Grid-Obstacle Representations with Connections to Staircase Guarding

In this paper, we study grid-obstacle representations of graphs where we assign grid-points to vertices and define obstacles such that an edge exists if and only if an $xy$-monotone grid path connects the two endpoints without hitting an obstacle or another vertex. It was previously argued that all planar graphs have a grid-obstacle representation in 2D, and all graphs have a grid-obstacle representation in 3D. In this paper, we show that such constructions are possible with significantly smaller grid-size than previously achieved. Then we study the variant where vertices are not blocking, and show that then grid-obstacle representations exist for bipartite graphs. The latter has applications in so-called staircase guarding of orthogonal polygons; using our grid-obstacle representations, we show that staircase guarding is \textsc{NP}-hard in 2D.Comment: To appear in the proceedings of the 25th International Symposium on Graph Drawing and Network Visualization (GD 2017

Inapproximability of maximal strip recovery

In comparative genomic, the first step of sequence analysis is usually to decompose two or more genomes into syntenic blocks that are segments of homologous chromosomes. For the reliable recovery of syntenic blocks, noise and ambiguities in the genomic maps need to be removed first. Maximal Strip Recovery (MSR) is an optimization problem proposed by Zheng, Zhu, and Sankoff for reliably recovering syntenic blocks from genomic maps in the midst of noise and ambiguities. Given $d$ genomic maps as sequences of gene markers, the objective of \msr{d} is to find $d$ subsequences, one subsequence of each genomic map, such that the total length of syntenic blocks in these subsequences is maximized. For any constant $d \ge 2$, a polynomial-time 2d-approximation for \msr{d} was previously known. In this paper, we show that for any $d \ge 2$, \msr{d} is APX-hard, even for the most basic version of the problem in which all gene markers are distinct and appear in positive orientation in each genomic map. Moreover, we provide the first explicit lower bounds on approximating \msr{d} for all $d \ge 2$. In particular, we show that \msr{d} is NP-hard to approximate within $\Omega(d/\log d)$. From the other direction, we show that the previous 2d-approximation for \msr{d} can be optimized into a polynomial-time algorithm even if $d$ is not a constant but is part of the input. We then extend our inapproximability results to several related problems including \cmsr{d}, \gapmsr{\delta}{d}, and \gapcmsr{\delta}{d}.Comment: A preliminary version of this paper appeared in two parts in the Proceedings of the 20th International Symposium on Algorithms and Computation (ISAAC 2009) and the Proceedings of the 4th International Frontiers of Algorithmics Workshop (FAW 2010

The Nylon Scintillator Containment Vessels for the Borexino Solar Neutrino Experiment

Borexino is a solar neutrino experiment designed to observe the 0.86 MeV Be-7 neutrinos emitted in the pp cycle of the sun. Neutrinos will be detected by their elastic scattering on electrons in 100 tons of liquid scintillator. The neutrino event rate in the scintillator is expected to be low (~0.35 events per day per ton), and the signals will be at energies below 1.5 MeV, where background from natural radioactivity is prominent. Scintillation light produced by the recoil electrons is observed by an array of 2240 photomultiplier tubes. Because of the intrinsic radioactive contaminants in these PMTs, the liquid scintillator is shielded from them by a thick barrier of buffer fluid. A spherical vessel made of thin nylon film contains the scintillator, separating it from the surrounding buffer. The buffer region itself is divided into two concentric shells by a second nylon vessel in order to prevent inward diffusion of radon atoms. The radioactive background requirements for Borexino are challenging to meet, especially for the scintillator and these nylon vessels. Besides meeting requirements for low radioactivity, the nylon vessels must also satisfy requirements for mechanical, optical, and chemical properties. The present paper describes the research and development, construction, and installation of the nylon vessels for the Borexino experiment

Constant-degree graph expansions that preserve the treewidth

Many hard algorithmic problems dealing with graphs, circuits, formulas and constraints admit polynomial-time upper bounds if the underlying graph has small treewidth. The same problems often encourage reducing the maximal degree of vertices to simplify theoretical arguments or address practical concerns. Such degree reduction can be performed through a sequence of splittings of vertices, resulting in an _expansion_ of the original graph. We observe that the treewidth of a graph may increase dramatically if the splittings are not performed carefully. In this context we address the following natural question: is it possible to reduce the maximum degree to a constant without substantially increasing the treewidth? Our work answers the above question affirmatively. We prove that any simple undirected graph G=(V, E) admits an expansion G'=(V', E') with the maximum degree <= 3 and treewidth(G') <= treewidth(G)+1. Furthermore, such an expansion will have no more than 2|E|+|V| vertices and 3|E| edges; it can be computed efficiently from a tree-decomposition of G. We also construct a family of examples for which the increase by 1 in treewidth cannot be avoided.Comment: 12 pages, 6 figures, the main result used by quant-ph/051107

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

Measurement of Ultra-Low Potassium Contaminations with Accelerator Mass Spectrometry

Levels of trace radiopurity in active detector materials is a subject of major concern in low-background experiments. Among the radio-isotopes, \k40 is one of the most abundant and yet whose signatures are difficult to reject. Procedures were devised to measure trace potassium concentrations in the inorganic salt CsI as well as in organic liquid scintillator (LS) with Accelerator Mass Spectrometry (AMS), giving, respectively, the \k40-contamination levels of $\sim 10^{-10}$ and $\sim 10^{-13}$ g/g. Measurement flexibilities and sensitivities are improved over conventional methods. The projected limiting sensitivities if no excess of potassium signals had been observed over background are $8 \times 10^{-13}$ g/g and $3 \times 10^{-17}$ g/g for the CsI and LS, respectively. Studies of the LS samples indicate that the radioactive contaminations come mainly in the dye solutes, while the base solvents are orders of magnitude cleaner. The work demonstrate the possibilities of measuring naturally-occurring isotopes with the AMS techniques.Comment: 18 pages, 4 figures, 3 table

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

Neutral B Flavor Tagging for the Measurement of Mixing-induced CP Violation at Belle

We describe a flavor tagging algorithm used in measurements of the CP violation parameter sin2phi_1 at the Belle experiment. Efficiencies and wrong tag fractions are evaluated using flavor-specific B meson decays into hadronic and semileptonic modes. We achieve a total effective efficiency of $ 28.8 +- 0.6 %.Comment: 28 pages, 9 figure

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

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.