The higher rank numerical range of nonnegative matrices

In this article the rank-k numerical range ∧ _k (A) of an entrywise nonnegative matrix A is investigated. Extending the notion of elements of maximum modulus in ∧ _k (A), we examine their location on the complex plane. Further, an application of this theory to ∧ _k (L(λ)) of a Perron polynomial L(λ) is elaborated via its companion matrix C _L .     

Self-Supervised Variational Auto-Encoders

Density estimation, compression, and data generation are crucial tasks in artificial intelligence. Variational Auto-Encoders (VAEs) constitute a single framework to achieve these goals. Here, we present a novel class of generative models, called self-supervised Variational Auto-Encoder (selfVAE), which utilizes deterministic and discrete transformations of data. This class of models allows both conditional and unconditional sampling while simplifying the objective function. First, we use a single self-supervised transformation as a latent variable, where the transformation is either downscaling or edge detection. Next, we consider a hierarchical architecture, i.e., multiple transformations, and we show its benefits compared to the VAE. The flexibility of selfVAE in data reconstruction finds a particularly interesting use case in data compression tasks, where we can trade-off memory for better data quality and vice-versa. We present the performance of our approach on three benchmark image data (Cifar10, Imagenette64, and CelebA).     

Biomimetic Approaches to “Transparent” Photovoltaics: Current and Future Applications

There has been a surge in the interest for (semi)transparent photovoltaics (sTPVs) in recent years, since the more traditional, opaque, devices are not ideally suited for a variety of innovative applications spanning from smart and self-powered windows for buildings to those for vehicle integration. Additional requirements for these photovoltaic applications are a high conversion efficiency (despite the necessary compromise to achieve a degree of transparency) and an aesthetically pleasing design. One potential realm to explore in the attempt to meet such challenges is the biological world, where evolution has led to highly efficient and fascinating light-management structures. In this mini-review, we explore some of the biomimetic approaches that can be used to improve both transparent and semi-transparent photovoltaic cells, such as moth-eye inspired structures for improved performance and stability or tunable, coloured, and semi-transparent devices inspired by beetles’ cuticles. Lastly, we briefly discuss possible future developments for bio-inspired and potentially bio-compatible sTPVs.     

A new rhodium complex with a nitrogen‐containing bis(phosphine oxide) ligand as an efficient catalyst for the hydroformylation of styrene

A new rhodium complex with a nitrogen‐containing bis(phosphine oxide) ligand has been synthesized. The complex was applied to hydroformylation of styrene and displayed high activity and regioselectivity towards the branched aldehyde, which was found to be higher than those of the tertiary bis(phosphine) analogue. Copyright © 2006 John Wiley & Sons, Ltd.     

Rhodium complexes with a new chiral nitrogen‐containing BINOL‐based diphosphite or phosphonite ligand: synthesis and application to hydroformylation of styrene and/or hydrogenation of prochiral olefins

Two new cationic rhodium(I) complexes with a chiral nitrogen‐containing BINOL‐based diphosphite or phosphonite ligand have been synthesized. Chiral diphosphite was prepared by the reaction of N‐phenyldiethanolamine with two equivalents of [(R)‐(1,1′‐binaphthalene‐2,2′‐diyl)]chlorophosphite. In its rhodium complex the ligand is bound to the metal via both phosphorus atoms, and a Rh–N interaction is also possible. Synthesis of the chiral phosphonite was achieved by the reaction of 2‐(N,N‐dimethylaminophenyl)‐bis(diethylamino)phosphine with one equivalent of R‐BINOL. In its rhodium complex, the ligand is P,N‐bonded, forming a five‐membered chelate ring. The first complex was applied to hydroformylation of styrene and displayed high activity and chemo‐ and regioselectivity, but unfortunately no asymmetric induction was found. Both complexes were evaluated in the hydrogenation of prochiral olefins with moderate activities and low enantioselectivities. Copyright © 2005 John Wiley & Sons, Ltd.     

Excitonic Bands in the Spectra of Some Organic-Inorganic Hybrid Compounds Based on Metal Halide Units

Summary.  The optical absorption, photoluminescence, and photoconductivity spectra of some compounds of the formulas [R(CH₂) _n NH₃] _x M _y X _z , [R(CH₂) _n NH(CH₃)₂] _x M _y X _z , [R(CH₂) _n S(CH₃)₂] _x M _y X _z , [R(CH₂) _n SC(NH₂)₂] _x M _y X _z , and [R(CH₂) _n SeC(NH₂)₂] _x M _y X _z (R = organic residue; M = Bi(III), Pb(II), Sn(II), Cu(I), Ag(I) etc; X = I, Br, Cl; n, x, y, z = 0, 1, 2, 3, …) are briefly reviewed, and some new results are reported. The position, intensity, and shape of the excitonic bands depend on the dimensionality and size of the inorganic network as well as on the nature of the M, X, R, and onium moieties. Received June 23, 2000. Accepted August 1, 2000     

Design of cellular manufacturing systems using Latent Semantic Indexing and Self Organizing Maps

A new, efficient clustering method for solving the cellular manufacturing problem is presented in this paper. The method uses the part-machine incidence matrix of the manufacturing system to form machine cells, each of which processes a family of parts. By doing so, the system is decomposed into smaller semi-independent subsystems that are managed more effectively improving overall performance. The proposed method uses Self Organizing Maps (SOMs), a class of unsupervised learning neural networks, to perform direct clustering of machines into cells, without first resorting to grouping parts into families as done by previous approaches. In addition, Latent Semantic Indexing (LSI) is employed to significantly reduce the complexity of the problem resulting in more effective training of the network, significantly improved computational efficiency, and, in many cases, improved solution quality. The robustness of the method and its computational efficiency has been investigated with respect to the dimension of the problem and the degree of dimensionality reduction. The effectiveness of grouping has been evaluated by comparing the results obtained with those of the k-means classical clustering algorithm.AMS classification: 62H30