Mesoscale and clusters of synchrony in networks of bursting neurons

We study the role of network architecture in the formation of synchronous clusters in synaptically coupled networks of bursting neurons. We give a simple combinatorial algorithm that finds the largest synchronous clusters from the network topology. We demonstrate that networks with a certain degree of internal symmetries are likely to have cluster decompositions with relatively large clusters, leading potentially to cluster synchronization at the mesoscale network level. We also address the asymptotic stability of cluster synchronization in excitatory networks of Hindmarsh-Rose bursting neurons and derive explicit thresholds for the coupling strength that guarantees stable cluster synchronization.     

A compact permanent magnet array with a remote homogeneous field

We present the design and construction of a single sided magnet array generating a homogeneous field in a remote volume. The compact array measures 11.5 cm by 10 cm by 6 cm and weights approximately 5 kg. It produces a B(0) field with a 'sweet spot' at a point 1cm above its surface, where its first and second spatial derivatives are approximately zero. Unlike other sweet spot magnets of this general type, our array has B(0) oriented parallel to its surface. This allows an ordinary surface coil to be used for unilateral measurements, giving the potential for dramatic SNR improvement.     

Continuous monitoring of dough fermentation and bread baking by magnetic resonance microscopy

The consumer quality of baked products is closely related with dough structure properties. These are developed during dough fermentation and finalized during its baking. In this study, magnetic resonance microscopy (MRM) was employed in a study of dough fermentation and baking. A small hot air oven was installed inside a 2.35-T horizontal bore superconducting magnet. Four different samples of commercial bread mixes for home baking were used to prepare small samples of dough that were inserted in the oven and allowed to rise at 33°C for 112 min; this was followed by baking at 180°C for 49 min. The entire process was followed by dynamic T₁-weighted 3D magnetic resonance imaging with 7 min of temporal resolution and 0.23×0.23×1.5 mm³ of spatial resolution. Acquired images were analyzed to determine time courses of dough pore distribution, dough volume and bread crust thickness. Image analysis showed that both the number of dough pores and the normalized dough volume increased in a sigmoid-like fashion during fermentation and decreased during baking due to the bread crust formation. The presented magnetic resonance method was found to be efficient in analysis of dough structure properties and in discrimination between different dough types.     

Isomorphism of two realizations of quantum affine algebraU_q (\widehat{\mathfrak{g}\mathfrak{l}{\text{(}}n{\text{)}}})

We establish an explicit isomorphism between two realizations of the quantum affine algebra given previously by Drinfeld and Reshetikhin-Semenov-Tian-Shansky. Our result can be considered as an affine version of the isomorphism between the Drinfield/Jimbo and the Faddeev-Reshetikhin-Takhtajan constructions of the quantum algebra .     

Superradiance of trapped atoms

A new method for calculating the total power of the spontaneous emission of a few motionless two-level atoms located at a distance of the order of the resonance-radiation wavelength with dipole-dipole interaction is suggested. The method is based on the Schrödinger representation. It is shown, as an example, that two trapped atoms cannot emit a pulse of superradiance under any conditions, while four atoms can emit such a pulse at certain conditions. Different ways of introducing the quasi-stationary states of atoms along with the generalization of the proposed method to other resonance systems are discussed.     

Distortion-free single point imaging of multi-layered composite sandwich panel structures

The results of a magnetic resonance imaging (MRI) investigation concerning the effects of an aluminum honeycomb sandwich panel on the B1 and B0 fields and on subsequent image quality are presented. Although the sandwich panel structure, representative of an aircraft composite material, distorts B0 and attenuates B1, distortion-free imaging is possible using single point (constant time) imaging techniques. A new expression is derived for the error caused by gradient field distortion due to the heterogeneous magnetic susceptibility within a sample and this error is shown not to cause geometric distortion in the image. The origin of the B0 distortion in the sample under investigation was also examined. The graphite-epoxy 'skin' of the panel is the principal source of the B0 distortion. Successful imaging of these structures sets the stage for the development of methods for detecting moisture ingress and degradation within composite sandwich structures.     

Mechanical properties of silk: interplay of deformation on macroscopic and molecular length scales

Using an in situ combination of tensile tests and x-ray diffraction, we have determined the mechanical properties of both the crystalline and the disordered phase of the biological nanocomposite silk by adapting a model from linear viscoelastic theory to the semicrystalline morphology of silk. We observe a strong interplay between morphology and mechanical properties. Silk's high extensibility results principally from the disordered phase; however, the crystals are also elastically deformed.     

Algorithmic boundedness-from-below conditions for generic scalar potentials

Checking that a scalar potential is bounded from below (BFB) is an ubiquitous and notoriously difficult task in many models with extended scalar sectors. Exact analytic BFB conditions are known only in simple cases. In this work, we present a novel approach to algorithmically establish the BFB conditions for any polynomial scalar potential. The method relies on elements of multivariate algebra, in particular, on resultants and on the spectral theory of tensors, which is being developed by the mathematical community. We give first a pedagogical introduction to this approach, illustrate it with elementary examples, and then present the working Mathematica implementation publicly available at GitHub. Due to the rapidly increasing complexity of the problem, we have not yet produced ready-to-use analytical BFB conditions for new multi-scalar cases. But we are confident that the present implementation can be dramatically improved and may eventually lead to such results.