Some images corresponding to a diffuse axonal injury (DAI) are processed using several quantum filters such as Hermite Weibull and Morse. Diffuse axonal injury is a particular, common and severe case of traumatic brain injury (TBI). DAI involves global damage on microscopic scale of brain tissue and causes serious neurologic abnormalities. New imaging techniques provide excellent images showing cellular damages related to DAI. Said images can be processed with quantum filters, which accomplish high resolutions of dendritic and axonal structures both in normal and pathological state. Using the Laplacian operators from the new quantum filters, excellent edge detectors for neurofiber resolution are obtained. Image quantum processing of DAI images is made using computer algebra, specifically Maple. Quantum filter plugins construction is proposed as a future research line, which can incorporated to the ImageJ software package, making its use simpler for medical personnel.
A model of transient flow with memory in a nanocapillar is formulated and anallitically solved. Nanofluidics behavior
is described by Navier-Stokes Equation when viscosity is a radially modulated parameter and by a border condition
corresponding with hysteretic sliding on the nanocapillar wall. Solution is obtained using the Laplace Transform, and
Bromwich Integral and the Residue Theorem for the Inverse Laplace Transform; with the final result being expressed
as an infinite series of Bessel Functions. The analytic solution for the case with material memory is compared with the
analytic solution for the case with no material memory and with constant viscosity. A formula for the development of
nanodynamic impedance is deduced. Analytic results are shown to be relevant in the design of nanofluidics devices
with applications in general nanotechnologies and pharmaceutical engineering in particular. Future lines of research
are also suggested.
Biologic processes are represented as Boolean networks, in a discrete time. The dynamics within these networks
are approached with the help of SMT Solvers and the use of computer algebra. Software such as Maple and Z3
was used in this case. The number of stationary states for each network was calculated. The network studied
here corresponds to the immune system under the effects of drastic mood changes. Mood is considered as a
Boolean variable that affects the entire dynamics of the immune system, changing the Boolean satisfiability and
the number of stationary states of the immune network. Results obtained show Z3’s great potential as a SMT
Solver. Some of these results were verified in Maple, even though it showed not to be as suitable for the problem
approach. The solving code was constructed using Z3-Python and Z3-SMT-LiB. Results obtained are important
in biology systems and are expected to help in the design of immune therapies. As a future line of research,
more complex Boolean network representations of the immune system as well as the whole psychological
apparatus are suggested.
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