Here we ‘close the loop’ of the relationship between MSN responses and behaviour. That is, having established desired MSN response profiles from a behavioural analysis of basal ganglia output (Figure 1), we now seek to confirm that the MSNs derived from our learning rules give basal ganglia output of the required form. Our goal here is to show that the responsiveness of the spiking D1 and D2 MS...

Let a, b, c be fixed positive integers satisfying a2 + ab + b2 = c with gcd(a, b) = 1. We show that the Diophantine equation a2x+axby+b2y = cz has only the positive integer solution (x, y, z) = (1, 1, 1) under some conditions. The proof is based on elementary methods and Cohn’s ones concerning the Diophantine equation x2 + C = yn. Mathematics Subject Classification: 11D61

In this paper, we study the dynamics of FitzHugh–Nagumo system $$\dot{x}=z,\;\dot{y}=b\left( x-dy\right) ,\;\dot{z}=x\left( x-1\right) \left( x-a\right) +y+cz$$ having invariant algebraic surfaces. This has four different types The two these classes surfaces have been characterized in Valls (J Nonlinear Math Phys 26:569–578, 2019). Using quasi-homogeneous directional blow-up and Poincaré compac...

A strain of Mexican Boophilus microplus (Cz) collected near Coatzacoalcos, Veracruz, Mexico, exhibits a moderate, but significant, level of permethrin resistance. Unlike other highly permethrin resistant strains, the Cz strain does not have a mutation within the sodium channel gene that results in target-site insensitivity. However, the Cz strain possesses a substantial increase in general and ...

A boronic acid-functionalized mesoporous silica nanoparticle-based drug delivery system (BA-MSN) for glucose-responsive controlled release of both insulin and cyclic adenosine monophosphate (cAMP) was synthesized. Fluorescein isothiocyanate-labeled, gluconic acid-modified insulin (FITC-G-Ins) proteins were immobilized on the exterior surface of BA-MSN and also served as caps to encapsulate cAMP...

Mesoporous silica nanoparticles (MSNs) exhibit unique drug delivery properties and are thus considered as promising candidates for next generation nano-medicines. In particular, inhalation into the lungs represents a direct, non-invasive delivery route for treating lung disease. To assess MSN biocompatibility in the lung, we investigated the bioresponse of avidin-coated MSNs (MSN-AVI), as well ...

Increasing production of nanomaterials in industrial quantities has led to public health concerns regarding exposure, particularly among pregnant women and developing fetuses. Information regarding the barrier capacity of the placenta for various nanomaterials is limited due to challenges working with ex vivo human placentas or in vivo animal models. To facilitate real-time in vivo imaging of p...