Resource Competition on Integral Polymatroids

We study competitive resource allocation problems in which players distribute their demands integrally on a set of resources subject to player-specific submodular capacity constraints. Each player has to pay for each unit of demand a cost that is a nondecreasing and convex function of the total allocation of that resource. This general model of resource allocation generalizes both singleton congestion games with integer-splittable demands and matroid congestion games with player-specific costs. As our main result, we show that in such general resource allocation problems a pure Nash equilibrium is guaranteed to exist by giving a pseudo-polynomial algorithm computing a pure Nash equilibrium.Comment: 17 page

Acceptability to patients, carers and clinicians of an mHealth platform for the management of Parkinson's disease (PD_Manager): study protocol for a pilot randomised controlled trial.

BACKGROUND: Parkinson's disease is a degenerative neurological condition causing multiple motor and non-motor symptoms that have a serious adverse effect on quality of life. Management is problematic due to the variable and fluctuating nature of symptoms, often hourly and daily. The PD_Manager mHealth platform aims to provide a continuous feed of data on symptoms to improve clinical understanding of the status of any individual patient and inform care planning. The objectives of this trial are to (1) assess patient (and family carer) perspectives of PD_Manager regarding comfort, acceptability and ease of use; (2) assess clinician views about the utility of the data generated by PD_Manager for clinical decision making and the acceptability of the system in clinical practice. METHODS/DESIGN: This trial is an unblinded, parallel, two-group, randomised controlled pilot study. A total of 200 persons with Parkinson's disease (Hoehn and Yahr stage 3, experiencing motor fluctuations at least 2 h per day), with primary family carers, in three countries (110 Rome, 50 Venice, Italy; 20 each in Ioannina, Greece and Surrey, England) will be recruited. Following informed consent, baseline information will be gathered, including the following: age, gender, education, attitudes to technology (patient and carer); time since Parkinson's diagnosis, symptom status and comorbidities (patient only). Randomisation will assign participants (1:1 in each country), to PD_Manager vs control, stratifying by age (1 ≤ 70 : 1 > 70) and gender (60% M: 40% F). The PD_Manager system captures continuous data on motor symptoms, sleep, activity, speech quality and emotional state using wearable devices (wristband, insoles) and a smartphone (with apps) for storing and transmitting the information. Control group participants will be asked to keep a symptom diary covering the same elements as PD_Manager records. After a minimum of two weeks, each participant will attend a consultation with a specialist doctor for review of the data gathered (by either means), and changes to management will be initiated as indicated. Patients, carers and clinicians will be asked for feedback on the acceptability and utility of the data collection methods. The PD_Manager intervention, compared to a symptom diary, will be evaluated in a cost-consequences framework. DISCUSSION: Information gathered will inform further development of the PD_Manager system and a larger effectiveness trial. TRIAL REGISTRATION: ISRCTN Registry, ISRCTN17396879 . Registered on 15 March 2017