Connections on modules over quasi-homogeneous plane curves

Let k be an algebraically closed field of characteristic 0, and let $A = k[x,y]/(f)$ be a quasi-homogeneous plane curve. We show that for any graded torsion free A-module M, there exists a natural graded integrable connection, i.e. a graded A-linear homomorphism $\nabla: \operatorname{Der}_k(A) \to \operatorname{End}_k(M)$ that satisfy the derivation property and preserves the Lie product. In particular, a torsion free module N over the complete local ring $B = \hat A$ admits a natural integrable connection if A is a simple curve singularity, or if A is irreducible and N is a gradable module.Comment: AMS-LaTeX, 12 pages, minor changes. To appear in Comm. Algebr

Research priorities for data collection and management within global acute and emergency care systems.

Barriers to global emergency care development include a critical lack of data in several areas, including limited documentation of the acute disease burden, lack of agreement on essential components of acute care systems, and a lack of consensus on key analytic elements, such as diagnostic classification schemes and regionally appropriate metrics for impact evaluation. These data gaps obscure the profound health effects of lack of emergency care access in low- and middle-income countries (LMICs). As part of the Academic Emergency Medicine consensus conference "Global Health and Emergency Care: A Research Agenda," a breakout group sought to develop a priority research agenda for data collection and management within global emergency care systems

Diffusion Tensor Imaging Predictors of Episodic Memory Decline in Healthy Elders at Genetic Risk for Alzheimer’s Disease

Objectives: White matter (WM) integrity within the mesial temporal lobe (MTL) is important for episodic memory (EM) functioning. The current study investigated the ability of diffusion tensor imaging (DTI) in MTL WM tracts to predict 3-year changes in EM performance in healthy elders at disproportionately higher genetic risk for Alzheimer’s disease (AD). Methods: Fifty-one cognitively intact elders (52% with family history (FH) of dementia and 33% possessing an Apolipoprotein E ε4 allelle) were administered the Rey Auditory Verbal Learning Test (RAVLT) at study entry and at 3-year follow-up. DTI scanning, conducted at study entry, examined fractional anisotropy and mean, radial and axial diffusion within three MTL WM tracts: uncinate fasciculus (UNC), cingulate-hippocampal (CHG), and fornix-stria terminalis (FxS). Correlations were performed between residualized change scores computed from RAVLT trials 1–5, immediate recall, and delayed recall scores and baseline DTI measures; MTL gray matter (GM) and WM volumes; demographics; and AD genetic and metabolic risk factors. Results: Higher MTL mean and axial diffusivity at baseline significantly predicted 3-year changes in EM, whereas baseline MTL GM and WM volumes, FH, and metabolic risk factors did not. Both ε4 status and DTI correlated with change in immediate recall. Conclusions: Longitudinal EM changes in cognitively intact, healthy elders can be predicted by disruption of the MTL WM microstructure. These results are derived from a sample with a disproportionately higher genetic risk for AD, suggesting that the observed WM disruption in MTL pathways may be related to early neuropathological changes associated with the preclinical stage of AD. (JINS, 2016, 22, 1005–1015

The Contribution of Blood Serum Biomarkers to the Prediction of Cognitive Decline by fMRI and Apolipoprotein-E in Healthy Older Adults

Biomarkers are a promising approach to the prediction and early intervention of Alzheimer\u27s disease. We demonstrated that cortical functional MRI (fMRI) activation during a semantic memory task and apolipoprotein-E ?4 allele inheritance (APOE?4) effectively predicted cognitive decline after 18-months in healthy, asymptomatic elders. Hippocampal volume added modest prediction, while AD family history and demographics were ineffective. Previous studies have linked plasma homocysteine (tHcy), vitamin B12 and creatinine values to cognitive funcitoning, cortical atrophy, hippocampal atrophy and neuropathology, and vascular integrity. Here we incorporated total plasma homocysteine (tHcy), B12 creatinine values into our previous predictive models. Of 78 healthy elders, 27 (34.6%) exhibited significant cognitive decline after 18-months. tHcy, but not B12 or creatinine, was marginally positively correlated with cortical semantic memory fMRI activation, particularly in stable participants. Logistic regression showed that tHcy, when added to APOE?4 and cortical fMRI, was a significant predictor of outcome and strengthed the already significant model (p = .007; C = .80 and R2 = .37). However, control for B12 and creatinine covariates diminished tHcy as a predictor (p = .084), though the model was still stronger than without this factor (C = .78 and R = 31). tHcy did not significantly interact with APOE?4, as has previously been reported. Neither B12 nor creatinine was similarly effective as a predictor. These results suggest that commonly investigated blood serum biomarkers are at best weakly associated with predicting age- and dementia-related cognitive decline in healthy, asymptomatic elders. fMRI and APOE?4 presently provided the best predictive model

The Contribution of Blood Serum Biomarkers to the Prediction of Cognitive Decline by fMRI and Apolipoprotein-E in Healthy Older Adults

