Trades in complex Hadamard matrices

A trade in a complex Hadamard matrix is a set of entries which can be changed to obtain a different complex Hadamard matrix. We show that in a real Hadamard matrix of order $n$ all trades contain at least $n$ entries. We call a trade rectangular if it consists of a submatrix that can be multiplied by some scalar $c \neq 1$ to obtain another complex Hadamard matrix. We give a characterisation of rectangular trades in complex Hadamard matrices of order $n$ and show that they all contain at least $n$ entries. We conjecture that all trades in complex Hadamard matrices contain at least $n$ entries.Comment: 9 pages, no figure

Pathogenic Variants in Fucokinase Cause a Congenital Disorder of Glycosylation

FUK encodes fucokinase, the only enzyme capable of converting L-fucose to fucose-1-phosphate, which will ultimately be used for synthesizing GDP-fucose, the donor substrate for all fucosyltransferases. Although it is essential for fucose salvage, this pathway is thought to make only a minor contribution to the total amount of GDP-fucose. A second pathway, the major de novo pathway, involves conversion of GDP-mannose to GDP-fucose. Here we describe two unrelated individuals who have pathogenic variants in FUK and who presented with severe developmental delays, encephalopathy, intractable seizures, and hypotonia. The first individual was compound heterozygous for c.667T>C (p.Ser223Pro) and c.2047C>T (p.Arg683Cys), and the second individual was homozygous for c.2980A>C (p.Lys994Gln). Skin fibroblasts from the first individual confirmed the variants as loss of function and showed significant decreases in total GDP-[3H] fucose and [3H] fucose-1-phosphate. There was also a decrease in the incorporation of [5,6-3H]-fucose into fucosylated glycoproteins. Lys994 has previously been shown to be an important site for ubiquitin conjugation. Here, we show that loss-of-function variants in FUK cause a congenital glycosylation disorder characterized by a defective fucose-salvage pathway

Preassociative aggregation functions

The classical property of associativity is very often considered in aggregation function theory and fuzzy logic. In this paper we provide axiomatizations of various classes of preassociative functions, where preassociativity is a generalization of associativity recently introduced by the authors. These axiomatizations are based on existing characterizations of some noteworthy classes of associative operations, such as the class of Acz\'elian semigroups and the class of t-norms.Comment: arXiv admin note: text overlap with arXiv:1309.730

Exotic complex Hadamard matrices, and their equivalence

In this paper we use a design theoretical approach to construct new, previously unknown complex Hadamard matrices. Our methods generalize and extend the earlier results of de la Harpe--Jones and Munemasa--Watatani and offer a theoretical explanation for the existence of some sporadic examples of complex Hadamard matrices in the existing literature. As it is increasingly difficult to distinguish inequivalent matrices from each other, we propose a new invariant, the fingerprint of complex Hadamard matrices. As a side result, we refute a conjecture of Koukouvinos et al. on (n-8)x(n-8) minors of real Hadamard matrices.Comment: 10 pages. To appear in Cryptography and Communications: Discrete Structures, Boolean Functions and Sequence

All Teleportation and Dense Coding Schemes

We establish a one-to-one correspondence between (1) quantum teleportation schemes, (2) dense coding schemes, (3) orthonormal bases of maximally entangled vectors, (4) orthonormal bases of unitary operators with respect to the Hilbert-Schmidt scalar product, and (5) depolarizing operations, whose Kraus operators can be chosen to be unitary. The teleportation and dense coding schemes are assumed to be ``tight'' in the sense that all Hilbert spaces involved have the same finite dimension d, and the classical channel involved distinguishes d^2 signals. A general construction procedure for orthonormal bases of unitaries, involving Latin Squares and complex Hadamard Matrices is also presented.Comment: 21 pages, LaTe

TSPO interacts with VDAC1 and triggers a ROS-mediated inhibition of mitochondrial quality control

