Phase transition in the one-dimensional Kondo lattice model with attractive electron-electron interaction

The one-dimensional Kondo lattice model with attractive interaction among the conduction electrons is analyzed in the case of half-filling. It is shown that there are three distinct phases depending on the coupling constants of the model. Two phases have a spin and charge gap. While one shows a clear separation of the spin and charge excitation spectrum the other phase may be characterized as a band insulator type where both excitations are due to two-particle states. The third phase is gapless in both channels and has quasi long-range order in the spin and charge density wave correlation. In this phase the spin and charge excitations have again a clearly separated spectrum. For the analysis we discuss first two limiting cases. Then a density matrix renormalization group calculation on finite systems is applied to determine the phase diagram and the correlation functions in the gapped and gapless phase for general couplding constants.Comment: 9 pages, 7 Postscript figures, REVTe

A Machine Checked Model of Idempotent MGU Axioms For Lists of Equational Constraints

We present formalized proofs verifying that the first-order unification algorithm defined over lists of satisfiable constraints generates a most general unifier (MGU), which also happens to be idempotent. All of our proofs have been formalized in the Coq theorem prover. Our proofs show that finite maps produced by the unification algorithm provide a model of the axioms characterizing idempotent MGUs of lists of constraints. The axioms that serve as the basis for our verification are derived from a standard set by extending them to lists of constraints. For us, constraints are equalities between terms in the language of simple types. Substitutions are formally modeled as finite maps using the Coq library Coq.FSets.FMapInterface. Coq's method of functional induction is the main proof technique used in proving many of the axioms.Comment: In Proceedings UNIF 2010, arXiv:1012.455

Die Rolle der mathematischen Logik in der Künstlichen Intelligenz

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Atrial Fibrillation: A New Indicator for Advanced Colorectal Neoplasia in Screening Colonoscopy

BACKGROUND Colorectal cancer (CRC) is a common and potentially preventable malignancy. Evidence has emerged that coronary artery disease patients are at increased risk for developing CRC by shared risk factors. Here we investigated an association between CRC and atrial fibrillation (AF), a surrogate marker of cardiovascular risk, in the setting of routine screening colonoscopy. METHODS We investigated 1949 asymptomatic participants (median age 61 [54-67] years, 49% females) undergoing screening colonoscopy within the SAKKOPI registry (Salzburg Colon Cancer Prevention Initiative). Forty-six participants with AF (2.4%) were identified, and colonoscopy findings were compared to non-AF participants. Propensity Score Matching (PSM) was used to create 1:1 and 3:1 age- and gender-matched couples. RESULTS Abnormal findings on screening colonoscopy (any form of adenoma or carcinoma) were more common in AF participants with an odds ratios (OR) of 2.4 [1.3-4.3] in the unmatched analysis, and 2.6 [1.1-6.3] and 2.0 [1.1-4.0] in the 1:1 and 3:1 matched groups, respectively. Correspondingly, the odds of finding advanced adenomas or carcinomas was elevated about three-fold across the different matched and unmatched analyses (OR 3.3 [1.1-10.8] for 3:1 matched participants). At the same time, the prevalence and number of colonic lesions were significantly higher in AF participants (63.0% vs. 33.4% for 3:1 matched participants, p < 0.001). Non-CRC related findings on colonoscopy, like diverticulosis, were non-different between groups. CONCLUSION Participants with AF had a higher burden of advanced premalignant adenomas and CRC in routine colonoscopy screening. Our data suggest that practitioners should monitor the CRC screening status, especially in AF patients

Changing Metabolic Patterns along the Colorectal Adenoma-Carcinoma Sequence

Colorectal cancer (CRC) is a major public health burden and one of the leading causes of cancer-related deaths worldwide. Screening programs facilitate early diagnosis and can help to reduce poor outcomes. Serum metabolomics can extract vital molecular information that may increase the sensitivity and specificity of colonoscopy in combination with histopathological examination. The present study identifies serum metabolite patterns of treatment-naïve patients, diagnosed with either advanced adenoma (AA) or CRC in colonoscopy screenings, in the framework of the SAKKOPI (Salzburg Colon Cancer Prevention Initiative) program. We used a targeted flow injection analysis and liquid chromatography-tandem mass spectrometry metabolomics approach (FIA- and LC-MS/MS) to characterise the serum metabolomes of an initial screening cohort and two validation cohorts (in total 66 CRC, 76 AA and 93 controls). The lipidome was significantly perturbed, with a proportion of lipid species being downregulated in CRC patients, as compared to AA and controls. The predominant alterations observed were in the levels of lyso-lipids, glycerophosphocholines and acylcarnitines, but additionally, variations in the quantity of hydroxylated sphingolipids could be detected. Changed amino acid metabolism was restricted mainly to metabolites of the arginine/dimethylarginine/NO synthase pathway. The identified metabolic divergences observed in CRC set the foundation for mechanistic studies to characterise biochemical pathways that become deregulated during progression through the adenoma to carcinoma sequence and highlight the key importance of lipid metabolites. Biomarkers related to these pathways could improve the sensitivity and specificity of diagnosis, as well as the monitoring of therapies