On the Multi-Kind BahnCard Problem

The BahnCard problem is an important problem in the realm of online decision making. In its original form, there is one kind of BahnCard associated with a certain price, which upon purchase reduces the ticket price of train journeys for a certain factor over a certain period of time. The problem consists of deciding on which dates BahnCards should be purchased such that the overall cost, that is, BahnCard prices plus (reduced) ticket prices, is minimized without having knowledge about the number and prices of future journeys. In this paper, we extend the problem such that multiple kinds of BahnCards are available for purchase. We provide an optimal offline algorithm, as well as online strategies with provable competitiveness factors. Furthermore, we describe and implement several heuristic online strategies and compare their competitiveness in realistic scenarios

Longitudinal Study of the Transition From Healthy Aging to Alzheimer Disease

BACKGROUND: Detection of the earliest cognitive changes signifying Alzheimer disease is difficult. OBJECTIVE: To model the cognitive decline in preclinical Alzheimer disease. DESIGN: Longitudinal archival study comparing individuals who became demented during follow-up and people who remained nondemented on each of 4 cognitive factors: global, verbal memory, visuospatial, and working memory. SETTING: Alzheimer Disease Research Center, Washington University School of Medicine, St Louis, Missouri. PARTICIPANTS: One hundred thirty-four individuals who became demented during follow-up and 310 who remained nondemented. MAIN OUTCOME MEASURES: Inflection point in longitudinal cognitive performance. RESULTS: The best-fitting model for each of the 4 factors in the stable group was linear, with a very slight downward trend on all but the Visuospatial factor. In contrast, a piecewise model with accelerated slope after a sharp inflection point provided the best fit for the group that progressed. The optimal inflection point for all 4 factors was prior to diagnosis of dementia: Global, 2 years; Verbal and Working Memory, 1 year; and Visuospatial, 3 years. These results were also obtained when data were limited to the subset (n = 44) with autopsy-confirmed Alzheimer disease. CONCLUSIONS: There is a sharp inflection point followed by accelerating decline in multiple domains of cognition, not just memory, in the preclinical period in Alzheimer disease when there is insufficient cognitive decline to warrant clinical diagnosis using conventional criteria. Early change was seen in tests of visuospatial ability, most of which were speeded. Research into early detection of cognitive disorders using only episodic memory tasks may not be sensitive to all of the early manifestations of disease

Map Matching for Semi-Restricted Trajectories

We consider the problem of matching trajectories to a road map, giving particular consideration to trajectories that do not exclusively follow the underlying network. Such trajectories arise, for example, when a person walks through the inner part of a city, crossing market squares or parking lots. We call such trajectories semi-restricted. Sensible map matching of semi-restricted trajectories requires the ability to differentiate between restricted and unrestricted movement. We develop in this paper an approach that efficiently and reliably computes concise representations of such trajectories that maintain their semantic characteristics. Our approach utilizes OpenStreetMap data to not only extract the network but also areas that allow for free movement (as e.g. parks) as well as obstacles (as e.g. buildings). We discuss in detail how to incorporate this information in the map matching process, and demonstrate the applicability of our method in an experimental evaluation on real pedestrian and bicycle trajectories

Diabetic Myonecrosis: An Uncommon Complication of a Common Condition

Introduction: Diabetic myonecrosis is an uncommon complication of diabetes mellitus, most often occurring in patients with poorly controlled, insulin-dependent diabetes. Its etiology is poorly understood, with many suggesting microvascular occlusion to be a key factor resulting in necrosis of skeletal muscle. Case presentation: A 28-year-old male with a history of poorly controlled type I diabetes mellitus and end-stage renal disease requiring dialysis presented to the emergency department with severe pain of the lower extremities bilaterally. Results: Work-up included an x-ray, which demonstrated no acute fractures but extensive vascular calcification of the lower extremities, and Doppler ultrasonography, which showed no DVT. MRI demonstrated severe muscular edema with patchy, geographic areas of sparing, which, in conjunction with the patient’s clinical presentation, allowed for a diagnosis of diabetic myonecrosis. He underwent conservative treatment, consisting of rest and pain management, leading to resolution of symptoms. Discussion: Diabetic myonecrosis, although uncommon, can be easily diagnosed with a high degree of clinical suspicion. It typically presents in a patient with poorly controlled diabetes, and will commonly involve the proximal muscles of the lower extremity unilaterally, but may present bilaterally and involve the distal muscles, as demonstrated in this case. Diagnosis is made via MRI, and it is treated conservatively with pain management and rest. Most cases resolve with conservative management but recurrence is common

Habitual physical activity (HPA) as a factor in sustained executive function in Alzheimer-type dementia: a cohort study

Evidence from studies on healthy older adults and mild cognitive impairment (MCI) populations suggests that physical activity interventions have a positive effect on executive function. In this study, we consider whether HPA is positively associated with executive function in Alzheimer's disease (AD). Eighty-two participants with a diagnosis of mild to moderate AD completed six measures of executive function. Objective measures of physical status were taken. In addition, informants completed questionnaires on the participants’ HPA and other lifestyle factors. A composite measure of executive function was the primary outcome. A multistage multiple regression was used to determine how much variance HPA accounted for. The final model comprised disease severity, cognitive reserve, cognitive activities, neuropsychiatric status and HPA status. The final model accounted for a total of 57% of the variance of executive performance, of which HPA itself accounted for 8% of the variance. HPA status is associated executive performance in an AD population even after controlling for key covariates. The findings encourage clinicians to recommend HPA and its cognitive benefits to AD patients and their carers

Outcomes after Diagnosis of Mild Cognitive Impairment in a Large Autopsy Series

OBJECTIVE: To determine clinical and neuropathological outcomes following a clinical diagnosis of mild cognitive impairment (MCI). METHODS: Data were drawn from a large autopsy series (N = 1,337) of individuals followed longitudinally from normal or MCI status to death, derived from 4 Alzheimer Disease (AD) Centers in the United States. RESULTS: Mean follow‐up was 7.9 years. Of the 874 individuals ever diagnosed with MCI, final clinical diagnoses were varied: 39.2% died with an MCI diagnosis, 46.8% with a dementia diagnosis, and 13.9% with a diagnosis of intact cognition. The latter group had pathological features resembling those with a final clinical diagnosis of MCI. In terms of non‐AD pathologies, both primary age‐related tauopathy (p \u3c 0.05) and brain arteriolosclerosis pathology (p \u3c 0.001) were more severe in MCI than cognitively intact controls. Among the group that remained MCI until death, mixed AD neuropathologic changes (ADNC; ≥1 comorbid pathology) were more frequent than “pure” ADNC pathology (55% vs 22%); suspected non‐Alzheimer pathology comprised the remaining 22% of cases. A majority (74%) of subjects who died with MCI were without “high”‐level ADNC, Lewy body disease, or hippocampal sclerosis pathologies; this group was enriched in cerebrovascular pathologies. Subjects who died with dementia and were without severe neurodegenerative pathologies tended to have cerebrovascular pathology and carry the MCI diagnosis for a longer interval. INTERPRETATION: MCI diagnosis usually was associated with comorbid neuropathologies; less than one-quarter of MCI cases showed pure AD at autopsy. Ann Neurol 2017;81:549-559