Reduction and Realization in Toda and Volterra

We construct a new symplectic, bi-hamiltonian realization of the KM-system by reducing the corresponding one for the Toda lattice. The bi-hamiltonian pair is constructed using a reduction theorem of Fernandes and Vanhaecke. In this paper we also review the important work of Moser on the Toda and KM-systems.Comment: 17 page

Bayesian Optimisation for Safe Navigation under Localisation Uncertainty

In outdoor environments, mobile robots are required to navigate through terrain with varying characteristics, some of which might significantly affect the integrity of the platform. Ideally, the robot should be able to identify areas that are safe for navigation based on its own percepts about the environment while avoiding damage to itself. Bayesian optimisation (BO) has been successfully applied to the task of learning a model of terrain traversability while guiding the robot through more traversable areas. An issue, however, is that localisation uncertainty can end up guiding the robot to unsafe areas and distort the model being learnt. In this paper, we address this problem and present a novel method that allows BO to consider localisation uncertainty by applying a Gaussian process model for uncertain inputs as a prior. We evaluate the proposed method in simulation and in experiments with a real robot navigating over rough terrain and compare it against standard BO methods.Comment: To appear in the proceedings of the 18th International Symposium on Robotics Research (ISRR 2017

Review of Protocols Used in Ultrasound Thrombolysis

Objectives: This paper focuses on the review of protocols used in thrombolysis studies with ultrasound. Materials and methods: Data from peer-review articles were acquired. Results: The protocols of several published reports are summarized in 3 tables (in vitro, in vivo, and clinical), providing detailed information concerning clot model, thrombolytic drug, treatment mode, sonication parameters, evaluation method, thrombolysis outcome, side effects, and conclusions. Conclusions: The aim of this review was to give an overview of the different protocols used so far in the field of sonothrombolysis and investigate the impact of several aspects involved on sonothrombolysis outcome

The last integrable case of kozlov-Treshchev Birkhoff integrable potentials

We establish the integrability of the last open case in the Kozlov-Treshchev classification of Birkhoff integrable Hamiltonian systems. The technique used is a modification of the so called quadratic Lax pair for $D_n$ Toda lattice combined with a method used by M. Ranada in proving the integrability of the Sklyanin case.Comment: 13 page

Multiple Hamiltonian structure of Bogoyavlensky-Toda lattices

This paper is mainly a review of the multi--Hamiltonian nature of Toda and generalized Toda lattices corresponding to the classical simple Lie groups but it includes also some new results. The areas investigated include master symmetries, recursion operators, higher Poisson brackets, invariants and group symmetries for the systems. In addition to the positive hierarchy we also consider the negative hierarchy which is crucial in establishing the bi--Hamiltonian structure for each particular simple Lie group. Finally, we include some results on point and Noether symmetries and an interesting connection with the exponents of simple Lie groups. The case of exceptional simple Lie groups is still an open problem.Comment: 65 pages, 67 reference

iCub visual memory inspector: Visualising the iCub’s thoughts

This paper describes the integration of multiple sensory recognition models created by a Synthetic Autobiographical Memory into a structured system. This structured system provides high level control of the overall architecture and interfaces with an iCub simulator based in Unity which provides a virtual space for the display of recollected events

Evaluation of fast spin echo MRI sequence for an MRI guided high intensity focused ultrasound system for in vivo rabbit liver ablation

The effectiveness of magnetic resonance imaging (MRI) to monitor thermal lesions created by High Intensity Focused Ultrasound (HIFU) in rabbit liver in vivo is investigated. The MRI sequences of T1-weighted, and T2-weighted fast spin echo (FSE) were evaluated. The main goal in this paper was to find the range of repetition time (TR) and range of echo time (TE) which maximizes the contrast to noise ratio (CNR). An ultrasonic transducer operating at 2 MHz was used, which is navigated using a positioning device. With T1W FSE the range of TR under which CNR is maximized ranges from 400 to 900 ms. The maximum contrast measured is approximately 25. With T2W FSE the range of TE that establishes maximum contrast is between 40 ms and 80 ms, with CNR of approximately 14. T1W FSE is much better than T2W FSE in detecting thermal lesions in liver. Both T1W and T2 W FSE were proven successful to image thermal lesions created by HIFU in rabbit liver in vivo

Heart ablation using a planar rectangular high intensity ultrasound transducer and MRI guidance

The aim of this study was to evaluate a flat rectangular (3 × 10 mm2) MRI compatible transducer operating at 5 MHz. The main task was to explore the feasibility of creating deep lesions in heart at a depth of at least 15 mm. The size of thermal necrosis in heart tissue was estimated as a function of power and time using a simulation model. The system was then tested in an excised lamb heart. In this study, we were able to create lesions of 15 mm deep with acoustic power of 6 W for an exposure of approximately 1 min. The contrast to noise ratio (CNR) between lesion and heart tissue was evaluated using fast spin echo (FSE). The CNR value was approximately 22 using T1 W FSE. Maximum CNR was achieved with repetition time (TR) between 300 and 800 ms. Using T2W FSE, the corresponding CNR was approximately 13 for the 14 in vivo experiments. The average lesion depth was 11.93 mm with a standard deviation of 0.62 mm. In vivo irradiation conditions were 6 W for 60 s. The size of the lesion in the other two dimensions was close to 3 × 10 mm2 (size of the transducer element)

MRI monitoring of lesions created at temperature below the boiling point and of lesions created above the boiling point using high intensity focused ultrasound

Magnetic Resonance Imaging (MRI) was utilized to monitor lesions created at temperature below the boiling point and lesions created at temperature above the boiling point using High Intensity Focused Ultrasound (HIFU) in freshly excised kidney, liver and brain and in vivo rabbit kidney and brain. T2-weighted fast spin echo (FSE) was proven as an excellent MRI sequence that can detect lesions with temperature above the boiling point in kidney. This advantage is attributed to the significant difference in signal intensity between the cavity and the thermal lesion. In liver the MRI sequence of Proton Density is recommended to detect lesions above boiling. In brain T1-W FSE was the optimum pulse sequence to detect lesions of either type. In order to monitor the temperature elevation during a HIFU exposure, T1-weighted fast spoiled gradient (FSPGR) was used. The shape of the focal temperature distribution was uniform with the absence of boiling, whereas with an exposure affected by boiling, the temperature distribution could be of irregular shape, demonstrating the drastic effects taking place during boiling. In order to confirm that boiling occurred, the temperature was estimated using the widely used method of Proton Resonance Frequency (PRF) shift