On Hadamard Product of Hypercomplex Numbers

Certain product rules take various forms in the set of hypercomplex numbers. In this paper, we introduce a new multiplication form of the hypercomplex numbers that will be called «the Hadamard product», inspired by the analogous product in the real matrix space, and investigate some algebraic properties of that, including the norm of inequality. In particular, we extend our new definition and its applications to the complex matrix theory.

NME6 is a phosphotransfer-inactive, monomeric NME/NDPK family member and functions in complexes at the interface of mitochondrial inner membrane and matrix

Background NME6 is a member of the nucleoside diphosphate kinase (NDPK/NME/Nm23) family which has key roles in nucleotide homeostasis, signal transduction, membrane remodeling and metastasis suppression. The well-studied NME1-NME4 proteins are hexameric and catalyze, via a phospho-histidine intermediate, the transfer of the terminal phosphate from (d)NTPs to (d)NDPs (NDP kinase) or proteins (protein histidine kinase). For the NME6, a gene/protein that emerged early in eukaryotic evolution, only scarce and partially inconsistent data are available. Here we aim to clarify and extend our knowledge on the human NME6. Results We show that NME6 is mostly expressed as a 186 amino acid protein, but that a second albeit much less abundant isoform exists. The recombinant NME6 remains monomeric, and does not assemble into homo-oligomers or hetero-oligomers with NME1-NME4. Consequently, NME6 is unable to catalyze phosphotransfer: it does not generate the phospho-histidine intermediate, and no NDPK activity can be detected. In cells, we could resolve and extend existing contradictory reports by localizing NME6 within mitochondria, largely associated with the mitochondrial inner membrane and matrix space. Overexpressing NME6 reduces ADP-stimulated mitochondrial respiration and complex III abundance, thus linking NME6 to dysfunctional oxidative phosphorylation. However, it did not alter mitochondrial membrane potential, mass, or network characteristics. Our screen for NME6 protein partners revealed its association with NME4 and OPA1, but a direct interaction was observed only with RCC1L, a protein involved in mitochondrial ribosome assembly and mitochondrial translation, and identified as essential for oxidative phosphorylation. Conclusions NME6, RCC1L and mitoribosomes localize together at the inner membrane/matrix space where NME6, in concert with RCC1L, may be involved in regulation of the mitochondrial translation of essential oxidative phosphorylation subunits. Our findings suggest new functions for NME6, independent of the classical phosphotransfer activity associated with NME proteins.

Compositional matrix-space models of language: Definitions, properties, and learning methods

We give an in-depth account of compositional matrix-space models (CMSMs), a type of generic models for natural language, wherein compositionality is realized via matrix multiplication. We argue for the structural plausibility of this model and show that it is able to cover and combine various common compositional natural language processing approaches. Then, we consider efficient task-specific learning methods for training CMSMs and evaluate their performance in compositionality prediction and sentiment analysis.

Functionalized Biomimetic Hydrogels Enhance Salivary Stem/Progenitor Cell Organization

Complex branched salivary structures remain challenging to replicate within implant ready hydrogels. We showed previously that hyaluronic acid (HA)-based hydrogels enable growth and organization of primary salivary-derived human stem/progenitor cells (hS/PCs) into multicellular spheroids. Here, we systematically functionalized three components of migration-permissive hydrogels to foster salivary tissue morphogenesis. We separately analyzed contributions of an enzymatically degradable crosslinker, a pendant integrin-binding site, and hydrogel porosity to best support high viability, integrin-dependent cell adhesion and migration. Structure size, frequency, and morphology were all affected by hydrogel crosslink density and integration of biofunctional peptides. Viability and proliferation data suggested that integration of integrin binding sites had the greatest effect on hS/PCs behavior. A larger internal matrix space, created by increasing both crosslinker length and PEG content, was needed to form large multicellular hS/PC structures. Peptide-modified hydrogels with more internal space shifted hS/PC organization from spheroidal, surrounded by thick basement membrane, to an asymmetric arrangement with punctate matrix proteins defining a "wrinkled" perimeter. Integrin-binding peptides activated integrin β1, with highest activation observed in hydrogels having both cleavable peptide and integrin ligand. The design parameters we prescribe allowed us to encapsulate hS/PCs in a humanized biomimetic hydrogel matrix able to support morphogenesis needed for salivary restoration.

