A weighted cellular matrix-tree theorem, with applications to complete colorful and cubical complexes

We present a version of the weighted cellular matrix-tree theorem that is suitable for calculating explicit generating functions for spanning trees of highly structured families of simplicial and cell complexes. We apply the result to give weighted generalizations of the tree enumeration formulas of Adin for complete colorful complexes, and of Duval, Klivans and Martin for skeleta of hypercubes. We investigate the latter further via a logarithmic generating function for weighted tree enumeration, and derive another tree-counting formula using the unsigned Euler characteristics of skeleta of a hypercube and the Crapo $\beta$-invariant of uniform matroids.Comment: 22 pages, 2 figures. Sections 6 and 7 of previous version simplified and condensed. Final version to appear in J. Combin. Theory Ser.

Electrical control of spins and giant g-factors in ring-like coupled quantum dots

Emerging theoretical concepts for quantum technologies have driven a continuous search for structures where a quantum state, such as spin, can be manipulated efficiently. Central to many concepts is the ability to control a system by electric and magnetic fields, relying on strong spin-orbit interaction and a large g-factor. Here, we present a new mechanism for spin and orbital manipulation using small electric and magnetic fields. By hybridizing specific quantum dot states at two points inside InAs nanowires, nearly perfect quantum rings form. Large and highly anisotropic effective g-factors are observed, explained by a strong orbital contribution. Importantly, we find that the orbital and spin-orbital contributions can be efficiently quenched by simply detuning the individual quantum dot levels with an electric field. In this way, we demonstrate not only control of the effective g-factor from 80 to almost 0 for the same charge state, but also electrostatic change of the ground state spin

Consciousness Detection in a Complete Locked-in Syndrome Patient through Multiscale Approach Analysis

Completely locked-in state (CLIS) patients are unable to speak and have lost all muscle movement. From the external view, the internal brain activity of such patients cannot be easily perceived, but CLIS patients are considered to still be conscious and cognitively active. Detecting the current state of consciousness of CLIS patients is non-trivial, and it is difficult to ascertain whether CLIS patients are conscious or not. Thus, it is important to find alternative ways to re-establish communication with these patients during periods of awareness, and one such alternative is through a brain–computer interface (BCI). In this study, multiscale-based methods (multiscale sample entropy, multiscale permutation entropy and multiscale Poincaré plots) were applied to analyze electrocorticogram signals from a CLIS patient to detect the underlying consciousness level. Results from these different methods converge to a specific period of awareness of the CLIS patient in question, coinciding with the period during which the CLIS patient is recorded to have communicated with an experimenter. The aim of the investigation is to propose a methodology that could be used to create reliable communication with CLIS patients

Characterisation of precipitation and carbide coarsening in low carbon low alloy Q&T steels during the early stages of tempering

In order to ensure that appropriate tempering conditions are used to obtain desired strength and toughness for low carbon low alloy quench and tempered (Q&T) steel plates in a range of thickness, it is desirable to be able to predict the effect of composition and tempering conditions (time and temperature) on the microstructure and hence the hardness evolution for these steels. In this paper, carbide precipitation and coarsening behaviour in three low carbon low alloy Q&T steels have been investigated during tempering at 600 °C up to 16 hours to determine the role of alloying additions of Mo, V, Cr and Si. It has been found that auto-tempering occurs during water quenching with ε’-carbide and cementite being present within the martensite laths for all three steels. In the Base steel, cementite becomes the stable second phase after 2 hours tempering and has an elliptical (sometimes spherical) shape, which coarsens with time during tempering from 2 h to 16 h. However, in the Base-Mo-V and Base-Cr-Mo-V-Si steels, elliptical and needle-shaped cementite (shown to contain Mn, Mo and Cr) both exist during tempering; furthermore, finer elliptical secondary Mo-V-rich carbides are observed after tempering for 4 h. The coarsening of cementite contributing to the softening process in the three steels has been quantified with, most significantly, the inter- and intra-lath carbides coarsening independently. Although fine secondary alloy carbides are observed after 4 hours tempering, they do not result in any noticeable secondary hardening peak in the Base-Mo-V and Base-Cr-Mo-V-Si steels