LambdaRank has proven effective for optimizing information retrieval metrics such as Normalized Discounted Cumulative Gain (NDCG). However, its application to Precision at document k (P@k) poses significant challenges because of the metric’s unique definition, which heavily restricts the number of effective training document pairs. This limitation diminishes the learning signal for relevant documents beyond the top k, potentially resulting in suboptimal performance. To overcome this, we propose LambdaGap, a ranking algorithm inspired by LambdaRank specifically tailored for optimizing P@k. LambdaGap replaces the pairwise weighting scheme in LambdaRank by one where pairs of documents within k positions in the ranking are masked out. We establish a theoretical link between LambdaGap and P@k by identifying the implicit metric optimized by the model. Furthermore, we introduce a new metric, Average Relevance Position beyond document k, which can be used in conjunction with LambdaRank to indirectly optimize for P@k. Our extensive experiments on publicly available datasets demonstrate the effectiveness of the proposed methods, yielding statistically significant improvements in P@k performance and highlighting their potential for more efficient training.

Wind field is a critical issue in forest fire propagation prediction. However, wind field calculation is a complex problem that, for large terrains, involves solving huge linear systems. To solve such systems, the Preconditioned Conjugate Gradient (PCG) solver is applied. SSOR and Jacobi preconditioners are usually used, but solving such systems takes too much time and makes the approach unfeasible in real time operation. Parallelization appears as a way to make the approach operational in real time. The PCG with both preconditioners has been parallelized to accelerate the execution. However, the improvement in execution time is not enough, and the Schwarz alternating domain decomposition has been applied to exploit a second level of parallelism. Using this method, the linear system is decomposed in a set of overlapped subdomains that can be solved in parallel using a Master/Worker paradigm, where each worker exploits the PCG solver parallelism. As a result, the wind field calculation time is significantly reduced; for example, a large map of 1200×1200 cells, whose solution took more than 2000 seconds in the original WindNinja, can now be solved in less than 240 seconds using 4 subdomain and 4 cores per subdomain.

Wind field calculation is a critical issue in reaching accurate forest fire propagation predictions. However, when the involved terrain map is large, the amount of memory and the execution time can prevent them from being useful in an operational environment. Wind field calculation involves sparse matrices that are usually stored in CSR storage format. This storage format can cause sparse matrix-vector multiplications to create a bottleneck due to the number of cache misses involved. Moreover, the matrices involved are extremely sparse and follow a very well-defined pattern. Therefore, a new storage system has been designed to reduce memory requirements and cache misses in this particular sparse matrix-vector multiplication. Sparse matrix-vector multiplication has been implemented using this new storage format and taking advantage of the inherent parallelism of the operation. The new method has been implemented in OpenMP, MPI and CUDA and has been tested on different hardware configurations. The results are very promising and the execution time and memory requirements are significantly reduced.

• Predicting forest fire propagation is a crucial issue to mitigate fire damages. • Wind significantly affects forest fire propagation. • Wind field calculation implies solving extremely large systems of equations. • The Schur method has been applied to accelerate wind field calculation. • Execution time is reduced to accomplish operational requirements. Forest fire are natural hazards that every year cause significant looses. Predicting the evolution of a forest fire is a critical issue in mitigating its effects. Such predictions must accomplish strict real time constraints to be effective. Wind field calculation is a key issue in providing accurate forest fire propagation predictions. However, it implies solving large linear systems with 10 5 to 10 8 variables that takes too long using conventional methods. Therefore, the domain decomposition Schur method has been applied to accelerate wind field calculation. Using the Schur method, the linear system is significantly reduced and several phases can be parallelised exploiting cluster computing capabilities. Results show that the execution time for the wind field calculation of a map of 800 × 800 cells has been reduced from 400 s to 90 s using 10 nodes.