BACKGROUND An essential phenomenon during brain development is the extension of long collateral branches by axons. How the local cellular environment contributes to the initial sprouting of these branches in specific points of an axonal shaft remains unclear. METHODOLOGY/PRINCIPAL FINDINGS The principal mammillary tract (pm) is a landmark axonal bundle connecting ventral diencephalon to brain...

In this study, it was attempted to design a high-performance single-walled carbon nanotube (SWCNT) bundle interconnects in a full adder. For this purpose, the circuit performance was investigated using simulation in HSPICE software and considering the technology of 32-nm. Next, the effects of geometric parameters including the diameter of a nanotube, distance between nanotubes in a bundle, and ...

We present two classes of examples Hopf algebroids associated with non-commutative principal bundles. The first comes from deforming the bundle while leaving unchanged structure algebra. second is related to a quantum homogeneous space; this needs careful deformation algebra in order preserve compatibilities between operations.

We construct a natural L-metric on the perturbed Seiberg-Witten moduli spaces Mμ+ of a compact 4-manifold M , and we study the resulting Riemannian geometry of Mμ+ . We derive a formula which expresses the sectional curvature of Mμ+ in terms of the Green operators of the deformation complex of the Seiberg-Witten equations. In case M is simply connected, we construct a Riemannian metric on the S...

Let EG be a holomorphic principal G–bundle over a compact connected Riemann surface, where G is a connected reductive affine algebraic group defined over C, such that EG admits a holomorphic connection. Take any β ∈ H(X, ad(EG)), where ad(EG) is the adjoint vector bundle for EG, such that the conjugacy class β(x) ∈ g/G, x ∈ X , is independent of x. We give a sufficient condition for the existen...

We introduce the notions of multiplier C*-category and continuous bundle of C*-categories, as the categorical analogues of the corresponding C*-algebraic notions. Every symmetric tensor C*-category with conjugates is a continuous bundle of C*-categories, with base space the spectrum of the C*-algebra associated with the identity object. We classify tensor C*-categories with fibre the dual of a ...

Let V be any vector bundle over the sphere S n which is associated to the principal bundle of oriented orthonormal frames, or to that of spin frames. We give an explicit formula for the spectrum, with multiplicity, of the Bochner Laplacian r r on V , where r is the Riemannian or Riemannian spin connection. In the case of tensor bundles, we also give the spectrum of the Lichnerowicz Laplacian. T...

Utilizing gauge symmetries, the Geometric Arbitrage Theory reformulates any asset model, allowing for arbitrage by means of a stochastic principal fibre bundle with connection whose curvature measures “instantaneous capability”. The cash flow is associated vector bundle. zero eigenspace its Laplacian parameterizes all risk-neutral equivalent to statistical one. A market satisfies No-Free-Lunch-...

The quantization of gauge-affine gravity within the superfibre bundle formalism is proposed. By introducing an even pseudotensorial 1-superform over a principal superfibre bundle with superconnection, we obtain the geometrical BRST and anti-BRST transformations of the fields occurring in such a theory. Reducing the four-dimensional general affine group double-covering GA(4, R) to the Poincaré g...

The quantization of gauge-affine gravity within the superfiber bundle formalism is proposed. By introducing an even pseudotensorial 1-superform over a principal superfiber bundle with superconnection, we obtain the geometrical Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST transformations of the fields occurring in such a theory. Reducing the four-dimensional general affine group double-coverin...