Achieving New Upper Bounds for the Hypergraph Duality Problem through Logic

The hypergraph duality problem DUAL is defined as follows: given two simple hypergraphs $\mathcal{G}$ and $\mathcal{H}$, decide whether $\mathcal{H}$ consists precisely of all minimal transversals of $\mathcal{G}$ (in which case we say that $\mathcal{G}$ is the dual of $\mathcal{H}$). This problem is equivalent to deciding whether two given non-redundant monotone DNFs are dual. It is known that non-DUAL, the complementary problem to DUAL, is in $\mathrm{GC}(\log^2 n,\mathrm{PTIME})$, where $\mathrm{GC}(f(n),\mathcal{C})$ denotes the complexity class of all problems that after a nondeterministic guess of $O(f(n))$ bits can be decided (checked) within complexity class $\mathcal{C}$. It was conjectured that non-DUAL is in $\mathrm{GC}(\log^2 n,\mathrm{LOGSPACE})$. In this paper we prove this conjecture and actually place the non-DUAL problem into the complexity class $\mathrm{GC}(\log^2 n,\mathrm{TC}^0)$ which is a subclass of $\mathrm{GC}(\log^2 n,\mathrm{LOGSPACE})$. We here refer to the logtime-uniform version of $\mathrm{TC}^0$, which corresponds to $\mathrm{FO(COUNT)}$, i.e., first order logic augmented by counting quantifiers. We achieve the latter bound in two steps. First, based on existing problem decomposition methods, we develop a new nondeterministic algorithm for non-DUAL that requires to guess $O(\log^2 n)$ bits. We then proceed by a logical analysis of this algorithm, allowing us to formulate its deterministic part in $\mathrm{FO(COUNT)}$. From this result, by the well known inclusion $\mathrm{TC}^0\subseteq\mathrm{LOGSPACE}$, it follows that DUAL belongs also to $\mathrm{DSPACE}[\log^2 n]$. Finally, by exploiting the principles on which the proposed nondeterministic algorithm is based, we devise a deterministic algorithm that, given two hypergraphs $\mathcal{G}$ and $\mathcal{H}$, computes in quadratic logspace a transversal of $\mathcal{G}$ missing in $\mathcal{H}$.Comment: Restructured the presentation in order to be the extended version of a paper that will shortly appear in SIAM Journal on Computin

Wind power forecasting using historical data and artificial neural networks modeling

One of the main parameters affecting the reliability of the renewable energy sources (RES) system, compared to the local conventional power station, is the ability to forecast the RES availability for a few hours ahead. To this end, the main objective of this work is the prognosis of the mean, maximum and minimum hourly wind power (WP) 8hours ahead. For this purpose, Artificial Neural Networks (ANN) modeling is applied. For the appropriate training of the developed ANN models hourly meteorological data are used. These data have been recorded by a meteorological mast in Tilos Island, Greece. For the evaluation of the developed ANN forecasting models proper statistical evaluation indices are used. According to the results, the coefficient of the determination ranges from 0.285 up to 0.768 (mean hourly WP), from 0.227 up to 0.798 (maximum hourly WP) and from 0.025 up to 0.398 (minimum hourly WP). Furthermore, the proposed forecasting methodology shows that is able to give sufficient and adequate prognosis of WP by a wind turbine in a specific location 8 hours ahead. This will be a useful tool for the operator of a RES system in order to achieve a better monitoring and a better management of the whole system

Trace Spaces: an Efficient New Technique for State-Space Reduction

State-space reduction techniques, used primarily in model-checkers, all rely on the idea that some actions are independent, hence could be taken in any (respective) order while put in parallel, without changing the semantics. It is thus not necessary to consider all execution paths in the interleaving semantics of a concurrent program, but rather some equivalence classes. The purpose of this paper is to describe a new algorithm to compute such equivalence classes, and a representative per class, which is based on ideas originating in algebraic topology. We introduce a geometric semantics of concurrent languages, where programs are interpreted as directed topological spaces, and study its properties in order to devise an algorithm for computing dihomotopy classes of execution paths. In particular, our algorithm is able to compute a control-flow graph for concurrent programs, possibly containing loops, which is "as reduced as possible" in the sense that it generates traces modulo equivalence. A preliminary implementation was achieved, showing promising results towards efficient methods to analyze concurrent programs, with very promising results compared to partial-order reduction techniques

Polynomial Delay Algorithm for Listing Minimal Edge Dominating sets in Graphs

The Transversal problem, i.e, the enumeration of all the minimal transversals of a hypergraph in output-polynomial time, i.e, in time polynomial in its size and the cumulated size of all its minimal transversals, is a fifty years old open problem, and up to now there are few examples of hypergraph classes where the problem is solved. A minimal dominating set in a graph is a subset of its vertex set that has a non empty intersection with the closed neighborhood of every vertex. It is proved in [M. M. Kant\'e, V. Limouzy, A. Mary, L. Nourine, On the Enumeration of Minimal Dominating Sets and Related Notions, In Revision 2014] that the enumeration of minimal dominating sets in graphs and the enumeration of minimal transversals in hypergraphs are two equivalent problems. Hoping this equivalence can help to get new insights in the Transversal problem, it is natural to look inside graph classes. It is proved independently and with different techniques in [Golovach et al. - ICALP 2013] and [Kant\'e et al. - ISAAC 2012] that minimal edge dominating sets in graphs (i.e, minimal dominating sets in line graphs) can be enumerated in incremental output-polynomial time. We provide the first polynomial delay and polynomial space algorithm that lists all the minimal edge dominating sets in graphs, answering an open problem of [Golovach et al. - ICALP 2013]. Besides the result, we hope the used techniques that are a mix of a modification of the well-known Berge's algorithm and a strong use of the structure of line graphs, are of great interest and could be used to get new output-polynomial time algorithms.Comment: proofs simplified from previous version, 12 pages, 2 figure

