Continuous Probabilistic Nearest-Neighbor Queries for Uncertain Trajectories

This work addresses the problem of processing continuous nearest neighbor (NN) queries for moving objects trajectories when the exact position of a given object at a particular time instant is not known, but is bounded by an uncertainty region. As has already been observed in the literature, the answers to continuous NN-queries in spatio-temporal settings are time parameterized in the sense that the objects in the answer vary over time. Incorporating uncertainty in the model yields additional attributes that affect the semantics of the answer to this type of queries. In this work, we formalize the impact of uncertainty on the answers to the continuous probabilistic NN-queries, provide a compact structure for their representation and efficient algorithms for constructing that structure. We also identify syntactic constructs for several qualitative variants of continuous probabilistic NN-queries for uncertain trajectories and present efficient algorithms for their processing. 1

First Laboratory Detection of N13CO-and Semiexperimental Equilibrium Structure of the NCO-Anion

The cyanate anion (NCO-) is a species of considerable astrophysical relevance. It is widely believed to be embedded in interstellar ices present in young stellar objects but has not yet been detected in the dense gas of the interstellar medium. Here we report highly accurate laboratory measurements of the rotational spectrum of the N13CO-isotopologue at submillimeter wavelengths along with the detection of three additional lines of the parent isotopologue up to 437.4 GHz. With this new data, the rotational spectrum of both isotopologues can be predicted to better 0.25 km s-1in equivalent radial velocity up to 1 THz, more than adequate for an astronomical search in any source. Moreover, a semiexperimental equilibrium structure of the anion is derived by combining the experimental ground-state rotational constants of the two isotopologues with theoretical vibrational corrections, obtained by using the coupled-cluster method with inclusion of single and double excitations and perturbative inclusion of triple excitations (CCSD(T)). The estimated accuracy of the two bond distances is on the order of 5 × 10-4Å: a comparison to the values obtained by geometry optimization with the CCSD(T) method and the use of a composite scheme, including additivity and basis-set extrapolation techniques, reveals that this theoretical procedure is very accurate

High resolution infrared and Raman spectra of 13C12CD2: The CD stretching fundamentals and associated combination and hot bands

11 pags.; 4 figs.; 9 tabs.© 2015 AIP Publishing LLC. Infrared and Raman spectra of mono 13C fully deuterated acetylene, 13C12CD2, have been recorded and analysed to obtain detailed information on the C—D stretching fundamentals and associated combination, overtone, and hot bands. Infrared spectra were recorded at an instrumental resolution ranging between 0.006 and 0.01 cm−1 in the region 1800–7800 cm−1. Sixty new bands involving the ν 1 and ν 3 C—D stretching modes also associated with the ν 4 and ν 5 bending vibrations have been observed and analysed. In total, 5881 transitions have been assigned in the investigated spectral region. In addition, the Q branch of the ν 1 fundamental was recorded using inverse Raman spectroscopy, with an instrumental resolution of about 0.003 cm−1. The transitions relative to each stretching mode, i.e., the fundamental band, its first overtone, and associated hot and combination bands involving bending states with υ 4 + υ 5 up to 2 were fitted simultaneously. The usual Hamiltonian appropriate to a linear molecule, including vibration and rotation l-type and the Darling–Dennison interaction between υ 4 = 2 and υ 5 = 2 levels associated with the stretching states, was adopted for the analysis. The standard deviation for each global fit is ≤0.0004 cm−1, of the same order of magnitude of the measurement precision. Slightly improved parameters for the bending and the ν 2 manifold have been also determined. Precise values of spectroscopic parameters deperturbed from the resonance interactions have been obtained. They provide quantitative information on the anharmonic character of the potential energy surface, which can be useful, in addition to those reported in the literature, for the determination of a general anharmonic force field for the molecule. Finally, the obtained values of the Darling–Dennison constants can be valuable for understanding energy flows between independent vibrations.The Bologna authors acknowledge the Università di Bologna and the financial support of the Ministero dell’ Istruzione dell’Università e della Ricerca (PRIN 2012 “Spettroscopia e Tecniche computazionali per la ricerca Astrofisica, atmosferica e Radioastronomica”). D.B. and R.Z.M. acknowledge the financial support of the Ministry of Economy and Competitiveness through Research Grant No. FIS2012-38175.Peer Reviewe

