On Tarski's axiomatic foundations of the calculus of relations

It is shown that Tarski's set of ten axioms for the calculus of relations is independent in the sense that no axiom can be derived from the remaining axioms. It is also shown that by modifying one of Tarski's axioms slightly, and in fact by replacing the right-hand distributive law for relative multiplication with its left-hand version, we arrive at an equivalent set of axioms which is redundant in the sense that one of the axioms, namely the second involution law, is derivable from the other axioms. The set of remaining axioms is independent. Finally, it is shown that if both the left-hand and right-hand distributive laws for relative multiplication are included in the set of axioms, then two of Tarski's other axioms become redundant, namely the second involution law and the distributive law for converse. The set of remaining axioms is independent and equivalent to Tarski's axiom system

The extension problem for partial Boolean structures in Quantum Mechanics

Alternative partial Boolean structures, implicit in the discussion of classical representability of sets of quantum mechanical predictions, are characterized, with definite general conclusions on the equivalence of the approaches going back to Bell and Kochen-Specker. An algebraic approach is presented, allowing for a discussion of partial classical extension, amounting to reduction of the number of contexts, classical representability arising as a special case. As a result, known techniques are generalized and some of the associated computational difficulties overcome. The implications on the discussion of Boole-Bell inequalities are indicated.Comment: A number of misprints have been corrected and some terminology changed in order to avoid possible ambiguitie

V*-algebras, independence algebras and logic

Independence algebras were introduced in the early 1990s by specialists in semigroup theory, as a tool to explain similarities between the transformation monoid on a set and the endomorphism monoid of a vector space. It turned out that these algebras had already been defined and studied in the 1960s, under the name of v*-algebras, by specialists in universal algebra (and statistics). Our goal is to complete this picture by discussing how, during the middle period, independence algebras began to play a very important role in logic

Bell inequalities from variable elimination methods

Tight Bell inequalities are facets of Pitowsky's correlation polytope and are usually obtained from its extreme points by solving the hull problem. Here we present an alternative method based on a combination of algebraic results on extensions of measures and variable elimination methods, e.g., the Fourier-Motzkin method. Our method is shown to overcome some of the computational difficulties associated with the hull problem in some non-trivial cases. Moreover, it provides an explanation for the arising of only a finite number of families of Bell inequalities in measurement scenarios where one experimenter can choose between an arbitrary number of different measurements

Tarski monoids: Matui's spatial realization theorem

We introduce a class of inverse monoids, called Tarski monoids, that can be regarded as non-commutative generalizations of the unique countable, atomless Boolean algebra. These inverse monoids are related to a class of etale topological groupoids under a non-commutative generalization of classical Stone duality and, significantly, they arise naturally in the theory of dynamical systems as developed by Matui. We are thereby able to reinterpret a theorem of Matui on a class of \'etale groupoids as an equivalent theorem about a class of Tarski monoids: two simple Tarski monoids are isomorphic if and only if their groups of units are isomorphic. The inverse monoids in question may also be viewed as countably infinite generalizations of finite symmetric inverse monoids. Their groups of units therefore generalize the finite symmetric groups and include amongst their number the classical Thompson groups.Comment: arXiv admin note: text overlap with arXiv:1407.147

Extraribosomal functions associated with the C terminus of the 37/67 kDa laminin receptor are required for maintaining cell viability

The 37/67 kDa laminin receptor (LAMR) is a multifunctional protein, acting as an extracellular receptor, localizing to the nucleus, and playing roles in rRNA processing and ribosome assembly. LAMR is important for cell viability; however, it is unclear which of its functions are essential. We developed a silent mutant LAMR construct, resistant to siRNA, to rescue the phenotypic effects of knocking down endogenous LAMR, which include inhibition of protein synthesis, cell cycle arrest, and apoptosis. In addition, we generated a C-terminal-truncated silent mutant LAMR construct structurally homologous to the Archaeoglobus fulgidus S2 ribosomal protein and missing the C-terminal 75 residues of LAMR, which displays more sequence divergence. We found that HT1080 cells stably expressing either silent mutant LAMR construct still undergo arrest in the G1 phase of the cell cycle when treated with siRNA. However, the expression of full-length silent mutant LAMR rescues cell viability, whereas the expression of the C-terminal-truncated LAMR does not. Interestingly, we also found that both silent mutant constructs restore protein translation and localize to the nucleus. Our findings indicate that the ability of LAMR to regulate viability is associated with its C-terminal 75 residues. Furthermore, this function is distinct from its role in cell proliferation, independent of its ribosomal functions, and may be regulated by a nonnuclear localization

