Non-commutative Painleve' equations and Hermite-type matrix orthogonal polynomials

We study double integral representations of Christoffel-Darboux kernels associated with two examples of Hermite-type matrix orthogonal polynomials. We show that the Fredholm determinants connected with these kernels are related through the Its-Izergin-Korepin-Slavnov (IIKS) theory with a certain Riemann-Hilbert problem. Using this Riemann-Hilbert problem we obtain a Lax pair whose compatibility conditions lead to a non-commutative version of the Painleve' IV differential equation for each family.Comment: Final version, accepted for publication on CMP: Communications in Mathematical Physics. 24 pages, 1 figur

GUIDER: a GUI for semiautomatic, physiologically driven EEG feature selection for a rehabilitation BCI

GUIDER is a graphical user interface developed in MATLAB software environment to identify electroencephalography (EEG)-based brain computer interface (BCI) control features for a rehabilitation application (i.e. post-stroke motor imagery training). In this context, GUIDER aims to combine physiological and machine learning approaches. Indeed, GUIDER allows therapists to set parameters and constraints according to the rehabilitation principles (e.g. affected hemisphere, sensorimotor relevant frequencies) and foresees an automatic method to select the features among the defined subset. As a proof of concept, we compared offline performances between manual, just based on operator’s expertise and experience, and GUIDER semiautomatic features selection on BCI data collected from stroke patients during BCI-supported motor imagery training. Preliminary results suggest that this semiautomatic approach could be successfully applied to support the human selection reducing operator dependent variability in view of future multi-centric clinical trials

BCI-assisted training for upper limb motor rehabilitation: estimation of effects on individual brain connectivity and motor functions

The aim of the study is to quantify individual changes in scalp connectivity patterns associated to the affected hand movement in stroke patients after a 1-month training based on BCIsupported motor imagery to improve upper limb motor recovery. To perform the statistical evaluation between pre- and post-training conditions at the single subject level, a resampling approach was applied to EEG datasets acquired from 12 stroke patients during the execution of a motor task with the stroke affected hand before and after the rehabilitative intervention. Significant patterns of the network reinforced after the training were extracted and a significant correlation was found between indices related to the reinforced pattern and the clinical outcome indicated by clinical scales

Identification of new orbits to enable future mission oppportunities for the human exploration of the Martian moon Phobos

One of the paramount stepping stones towards NASA's long-term goal of undertaking human missions to Mars is the exploration of the Martian moons. Since a precursor mission to Phobos would be easier than landing on Mars itself, NASA is targeting this moon for future exploration, and ESA has also announced Phootprint as a candidate Phobos sample-and-return mission. Orbital dynamics around small planetary satellites are particularly complex because many strong perturbations are involved, and the classical circular restricted three-body problem (R3BP) does not provide an accurate approximation to describe the system's dynamics. Phobos is a special case, since the combination of a small mass-ratio and length-scale means that the sphere-of-influence of the moon moves very close to its surface. Thus, an accurate nonlinear model of a spacecraft's motion in the vicinity of this moon must consider the additional perturbations due to the orbital eccentricity and the complete gravity field of Phobos, which is far from a spherical-shaped body, and it is incorporated into an elliptic R3BP using the gravity harmonics series-expansion (ER3BPGH). In this paper, a showcase of various classes of non-keplerian orbits are identified and a number of potential mission applications in the Mars-Phobos system are proposed: these results could be exploited in upcoming unmanned missions targeting the exploration of this Martian moon. These applications include: low-thrust hovering and orbits around Phobos for close-range observations; the dynamical substitutes of periodic and quasi-periodic Libration Point Orbits in the ER3BP-GH to enable unique low-cost operations for space missions in the proximity of Phobos; their manifold structure for high-performance landing / take-off maneuvers to and from Phobos' surface and for transfers from and to Martian orbits; Quasi-Satellite Orbits for long-period station-keeping and maintenance. In particular, these orbits could exploit Phobos' occulting bulk and shadowing wake as a passive radiation shield during future manned flights to Mars to reduce human exposure to radiation, and the latter orbits can be used as an orbital garage, requiring no orbital maintenance, where a spacecraft could make planned pit-stops during a round-trip mission to Mars

Attentional processes during P3-based Brain Computer Interface task in amyotrophic lateral sclerosis patients

To be available for a wide range of end-users a brain-computer interface (BCI) should be flexible and adaptable to end-users’ cognitive strengths and weaknesses. People’s cognitive abilities change according to the disease they are affected by, and people suffering from the same disease could have different cognitive capacities. We aimed at investigating how the amyotrophic lateral sclerosis (ALS) disease, and two different cognitive attentional aspects [1] influenced the usage of a P3-based BC

What Constitutes an Effective Instructional Video When Incorporated in Simulation Software Packages

Many studies have shown that instructional videos can be a highly effective educational tool (e.g., Kay, 2012; Lloyd and Robertson, 2012; Rackaway, 2012; Hsin and Cigas, 2013). In particular, Hsin and Cigas, (2013) describes the outcome derived from using video mini-lectures in an introductory course in computer science/mathematics. Student withdrawal, the failure rate, time-intensive interactive chats and written communication by the instructor was reduced after adding the videos to the class. Students were more satisfied with the course and average grades in the course increased slightly. This study expands the use of video mini-lectures to using a simulation software package that includes observing a video, practice the steps in the video and apply skills in simulated environments. It will define and measure the elements and use of video demonstrations included in a commercial simulation software package