Principal Bundle Structure of Matrix Manifolds

In this paper, we introduce a new geometric description of the manifolds of matrices of fixed rank. The starting point is a geometric description of the Grassmann manifold Gr(Rk) of linear subspaces of dimension r<k in Rk, which avoids the use of equivalence classes. The set Gr(Rk) is equipped with an atlas, which provides it with the structure of an analytic manifold modeled on R(k−r)×r. Then, we define an atlas for the set Mr(Rk×r) of full rank matrices and prove that the resulting manifold is an analytic principal bundle with base Gr(Rk) and typical fibre GLr, the general linear group of invertible matrices in Rk×k. Finally, we define an atlas for the set Mr(Rn×m) of non-full rank matrices and prove that the resulting manifold is an analytic principal bundle with base Gr(Rn)×Gr(Rm) and typical fibre GLr. The atlas of Mr(Rn×m) is indexed on the manifold itself, which allows a natural definition of a neighbourhood for a given matrix, this neighbourhood being proved to possess the structure of a Lie group. Moreover, the set Mr(Rn×m) equipped with the topology induced by the atlas is proven to be an embedded submanifold of the matrix space Rn×m equipped with the subspace topology. The proposed geometric description then results in a description of the matrix space Rn×m, seen as the union of manifolds Mr(Rn×m), as an analytic manifold equipped with a topology for which the matrix rank is a continuous map.

Vitamin K Vitamers Differently Affect Energy Metabolism in IPEC-J2 Cells

The fat-soluble vitamin K (VK) has long been known as a requirement for blood coagulation, but like other vitamins, has been recently recognized to play further physiological roles, particularly in cell development and homeostasis. Vertebrates cannot de novo synthesize VK, which is essential, and it can only be obtained from the diet or by the activity of the gut microbiota. The IPEC-J2 cell line, obtained from porcine small intestine, which shows strong similarities to the human one, represents an excellent functional model to in vitro study the effect of compounds at the intestinal level. The acute VK treatments on the bioenergetic features of IPEC-J2 cells were evaluated by Seahorse XP Agilent technology. VK exists in different structurally related forms (vitamers), all featured by a naphtoquinone moiety, but with distinct effects on IPEC-J2 energy metabolism. The VK1, which has a long hydrocarbon chain, at both concentrations (5 and 10 μM), increases the cellular ATP production due to oxidative phosphorylation (OXPHOS) by 5% and by 30% through glycolysis. The VK2 at 5 μM only stimulates ATP production by OXPHOS. Conversely, 10 μM VK3, which lacks the long side chain, inhibits OXPHOS by 30% and glycolysis by 45%. However, even if IPEC-J2 cells mainly prefer OXPHOS to glycolysis to produce ATP, the OXPHOS/glycolysis ratio significantly decreases in VK1-treated cells, is unaffected by VK2, and only significantly increased by 10 μM VK3. VK1, at the two concentrations tested, does not affect the mitochondrial bioenergetic parameters, while 5 μM VK2 increases and 5 μM VK3 reduces the mitochondrial respiration (i.e., maximal respiration and spare respiratory capacity). Moreover, 10 μM VK3 impairs OXPHOS, as shown by the increase in the proton leak, namely the proton backward entry to the matrix space, thus pointing out mitochondrial toxicity. Furthermore, in the presence of both VK1 and VK2 concentrations, the glycolytic parameters, namely the glycolytic capacity and the glycolytic reserve, are unaltered. In contrast, the inhibition of glycoATP production by VK3 is linked to the 80% inhibition of glycolysis, resulting in a reduced glycolytic capacity and reserve. These data, which demonstrate the VK ability to differently modulate IPEC-J2 cell energy metabolism according to the different structural features of the vitamers, can mirror VK modulatory effects on the cell membrane features and, as a cascade, on the epithelial cell properties and gut functions: balance of salt and water, macromolecule cleavage, detoxification of harmful compounds, and nitrogen recycling.