Interleukins, laminin and epstein - barr virus latent membrane protein 1 (EBV LMP1) Promote metastatic phenotype in nasopharyngeal carcinoma

<p>Abstract</p> <p>Background</p> <p>Nasopharyngeal carcinoma (NPC) is a type of neoplasm that is highly prevalent in East Asia and Africa with Epstein-Barr virus (EBV), genetic, and dietary factors implicated as possible aetiologic factors. Previous studies suggested the association of certain cytokines with the invasion and metastatic properties of NPC. The present study examined the roles of EBV latent membrane protein-1 (LMP1), interleukin-6 (IL-6), interleukin-10 (IL-10), transforming growth factor-beta 1 (TGF-β1) and laminin in the regulation of matrix-metalloproteinases (MMPs) and vascular endothelial growth factor (VEGF) in NPC. The effects of these factors on <it>bmi-1</it>, an oncogene, and <it>ngx6</it>, a tumour suppressor gene, were also investigated.</p> <p>Methods</p> <p>TW01 cells expressing LMP1 (TW01-LMP1) were established via transfection with the B95.8 EBV LMP1 gene. Both TW01 and TW01-LMP1 cells were treated with 100 pg/ml IL-6, 1000 pg/ml IL-10 and 100 pg/ml TGF-β1, separately and also in combination at their respective concentration for 48 hours. Treated cells were subjected to laminin adherence assay. The cells were also cultured with and without laminin and assayed for MMP-3, MMP-9 and VEGF production using enzyme-linked immunosorbent assay (ELISA). The cellular apoptotic property was analysed using caspase-3 apoptosis assay. The expression of <it>bmi-1 </it>and <it>ngx6 </it>gene was investigated using real time reverse transcriptase polymerase chain reaction.</p> <p>Results</p> <p>LMP1 was found to reduce the adherence of NPC cells towards laminin (p < 0.05) as compared to control. Treatment with IL-6 at 100 pg/ml enhanced the production of MMP-9 in both TW01 and TW01-LMP1 cells (p < 0.05). When cultured on laminin, the levels of MMP-3 and VEGF were significantly increased (p < 0.05) in TW01-LMP1 cells. TW01-LMP1 cells had relatively greater resistance to apoptosis as compared to TW01 cells (p < 0.05). Laminin, IL-6 and LMP1 were found to up-regulate the expression of <it>bmi-1 </it>and suppressed the expression of <it>ngx6</it>.</p> <p>Conclusions</p> <p>We conclude that IL-6 reduced cell adherence towards laminin and increased MMP-9 production in NPC cells. Our data suggested that EBV LMP1 was able to confer resistance of apoptosis and increased MMP-9 production in NPC cells. When cultured on laminin, TW01 cells expressing the EBV LMP1 (TW0-LMP1) that were treated with IL-6 at 100 pg/ml displayed increased MMP-9 production, up-regulation of <it>bmi-1 </it>oncogene expression and down-regulation of <it>ngx6 </it>tumour suppressor gene expression. These findings implicate the roles of EBV LMP1, laminin and IL-6 in the promotion of invasion and metastasis in NPC.</p

Collagen I but not Matrigel matrices provide an MMP-dependent barrier to ovarian cancer cell penetration

Abstract Background The invasive potential of cancer cells is usually assessed in vitro using Matrigel as a surrogate basement membrane. Yet cancer cell interaction with collagen I matrices is critical, particularly for the peritoneal metastatic route undertaken by several cancer types including ovarian. Matrix metalloprotease (MMP) activity is important to enable cells to overcome the barrier constraints imposed by basement membranes and stromal matrices in vivo. Our objective was to compare matrices reconstituted from collagen I and Matrigel as representative barriers for ovarian cancer cell invasion. Methods The requirement of MMP activity for ovarian cancer cell penetration of Matrigel and collagen matrices was assessed in 2D transwell and 3D spheroid culture systems. Results The broad range MMP inhibitor GM6001 completely prevented cell perforation of polymerised collagen I-coated transwell membranes. In contrast, GM6001 decreased ES-2 cell penetration of Matrigel by only ~30% and had no effect on HEY cell Matrigel penetration. In 3D culture, ovarian cancer cells grown as spheroids also migrated into surrounding Matrigel matrices despite MMP blockade. In contrast, MMP activity was required for invasion into 3D matrices of collagen I reconstituted from acid-soluble rat-tail collagen I, but not from pepsin-extracted collagen I (Vitrogen/Purecol), which lacks telopeptide regions. Conclusion Matrigel does not form representative barriers to ovarian cancer cells in either 2D or 3D culture systems. Our findings support the use of collagen I rather than Matrigel as a matrix barrier for invasion studies to better approximate critical interactions and events associated with peritoneal metastasis