Two algorithms to find a power integral basis

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A Model-to-model analysis of the repeated Prisoners' Dilemma: genetic algorithms vs. evolutionary dynamics

We study the properties of the well known Replicator Dynamics when applied to a finitely repeated version of the Prisoners' Dilemma game. We characterize the behavior of such dynamics under strongly simplifying assumptions (i.e. only 3 strategies are available) and show that the basin of attraction of defection shrinks as the number of repetitions increases. After discussing the difficulties involved in trying to relax the 'strongly simplifying assumptions' above, we approach the same model by means of simulations based on genetic algorithms. The resulting simulations describe a behavior of the system very close to the one predicted by the replicator dynamics without imposing any of the assumptions of the analytical model. Our main conclusion is that analytical and computational models are good complements for research in social sciences. Indeed, while on the one hand computational models are extremely useful to extend the scope of the analysis to complex scenar

Multi-scale support vector algorithms for hot spot detection and modelling

The algorithmic approach to data modelling has developed rapidly these last years, in particular methods based on data mining and machine learning have been used in a growing number of applications. These methods follow a data-driven methodology, aiming at providing the best possible generalization and predictive abilities instead of concentrating on the properties of the data model. One of the most successful groups of such methods is known as Support Vector algorithms. Following the fruitful developments in applying Support Vector algorithms to spatial data, this paper introduces a new extension of the traditional support vector regression (SVR) algorithm. This extension allows for the simultaneous modelling of environmental data at several spatial scales. The joint influence of environmental processes presenting different patterns at different scales is here learned automatically from data, providing the optimum mixture of short and large-scale models. The method is adaptive to the spatial scale of the data. With this advantage, it can provide efficient means to model local anomalies that may typically arise in situations at an early phase of an environmental emergency. However, the proposed approach still requires some prior knowledge on the possible existence of such short-scale patterns. This is a possible limitation of the method for its implementation in early warning systems. The purpose of this paper is to present the multi-scale SVR model and to illustrate its use with an application to the mapping of Cs137 activity given the measurements taken in the region of Briansk following the Chernobyl accident.

Predicting hematologic toxicity in patients undergoing radioimmunotherapy with 90Y-ibritumomab tiuxetan or 131I-tositumomab.

This study aimed at identifying clinical factors for predicting hematologic toxicity after radioimmunotherapy with (90)Y-ibritumomab tiuxetan or (131)I-tositumomab in clinical practice. Hematologic data were available from 14 non-Hodgkin lymphoma patients treated with (90)Y-ibritumomab tiuxetan and 18 who received (131)I-tositumomab. The percentage baseline at nadir and 4 wk post nadir and the time to nadir were selected as the toxicity indicators for both platelets and neutrophils. Multiple linear regression analysis was performed to identify significant predictors (P < 0.05) of each indicator. For both platelets and neutrophils, pooled and separate analyses of (90)Y-ibritumomab tiuxetan and (131)I-tositumomab data yielded the time elapsed since the last chemotherapy as the only significant predictor of the percentage baseline at nadir. The extent of bone marrow involvement was not a significant factor in this study, possibly because of the short time elapsed since the last chemotherapy of the 7 patients with bone marrow involvement. Because both treatments were designed to deliver a comparable bone marrow dose, this factor also was not significant. None of the 14 factors considered was predictive of the time to nadir. The R(2) value for the model predicting percentage baseline at nadir was 0.60 for platelets and 0.40 for neutrophils. This model predicted the platelet and neutrophil toxicity grade to within ±1 for 28 and 30 of the 32 patients, respectively. For the 7 patients predicted with grade I thrombocytopenia, 6 of whom had actual grade I-II, dosing might be increased to improve treatment efficacy. The elapsed time since the last chemotherapy can be used to predict hematologic toxicity and customize the current dosing method in radioimmunotherapy.

