Matrix data sets are common nowadays like in biomedical imaging where the Diffusion Tensor Magnetic Resonance Imaging (DT-MRI) modality produces data sets of 3D symmetric positive definite matrices anchored at voxel positions capturing the anisotropic diffusion properties of water molecules in biological tissues. The space of symmetric matrices can be partially ordered using the Löwner ordering...

We survey recent results on first-passage processes in unbounded cones and their applications to ordering of particles undergoing Brownian motion in one dimension. We first discuss the survival probability S(t) that a diffusing particle, in arbitrary spatial dimension, remains inside a conical domain up to time t. In general, this quantity decays algebraically S ∼ t in the long-time limit. The ...

We propose an experimental setup of ultracold fermions in an optical lattice to determine the pairing gap in a superfluid state and the spin ordering in a Mott-insulating state. The idea is to apply a periodic modulation of the lattice potential and to use the thereby induced double occupancy to probe the system. We show by full time-dependent calculation using the adaptive time-dependent densi...

Introduction: Semaphorin 3A (Sema 3A) is a secreted protein, which plays an integral part in developing the nervous system. It has collapse activity on the growth cone of dorsal root ganglia. After the development of the nervous system, Sema 3A expression decreases. Neuropilin 1 is a membrane receptor of Sema 3A. When semaphorin binds to neuropilin 1, the recruitment of oligodendrocyte precurso...

we consider the semigroup $s$ of highest weights appearing in tensor powers $v^{otimes k}$ of a finite dimensional representation $v$ of a connected reductive group. we describe the cone generated by $s$ as the cone over the weight polytope of $v$ intersected with the positive weyl chamber. from this we get a description for the asymptotic of the number of highest weights appearing in $v^{otime...

The correlation between orientation ordering of polymer chains in the bulk of polymer film and at the polymer-liquid-crystal (LC) interface has been studied to determine it's role in LC alignment. The bulk and surface ordering of polymer were investigated by null ellipsometry and x-ray reflectivity, respectively. Two kinds of liquid-crystalline polymers were used; side-chain azopolymers with az...

The transcription factor p53 suppresses tumorgenesis by regulating cell proliferation and migration. We investigated whether p53 could also control cell motility in postmitotic neurons. p53 isoforms recognized by phospho-p53-specific (at Ser-15) or "mutant" conformation-specific antibodies were highly and specifically expressed in axons and axonal growth cones in primary hippocampal neurons. In...

In this paper, we first present new existence theorems of cone-supremum/infimum for directed convex and/or free disposal subsets in their closure. Then, we provide various conditions through which this kind of subsets admits a cone-maximum/minimum point, the so-called strongly maximal/minimal or ideal efficient points with respect to a cone. Next, we present a unifying result on the existence o...

The underlying mechanisms of polarization sensitivity (PS) have long remained elusive. For rhabdomeric photoreceptors, questions remain over the high levels of PS measured experimentally. In ciliary photoreceptors, and specifically cones, little direct evidence supports any type of mechanism. In order to promote a greater interest in these fundamental aspects of polarization vision, we examined...