Summary and highlights

Energy means development, and access to energy and electricity should be possible for everyone. The energy challenge for the years to come is to have a sustainable energy supply and after the week spent in Varenna it is clear that "sustainable" cannot be identified with green gas emission reduction only: it has to be an energy supply system respectful of the environment and the humankind, able to provide reliable and affordable energy to the whole world population. This is definitely not an easy challenge: no single energy technology will suffice to safeguard our future and any possible solution has to be exploited at its best, from renewable to nuclear energy, from clean fossil fuels to biofuels. Last but not least, it is the energy efficiency that, given the actual technology, may give the most important and immediate contribution to this challenge. Meanwhile researchers must examine a broad range of options and develop different kinds of technologies: only new investments on R&D can allow to meet the growing demand for energy in a responsible, equitable, and sustainable way

Geoneutrinos in Borexino

This paper describes the Borexino detector and the high-radiopurity studies and tests that are integral part of the Borexino technology and development. The application of Borexino to the detection and studies of geoneutrinos is discussed.Comment: Conference: Neutrino Geophysics Honolulu, Hawaii December 14-16, 200

Neutrino Physics: Open Theoretical Questions

We know that neutrino mass and mixing provide a window to physics beyond the Standard Model. Now this window is open, at least partly. And the questions are: what do we see, which kind of new physics, and how far "beyond"? I summarize the present knowledge of neutrino mass and mixing, and then formulate the main open questions. Following the bottom-up approach, properties of the neutrino mass matrix are considered. Then different possible ways to uncover the underlying physics are discussed. Some results along the line of: see-saw, GUT and SUSY GUT are reviewed.Comment: 17 pages, latex, 12 figures. Talk given at the XXI International Symposium on Lepton and Photon Interactions at High Energies, ``Lepton Photon 2003", August 11-16, 2003 - Fermilab, Batavia, IL US

On Approximating Restricted Cycle Covers

A cycle cover of a graph is a set of cycles such that every vertex is part of exactly one cycle. An L-cycle cover is a cycle cover in which the length of every cycle is in the set L. The weight of a cycle cover of an edge-weighted graph is the sum of the weights of its edges. We come close to settling the complexity and approximability of computing L-cycle covers. On the one hand, we show that for almost all L, computing L-cycle covers of maximum weight in directed and undirected graphs is APX-hard and NP-hard. Most of our hardness results hold even if the edge weights are restricted to zero and one. On the other hand, we show that the problem of computing L-cycle covers of maximum weight can be approximated within a factor of 2 for undirected graphs and within a factor of 8/3 in the case of directed graphs. This holds for arbitrary sets L.Comment: To appear in SIAM Journal on Computing. Minor change

Tropical Dominating Sets in Vertex-Coloured Graphs

Given a vertex-coloured graph, a dominating set is said to be tropical if every colour of the graph appears at least once in the set. Here, we study minimum tropical dominating sets from structural and algorithmic points of view. First, we prove that the tropical dominating set problem is NP-complete even when restricted to a simple path. Then, we establish upper bounds related to various parameters of the graph such as minimum degree and number of edges. We also give upper bounds for random graphs. Last, we give approximability and inapproximability results for general and restricted classes of graphs, and establish a FPT algorithm for interval graphs.Comment: 19 pages, 4 figure

On the possiblity of detecting Solar pp-neutrino with a large volume liquid organic scintillator detector

It is shown that a large volume liquid organic scintillator detector with an energy resolution of 10 keV at 200 keV 1 sigma will be sensitive to solar pp-neutrino, if operated at the target radiopurity levels for the Borexino detector, or the solar neutrino project of KamLAND.Comment: 18 pages, 2 figures, 4 tables. Contributed paper to the Nonaccelerating New Neutrino Physic. NANP-2003, Dubna. To be published in Phys.At.Nucl.(2004

