Accessing written math content can be difficult for students with Developmental Learning Disorders. Through a user study with 19 representative participants, we investigate how text-to-speech access compares to reading for these students in terms of math syntax memorability, as well as the perceived accessibility, ease of access, and usefulness. Results show that text-to-speech is regarded as significantly easier and more useful for accessing math content, compared to reading access. The perceived accessibility of math content is also higher for text-to-speech access, but actual improvement could not be verified as much of the content was correctly memorized in both conditions. However, some of the considered content was consistently better memorized through text-to-speech, indicating promising future applications of this technology.
For a one-dimensional diffusion process X, we derive the Laplace transform and the moments of the first time at which the age of an excursion above (or below) the level x is longer than u. The result is then illustrated for diffusion processes that are found relevant in applications. In the context of pricing Parisian options, the Brownian motion and the Geometric Brownian motion are considered and the Laplace transform can be made explicit and explicit expression for the moments can be derived. In the context of neuronal modeling, the Ornstein–Uhlenbeck process and the Cox–Ingersoll–Ross process are considered and the Laplace transform and the moments must be approximated by numerical inversion.
A new definition of firing time is given in the framework of Integrate and Fire neuronal models. The classical absorption condition at the threshold is relaxed and the firing time is defined as the first time the membrane potential process lies above a fixed depolarisation level for a sufficiently long time. The mathematical properties of the new firing time are investigated both for the Perfect Integrator and the Leaky Integrator. In the latter case, a simulation study is presented to complete the analysis where analytical results are not yet achieved.
