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

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

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

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

The Kr2Det project: Search for mass-3 state contribution |U_{e3}|^2 to the electron neutrino using a one reactor - two detector oscillation experiment at Krasnoyarsk underground site

The main physical goal of the project is to search with reactor antineutrinos for small mixing angle oscillations in the atmospheric mass parameter region around {\Delta}m^{2}_{atm} ~ 2.5 10^{-3} eV^2 in order to find the element U_{e3} of the neutrino mixing matrix or to set a new more stringent constraint (U_{e3} is the contribution of mass-3 state to the electron neutrino flavor state). To achieve this we propose a "one reactor - two detector" experiment: two identical antineutrino spectrometers with $\sim$50 ton liquid scintillator targets located at ~100 m and ~1000 m from the Krasnoyarsk underground reactor (~600 mwe). In no-oscillation case ratio of measured positron spectra of the \bar{{\nu}_e} + p \to e^{+} + n reaction is energy independent. Deviation from a constant value of this ratio is the oscillation signature. In this scheme results do not depend on the exact knowledge of the reactor power, nu_e spectra, burn up effects, target volumes and, which is important, the backgrounds can periodically be measured during reactor OFF periods. In this letter we present the Krasnoyarsk reactor site, give a schematic description of the detectors, calculate the neutrino detection rates and estimate the backgrounds. We also outline the detector monitoring and calibration procedures, which are of a key importance. We hope that systematic uncertainties will not accede 0.5% and the sensitivity U^{2}_{e3} ~4 10^{-3} (at {\Delta}m^{2} = 2.5 10^{-3} eV^2) can be achieved.Comment: Latex 2e, 9 pages and 5 ps figure

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

New limits on nucleon decays into invisible channels with the BOREXINO Counting Test Facility

The results of background measurements with the second version of the BOREXINO Counting Test Facility (CTF-II), installed in the Gran Sasso Underground Laboratory, were used to obtain limits on the instability of nucleons, bounded in nuclei, for decays into invisible channels ($inv$): disappearance, decays to neutrinos, etc. The approach consisted of a search for decays of unstable nuclides resulting from $N$ and $NN$ decays of parents $^{12}$C, $^{13}$C and $^{16}$O nuclei in the liquid scintillator and the water shield of the CTF. Due to the extremely low background and the large mass (4.2 ton) of the CTF detector, the most stringent (or competitive) up-to-date experimental bounds have been established: $\tau(n \to inv) > 1.8 \cdot 10^{25}$ y, $\tau(p \to inv) > 1.1 \cdot 10^{26}$ y, $\tau(nn \to inv) > 4.9 \cdot 10^{25}$ y and $\tau(pp \to inv) > 5.0 \cdot 10^{25}$ y, all at 90% C.L.Comment: 22 pages, 3 figures,submitted to Phys.Lett.

Constraining Non-Standard Interactions of the Neutrino with Borexino

We use the Borexino 153.6 ton.year data to place constraints on non-standard neutrino-electron interactions, taking into account the uncertainty in the 7Be solar neutrino flux, and backgrounds due to 85Kr and 210Bi beta-decay. We find that the bounds are comparable to existing bounds from all other experiments. Further improvement can be expected in Phase II of Borexino due to the reduction in the 85Kr background.Comment: 21 pages, 16 pdf figures, 2 tables. Analysis updated including the uncertainty in sin^2\theta_{23}. Accepted in JHE

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 $3$