Algorithmic aspects of disjunctive domination in graphs

For a graph $G=(V,E)$, a set $D\subseteq V$ is called a \emph{disjunctive dominating set} of $G$ if for every vertex $v\in V\setminus D$, $v$ is either adjacent to a vertex of $D$ or has at least two vertices in $D$ at distance $2$ from it. The cardinality of a minimum disjunctive dominating set of $G$ is called the \emph{disjunctive domination number} of graph $G$, and is denoted by $\gamma_{2}^{d}(G)$. The \textsc{Minimum Disjunctive Domination Problem} (MDDP) is to find a disjunctive dominating set of cardinality $\gamma_{2}^{d}(G)$. Given a positive integer $k$ and a graph $G$, the \textsc{Disjunctive Domination Decision Problem} (DDDP) is to decide whether $G$ has a disjunctive dominating set of cardinality at most $k$. In this article, we first propose a linear time algorithm for MDDP in proper interval graphs. Next we tighten the NP-completeness of DDDP by showing that it remains NP-complete even in chordal graphs. We also propose a $(\ln(\Delta^{2}+\Delta+2)+1)$-approximation algorithm for MDDP in general graphs and prove that MDDP can not be approximated within $(1-\epsilon) \ln(|V|)$ for any $\epsilon>0$ unless NP $\subseteq$ DTIME$(|V|^{O(\log \log |V|)})$. Finally, we show that MDDP is APX-complete for bipartite graphs with maximum degree $3$

Approximating Clustering of Fingerprint Vectors with Missing Values

The problem of clustering fingerprint vectors is an interesting problem in Computational Biology that has been proposed in (Figureroa et al. 2004). In this paper we show some improvements in closing the gaps between the known lower bounds and upper bounds on the approximability of some variants of the biological problem. Namely we are able to prove that the problem is APX-hard even when each fingerprint contains only two unknown position. Moreover we have studied some variants of the orginal problem, and we give two 2-approximation algorithm for the IECMV and OECMV problems when the number of unknown entries for each vector is at most a constant.Comment: 13 pages, 4 figure

KamLAND, terrestrial heat sources and neutrino oscillations

We comment on the first indication of geo-neutrino events from KamLAND and on the prospects for understanding Earth energetics. Practically all models of terrestrial heat production are consistent with data within the presently limited statistics, the fully radiogenic model being closer to the observed value ($\approx 9$ geo-events). In a few years KamLAND should collect sufficient data for a clear evidence of geo-neutrinos, however discrimination among models requires a detector with the class and size of KamLAND far away from nuclear reactors. We also remark that the event ratio from Thorium and Uranium decay chains is well fixed $N(Th)/N(U) \simeq 0.25$, a constraint that can be useful for determining neutrino oscillation parameters. We show that a full spectral analysis, including this constraint, further reduces the oscillation parameter space compared to an analysis with an energy threshold $E_{vis}>2.6 MeV$.Comment: 12 pages, RevTeX file, 3 ps figures included in the correct order, corrected some typos and added references. Accepted for publication on Phys. Lett.

Parameterized Complexity of the k-anonymity Problem

The problem of publishing personal data without giving up privacy is becoming increasingly important. An interesting formalization that has been recently proposed is the $k$-anonymity. This approach requires that the rows of a table are partitioned in clusters of size at least $k$ and that all the rows in a cluster become the same tuple, after the suppression of some entries. The natural optimization problem, where the goal is to minimize the number of suppressed entries, is known to be APX-hard even when the records values are over a binary alphabet and $k=3$, and when the records have length at most 8 and $k=4$ . In this paper we study how the complexity of the problem is influenced by different parameters. In this paper we follow this direction of research, first showing that the problem is W[1]-hard when parameterized by the size of the solution (and the value $k$). Then we exhibit a fixed parameter algorithm, when the problem is parameterized by the size of the alphabet and the number of columns. Finally, we investigate the computational (and approximation) complexity of the $k$-anonymity problem, when restricting the instance to records having length bounded by 3 and $k=3$. We show that such a restriction is APX-hard.Comment: 22 pages, 2 figure