Fast numerical algorithms for the computation of invariant tori in Hamiltonian systems

In this paper, we develop numerical algorithms that use small requirements of storage and operations for the computation of invariant tori in Hamiltonian systems (exact symplectic maps and Hamiltonian vector fields). The algorithms are based on the parameterization method and follow closely the proof of the KAM theorem given in [LGJV05] and [FLS07]. They essentially consist in solving a functional equation satisfied by the invariant tori by using a Newton method. Using some geometric identities, it is possible to perform a Newton step using little storage and few operations. In this paper we focus on the numerical issues of the algorithms (speed, storage and stability) and we refer to the mentioned papers for the rigorous results. We show how to compute efficiently both maximal invariant tori and whiskered tori, together with the associated invariant stable and unstable manifolds of whiskered tori. Moreover, we present fast algorithms for the iteration of the quasi-periodic cocycles and the computation of the invariant bundles, which is a preliminary step for the computation of invariant whiskered tori. Since quasi-periodic cocycles appear in other contexts, this section may be of independent interest. The numerical methods presented here allow to compute in a unified way primary and secondary invariant KAM tori. Secondary tori are invariant tori which can be contracted to a periodic orbit. We present some preliminary results that ensure that the methods are indeed implementable and fast. We postpone to a future paper optimized implementations and results on the breakdown of invariant tori.

A Survey of Active Learning Algorithms for Supervised Remote Sensing Image Classification

Defining an efficient training set is one of the most delicate phases for the success of remote sensing image classification routines. The complexity of the problem, the limited temporal and financial resources, as well as the high intraclass variance can make an algorithm fail if it is trained with a suboptimal dataset. Active learning aims at building efficient training sets by iteratively improving the model performance through sampling. A user-defined heuristic ranks the unlabeled pixels according to a function of the uncertainty of their class membership and then the user is asked to provide labels for the most uncertain pixels. This paper reviews and tests the main families of active learning algorithms: committee, large margin, and posterior probability-based. For each of them, the most recent advances in the remote sensing community are discussed and some heuristics are detailed and tested. Several challenging remote sensing scenarios are considered, including very high spatial resolution and hyperspectral image classification. Finally, guidelines for choosing the good architecture are provided for new and/or unexperienced user.

Less frequent dosing of erythropoiesis stimulating agents in patients undergoing dialysis: a European multicentre cost study.

OBJECTIVE: To calculate the variable costs involved with the process of delivering erythropoiesis stimulating agents (ESA) in European dialysis practices. METHODS: A conceptual model was developed to classify the processes and sub-processes followed in the pharmacy (ordering from supplier, receiving/storing/delivering ESA to the dialysis unit), dialysis unit (dose determination, ordering, receipt, registration, storage, administration, registration) and waste disposal unit. Time and material costs were recorded. Labour costs were derived from actual local wages while material costs came from the facilities' accounting records. Activities associated with ESA administration were listed and each activity evaluated to determine if dosing frequency affected the amount of resources required. RESULTS: A total of 21 centres in 8 European countries supplied data for 142 patients (mean) per hospital (range 42-648). Patients received various ESA regimens (thrice-weekly, twice-weekly, once-weekly, once every 2 weeks and once-monthly). Administering ESA every 2 weeks, the mean costs per patient per year for each process and the estimates of the percentage reduction in costs obtainable, respectively, were: pharmacy labour (10.1 euro, 39%); dialysis unit labour (66.0 euro, 65%); dialysis unit materials (4.11 euro, 61%) and waste unit materials (0.43 euro, 49%). LIMITATION: Impact on financial costs was not measured. CONCLUSION: ESA administration has quantifiable labour and material costs which are affected by dosing frequency.

Guidelines for the clinical management of atrial fibrillation: a practical perspective.

Since the management of atrial fibrillation may be difficult in the individual patient, our purpose was to develop simple clinical recommendations to help the general internist manage this common clinical problem. Systematic review of the literature with evaluation of data-related evidence and framing of graded recommendations. Atrial fibrillation affects some 1% of the population in Western countries and is linked to a significant increase in morbidity and mortality. The management of atrial fibrillation requires individualised evaluation of the risks and benefits of therapeutic modalities, relying whenever possible on simple and validated tools. The two main points requiring a decision in clinical management are 1) whether or not to implement thromboembolic prevention therapy, and 2) whether preference should be given to a "rate control" or "rhythm control" strategy. Thromboembolic prophylaxis should be prescribed after individualised risk assessment: for patients at risk, oral anticoagulation with warfarin decreases the rate of embolic complications by 60% and aspirin by 20%, at the expense of an increased incidence of haemorrhagic complications. "Rate control" and "rhythm control" strategies are probably equivalent, and the choice should also be made on an individualised basis. To assist the physician in making his choices for the care of an atrial fibrillation patient we propose specific tables and algorithms, with graded recommendations. On the evidence of data from the literature we propose simple algorithms and tables for the clinical management of atrial fibrillation in the individual patient.

Hard instances of algorithms and proof systems

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