Mechanisms for Robust Local Differential Privacy.

We consider privacy mechanisms for releasing data X=(S,U), where S is sensitive and U is non-sensitive. We introduce the robust local differential privacy (RLDP) framework, which provides strong privacy guarantees, while preserving utility. This is achieved by providing robust privacy: our mechanisms do not only provide privacy with respect to a publicly available estimate of the unknown true distribution, but also with respect to similar distributions. Such robustness mitigates the potential privacy leaks that might arise from the difference between the true distribution and the estimated one. At the same time, we mitigate the utility penalties that come with ordinary differential privacy, which involves making worst-case assumptions and dealing with extreme cases. We achieve robustness in privacy by constructing an uncertainty set based on a Rényi divergence. By analyzing the structure of this set and approximating it with a polytope, we can use robust optimization to find mechanisms with high utility. However, this relies on vertex enumeration and becomes computationally inaccessible for large input spaces. Therefore, we also introduce two low-complexity algorithms that build on existing LDP mechanisms. We evaluate the utility and robustness of the mechanisms using numerical experiments and demonstrate that our mechanisms provide robust privacy, while achieving a utility that is close to optimal.

Shannon Entropy as an Indicator for Sorting Processes in Hydrothermal Systems.

Hydrothermal processes modify the chemical and mineralogical composition of rock. We studied and quantified the effects of hydrothermal processes on the composition of volcanic rocks by a novel application of the Shannon entropy, which is a measure of uncertainty and commonly applied in information theory. We show here that the Shannon entropies calculated on major elemental chemical composition data and short-wave infrared (SWIR) reflectance spectra of hydrothermally altered rocks are lower than unaltered rocks with a comparable primary composition. The lowering of the Shannon entropy indicates chemical and spectral sorting during hydrothermal alteration of rocks. The hydrothermal processes described in this study present a natural mechanism for transforming energy from heat to increased order in rock. The increased order is manifest as the increased sorting of chemical elements and SWIR absorption features of the rock, and can be measured and quantified by the Shannon entropy. The results are useful for the study of hydrothermal mineral deposits, early life environments and the effects of hydrothermal processes on rocks.

Evaluation of the cognitive-motor performance of adults with Duchenne Muscular Dystrophy in a hand-related task.

Duchenne muscular Dystrophy (DMD) is a progressive degenerative muscle disease, affecting, among others, the upper extremities. Effective hand rehabilitation can improve the hand function of people with DMD. To reach this goal, we first need to gain more insight into the hand cognitive-motor performance of people with DMD. This is the first study employing a systematic analysis on multi-finger, cognitive-motor performance of people with DMD. For this purpose, we propose an active dynamic visuo-motor task. The task employed six visual stimuli, a subset of which was activated at each trial. The stimuli were activated with a frequency of 1, 2, 3 and 4 Hz. Eight healthy participants and three participants with DMD performed the task. Additionally, the healthy participants performed seven sessions, and we assessed the training effects. Task-related cognitive-motor performance was evaluated using information transfer rate (ITR) and perceived workload. Regarding ITR, healthy participants performed significantly better than DMD participants; however, this was more evident for trials involving more than three fingers. Workload showed no difference between the healthy and the DMD groups. Healthy participants significantly improved their performance during training. Our results suggest that hand rehabilitation of people with DMD should consider multi-finger dynamic training. However, additional research with more people with DMD is needed for further generalization of our conclusions.

Quantification of information transfer rate of the human hand during a mouse clicking task with healthy adults and one adult with Duchenne muscular Dystrophy.

Duchenne muscular Dystrophy (DMD) Is a progressive muscle degenerative disease. Active hand assistive devices, can improve the quality of life of people with DMD. Such devices show a rejection rate due to complexity. Our hypothesis is, that a simple orthosis might prove more functional and realistic in assisting people with DMD. To investigate, we developed a portable setup that provides various visual stimuli and records the response of the subjects' fingers through a mouse clicking task. Six LEDs served as visual stimuli. The subjects' responses were obtained through mechanical interaction with two vertical mice. Different combinations of frequencies and numbers of stimuli were tested with 8 healthy subjects and one with DMD. Performance was evaluated in terms of information transfer rate (ITR), pattern accuracy and perceived workload. The outcome shows that lower complexity results in lower ITR and lower workload for all subjects. While for healthy subjects, maximum ITR was 4.3 bits/s, for DMD maximum ITR was 2.5 bits/s. Both maxima were achieved at the same trial (3 fingers at 2 Hz). This trial agrees with a pareto optimization analysis of ITR with respect to workload. The results support our hypothesis for a simple yet functional solution. Furthermore healthy subjects and the individual with DMD, in principal show similar finger control, albeit with lower absolute performance.