The 18-kDa TSPO (translocator protein) localizes on the outer mitochondrial membrane (OMM) and participates in cholesterol transport. Here, we report that TSPO inhibits mitochondrial autophagy downstream of the PINK1-PARK2 pathway, preventing essential ubiquitination of proteins. TSPO abolishes mitochondrial relocation of SQSTM1/p62 (sequestosome 1), and consequently that of the autophagic marker LC3 (microtubule-associated protein 1 light chain 3), thus leading to an accumulation of dysfunctional mitochondria, altering the appearance of the network. Independent of cholesterol regulation, the modulation of mitophagy by TSPO is instead dependent on VDAC1 (voltage-dependent anion channel 1), to which TSPO binds, reducing mitochondrial coupling and promoting an overproduction of reactive oxygen species (ROS) that counteracts PARK2-mediated ubiquitination of proteins. These data identify TSPO as a novel element in the regulation of mitochondrial quality control by autophagy, and demonstrate the importance for cell homeostasis of its expression ratio with VDAC1

On quaternary complex Hadamard matrices of small orders

One of the main goals of design theory is to classify, characterize and count various combinatorial objects with some prescribed properties. In most cases, however, one quickly encounters a combinatorial explosion and even if the complete enumeration of the objects is possible, there is no apparent way how to study them in details, store them efficiently, or generate a particular one rapidly. In this paper we propose a novel method to deal with these difficulties, and illustrate it by presenting the classification of quaternary complex Hadamard matrices up to order 8. The obtained matrices are members of only a handful of parametric families, and each inequivalent matrix, up to transposition, can be identified through its fingerprint.Comment: 7 page

YY1 haploinsufficiency causes an intellectual disability syndrome featuring transcriptional and chromatin dysfunction

Yin and yang 1 (YY1) is a well-known zinc-finger transcription factor with crucial roles in normal development and malignancy. YY1 acts both as a repressor and as an activator of gene expression. We have identified 23 individuals with de novo mutations or deletions of YY1 and phenotypic features that define a syndrome of cognitive impairment, behavioral alterations, intrauterine growth restriction, feeding problems, and various congenital malformations. Our combined clinical and molecular data define "YY1 syndrome" as a haploinsufficiency syndrome. Through immunoprecipitation of YY1-bound chromatin from affected individuals' cells with antibodies recognizing both ends of the protein, we show that YY1 deletions and missense mutations lead to a global loss of YY1 binding with a preferential retention at high-occupancy sites. Finally, we uncover a widespread loss of H3K27 acetylation in particular on the YY1-bound enhancers, underscoring a crucial role for YY1 in enhancer regulation. Collectively, these results define a clinical syndrome caused by haploinsufficiency of YY1 through dysregulation of key transcriptional regulators.Michele Gabriele, Anneke T. Vulto-van Silfhout, Pierre-Luc Germain, Alessandro Vitriolo, Raman Kumar, Evelyn Douglas, Eric Haan, Kenjiro Kosaki, Toshiki Takenouchi, Anita Rauch, Katharina Steindl, Eirik Frengen, Doriana Misceo, Christeen Ramane J. Pedurupillay, Petter Stromme, Jill A. Rosenfeld, Yunru Shao, William J. Craigen, Christian P. Schaaf, David Rodriguez-Buritica, Laura Farach, Jennifer Friedman, Perla Thulin, Scott D. McLean, Kimberly M. Nugent, Jenny Morton, Jillian Nicholl, Joris Andrieux, Asbjørg Stray-Pedersen, Pascal Chambon, Sophie Patrier, Sally A. Lynch, Susanne Kjaergaard, Pernille M. Tørring, Charlotte Brasch-Andersen, Anne Ronan, Arie van Haeringen, Peter J. Anderson, Zöe Powis, Han G. Brunner, Rolph Pfundt, Janneke H.M. Schuurs-Hoeijmakers, Bregje W.M. van Bon, Stefan Lelieveld, Christian Gilissen, Willy M. Nillesen, Lisenka E.L.M. Vissers, Jozef Gecz, David A. Koolen, Giuseppe Testa, Bert B.A. de Vrie