Beyond Hypergraph Dualization

International audienceThis problem concerns hypergraph dualization and generalization to poset dualization. A hypergraph H = (V, E) consists of a finite collection E of sets over a finite set V , i.e. E ⊆ P(V) (the powerset of V). The elements of E are called hyperedges, or simply edges. A hypergraph is said simple if none of its edges is contained within another. A transversal (or hitting set) of H is a set T ⊆ V that intersects every edge of E. A transversal is minimal if it does not contain any other transversal as a subset. The set of all minimal transversal of H is denoted by T r(H). The hypergraph (V, T r(H)) is called the transversal hypergraph of H. Given a simple hypergraph H, the hypergraph dualization problem (Trans-Enum for short) concerns the enumeration without repetitions of T r(H). The Trans-Enum problem can also be formulated as a dualization problem in posets. Let (P, ≤) be a poset (i.e. ≤ is a reflexive, antisymmetric, and transitive relation on the set P). For A ⊆ P , ↓ A (resp. ↑ A) is the downward (resp. upward) closure of A under the relation ≤ (i.e. ↓ A is an ideal and ↑ A a filter of (P, ≤)). Two antichains (B + , B −) of P are said to be dual if ↓ B + ∪ ↑ B − = P and ↓ B + ∩ ↑ B − = ∅. Given an implicit description of a poset P and an antichain B + (resp. B −) of P , the poset dualization problem (Dual-Enum for short) enumerates the set B − (resp. B +), denoted by Dual(B +) = B − (resp. Dual(B −) = B +). Notice that the function dual is self-dual or idempotent, i.e. Dual(Dual(B)) = B

CO2GeoNet, the unique role of the European scientific body on CO2 geological storage

CO2GeoNet is a Network of Excellence on the geological storage of CO2, initiated by the EC's 6th research framework programme in 2004 and integrating Europe's key research institutes to create a scientific reference body dedicated to the development of CO2 geological storage as a viable option for mitigating climate change. It has gained international recognition through bodies such as CSLF and IEA-GHG. It emerges as the world's largest integrated scientific community on this theme. In 2008, the network has been transformed into a legally registered Association, thus reinforcing its identity as a durable entity engaged for the safe and reliable deployment of CO2 geological storage. CO2GeoNet's activities encompass joint research, training, scientific advice, and information and communication on CO2 geological storage. © 2009 Elsevier Ltd. All rights reserved

GRS 1915+105 : High-energy Insights with SPI/INTEGRAL

We report on results of two years of INTEGRAL/SPI monitoring of the Galactic microquasar GRS 1915+105. From September 2004 to May 2006, the source has been observed twenty times with long (approx 100 ks) exposures. We present an analysis of the SPI data and focus on the description of the high-energy (> 20 keV) output of the source. We found that the 20 - 500 keV spectral emission of GRS 1915+105 was bound between two states. It seems that these high-energy states are not correlated with the temporal behavior of the source, suggesting that there is no direct link between the macroscopic characteristics of the coronal plasma and the the variability of the accretion flow. All spectra are well fitted by a thermal comptonization component plus an extra high-energy powerlaw. This confirms the presence of thermal and non-thermal electrons around the black hole.Comment: 7 pages, 8 figures, 2 tables; accepted (09/11/2008) for publication in A&

Structural and functional analysis of cellular networks with CellNetAnalyzer

BACKGROUND: Mathematical modelling of cellular networks is an integral part of Systems Biology and requires appropriate software tools. An important class of methods in Systems Biology deals with structural or topological (parameter-free) analysis of cellular networks. So far, software tools providing such methods for both mass-flow (metabolic) as well as signal-flow (signalling and regulatory) networks are lacking. RESULTS: Herein we introduce CellNetAnalyzer, a toolbox for MATLAB facilitating, in an interactive and visual manner, a comprehensive structural analysis of metabolic, signalling and regulatory networks. The particular strengths of CellNetAnalyzer are methods for functional network analysis, i.e. for characterising functional states, for detecting functional dependencies, for identifying intervention strategies, or for giving qualitative predictions on the effects of perturbations. CellNetAnalyzer extends its predecessor FluxAnalyzer (originally developed for metabolic network and pathway analysis) by a new modelling framework for examining signal-flow networks. Two of the novel methods implemented in CellNetAnalyzer are discussed in more detail regarding algorithmic issues and applications: the computation and analysis (i) of shortest positive and shortest negative paths and circuits in interaction graphs and (ii) of minimal intervention sets in logical networks. CONCLUSION: CellNetAnalyzer provides a single suite to perform structural and qualitative analysis of both mass-flow- and signal-flow-based cellular networks in a user-friendly environment. It provides a large toolbox with various, partially unique, functions and algorithms for functional network analysis.CellNetAnalyzer is freely available for academic use