Weakly Nonextensive Thermostatistics and the Ising Model with Long--range Interactions

We introduce a nonextensive entropic measure $S_{\chi}$ that grows like $N^{\chi}$, where $N$ is the size of the system under consideration. This kind of nonextensivity arises in a natural way in some $N$-body systems endowed with long-range interactions described by $r^{-\alpha}$ interparticle potentials. The power law (weakly nonextensive) behavior exhibited by $S_{\chi}$ is intermediate between (1) the linear (extensive) regime characterizing the standard Boltzmann-Gibbs entropy and the (2) the exponential law (strongly nonextensive) behavior associated with the Tsallis generalized $q$-entropies. The functional $S_{\chi}$ is parametrized by the real number $\chi \in[1,2]$ in such a way that the standard logarithmic entropy is recovered when $\chi=1$ >. We study the mathematical properties of the new entropy, showing that the basic requirements for a well behaved entropy functional are verified, i.e., $S_{\chi}$ possesses the usual properties of positivity, equiprobability, concavity and irreversibility and verifies Khinchin axioms except the one related to additivity since $S_{\chi}$ is nonextensive. For $1<\chi<2$, the entropy $S_{\chi}$ becomes superadditive in the thermodynamic limit. The present formalism is illustrated by a numerical study of the thermodynamic scaling laws of a ferromagnetic Ising model with long-range interactions.Comment: LaTeX file, 20 pages, 7 figure

The impact of motor symptoms on self-reported anxiety in Parkinson's disease

OBJECTIVE: Anxiety is commonly endorsed in Parkinson's disease (PD) and significantly affects quality of life. The Beck Anxiety Inventory (BAI) is often used but contains items that overlap with common PD motor symptoms (e.g., “hands trembling”). Because of these overlapping items, we hypothesized that PD motor symptoms would significantly affect BAI scores. METHODS: One hundred non-demented individuals with PD and 74 healthy control participants completed the BAI. PD motor symptoms were assessed by the Unified Parkinson's Disease Rating Scale (UPDRS). Factor analysis of the BAI assessed for a PD motor factor, and further analyses assessed how this factor affected BAI scores. RESULTS: BAI scores were significantly higher for PD than NC. A five-item PD motor factor correlated with UPDRS observer-rated motor severity and mediated the PD-control difference on BAI total scores. An interaction occurred, whereby removal of the PD motor factor resulted in a significant reduction in BAI scores for PD relative to NC. The correlation between the BAI and UPDRS significantly declined when controlling for the PD motor factor. CONCLUSIONS: The results indicate that commonly endorsed BAI items may reflect motor symptoms such as tremor instead of, or in addition to, genuine mood symptoms. These findings highlight the importance of considering motor symptoms in the assessment of anxiety in PD and point to the need for selecting anxiety measures that are less subject to contamination by the motor effects of movement disorders.Published versio

Optimization of Total Variation regularization to improve the accuracy of the characterization of vertical cracks by lock-in vibrothermography

We use lock-in vibrothermography to characterize vertical cracks. In the presence of ultrasounds, the rubbing of the crack faces produces heat which induces a temperature rise at the surface that is measured with an infrared camera. We fit data obtained by modulating the amplitude of the ultrasounds at several modulation frequencies. The inverse problem consisting of finding the geometry and location of the heat source from vibrothermography data is ill-posed, which makes it necessary to stabilize the inversion algorithm. We analyze the effect of the stabilizing term on the accuracy of the reconstructions

Low-cost sensors data fusion for small size unmanned aerial vehicles navigation and guidance

A new integrated navigation system designed for small size Unmanned Aerial Vehicles (UAVs) is presented. The proposed system is based on a number of low-cost avionics sensors, including Global Navigation Satellite Systems (GNSS), Micro-Electro-Mechanical System (MEMS) based Inertial Measurement Unit (IMU) and Vision Based Sensors (VBS). The use of an Aircraft Dynamics Models (ADMs) to provide additional information to compensate for the shortcomings of Vision Based Navigation (VBN) and MEMS-IMU sensors in high-dynamics attitude determination tasks is also considered. Additionally, the research concentrates on the potential of carrier-phase GNSS for Attitude Determination (GAD) using interferometric techniques. The main objective is to design a compact, light and relatively inexpensive system capable of providing the required navigation performance (position and attitude data) in all phases of flight of small UAVs, with a special focus on precision approach and landing, where VBN techniques can be fully exploited in a multi-sensor data fusion architecture. An Extended Kalman Filter (EKF) is developed to integrate the information provided by the different sensors and to provide estimates of position, velocity and attitude of the UAV platform in real-time. Three different integrated navigation system architectures are implemented. The first architecture uses VBN at 20 Hz and GNSS at 1 Hz to augment the MEMS-IMU running at 100 Hz. The second mode also includes the ADM (computations performed at 100 Hz) to provide augmentation of the attitude channel. The third fusion architecture uses GNSS based attitude values. The simulations are carried out on the AEROSONDE UAV performing high-dynamics manoeuvres repre-sentative of the UAV operational flight envelope. Simulation of the VBN-IMU-GNSS (VIG) integrated navigation system shows that the system can attain position, velocity and attitude accuracies complying with Category Two (CAT II) precision approach requirements. Simulation of the VBN-IMU-GNSS-ADM (VIGA) system also shows promising results, since the achieved attitude accuracy is higher using the ADM-VBN-IMU than using VBN-IMU only. However, due to rapid divergence of the ADM virtual sensor, there is a need for frequent re-initialisation of the ADM data module, which is strongly dependent on the UAV flight dynamics and the specific manoeuvring transitions performed. In the simulation of the third integrated navigation system, the VIG system is augmented by employing the GAD, forming the VIG-GAD (VIGGA) system architecture. The performances achieved with the VIG, VIGA and VIGGA integrated Navigation and Guidance System (NGS) are presented and are in line with the International Civil Aviation Organization (ICAO) precision approach requirements