Convex Combinatorial Optimization

We introduce the convex combinatorial optimization problem, a far reaching generalization of the standard linear combinatorial optimization problem. We show that it is strongly polynomial time solvable over any edge-guaranteed family, and discuss several applications

Regression Driven F--Transform and Application to Smoothing of Financial Time Series

In this paper we propose to extend the definition of fuzzy transform in order to consider an interpolation of models that are richer than the standard fuzzy transform. We focus on polynomial models, linear in particular, although the approach can be easily applied to other classes of models. As an example of application, we consider the smoothing of time series in finance. A comparison with moving averages is performed using NIFTY 50 stock market index. Experimental results show that a regression driven fuzzy transform (RDFT) provides a smoothing approximation of time series, similar to moving average, but with a smaller delay. This is an important feature for finance and other application, where time plays a key role.Comment: IFSA-SCIS 2017, 5 pages, 6 figures, 1 tabl

The Development of Penetration Charges for Increasing the Efficiency of the Interventions of Fire Rescue Service Units

During building fires is often necessary to deliver nozzles with water to the desired point of intervention and the wall or ceiling must be penetrated for energy supply and the entrance of persons. Access openings for extinguishing are created with hand tools or explosives, but it is a very time-consuming activity and fragmented material may endanger persons. Another possibility is the use of charges with a water layer, which absorbs the shock wave of the explosion at the back and at the same time significantly suppresses the fragmentation of the building element on which the charge acts. The penetration charge developed in two versions allows a sufficient penetration of the partitio

A tree-decomposed transfer matrix for computing exact Potts model partition functions for arbitrary graphs, with applications to planar graph colourings

Combining tree decomposition and transfer matrix techniques provides a very general algorithm for computing exact partition functions of statistical models defined on arbitrary graphs. The algorithm is particularly efficient in the case of planar graphs. We illustrate it by computing the Potts model partition functions and chromatic polynomials (the number of proper vertex colourings using Q colours) for large samples of random planar graphs with up to N=100 vertices. In the latter case, our algorithm yields a sub-exponential average running time of ~ exp(1.516 sqrt(N)), a substantial improvement over the exponential running time ~ exp(0.245 N) provided by the hitherto best known algorithm. We study the statistics of chromatic roots of random planar graphs in some detail, comparing the findings with results for finite pieces of a regular lattice.Comment: 5 pages, 3 figures. Version 2 has been substantially expanded. Version 3 shows that the worst-case running time is sub-exponential in the number of vertice

A stabilized finite element method for the two-field and three-field Stokes eigenvalue problems

In this paper, the stabilized finite element approximation of the Stokes eigenvalue problems is considered for both the two-field (displacement-pressure) and the three-field (stress-displacement-pressure) formulations. The method presented is based on a subgrid scale concept, and depends on the approximation of the unresolvable scales of the continuous solution. In general, subgrid scale techniques consist in the addition of a residual based term to the basic Galerkin formulation. The application of a standard residual based stabilization method to a linear eigenvalue problem leads to a quadratic eigenvalue problem in discrete form which is physically inconvenient. As a distinguished feature of the present study, we take the space of the unresolved subscales orthogonal to the finite element space, which promises a remedy to the above mentioned complication. In essence, we put forward that only if the orthogonal projection is used, the residual is simplified and the use of term by term stabilization is allowed. Thus, we do not need to put the whole residual in the formulation, and the linear eigenproblem form is recovered properly. We prove that the method applied is convergent, and present the error estimates for the eigenvalues and the eigenfunctions. We report several numerical tests in order to illustrate that the theoretical results are validated

Convex Matroid Optimization

We consider a problem of optimizing convex functionals over matroid bases. It is richly expressive and captures certain quadratic assignment and clustering problems. While generally NP-hard, we show it is polynomial time solvable when a suitable parameter is restricted