Hard instances of algorithms and proof systems

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Approximation algorithms for two-state anti-ferromagnetic spin systems on bounded degree graphs

In a seminal paper [10], Weitz gave a deterministic fully polynomial approximation scheme for counting exponentially weighted independent sets (which is the same as approximating the partition function of the hard-core model from statistical physics) in graphs of degree at most d, up to the critical activity for the uniqueness of the Gibbs measure on the innite d-regular tree. ore recently Sly [8] (see also [1]) showed that this is optimal in the sense that if here is an FPRAS for the hard-core partition function on graphs of maximum egree d for activities larger than the critical activity on the innite d-regular ree then NP = RP. In this paper we extend Weitz's approach to derive a deterministic fully polynomial approximation scheme for the partition function of general two-state anti-ferromagnetic spin systems on graphs of maximum degree d, up to the corresponding critical point on the d-regular tree. The main ingredient of our result is a proof that for two-state anti-ferromagnetic spin systems on the d-regular tree, weak spatial mixing implies strong spatial mixing. his in turn uses a message-decay argument which extends a similar approach proposed recently for the hard-core model by Restrepo et al [7] to the case of general two-state anti-ferromagnetic spin systems.

Extreme Precipitation Modelling Using Geostatistics and Machine Learning Algorithms

The paper presents an approach for mapping of precipitation data. The main goal is to perform spatial predictions and simulations of precipitation fields using geostatistical methods (ordinary kriging, kriging with external drift) as well as machine learning algorithms (neural networks). More practically, the objective is to reproduce simultaneously both the spatial patterns and the extreme values. This objective is best reached by models integrating geostatistics and machine learning algorithms. To demonstrate how such models work, two case studies have been considered: first, a 2-day accumulation of heavy precipitation and second, a 6-day accumulation of extreme orographic precipitation. The first example is used to compare the performance of two optimization algorithms (conjugate gradients and Levenberg-Marquardt) of a neural network for the reproduction of extreme values. Hybrid models, which combine geostatistical and machine learning algorithms, are also treated in this context. The second dataset is used to analyze the contribution of radar Doppler imagery when used as external drift or as input in the models (kriging with external drift and neural networks). Model assessment is carried out by comparing independent validation errors as well as analyzing data patterns.

Machine learning algorithms for spatial data. Case studies: Environmental pollution, natural hazards, renewable resources

This paper presents general problems and approaches for the spatial data analysis using machine learning algorithms. Machine learning is a very powerful approach to adaptive data analysis, modelling and visualisation. The key feature of the machine learning algorithms is that they learn from empirical data and can be used in cases when the modelled environmental phenomena are hidden, nonlinear, noisy and highly variable in space and in time. Most of the machines learning algorithms are universal and adaptive modelling tools developed to solve basic problems of learning from data: classification/pattern recognition, regression/mapping and probability density modelling. In the present report some of the widely used machine learning algorithms, namely artificial neural networks (ANN) of different architectures and Support Vector Machines (SVM), are adapted to the problems of the analysis and modelling of geo-spatial data. Machine learning algorithms have an important advantage over traditional models of spatial statistics when problems are considered in a high dimensional geo-feature spaces, when the dimension of space exceeds 5. Such features are usually generated, for example, from digital elevation models, remote sensing images, etc. An important extension of models concerns considering of real space constrains like geomorphology, networks, and other natural structures. Recent developments in semi-supervised learning can improve modelling of environmental phenomena taking into account on geo-manifolds. An important part of the study deals with the analysis of relevant variables and models' inputs. This problem is approached by using different feature selection/feature extraction nonlinear tools. To demonstrate the application of machine learning algorithms several interesting case studies are considered: digital soil mapping using SVM, automatic mapping of soil and water system pollution using ANN; natural hazards risk analysis (avalanches, landslides), assessments of renewable resources (wind fields) with SVM and ANN models, etc. The dimensionality of spaces considered varies from 2 to more than 30. Figures 1, 2, 3 demonstrate some results of the studies and their outputs. Finally, the results of environmental mapping are discussed and compared with traditional models of geostatistics.