Linear Operators That Preserve Arctic Ranks of Boolean Matrices

We study some properties of arctic rank of Boolean matrices. We compare the arctic rank with Boolean rank and term rank of a given Boolean matrix. Furthermore, we obtain some characterizations of linear operators that preserve arctic rank on Boolean matrix space.

Atomic kernels as waves and catastrophes

The presentation of atomic kerrnels as particles requires for the physics duality principle that they get a wave description. This is due to presenting the SU (3) GellMann matrix space by octonians which are obtained by doubling the spacetime quaternions. Their multiplication table is different from the SU (3) matrices. The third presentation of this space is a complex 4-dimensional space where the real spacetime coordinates of a 4-dimensional Euclidean Hilbert space R4 are extended to C4. For getting from Deuteron Cooper pairs NP of a neutron and proton atomic kernels AK, the wave package superpositions for AK need the mass defect of neutrons where kg is changed to inner speeds or interaction energies. For kg octonians have a GF measuring base triple as Gleason operator. Using a projective geometrical norming, C4 is normed to CP³, a projective 3-dimensional space. Its cell C³ has spacetime coordinates C², extended by an Einstein energy plane z3 = (m,f), m mass, f = 1/∆t frequency where mass can be transformed into f by using mc² = hf. If C³ is presented as a real space R6, it can be real projective normed to a real projective space P5 for the field presentation of AK. As field the NP‘s have then a common group speed for AK wave packages superpositions with which AK moves in spacetime C² and also a presentation as a Ψ wave. As probability distribution where they can be energetically found in space serves Ψ* Ψ.

Modeling the Effects of Calcium Overload on Mitochondrial Ultrastructural Remodeling

Mitochondrial cristae are dynamic invaginations of the inner membrane and play a key role in its metabolic capacity to produce ATP. Structural alterations caused by either genetic abnormalities or detrimental environmental factors impede mitochondrial metabolic fluxes and lead to a decrease in their ability to meet metabolic energy requirements. While some of the key proteins associated with mitochondrial cristae are known, very little is known about how the inner membrane dynamics are involved in energy metabolism. In this study, we present a computational strategy to understand how cristae are formed using a phase-based separation approach of both the inner membrane space and matrix space, which are explicitly modeled using the Cahn–Hilliard equation. We show that cristae are formed as a consequence of minimizing an energy function associated with phase interactions which are subject to geometric boundary constraints. We then extended the model to explore how the presence of calcium phosphate granules, entities that form in calcium overload conditions, exert a devastating inner membrane remodeling response that reduces the capacity for mitochondria to produce ATP. This modeling approach can be extended to include arbitrary geometrical constraints, the spatial heterogeneity of enzymes, and electrostatic effects to mechanize the impact of ultrastructural changes on energy metabolism.

COGNITIVE FOUNDATIONS OF IMPLEMENTING NOVEL GENRE CHARACTERISTICS (based on the analysis of “Never Let Me Go” by Kazuo Ishiguro)

The article analyses the role of chronotope in implementing genre characteristics of different types of novels within the frame of one novel in a cognitive approach perspective. The authors proceed from the theoretical assumption that the content of any novel represents a multidimensional knowledge of the matrix format comprising various types of conceptual domains as specific cognitive contexts. These contexts refer to the knowledge not only about the plot and the composition of the novel, but also about its genre characteristics and their individual interpretation by the author of the novel. Accordingly, they choose cognitive matrix analysis as the methodological basis of the research. Particular attention is focused on the analysis of general principles and mechanisms of the author's individual interpretation and implementation of the concept of chronotope, suggested by M.M. Bakhtin, within the framework of a specific novel. In relation to the novel under discussion the authors of the article model chronotope in the form of the cognitive matrix SPACE-TIME CONTINUUM and analyze its conceptual structure as it is seen by the author of the novel, as well as his choice of means of its representation in language. The results of the cognitive matrix and linguistic analysis lead to the conclusion that typical genre features of the novel are implemented through characteristics of the basic concepts of the respective conceptual domains and means of their linguistic representation. The article also argues close relationship between all of these characteristics and the dominant role of some of them in relation to the others.