An application of lattice basis reduction to polynomial identities for algebraic structures

The authors` recent classification of trilinear operations includes, among other cases, a fourth family of operations with parameter q epsilon Q boolean OR {infinity}, and weakly commutative and weakly anticommutative operations. These operations satisfy polynomial identities in degree 3 and further identities in degree 5. For each operation, using the row canonical form of the expansion matrix E to find the identities in degree 5 gives extremely complicated results. We use lattice basis reduction to simplify these identities: we compute the Hermite normal form H of E(t), obtain a basis of the nullspace lattice from the last rows of a matrix U for which UE(t) = H, and then use the LLL algorithm to reduce the basis. (C) 2008 Elsevier Inc. All rights reserved.

Polynomial identities for the ternary cyclic sum

We simplify the results of Bremner and Hentzel [J. Algebra 231 (2000) 387-405] on polynomial identities of degree 9 in two variables satisfied by the ternary cyclic sum [a, b, c] abc + bca + cab in every totally associative ternary algebra. We also obtain new identities of degree 9 in three variables which do not follow from the identities in two variables. Our results depend on (i) the LLL algorithm for lattice basis reduction, and (ii) linearization operators in the group algebra of the symmetric group which permit efficient computation of the representation matrices for a non-linear identity. Our computational methods can be applied to polynomial identities for other algebraic structures.

Malcev dialgebras

We apply Kolesnikov's algorithm to obtain a variety of nonassociative algebras defined by right anticommutativity and a "noncommutative" version of the Malcev identity. We use computer algebra to verify that these identities are equivalent to the identities of degree up to 4 satisfied by the dicommutator in every alternative dialgebra. We extend these computations to show that any special identity for Malcev dialgebras must have degree at least 7. Finally, we introduce a trilinear operation which makes any Malcev dialgebra into a Leibniz triple system.

Dual processes in recognition: Does a focus on measurement operations provide a sufficient foundation?

Current theoretical thinking about dual processes in recognition relies heavily on the measurement operations embodied within the process dissociation procedure. We critically evaluate the ability of this procedure to support this theoretical enterprise. We show that there are alternative processes that would produce a rough invariance in familiarity (a key prediction of the dual-processing approach) and that the process dissociation procedure does not have the power to differentiate between these alternative possibilities. We also show that attempts to relate parameters estimated by the process dissociation procedure to subjective reports (remember-know judgments) cannot differentiate between alternative dual-processing models and that there are problems with some of the historical evidence and with obtaining converging evidence. Our conclusion is that more specific theories incorporating ideas about representation and process are required.

IS SPLENECTOMY A DYSLIPIDEMIC INTERVENTION? EXPERIMENTAL RESPONSE OF SERUM LIPIDS TO DIFFERENT DIETS AND OPERATIONS

Spleen removal may be recommended during organ transplantation in ABO-incompatible recipients as well as for hypoperfusion of the grafted liver, besides conventional surgical indications, but elevation of serum lipids has been observed in certain contexts. Aiming to analyze the influence of two dietary regimens on lipid profile, an experimental study was conducted. Methods: Male Wistar rats (n = 86, 333.0 +/- 32.2 g) were divided in four groups: group 1: controls; group 2: sham operation; group 3: total splenectomy; group 4: subtotal splenectomy with upper pole preservation; subgroups A (cholesterol reducing chow) and B (cholesterol-rich mixture) were established, and diet was given during 90 days. Total cholesterol (Tchol), high-density lipoprotein (HDL), low-density lipoprotein (LDL), very-low-density lipoprotein (VLDL), and triglycerides were documented. Results: After total splenectomy, hyperlipidemia ensued with cholesterol-reducing chow. Tchol, LDL, VLDL, triglycerides, and HDL changed from 56.4 +/- 9.2, 24.6 +/- 4.7, 9.7 +/- 2.2, 48.6 +/- 11.1, and 22.4 +/- 4.3 mg/dL to 66.9 +/- 11.4, 29.9 +/- 5.9, 10.9 +/- 2.3, 54.3 +/- 11.4, and 26.1 +/- 5.1 mg/dL, respectively. Upper pole preservation inhibited abnormalities of Tchol, HDL, VLDL, and triglycerides, and LDL decreased (23.6 +/- 4.9 vs. 22.1 +/- 5.1, P = 0.002). Higher concentrations were triggered by splenectomy and cholesterol-enriched diet (Tchol 59.4 +/- 10.1 vs. 83.9 +/- 14.3 mg/dL, P = 0.000), and upper-pole preservation diminished without abolishing hyperlipidemia (Tchol 55.9 +/- 10.0 vs. 62.3 +/- 7.8, P = 0.002). Conclusions: After splenectomy, hyperlipidemia occurred with both diets. Preservation of the upper pole tended to correct dyslipidemia in modality A and to attenuate it in subgroup B. (c) 2008 Wiley-Liss, Inc. Microsurgery 29:154-160, 2009.

A new proctoscope for transanal endoscopic operations

Transanal access is one of many currently used procedures for rectal cancer treatment. The techniques used for local excision include conventional transanal excision, posterior access, therapeutic colonoscopy and transanal endoscopic approaches. The aim of the present study was to present a new surgical proctoscope for the endoscopic transanal excision of rectal lesions. A cylindrical proctoscope with a diameter of 4 cm was devised and built. The end inserted into the anus has a bevelled aspect and rounded borders, allowing correct exposure of the anal lesion. The rectoscope is fixed to the anal border with surgical thread through perforations in the external end. A base screw holds a fibre-light which illuminates the operative field. Part of the equipment is a guide which is positioned inside the rectoscope on insertion into the anus. In operations utilizing this proctoscope, 17 adenomas, 25 adenocarcinomas, 1 carcinoid and 1 endometrioma were excised. The diameter of the lesions varied from 1 to 6 cm. The range of procedures that are possible with this new proctoscope are similar to those achieved with conventional techniques which, however, require more expensive equipment. Hence, the present study demonstrates that this newly devised low-cost proctoscope is an efficient tool for the transanal endoscopic excision of rectal lesions.

Causal and localizable quantum operations

We examine constraints on quantum operations imposed by relativistic causality. A bipartite superoperator is said to be localizable if it can be implemented by two parties (Alice and Bob) who share entanglement but do not communicate, it is causal if the superoperator does not convey information from Alice to Bob or from Bob to Alice. We characterize the general structure of causal complete-measurement superoperators, and exhibit examples that are causal but not localizable. We construct another class of causal bipartite superoperators that are not localizable by invoking bounds on the strength of correlations among the parts of a quantum system. A bipartite superoperator is said to be semilocalizable if it can be implemented with one-way quantum communication from Alice to Bob, and it is semicausal if it conveys no information from Bob to Alice. We show that all semicausal complete-measurement superoperators are semi localizable, and we establish a general criterion for semicausality. In the multipartite case, we observe that a measurement superoperator that projects onto the eigenspaces of a stabilizer code is localizable.