Spike-based decision learning of nash equilibria in two-player games

Humans and animals face decision tasks in an uncertain multi-agent environment where an agent's strategy may change in time due to the co-adaptation of others strategies. The neuronal substrate and the computational algorithms underlying such adaptive decision making, however, is largely unknown. We propose a population coding model of spiking neurons with a policy gradient procedure that successfully acquires optimal strategies for classical game-theoretical tasks. The suggested population reinforcement learning reproduces data from human behavioral experiments for the blackjack and the inspector game. It performs optimally according to a pure (deterministic) and mixed (stochastic) Nash equilibrium, respectively. In contrast, temporal-difference(TD)-learning, covariance-learning, and basic reinforcement learning fail to perform optimally for the stochastic strategy. Spike-based population reinforcement learning, shown to follow the stochastic reward gradient, is therefore a viable candidate to explain automated decision learning of a Nash equilibrium in two-player games.

Virtual implant planning in the edentulous maxilla: criteria for decision making of prosthesis design

OBJECTIVES To evaluate prosthetic parameters in the edentulous anterior maxilla for decision making between fixed and removable implant prosthesis using virtual planning software. MATERIAL AND METHODS CT- or DVT-scans of 43 patients (mean age 62 ± 8 years) with an edentulous maxilla were analyzed with the NobelGuide software. Implants (≥3.5 mm diameter, ≥10 mm length) were virtually placed in the optimal three-dimensional prosthetic position of all maxillary front teeth. Anatomical and prosthetic landmarks, including the cervical crown point (C-Point), the acrylic flange border (F-Point), and the implant-platform buccal-end (I-Point) were defined in each middle section to determine four measuring parameters: (1) acrylic flange height (FLHeight), (2) mucosal coverage (MucCov), (3) crown-Implant distance (CID) and (4) buccal prosthesis profile (ProsthProfile). Based on these parameters, all patients were assigned to one of three classes: (A) MucCov ≤ 0 mm and ProsthProfile≥45(0) allowing for fixed prosthesis, (B) MucCov = 0-5 mm and/or ProsthProfile = 30(0) -45(0) probably allowing for fixed prosthesis, and (C) MucCov ≥ 5 mm and/or ProsthProfile ≤ 30(0) where removable prosthesis is favorable. Statistical analyses included descriptive methods and non-parametric tests. RESULTS Mean values were for FLHeight 10.0 mm, MucCov 5.6 mm, CID 7.4 mm, and ProsthProfile 39.1(0) . Seventy percent of patients fulfilled class C criteria (removable), 21% class B (probably fixed), and 2% class A (fixed), while in 7% (three patients) bone volume was insufficient for implant planning. CONCLUSIONS The proposed classification and virtual planning procedure simplify the decision-making process regarding type of prosthesis and increase predictability of esthetic treatment outcomes. It was demonstrated that in the majority of cases, the space between the prosthetic crown and implant platform had to be filled with prosthetic materials.

Decision-making in aortic root surgery in Marfan syndrome: bleeding, thromboembolism and risk of reintervention after valve-sparing or mechanical aortic root replacement†

OBJECTIVES Valve-sparing root replacement (VSRR) is thought to reduce the rate of thromboembolic and bleeding events compared with aortic root replacement using a mechanical aortic root replacement (MRR) with a composite graft by avoiding oral anticoagulation. But as VSRR carries a certain risk for subsequent reinterventions, decision-making in the individual patient can be challenging. METHODS Of 100 Marfan syndrome (MFS) patients who underwent 169 aortic surgeries and were followed at our institution since 1995, 59 consecutive patients without a history of dissection or prior aortic surgery underwent elective VSRR or MRR and were retrospectively analysed. RESULTS VSRR was performed in 29 (David n = 24, Yacoub n = 5) and MRR in 30 patients. The mean age was 33 ± 15 years. The mean follow-up after VSRR was 6.5 ± 4 years (180 patient-years) compared with 8.8 ± 9 years (274 patient-years) after MRR. Reoperation rates after root remodelling (Yacoub) were significantly higher than after the reimplantation (David) procedure (60 vs 4.2%, P = 0.01). The need for reinterventions after the reimplantation procedure (0.8% per patient-year) was not significantly higher than after MRR (P = 0.44) but follow-up after VSRR was significantly shorter (P = 0.03). There was neither significant morbidity nor mortality associated with root reoperations. There were no neurological events after VSRR compared with four stroke/intracranial bleeding events in the MRR group (log-rank, P = 0.11), translating into an event rate of 1.46% per patient-year following MRR. CONCLUSION The calculated annual failure rate after VSRR using the reimplantation technique was lower than the annual risk for thromboembolic or bleeding events. Since the perioperative risk of reinterventions following VSRR is low, patients might benefit from VSRR even if redo surgery may become necessary during follow-up.

Objective consensus from decision trees

BackgroundConsensus-based approaches provide an alternative to evidence-based decision making, especially in situations where high-level evidence is limited. Our aim was to demonstrate a novel source of information, objective consensus based on recommendations in decision tree format from multiple sources.MethodsBased on nine sample recommendations in decision tree format a representative analysis was performed. The most common (mode) recommendations for each eventuality (each permutation of parameters) were determined. The same procedure was applied to real clinical recommendations for primary radiotherapy for prostate cancer. Data was collected from 16 radiation oncology centres, converted into decision tree format and analyzed in order to determine the objective consensus.ResultsBased on information from multiple sources in decision tree format, treatment recommendations can be assessed for every parameter combination. An objective consensus can be determined by means of mode recommendations without compromise or confrontation among the parties. In the clinical example involving prostate cancer therapy, three parameters were used with two cut-off values each (Gleason score, PSA, T-stage) resulting in a total of 27 possible combinations per decision tree. Despite significant variations among the recommendations, a mode recommendation could be found for specific combinations of parameters.ConclusionRecommendations represented as decision trees can serve as a basis for objective consensus among multiple parties.

Decision Support Models for Composing and Navigating through e-Learning Objects

Libraries of learning objects may serve as basis for deriving course offerings that are customized to the needs of different learning communities or even individuals. Several ways of organizing this course composition process are discussed. Course composition needs a clear understanding of the dependencies between the learning objects. Therefore we discuss the metadata for object relationships proposed in different standardization projects and especially those suggested in the Dublin Core Metadata Initiative. Based on these metadata we construct adjacency matrices and graphs. We show how Gozinto-type computations can be used to determine direct and indirect prerequisites for certain learning objects. The metadata may also be used to define integer programming models which can be applied to support the instructor in formulating his specifications for selecting objects or which allow a computer agent to automatically select learning objects. Such decision models could also be helpful for a learner navigating through a library of learning objects. We also sketch a graph-based procedure for manual or automatic sequencing of the learning objects.