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

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

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

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

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

Voltage-dependent Anion Channel-1 (VDAC-1) Contributes to ATP Release and Cell Volume Regulation in Murine Cells

Extracellular ATP regulates several elements of the mucus clearance process important for pulmonary host defense. However, the mechanisms mediating ATP release onto airway surfaces remain unknown. Mitochondrial voltage-dependent anion channels (mt-VDACs) translocate a variety of metabolites, including ATP and ADP, across the mitochondrial outer membrane, and a plasmalemmal splice variant (pl-VDAC-1) has been proposed to mediate ATP translocation across the plasma membrane. We tested the involvement of VDAC-1 in ATP release in a series of studies in murine cells. First, the full-length coding sequence was cloned from a mouse airway epithelial cell line (MTE7b−) and transfected into NIH 3T3 cells, and pl-VDAC-1-transfected cells exhibited higher rates of ATP release in response to medium change compared with mock-transfected cells. Second, ATP release was compared in cells isolated from VDAC-1 knockout [VDAC-1 (−/−)] and wild-type (WT) mice. Fibroblasts from VDAC-1 (−/−) mice released less ATP than WT mice in response to a medium change. Well-differentiated cultures from nasal and tracheal epithelia of VDAC-1 (−/−) mice exhibited less ATP release in response to luminal hypotonic challenge than WT mice. Confocal microscopy studies revealed that cell volume acutely increased in airway epithelia from both VDAC-1 (−/−) and WT mice after luminal hypotonic challenge, but VDAC-1 (−/−) cells exhibited a slower regulatory volume decrease (RVD) than WT cells. Addition of ATP or apyrase to the luminal surface of VDAC-1 (−/−) or WT cultures with hypotonic challenge produced similar initial cell height responses and RVD kinetics in both cell types, suggesting that involvement of VDAC-1 in RVD is through ATP release. Taken together, these studies suggest that VDAC-1, directly or indirectly, contributes to ATP release from murine cells. However, the observation that VDAC-1 knockout cells released a significant amount of ATP suggests that other molecules also play a role in this function