On the use of information theory for detecting upper limb motor dysfunction: An application to Parkinson’s disease

Parkinson’s disease (PD) is a chronic neurodegenerative disorder characterized by a selective loss of dopaminergic neurons in the substantia nigra, decreased striatal dopamine levels, and consequent extrapyramidal motor dysfunctions. Several potential early diagnostic markers of PD have been proposed. Since they have not been validated in presymptomatic PD, the diagnosis and monitoring of the disease is based on subjective clinical assessment of cognitive and motor symptoms. In this study, we investigated interjoint coordination synergies in the upper limb of healthy and parkinsonian subjects during the performance of unconstrained linear-periodic movements in a horizontal plane using the mutual information (MI). We found that the MI is a sensitive metric in detecting upper limb motor dysfunction, thus suggesting that this method might be applicable to quantitatively evaluating the effects of the antiparkinsonian medication and to monitor the disease progression.     

Application of Fermat’s Principle to Calculation of the Errors of Acoustic Flow-Rate Measurements for a Three-Dimensional Fluid Flow or Gas

Fermat’s variational principle is used for derivation of the formula for the time of propagation of a sonic signal between two set points A and B in a steady three-dimensional flow of a fluid or gas. It is shown that the fluid flow changes the time of signal reception by a value proportional to the flow rate independently of the velocity profile. The time difference in the reception of the signals from point B to point A and vice versa is proportional with a high accuracy to the flow rate. It is shown that the relative error of the formula does not exceed the square of the largest Mach number. This makes it possible to measure the flow rate of a fluid or gas with an arbitrary steady subsonic velocity field.     

On Convergence to SLE<Subscript>6</Subscript> II: Discrete Approximations and Extraction of Cardy’s Formula for General Domains

We show how to extract Cardy’s Formula for a general class of domains given the requisite interior analyticity statement. This is accomplished by a careful study of the interplay between discretization schemes and extraction of limiting boundary values. Of particular importance to the companion work (Binder et al. in J. Stat. Phys., 2010) we establish these results for slit domains and for the critical percolation models introduced in Chayes and Lei (Rev. Math. Phys. 19:511–565, 2007).