediatric population. This entity is a subject of interest also because histologically it can mimic other fibrohistiocytic lesions of bone such as non-ossifying fibroma. CLINICAL CASE: An 11-year-old patient admitted with swelling of the right thigh and intermittent pain. Radiological evaluation shows cystic lesion of the femur with a soap-bubble and a border of condensation. Histopathological examination of the biopsy sample established the diagnosis of benign fibrous histiocytoma. The patient underwent complete curettage of the lesion with bone graft. There is no recurrence 16 months after surgery. DISCUSSION: Benign fibrous histiocytoma is a rare bone tumor especially in children. Histologically it can mimic non-ossifying fibroma. Thus clinical and radiological features are important to differentiate these tumors in order to choose adequate treatment. CONCLUSIONS: Benign fibrous histiocytoma is probably underestimated in pediatric population. This diagnosis should be considered in any child or teenager who presents with a non-ossifying fibroma accompanied by unexplainable pain or a rapid growing.

P14.17 Conventional MRI criteria differentiate true tumour progression from treatment-induced effects in irradiated WHO grade 3 and 4 gliomas

BACKGROUND Post-treatment radiological deterioration of patients with an irradiated high-grade (WHO grade 3 and 4) glioma (HGG) may be the result of true progressive disease (PD) or treatment-induced effects (TIE). Differentiation between these two entities is of great importance, but remains a diagnostic challenge. This study assesses the diagnostic value of conventional MRI characteristics to differentiate PD from TIE in treated HGGs. MATERIAL AND METHODS In this single-centre, retrospective cohort study, we included adult patients with a HGG, who were treated with radiotherapy and subsequently developed a new or increasing contrast-enhancing lesion on conventional follow-up MRI. TIE and PD were defined radiologically as stable/decreased for a minimum of six weeks or progressive according to the RANO criteria, and histologically as predominantly TIE without viable tumour or PD. Demographic and clinical data were retrieved. Twenty-one preselected MRI characteristics of the progressive lesions were assessed by two neuroradiologists. The statistical analysis included logistic regression to develop a) a full multivariable model b) a diagnostic model with model reduction, and a Cohen’s Kappa interrater reliability coefficient. RESULTS 210 patients (median age 61, IQR=54–68, 189 males) with 284 lesions were included, of which 141 (50%) had PD. Median time to PD was 2 (0.7–6.1) and to TIE 0.9 (0.7–3.5) months after RT. In multivariable modelling and after model reduction, the following determinants were significant diagnostic factors: Radiation dose (Odds ratio (OR)=0.68, p=0.017), longer time since radiotherapy (OR=3.56, p&lt;0.0005), certain enhancement patterns (soap bubble enhancement: OR=2.63, p=0.003), isointense apparent diffusion coefficient-signal (OR=2.11, p=0.036), development of multiple new lesions (OR=1.68, p=0.088) and increased marginal enhancement (OR=2.04, p=0.027). ORs of &gt;1 indicate higher odds of PD. The Hosmer & Lemeshow test showed a good calibration (p=0.947) and the area under the ROC-curve was 0.722 (95%-CI=0.66–0.78). Interrater reliability analysis between neuroradiologists revealed moderate to near-perfect agreement for the significantly predictive items, but poor agreement for others. CONCLUSION In patients with irradiated high-grade gliomas, several characteristics from conventional MRI are significant predictors for the discrimination between true progression and treatment-induced effects. Interrater reliability for these characteristics was variable. Conventional MRI characteristics from this study should be incorporated into a multimodal diagnostic model that includes advanced imaging techniques. FUNDING INFORMATION Foundation Vrienden UMC Utrecht and The StophersenkankerNU Foundation.

Soap bubbles seeding for quantitative time resolved velocity measurements of a turbulent wake flow behind a cylinder

The wake flow behind a cylinder of 100mm diameter is investigated using time resolved 2D PIV technique applied to an air flow generated in a closed loop open test section wind tunnel. The flow is seeded using a micro soap bubble generator (BG-1000, TSI Inc.). The bubbles in the air flow were illuminated with a CW laser source and imaged using a high-speed camera. The main purpose of this study is to show features and advantages of using soap bubbles as seeding for a relatively large-scale PIV investigation under low power illumination conditions.

