Circulating anions usually associated with the Krebs cycle in patients with metabolic acidosis

Introduction: Acute metabolic acidosis of non-renal origin is usually a result of either lactic or ketoacidosis, both of which are associated with a high anion gap. There is increasing recognition, however, of a group of acidotic patients who have a large anion gap that is not explained by either keto- or lactic acidosis nor, in most cases, is inappropriate fluid resuscitation or ingestion of exogenous agents the cause. Methods: Plasma ultrafiltrate from patients with diabetic ketoacidosis, lactic acidosis, acidosis of unknown cause, normal anion gap metabolic acidosis, or acidosis as a result of base loss were examined enzymatically for the presence of low molecular weight anions including citrate, isocitrate, α-ketoglutarate, succinate, malate and d-lactate. The results obtained from the study groups were compared with those obtained from control plasma from normal volunteers. Results: In five patients with lactic acidosis, a significant increase in isocitrate (0.71 ± 0.35 mEq l-1), α-ketoglutarate (0.55 ± 0.35 mEq l-1), malate (0.59 ± 0.27 mEq l-1), and d-lactate (0.40 ± 0.51 mEq l-1) was observed. In 13 patients with diabetic ketoacidosis, significant increases in isocitrate (0.42 ± 0.35 mEq l-1), α-ketoglutarate (0.41 ± 0.16 mEq l-1), malate (0.23 ± 0.18 mEq l-1) and d-lactate (0.16 ± 0.07 mEq l-1) were seen. Neither citrate nor succinate levels were increased. Similar findings were also observed in a further five patients with high anion gap acidosis of unknown origin with increases in isocitrate (0.95 ± 0.88 mEq l-1), α-ketoglutarate (0.65 ± 0.20 mEq l-1), succinate (0.34 ± 0.13 mEq l-1), malate (0.49 ± 0.19 mEq l-1) and d-lactate (0.18 ± 0.14 mEq l-1) being observed but not in citrate concentration. In five patients with a normal anion gap acidosis, no increases were observed except a modest rise in d-lactate (0.17 ± 0.14 mEq l-1). Conclusion: The levels of certain low molecular weight anions usually associated with intermediary metabolism were found to be significantly elevated in the plasma ultrafiltrate obtained from patients with metabolic acidosis. Our results suggest that these hitherto unmeasured anions may significantly contribute to the generation of the anion gap in patients with lactic acidosis and acidosis of unknown aetiology and may be underestimated in diabetic ketoacidosis. These anions are not significantly elevated in patients with normal anion gap acidosis

Generalised Moore spectra in a triangulated category

In this paper we consider a construction in an arbitrary triangulated category T which resembles the notion of a Moore spectrum in algebraic topology. Namely, given a compact object C of T satisfying some finite tilting assumptions, we obtain a functor which "approximates" objects of the module category of the endomorphism algebra of C in T. This generalises and extends a construction of Jorgensen in connection with lifts of certain homological functors of derived categories. We show that this new functor is well-behaved with respect to short exact sequences and distinguished triangles, and as a consequence we obtain a new way of embedding the module category in a triangulated category. As an example of the theory, we recover Keller's canonical embedding of the module category of a path algebra of a quiver with no oriented cycles into its u-cluster category for u>1.Comment: 26 pages, improvement to exposition of the proof of Theorem 3.

Equivariant cohomology over Lie groupoids and Lie-Rinehart algebras

Using the language and terminology of relative homological algebra, in particular that of derived functors, we introduce equivariant cohomology over a general Lie-Rinehart algebra and equivariant de Rham cohomology over a locally trivial Lie groupoid in terms of suitably defined monads (also known as triples) and the associated standard constructions. This extends a characterization of equivariant de Rham cohomology in terms of derived functors developed earlier for the special case where the Lie groupoid is an ordinary Lie group, viewed as a Lie groupoid with a single object; in that theory over a Lie group, the ordinary Bott-Dupont-Shulman-Stasheff complex arises as an a posteriori object. We prove that, given a locally trivial Lie groupoid G and a smooth G-manifold f over the space B of objects of G, the resulting G-equivariant de Rham theory of f boils down to the ordinary equivariant de Rham theory of a vertex manifold relative to the corresponding vertex group, for any vertex in the space B of objects of G; this implies that the equivariant de Rham cohomology introduced here coincides with the stack de Rham cohomology of the associated transformation groupoid whence this stack de Rham cohomology can be characterized as a relative derived functor. We introduce a notion of cone on a Lie-Rinehart algebra and in particular that of cone on a Lie algebroid. This cone is an indispensable tool for the description of the requisite monads.Comment: 47 page

Representation theory of some infinite-dimensional algebras arising in continuously controlled algebra and topology

In this paper we determine the representation type of some algebras of infinite matrices continuously controlled at infinity by a compact metrizable space. We explicitly classify their finitely presented modules in the finite and tame cases. The algebra of row-column-finite (or locally finite) matrices over an arbitrary field is one of the algebras considered in this paper, its representation type is shown to be finite.Comment: 33 page

Quantum Geons and Noncommutative Spacetimes

Physical considerations strongly indicate that spacetime at Planck scales is noncommutative. A popular model for such a spacetime is the Moyal plane. The Poincar\`e group algebra acts on it with a Drinfel'd-twisted coproduct. But the latter is not appropriate for more complicated spacetimes such as those containing the Friedman-Sorkin (topological) geons. They have rich diffeomorphism groups and in particular mapping class groups, so that the statistics groups for N identical geons is strikingly different from the permutation group $S_N$. We generalise the Drinfel'd twist to (essentially) generic groups including to finite and discrete ones and use it to modify the commutative spacetime algebras of geons as well to noncommutative algebras. The latter support twisted actions of diffeos of geon spacetimes and associated twisted statistics. The notion of covariant fields for geons is formulated and their twisted versions are constructed from their untwisted versions. Non-associative spacetime algebras arise naturally in our analysis. Physical consequences, such as the violation of Pauli principle, seem to be the outcomes of such nonassociativity. The richness of the statistics groups of identical geons comes from the nontrivial fundamental groups of their spatial slices. As discussed long ago, extended objects like rings and D-branes also have similar rich fundamental groups. This work is recalled and its relevance to the present quantum geon context is pointed out.Comment: 41 page

Computing Matveev's complexity via crystallization theory: the orientable case

By means of a slight modification of the notion of GM-complexity introduced in [Casali, M.R., Topol. Its Appl., 144: 201-209, 2004], the present paper performs a graph-theoretical approach to the computation of (Matveev's) complexity for closed orientable 3-manifolds. In particular, the existing crystallization catalogue C-28 available in [Lins, S., Knots and Everything 5, World Scientific, Singapore, 1995] is used to obtain upper bounds for the complexity of closed orientable 3-manifolds triangulated by at most 28 tetrahedra. The experimental results actually coincide with the exact values of complexity, for all but three elements. Moreover, in the case of at most 26 tetrahedra, the exact value of the complexity is shown to be always directly computable via crystallization theory

Basic Module Theory over Non-Commutative Rings with Computational Aspects of Operator Algebras

The present text surveys some relevant situations and results where basic Module Theory interacts with computational aspects of operator algebras. We tried to keep a balance between constructive and algebraic aspects.Comment: To appear in the Proceedings of the AADIOS 2012 conference, to be published in Lecture Notes in Computer Scienc