Cake Cutting Algorithms for Piecewise Constant and Piecewise Uniform Valuations

Cake cutting is one of the most fundamental settings in fair division and mechanism design without money. In this paper, we consider different levels of three fundamental goals in cake cutting: fairness, Pareto optimality, and strategyproofness. In particular, we present robust versions of envy-freeness and proportionality that are not only stronger than their standard counter-parts but also have less information requirements. We then focus on cake cutting with piecewise constant valuations and present three desirable algorithms: CCEA (Controlled Cake Eating Algorithm), MEA (Market Equilibrium Algorithm) and CSD (Constrained Serial Dictatorship). CCEA is polynomial-time, robust envy-free, and non-wasteful. It relies on parametric network flows and recent generalizations of the probabilistic serial algorithm. For the subdomain of piecewise uniform valuations, we show that it is also group-strategyproof. Then, we show that there exists an algorithm (MEA) that is polynomial-time, envy-free, proportional, and Pareto optimal. MEA is based on computing a market-based equilibrium via a convex program and relies on the results of Reijnierse and Potters [24] and Devanur et al. [15]. Moreover, we show that MEA and CCEA are equivalent to mechanism 1 of Chen et. al. [12] for piecewise uniform valuations. We then present an algorithm CSD and a way to implement it via randomization that satisfies strategyproofness in expectation, robust proportionality, and unanimity for piecewise constant valuations. For the case of two agents, it is robust envy-free, robust proportional, strategyproof, and polynomial-time. Many of our results extend to more general settings in cake cutting that allow for variable claims and initial endowments. We also show a few impossibility results to complement our algorithms.Comment: 39 page

The Least-core and Nucleolus of Path Cooperative Games

Cooperative games provide an appropriate framework for fair and stable profit distribution in multiagent systems. In this paper, we study the algorithmic issues on path cooperative games that arise from the situations where some commodity flows through a network. In these games, a coalition of edges or vertices is successful if it enables a path from the source to the sink in the network, and lose otherwise. Based on dual theory of linear programming and the relationship with flow games, we provide the characterizations on the CS-core, least-core and nucleolus of path cooperative games. Furthermore, we show that the least-core and nucleolus are polynomially solvable for path cooperative games defined on both directed and undirected network

The value of computed tomography in detecting distal radioulnar joint instability after a distal radius fracture

This study evaluated the value of computed tomography scans for the diagnosis of distal radioulnar joint instability. A total of 46 patients, conservatively treated for a unilateral distal radius fracture, were evaluated. Clinical instability was tested using the stress test and clunk test. A computed tomography scan of both wrists was performed in pronation and supination. Two independent observers reviewed the computed tomography scans using: the radioulnar line, subluxation ratio, epicentre and radioulnar ratio methods. Radiological distal radioulnar joint instability was assessed by comparing the measurements of the injured wrist with those of the contralateral uninjured wrists. A

Body mass index and extent of MRI-detected inflammation: opposite effects in rheumatoid arthritis versus other arthritides and asymptomatic persons

Imaging- and therapeutic targets in neoplastic and musculoskeletal inflammatory diseas

Lack of Knowledge Contrasts the Willingness to Counteract Sarcopenia Among Community-Dwelling Adults

OBJECTIVE: Sarcopenia is highly prevalent in older adults. Knowledge among community-dwelling adults is important for effective prevention and treatment of sarcopenia. This study aims to assess current knowledge about sarcopenia, investigate willingness for treatment and prevention, and awareness of muscle health. METHOD: Participants who attended health educational events completed a questionnaire on knowledge about sarcopenia. Self-perceived muscle health was assessed by visual analog scale. Objective muscle measures included muscle mass, handgrip strength, and gait speed. RESULTS: Included participants were 197 (median aged 67.9 years [interquartile range = 57.0-75.1]). Eighteen participants (9%) reported to know what sarcopenia is. Participants' self-perceived muscle health showed a low correlation with all objective muscle measures. 76% were willing, in case of sarcopenia diagnosis, to start treatment and 71% were willing to prevent sarcopenia. DISCUSSION: Knowledge about sarcopenia is limited while participants were willing to start treatment and prevention. Strategies to increase knowledge among community-dwelling adults are needed

MRI lesions in the sacroiliac joints of patients with spondyloarthritis: an update of definitions and validation by the ASAS MRI working group

OBJECTIVES: The Assessment of SpondyloArthritis international Society (ASAS) MRI working group (WG) was convened to generate a consensus update on standardised definitions for MRI lesions in the sacroiliac joint (SIJ) of patients with spondyloarthritis (SpA), and to conduct preliminary validation. // METHODS: The literature pertaining to these MRI lesion definitions was discussed at three meetings of the group. 25 investigators (20 rheumatologists, 5 radiologists) determined which definitions should be retained or required revision, and which required a new definition. Lesion definitions were assessed in a multi-reader validation exercise using 278 MRI scans from the ASAS classification cohort by global assessment (lesion present/absent) and detailed scoring (inflammation and structural). Reliability of detection of lesions was analysed using kappa statistics and the intraclass correlation coefficient (ICC). // RESULTS: No revisions were made to the current ASAS definition of a positive SIJ MRI or definitions for subchondral inflammation and sclerosis. The following definitions were revised: capsulitis, enthesitis, fat lesion and erosion. New definitions were developed for joint space enhancement, joint space fluid, fat metaplasia in an erosion cavity, ankylosis and bone bud. The most frequently detected structural lesion, erosion, was detected almost as reliably as subchondral inflammation (κappa/ICC:0.61/0.54 and 0.60/0.83) . Fat metaplasia in an erosion cavity and ankylosis were also reliably detected despite their low frequency (κappa/ICC:0.50/0.37 and 0.58/0.97). // CONCLUSION: The ASAS-MRI WG concluded that several definitions required revision and some new definitions were necessary. Multi-reader validation demonstrated substantial reliability for the most frequently detected lesions and comparable reliability between active and structural lesions

Prevalence and clinical significance of lumbosacral transitional vertebra (LSTV) in a young back pain population with suspected axial spondyloarthritis: results of the SPondyloArthritis Caught Early (SPACE) cohort

Imaging- and therapeutic targets in neoplastic and musculoskeletal inflammatory diseas