Principal and syntactic congruences in congruence-distributive and congruence-permutable varieties

We give a new proof that a finitely generated congruence-distributive variety has finitely determined syntactic congruences (or, equivalently, term finite principal congruences), and show that the same does not hold for finitely generated congruence-permutable varieties, even under the additional assumption that the variety is residually very finite

Dualizability of automatic algebras

We make a start on one of George McNulty's Dozen Easy Problems: "Which finite automatic algebras are dualizable?" We give some necessary and some sufficient conditions for dualizability. For example, we prove that a finite automatic algebra is dualizable if its letters act as an abelian group of permutations on its states. To illustrate the potential difficulty of the general problem, we exhibit an infinite ascending chain $\mathbf A_1 \le \mathbf A_2 \le \mathbf A_3 \le ...b$ of finite automatic algebras that are alternately dualizable and non-dualizable

Relationship Between Quantitative MRI Biomarkers and Patient-Reported Outcome Measures After Cartilage Repair Surgery: A Systematic Review.

Background:Treatment of articular cartilage injuries remains a clinical challenge, and the optimal tools to monitor and predict clinical outcomes are unclear. Quantitative magnetic resonance imaging (qMRI) allows for a noninvasive biochemical evaluation of cartilage and may offer advantages in monitoring outcomes after cartilage repair surgery. Hypothesis:qMRI sequences will correlate with early pain and functional measures. Study Design:Systematic review; Level of evidence, 3. Methods:A PubMed search was performed with the following search terms: knee AND (cartilage repair OR cartilage restoration OR cartilage surgery) AND (delayed gadolinium-enhanced MRI OR t1-rho OR T2 mapping OR dgemric OR sodium imaging OR quantitative imaging). Studies were included if correlation data were included on quantitative imaging results and patient outcome scores. Results:Fourteen articles were included in the analysis. Eight studies showed a significant relationship between quantitative cartilage imaging and patient outcome scores, while 6 showed no relationship. T2 mapping was examined in 11 studies, delayed gadolinium-enhanced MRI of cartilage (dGEMRIC) in 4 studies, sodium imaging in 2 studies, glycosaminoglycan chemical exchange saturation transfer (gagCEST) in 1 study, and diffusion-weighted imaging in 1 study. Five studies on T2 mapping showed a correlation between T2 relaxation times and clinical outcome scores. Two dGEMRIC studies found a correlation between T1 relaxation times and clinical outcome scores. Conclusion:Multiple studies on T2 mapping, dGEMRIC, and diffusion-weighted imaging showed significant correlations with patient-reported outcome measures after cartilage repair surgery, although other studies showed no significant relationship. qMRI sequences may offer a noninvasive method to monitor cartilage repair tissue in a clinically meaningful way, but further refinements in imaging protocols and clinical interpretation are necessary to improve utility