Development of micro soap bubble generator for PIV tracer using home stereolithography 3D printer

A micro soap bubble generator for tracers for PIV measurement was developed using a home stereolithography 3D printer. The nozzle has a coaxial triple pipe structure, and an orifice cap is attached to the nozzle head. The inner diameter of the central pipe is 0.7 mm, and the wall thickness of the central pipe is 0.7 mm. From the comparison of the smoke wire visualization result of the flow around the cylinder placed under the mainstream flow velocity of 3 m/s and the PIV measurement result, it was confirmed that the generated micro soap bubbles have good followability to the flow. Generated bubbles’ particle size was estimated to be Φ0.2 mm at the minimum and Φ6.3 mm at the maximum. The most common was Φ0.9 mm ± 0.1 mm, accounting for more than 50% of the total.

Central Neurocytoma in the Fourth Ventricle: Case Report and Literature Review

Background: Central neurocytoma is a rare primary intracranial tumour that usually occurs in young people. Central neurocytoma is more common in the lateral ventricle, but it is rare in the fourth ventricle. Herein, we report a case of central neurocytoma in the fourth ventricle. To improve our understanding, diagnosis, and treatment of this disease, we reviewed the literature to analyse the age, gender, clinical manifestations, imaging characteristics, and surgical prognosis of CNC in the fourth ventricle.Case presentation: A 44-year-old Chinese women presented with headache and dizziness for 8 years, walking instability for 2 years, and aggravation for 1 month. MRI revealed a 3.0 cm × 3.6 cm ×3.4 cm lesion located in the fourth ventricle. The tumour was completely resected. Pathological results were consistent with central neurocytoma. The patient could not walk or speak fluently during post-operative period, and no recurrence was found during the seventh month of follow-up.Conclusions: Central neurocytoma in the fourth ventricle is a rare intracranial tumour that is difficult to diagnose preoperatively. However, it can be considered when cystic and solid lesions are present in the fourth ventricle, especially when the morphology is like a soap bubble. Surgery is the main treatment for CNC. Adjuvant radiotherapy can be considered for partial or subtotal resection cases, and the prognosis is good. No recurrence of central neurocytoma in the fourth ventricle has been reported thus far.

Control of Soap Bubble Ejection Robot Using Facial Expressions

This research has developed a soap bubble ejection robot as an amusement system that reads emotions from human facial expressions and controls the ejection of soap bubbles to improve human-robot interaction. A subject's response to soap bubble ejection is read by a built-in face recognition sensor which sends data to a control system which in turn controls the next ejection. Soap bubbles are often used to research children's emotions/emotional responses. First, evaluation experiments of the control system were performed using face photographs that show human emotions. The experimental results revealed that soap bubbles were ejected in the case of indifference, and the ejection stopped in the case of joy. Through the experimental results, it was confirmed that the control system worked properly when face photographs were used and also verified the effectiveness of the facial recognition sensor. Secondly, evaluation experiments were conducted with an actual human, and it was confirmed from the results that the control system operates as designed.

Physically Based Soap Bubble Synthesis for VR

To experience a real soap bubble show, materials and tools are required, as are skilled performers who produce the show. However, in a virtual space where spatial and temporal constraints do not exist, bubble art can be performed without real materials and tools to give a sense of immersion. For this, the realistic expression of soap bubbles is an interesting topic for virtual reality (VR). However, the current performance of VR soap bubbles is not satisfying the high expectations of users. Therefore, in this study, we propose a physically based approach for reproducing the shape of the bubble by calculating the measured parameters required for bubble modeling and the physical motion of bubbles. In addition, we applied the change in the flow of the surface of the soap bubble measured in practice to the VR rendering. To improve users’ VR experience, we propose that they should experience a bubble show in a VR HMD (Head Mounted Display) environment.