The geometry of rank decompositions of matrix multiplication II: 3 × 3 matrices

This is the second in a series of papers on rank decompositions of the matrix multiplication tensor. We present new rank 23 decompositions for the $3\times 3$ matrix multiplication tensor $M_{〈3〉}$. All our decompositions have symmetry groups that include the standard cyclic permutation of factors but otherwise exhibit a range of behavior. One of them has 11 cubes as summands and admits an unexpected symmetry group of order 12.We establish basic information regarding symmetry groups of decompositions and outline two approaches for finding new rank decompositions of $M_{〈\mathbf{n}〉}$ for larger n.     

Liquid electrolytes for dye-sensitized solar cells

The present review offers a survey of liquid electrolytes used in dye-sensitized solar cells from the beginning of photoelectrochemical cell research. It handles both the solvents employed, and the prerequisites identified for an ideal liquid solvent, as well as the various effects of electrolyte solutes in terms of redox systems and additives. The conclusions of the present review call for more detailed molecular insight into the electrolyte-electrode interface reactions and structures.     

Synchrotron research solves art mystery

An alliance of Australian scientists and conservators has made a quantum leap forward in the analysis of priceless artworks, revealing an earlier painting of a different woman beneath a French Impressionist masterpiece in unprecedented detail, using a technology combination unavailable anywhere else in the world.     

Singular lensing from the scattering on special space–time defects

It is well known that certain special classes of self-gravitating point-like defects, such as global (non gauged) monopoles, give rise to non-asymptotically flat space–times characterized by solid angle deficits, whose size depends on the details of the underlying microscopic models. The scattering of electrically neutral particles on such space–times is described by amplitudes that exhibit resonant behaviour when thescattering and deficit angles coincide. This, in turn, leads to ring-like structures where the cross sections are formally divergent (“singular lensing”). In this work, we revisit this particular phenomenon, with the twofold purpose of placing it in a contemporary and more general context, in view of renewed interest in the theory and general phenomenology of such defects, and, more importantly, of addressing certain subtleties that appear in the particular computation that leads to the aforementioned effect. In particular, by adopting a specific regularization procedure for the formally infinite Legendre series encountered, we manage to ensure the recovery of the Minkowski space–time, and thus the disappearance of the lensing phenomenon, in the no-defect limit, and the validity of the optical theorem for the elastic total cross section. In addition, the singular nature of the phenomenon is confirmed by means of an alternative calculation, which, unlike the original approach, makes no use of the generating function of the Legendre polynomials, but rather exploits the asymptotic properties of the Fresnel integrals.     

Aggregating multiple classification results using fuzzy integration and stochastic feature selection

Classifying magnetic resonance spectra is often difficult due to the curse of dimensionality; scenarios in which a high-dimensional feature space is coupled with a small sample size. We present an aggregation strategy that combines predicted disease states from multiple classifiers using several fuzzy integration variants. Rather than using all input features for each classifier, these multiple classifiers are presented with different, randomly selected, subsets of the spectral features. Results from a set of detailed experiments using this strategy are carefully compared against classification performance benchmarks. We empirically demonstrate that the aggregated predictions are consistently superior to the corresponding prediction from the best individual classifier.