UOC Algorithms

Aplicació per a iPad a mode de repositori de continguts relacionats amb l'ensenyament d'assignatures d'informàtica.

Evaluation of organ-specific peripheral doses after 2-dimensional, 3-dimensional and hybrid intensity modulated radiation therapy for breast cancer based on Monte Carlo and convolution/superposition algorithms: implications for secondary cancer risk assessment.

To make a comprehensive evaluation of organ-specific out-of-field doses using Monte Carlo (MC) simulations for different breast cancer irradiation techniques and to compare results with a commercial treatment planning system (TPS). Three breast radiotherapy techniques using 6MV tangential photon beams were compared: (a) 2DRT (open rectangular fields), (b) 3DCRT (conformal wedged fields), and (c) hybrid IMRT (open conformal+modulated fields). Over 35 organs were contoured in a whole-body CT scan and organ-specific dose distributions were determined with MC and the TPS. Large differences in out-of-field doses were observed between MC and TPS calculations, even for organs close to the target volume such as the heart, the lungs and the contralateral breast (up to 70% difference). MC simulations showed that a large fraction of the out-of-field dose comes from the out-of-field head scatter fluence (>40%) which is not adequately modeled by the TPS. Based on MC simulations, the 3DCRT technique using external wedges yielded significantly higher doses (up to a factor 4-5 in the pelvis) than the 2DRT and the hybrid IMRT techniques which yielded similar out-of-field doses. In sharp contrast to popular belief, the IMRT technique investigated here does not increase the out-of-field dose compared to conventional techniques and may offer the most optimal plan. The 3DCRT technique with external wedges yields the largest out-of-field doses. For accurate out-of-field dose assessment, a commercial TPS should not be used, even for organs near the target volume (contralateral breast, lungs, heart).

Multicast extension of unicast charging for QoS Services

In order to successfully deploy multicast services in QoS-aware networks, pricing architectures must take into account the particular characteristics of multicast sessions. With this objective, we propose a charging scheme for QoS multicast services, assuming that the unicast cost of each interconnecting link is determined and that such cost is expressed in terms of quality of service (QoS) parameters. Our scheme allows determining the cost distribution of a multicast session along a cost distribution tree (CDT), and basing such distribution in those pre-existing unicast cost functions. The paper discusses in detail the main characteristics of the problem in a realistic interdomain scenario and how the proposed scheme would contribute to its solution

A quality-based cost distribution charging scheme for QoS multicast networks

This paper presents a new charging scheme for cost distribution along a point-to-multipoint connection when destination nodes are responsible for the cost. The scheme focus on QoS considerations and a complete range of choices is presented. These choices go from a safe scheme for the network operator to a fair scheme to the customer. The in-between cases are also covered. Specific and general problems, like the incidence of users disconnecting dynamically is also discussed. The aim of this scheme is to encourage the users to disperse the resource demand instead of having a large number of direct connections to the source of the data, which would result in a higher than necessary bandwidth use from the source. This would benefit the overall performance of the network. The implementation of this task must balance between the necessity to offer a competitive service and the risk of not recovering such service cost for the network operator. Throughout this paper reference to multicast charging is made without making any reference to any specific category of service. The proposed scheme is also evaluated with the criteria set proposed in the European ATM charging project CANCAN

On the use of QoS requirements as base of multicast charging

We propose a charging scheme for cost distribution along a multicast tree when cost is the responsibility of the receivers. This scheme focuses on QoS considerations and it does not depend on any specific type of service. The scheme has been designed to be used as a bridge between unicast and multicast services, solving the problem of charging multicast services by means of unicast charging and existing QoS routing mechanisms. We also include a numerical comparison and discussions of the case of non-numerical or relative QoS and on the application to some service examples in order to give a better understanding of the proposal