A filtering method for the interval eigenvalue problem

We consider the general problem of computing intervals that contain the real eigenvalues of interval matrices. Given an outer estimation of the real eigenvalue set of an interval matrix, we propose a filtering method that improves the estimation. Even though our method is based on an sufficient regularity condition, it is very efficient in practice, and our experimental results suggest that, in general, improves significantly the input estimation. The proposed method works for general, as well as for symmetric matrices

An Algorithm for the Real Interval Eigenvalue Problem

In this paper we present an algorithm for approximating the range of the real eigenvalues of interval matrices. Such matrices could be used to model real-life problems, where data sets suffer from bounded variations such as uncertainties (e.g. tolerances on parameters, measurement errors), or to study problems for given states. The algorithm that we propose is a subdivision algorithm that exploits so- phisticated techniques from interval analysis. The quality of the computed approximation, as well as the running time of the algorithm depend on a given input accuracy. We also present an efficient C++ implementation and illustrate its efficiency on various data sets. In most of the cases we manage to compute efficiently the exact boundary points (limited by floating point representation)

The Worst Case Finite Optimal Value in Interval Linear Programming

We consider a linear programming problem, in which possibly all coefficients are subject to uncertainty in the form of deterministic intervals. The problem of computing the worst case optimal value has already been thoroughly investigated in the past. Notice that it might happen that the value can be infinite due to infeasibility of some instances. This is a serious drawback if we know a priori that all instances should be feasible. Therefore we focus on the feasible instances only and study the problem of computing the worst case finite optimal value. We present a characterization for the general case and investigate special cases, too. We show that the problem is easy to solve provided interval uncertainty affects the objective function only, but the problem becomes intractable in case of intervals in the righthand side of the constraints. We also propose a finite reduction based on inspecting candidate bases. We show that processing a given basis is still an NP-hard problem even with non-interval constraint matrix, however, the problem becomes tractable as long as uncertain coefficients are situated either in the objective function or in the right-hand side only

Optimization of Quadratic Forms and t-norm Forms on Interval Domain and Computational Complexity

We consider the problem of maximization of a quadratic form over a box. We identify the NP-hardness boundary for sparse quadratic forms: the problem is polynomially solvable for O(log n) nonzero entries, but it is NP-hard if the number of nonzero entries is of the order nε for an arbitrarily small ε \u3e 0. Then we inspect further polynomially solvable cases. We define a sunflower graph over the quadratic form and study efficiently solvable cases according to the shape of this graph (e.g. the case with small sunflower leaves or the case with a restricted number of negative entries). Finally, we define a generalized quadratic form, called t-norm form, where the quadratic terms are replaced by t-norms. We prove that the optimization problem remains NP-hard with an arbitrary Lipschitz continuous t-norm

Refining Subgames in Large Imperfect Information Games

The leading approach to solving large imperfect information games is to pre-calculate an approximate solution using a simplified abstraction of the full game; that solution is then used to play the original, full-scale game. The abstraction step is necessitated by the size of the game tree. However, as the original game progresses, the remaining portion of the tree (the subgame) becomes smaller. An appealing idea is to use the simplified abstraction to play the early parts of the game and then, once the subgame becomes tractable, to calculate a solution using a finer-grained abstraction in real time, creating a combined final strategy. While this approach is straightforward for perfect information games, it is a much more complex problem for imperfect information games. If the subgame is solved locally, the opponent can alter his play in prior to this subgame to exploit our combined strategy. To prevent this, we introduce the notion of subgame margin, a simple value with appealing properties. If any best response reaches the subgame, the improvement of exploitability of the combined strategy is (at least) proportional to the subgame margin. This motivates subgame refinements resulting in large positive margins. Unfortunately, current techniques either neglect subgame margin (potentially leading to a large negative subgame margin and drastically more exploitable strategies), or guarantee only non-negative subgame margin (possibly producing the original, unrefined strategy, even if much stronger strategies are possible). Our technique remedies this problem by maximizing the subgame margin and is guaranteed to find the optimal solution. We evaluate our technique using one of the top participants of the AAAI-14 Computer Poker Competition, the leading playground for agents in imperfect information settin

Co2-Spicer – Czech-Norwegian Project to Prepare a Co2 Storage Pilot in a Carbonate Reservoir

Carbon capture and storage (CCS) is one of key technologies to decarbonise the emission-intensive industries in the Czech Republic and reach the 2050 carbon-neutral economy target. An important step on the road to the deployment of the technology is to prepare and realise a CO2 storage pilot project in the country. The newly launched CO2- SPICER project has been designed to make significant progress in this direction. It is the first project in Europe, targeting an onshore hydrocarbon field situated in carbonates as a pilot CO2 storage site. Achieving the main project objective - to reach the implementation-ready stage of site development - would allow direct follow-up to project activities, using main project results as ready-made input. The target Zar-3 site is a hydrocarbon field located in the SE part of the Czech Republic. It is situated in an erosional relict of fractured carbonates of Jurassic age on the SE slopes of the Bohemian Massif, covered by Paleogene deposits and Carpathian flysch nappes. The field was discovered in 2001 and is now nearly depleted. This relatively “young age” of the field, together with active participation of field operator in the consortium and ongoing hydrocarbon production provide many advantages, such as direct access of the reservoir, availability of field monitoring data, generally good condition of wells, well-preserved core material and detailed reservoir description. However, the geology of naturally fractured carbonates brings specific research challenges. This paper provides a brief overview of the storage site and the project, its objectives, planned activities and expected outcomes

Peak neutron production from the 7Li(p,n) reaction in the 20-35 MeV range

New experimental data on the peak neutron production in the Li-7(p,n) reaction were collected during several irradiation campaigns at the NPI CAS. Time-of-flight method was used to measure the number of the peak neutrons in the forward direction, and the number of produced Be-7 nuclei was determined using gamma-spectrometry. The new measurement results are compared with experimental data from the literature and used for the validation of several different systematics and nuclear data libraries developed over the years