Biomarkers are a promising approach to the prediction and early intervention of Alzheimer\u27s disease. We demonstrated that cortical functional MRI (fMRI) activation during a semantic memory task and apolipoprotein-E ?4 allele inheritance (APOE?4) effectively predicted cognitive decline after 18-months in healthy, asymptomatic elders. Hippocampal volume added modest prediction, while AD family history and demographics were ineffective. Previous studies have linked plasma homocysteine (tHcy), vitamin B12 and creatinine values to cognitive funcitoning, cortical atrophy, hippocampal atrophy and neuropathology, and vascular integrity. Here we incorporated total plasma homocysteine (tHcy), B12 creatinine values into our previous predictive models. Of 78 healthy elders, 27 (34.6%) exhibited significant cognitive decline after 18-months. tHcy, but not B12 or creatinine, was marginally positively correlated with cortical semantic memory fMRI activation, particularly in stable participants. Logistic regression showed that tHcy, when added to APOE?4 and cortical fMRI, was a significant predictor of outcome and strengthed the already significant model (p = .007; C = .80 and R2 = .37). However, control for B12 and creatinine covariates diminished tHcy as a predictor (p = .084), though the model was still stronger than without this factor (C = .78 and R = 31). tHcy did not significantly interact with APOE?4, as has previously been reported. Neither B12 nor creatinine was similarly effective as a predictor. These results suggest that commonly investigated blood serum biomarkers are at best weakly associated with predicting age- and dementia-related cognitive decline in healthy, asymptomatic elders. fMRI and APOE?4 presently provided the best predictive model

Genetic Risk for Alzheimer\u27s Disease Alters the Five-Year Trajectory of Semantic Memory Activation in Cognitively Intact Elders

Healthy aging is associated with cognitive declines typically accompanied by increased task-related brain activity in comparison to younger counterparts. The Scaffolding Theory of Aging and Cognition (STAC) (Park and Reuter-Lorenz, 2009; Reuter-Lorenz and Park, 2014) posits that compensatory brain processes are responsible for maintaining normal cognitive performance in older adults, despite accumulation of aging-related neural damage. Cross-sectional studies indicate that cognitively intact elders at genetic risk for Alzheimer\u27s disease (AD) demonstrate patterns of increased brain activity compared to low risk elders, suggesting that compensation represents an early response to AD-associated pathology. Whether this compensatory response persists or declines with the onset of cognitive impairment can only be addressed using a longitudinal design. The current prospective, 5-year longitudinal study examined brain activation in APOE ε4 carriers (N = 24) and non-carriers (N = 21). All participants, ages 65–85 and cognitively intact at study entry, underwent task-activated fMRI, structural MRI, and neuropsychological assessments at baseline, 18, and 57 months. fMRI activation was measured in response to a semantic memory task requiring participants to discriminate famous from non-famous names. Results indicated that the trajectory of change in brain activation while performing this semantic memory task differed between APOE ε4 carriers and non-carriers. The APOE ε4 group exhibited greater activation than the Low Risk group at baseline, but they subsequently showed a progressive decline in activation during the follow-up periods with corresponding emergence of episodic memory loss and hippocampal atrophy. In contrast, the non-carriers demonstrated a gradual increase in activation over the 5-year period. Our results are consistent with the STAC model by demonstrating that compensation varies with the severity of underlying neural damage and can be exhausted with the onset of cognitive symptoms and increased structural brain pathology. Our fMRI results could not be attributed to changes in task performance, group differences in cerebral perfusion, or regional cortical atrophy

Interactive Effects of Physical Activity and APOE-ε4 On White Matter Tract Diffusivity in Healthy Elders

Older adult apolipoprotein-E epsilon 4 (APOE-ε4) allele carriers vary considerably in the expression of clinical symptoms of Alzheimer\u27s disease (AD), suggesting that lifestyle or other factors may offer protection from AD-related neurodegeneration. We recently reported that physically active APOE-ε4 allele carriers exhibit a stable cognitive trajectory and protection from hippocampal atrophy over 18 months compared to sedentary ε4 allele carriers. The aim of this study was to examine the interactions between genetic risk for AD and physical activity (PA) on white matter (WM) tract integrity, using diffusion tensor imaging (DTI) MRI, in this cohort of healthy older adults (ages of 65 to 89). Four groups were compared based on the presence or absence of an APOE-ε4 allele (High Risk; Low Risk) and self-reported frequency and intensity of leisure time physical activity (PA) (High PA; Low PA). As predicted, greater levels of PA were associated with greater fractional anisotropy (FA) and lower radial diffusivity in healthy older adults who did not possess the APOE-ε4 allele. However, the effects of PA were reversed in older adults who were at increased genetic risk for AD, resulting in significant interactions between PA and genetic risk in several WM tracts. In the High Risk-Low PA participants, who had exhibited episodic memory decline over the previous 18-months, radial diffusivity was lower and fractional anisotropy was higher, compared to the High Risk-High PA participants. In WM tracts that subserve learning and memory processes, radial diffusivity (DR) was negatively correlated with episodic memory performance in physically inactive APOE-ε4 carriers, whereas DR was positively correlated with episodic memory performance in physically active APOE-ε4 carriers and the two Low Risk groups. The common model of demyelination-induced increase in radial diffusivity cannot directly explain these results. Rather, we hypothesize that PA may protect APOE-ε4 allele carriers from selective neurodegeneration of individual fiber populations at locations of crossing fibers within projection and association WM fiber tracts