Local and nonlocal solvable structures in ODEs reduction

Solvable structures, likewise solvable algebras of local symmetries, can be used to integrate scalar ODEs by quadratures. Solvable structures, however, are particularly suitable for the integration of ODEs with a lack of local symmetries. In fact, under regularity assumptions, any given ODE always admits solvable structures even though finding them in general could be a very difficult task. In practice a noteworthy simplification may come by computing solvable structures which are adapted to some admitted symmetry algebra. In this paper we consider solvable structures adapted to local and nonlocal symmetry algebras of any order (i.e., classical and higher). In particular we introduce the notion of nonlocal solvable structure

A Spherical Active Joint for Humanoids and Humans

Both humanoid robotics and prosthetics rely on the possibility of implementing spherical active joints to build dexterous robots and useful prostheses. There are three possible kinematic implementations of spherical joints: serial, parallel, and hybrid, each one with its own advantages and disadvantages. In this letter, we propose a hybrid active spherical joint, that combines the advantages of parallel and serial kinematics, to try and replicate some of the features of biological articulations: large workspace, compact size, dynamical behavior, and an overall spherical shape. We compare the workspace of the proposed joint to that of human joints, showing the possibility of an almost-complete coverage by the device workspace, which is limited only by kinematic singularities. A first prototype is developed and preliminarly tested as part of a robotic shoulder joint

Transcranial Magnetic Resonance Imaging-Guided Focused Ultrasound Treatment at 1.5 T: A Retrospective Study on Treatment- and Patient-Related Parameters Obtained From 52 Procedures

Objective: To present a retrospective analysis of patient- and sonication-related parameters of a group of patients treated with a transcranial magnetic resonance imaging (MRI)-guided focused ultrasound (tcMRgFUS) system integrated with a 1.5-T MRI unit. Methods: The data obtained from 59 patients, who underwent the tcMRgFUS procedure from January 2015 to April 2019, were retrospectively reviewed for this study. The following data, among others, were mainly collected: skull density ratio (SDR), skull area (SA), number of available transducer elements (Tx), and estimated focal power at target (FP). For each of the four different treatment stages, we calculated the number of sonication processes (S-n), user-defined sonication power (S-p), effective measured power (S-mp), sonication duration (S-d), user-defined energy (E), effective measured energy (E-m), maximum temperature (T-max), and MR thermometry plane orientation. Furthermore, the time delay between each sonication (S-t) and the total treatment time (T-t) were recorded. Results: Fifty-two patients (40 males and 12 females; age 64.51 +/- SD 11.90 years; range 26-86 years), who underwent unilateral Vim thalamotomy (left = 50, 96.15%; right = 2, 3.85%) for medication-refractory essential tremor (n = 39; 78%) or Parkinson tremor (n = 13; 22%) were considered. A total of 1,068 (95.10%) sonication processes were included in our final analysis (average S-n per treatment: 20.65 +/- 6.18; range 13-41). The energy released onto the planned target was found to decrease with the SDR for all temperature ranges. A positive correlation was observed between the slope of T-max vs. E-m plot and the SDR (R-2 = 0.765; p < 0.001). In addition, the T-max was positively correlated with SDR (R-2 = 0.398; p < 0.005). On the contrary, no significant correlation was found between SDR and SA or Tx. An analysis of the MR thermometry scanning plane indicated that, at our site, the axial and the coronal planes were used (on average) 10.4 (SD +/- 3.8) and 7.7 (SD +/- 3.0) times, respectively, whereas the sagittal plane was used only 2.5 (SD +/- 3.0) times per treatment. Conclusion: Our results confirm the factors that significantly influence the course of a tcMRgFUS procedure even when a 1.5-T MRI scanner is used for procedure guidance. The experience we gained in this study indicates that the SDR remains one of the most significant technical parameters to be considered in a tcMRgFUS procedure. The possibility of prospectively setting the sonication energy according to the presented curves of energy delivery as a function of SDR for each treatment stage could provide a further understanding and a greater awareness of this emerging technology

A proxy cost model for tramway services

In this paper, we build a proxy cost model for tramway services. we estimate separately: (i) transport services production costs; (ii) infrastructure costs; (iii) maintenance costs; (iv) administrative and general costs and (v) the cost of capital. we apply the proposed methodology to estimate the standard cost of italian tramway services. detailed data about costs, technical and environmental characteristics were collected by means of questionnaires sent to italian companies providing 100% of tramway services in 2012. we perform a simulation study in order to highlight the marginal impact of efficiency gains obtained by manipulating cost-driving variables both under the control of the operators (trains and drivers productivity) and of the local authority who assigns the service (number of train revenue kilometers (trK) assigned within the service contract, average fleet age). the simulations show how the local authority should allocate extra resources if it wants to increase the quality-quantity mix of tramway services. our results might help the decision-maker to define the maximum economic compensation (auction base) in competitive tendering procedures or a benchmark for the bargaining with the local monopolist

Uniform non-stoichiometric titanium nitride thin films for improved kinetic inductance detector array

We describe the fabrication of homogeneous sub-stoichiometric titanium nitride films for microwave kinetic inductance detector (mKID) arrays. Using a 6 inch sputtering target and a homogeneous nitrogen inlet, the variation of the critical temperature over a 2 inch wafer was reduced to <25 %. Measurements of a 132-pixel mKID array from these films reveal a sensitivity of 16 kHz/pW in the 100 GHz band, comparable to the best aluminium mKIDs. We measured a noise equivalent power of NEP = 3.6e-15 W/Hz^(1/2). Finally, we describe possible routes to further improve the performance of these TiN mKID arrays.Comment: 7 pages, 4 figures, submitted to Journal of low temperature physics, Proceedings of LTD-1