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

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

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

Position Paper on Water, Energy, Food and Ecosystem (WEFE) Nexus and Sustainable development Goals (SDGs)

The EU and the international community is realising that the Water, Energy, Food and Ecosystem components are interlinked and require a joint planning in order to meet the daunting global challenges related to Water, Energy and Food security and maintaining the ecosystem health and in this way, reach the SDGs. If not dealt with, the world will not be able to meet the demand for water, energy and food in a not too far future and, in any case, in a not sustainable way. The strain on the ecosystems resulting from unsustainable single-sector planning will lead to increasing poverty, inequality and instability. The Nexus approach is fully aligned with and supportive of the EU Consensus on Development. Key elements of the Consensus will require collaborative efforts across sectors in ways that can be supported/implemented by a Nexus approach. In this way, transparent and accountable decision-making, involving the civil society is key and common to the European Consensus on Development and the Nexus approach. The Nexus approach will support the implementation of the SDG in particular SDG 2 (Food), SDG 6 (Water) and SDG 7 (Energy), but most SDGs have elements that link to food, water and energy in one or other way, and will benefit from a Nexus approach. The SDGs are designed to be cross-cutting and be implemented together, which is also reflected in a WEFE Nexus approach. A Nexus approach offers a sustainable way of addressing the effects of Climate Change and increase resilience. The WEFE Nexus has in it the main drivers of climate change (water, energy and food security) and the main affected sectors (water and the environment). Decisions around policy, infrastructure, … developed based on the WEFE Nexus assessments will be suitable as elements of climate change mitigation and adaptation. In fact, it is difficult to imagine solutions to the climate change issue that are not built on a form of Nexus approach. The Nexus approach is being implemented around the world, as examples in the literature demonstrate. These examples together with more examples from EU and member state development cooperation will help build experience that can be consolidated and become an important contribution to a Toolkit for WEFE Nexus Implementation. From the expert discussions, it appears that because of the novelty of the approach, a Toolkit will be an important element in getting the Nexus approach widely used. This should build on experiences from practical examples of NEXUS projects or similar inter-sectorial collaboration projects; and, there are already policy, regulation and practical experience to allow institutions and countries to start applying the Nexus concept.JRC.D.2-Water and Marine Resource

Popular Web Hot Spots Identification and Visualization

This work aims a two-fold contribution: it presents a software to analyse logfiles and visualize popular web hot spots and, additionally, presents an algorithm to use this information in order to identify subsets of the website that display large access patterns. Such information is extremely valuable to the site maintainer, since it indicates points that may need content intervention or/and site graph restructuring. Experimental validation verified that the visualization tool, when coupled with algorithms that infer frequent traversal patterns, is both effective in indicating popular hot spots and efficient in doing so by using graph-based representations of popular traversals