DC3_3N observations towards high-mass star-forming regions

We present the study of deuteration of cyanoacetylene (HC$_3$N) towards a sample of 28 high-mass star-forming cores divided into different evolutionary stages, from starless to evolved protostellar cores. We report for the first time the detection of DC$_3$N towards 15 high-mass cores. The abundance ratios of DC$_3$N with respect HC$_3$N range in the interval 0.003$-$0.022, lower than those found in low-mas protostars and dark clouds. No significant trend with the evolutionary stage, or with the kinetic temperature of the region, has been found. We compare the level of deuteration of HC$_3$N with those of other molecules towards the same sample, finding weak correlation with species formed only or predominantly in gas phase (N$_2$H$^+$ and HNC, respectively), and no correlation with species formed only or predominantly on dust grains (CH$_3$OH and NH$_3$, respectively). We also present a single-dish map of DC$_3$N towards the protocluster IRAS 05358+3543, which shows that DC$_3$N traces an extended envelope ($\sim$0.37 pc) and peaks towards two cold condensations separated from the positions of the protostars and the dust continuum. The observations presented in this work suggest that deuteration of HC$_3$N is produced in the gas of the cold outer parts of massive star-forming clumps, giving us an estimate of the deuteration factor prior to the formation of denser gas.Comment: Accepted in Monthly Notices of the Royal Astronomical Society -- 11 pages, 7 Figures, 2 Tables. Version with some typos correcte

The Partial Visibility Representation Extension Problem

For a graph $G$, a function $\psi$ is called a \emph{bar visibility representation} of $G$ when for each vertex $v \in V(G)$, $\psi(v)$ is a horizontal line segment (\emph{bar}) and $uv \in E(G)$ iff there is an unobstructed, vertical, $\varepsilon$-wide line of sight between $\psi(u)$ and $\psi(v)$. Graphs admitting such representations are well understood (via simple characterizations) and recognizable in linear time. For a directed graph $G$, a bar visibility representation $\psi$ of $G$, additionally, puts the bar $\psi(u)$ strictly below the bar $\psi(v)$ for each directed edge $(u,v)$ of $G$. We study a generalization of the recognition problem where a function $\psi'$ defined on a subset $V'$ of $V(G)$ is given and the question is whether there is a bar visibility representation $\psi$ of $G$ with $\psi(v) = \psi'(v)$ for every $v \in V'$. We show that for undirected graphs this problem together with closely related problems are \NP-complete, but for certain cases involving directed graphs it is solvable in polynomial time.Comment: Appears in the Proceedings of the 24th International Symposium on Graph Drawing and Network Visualization (GD 2016

Visibility Representations of Boxes in 2.5 Dimensions

We initiate the study of 2.5D box visibility representations (2.5D-BR) where vertices are mapped to 3D boxes having the bottom face in the plane $z=0$ and edges are unobstructed lines of sight parallel to the $x$- or $y$-axis. We prove that: $(i)$ Every complete bipartite graph admits a 2.5D-BR; $(ii)$ The complete graph $K_n$ admits a 2.5D-BR if and only if $n \leq 19$; $(iii)$ Every graph with pathwidth at most $7$ admits a 2.5D-BR, which can be computed in linear time. We then turn our attention to 2.5D grid box representations (2.5D-GBR) which are 2.5D-BRs such that the bottom face of every box is a unit square at integer coordinates. We show that an $n$-vertex graph that admits a 2.5D-GBR has at most $4n - 6 \sqrt{n}$ edges and this bound is tight. Finally, we prove that deciding whether a given graph $G$ admits a 2.5D-GBR with a given footprint is NP-complete. The footprint of a 2.5D-BR $\Gamma$ is the set of bottom faces of the boxes in $\Gamma$.Comment: Appears in the Proceedings of the 24th International Symposium on Graph Drawing and Network Visualization (GD 2016

External-Memory Graph Algorithms

We present a collection of new techniques for designing and analyzing efficient external-memory algorithms for graph problems and illustrate how these techniques can be applied to a wide variety of specific problems. Our results include: Proximate-neighboring. We present a simple method for deriving external-memory lower bounds via reductions from a problem we call the “proximate neighbors” problem. We use this technique to derive non-trivial lower bounds for such problems as list ranking, expression tree evaluation, and connected components. PRAM simulation. We give methods for efficiently simulating PRAM computations in external memory, even for some cases in which the PRAM algorithm is not work-optimal. We apply this to derive a number of optimal (and simple) external-memory graph algorithms. Time-forward processing. We present a general technique for evaluating circuits (or “circuit-like” computations) in external memory. We also usethis in a deterministic list ranking algorithm. Deterministic 3-coloring of a cycle. We give several optimal methods for 3-coloring a cycle, which can be used as a subroutine for finding large independent sets for list ranking. Our ideas go beyond a straightforward PRAM simulation, and may be of independent interest. External depth-first search. We discuss a method for performing depth first search and solving related problems efficiently in external memory. Our technique can be used in conjunction with ideas due to Ullman and Yannakakis in order to solve graph problems involving closed semi-ring computations even when their assumption that vertices fit in main memory does not hold. Our techniques apply to a number of problems, including list ranking, which we discuss in detail, finding Euler tours, expression-tree evaluation, centroid decomposition of a tree, least-common ancestors, minimum spanning tree verification, connected and biconnected components, minimum spanning forest, ear decomposition, topological sorting, reachability, graph drawing, and visibility representation

Field Representations of Vector Supersymmetry

We study some field representations of vector supersymmetry with superspin Y=0 and Y=1/2 and nonvanishing central charges. For Y=0, we present two multiplets composed of four spinor fields, two even and two odd, and we provide a free action for them. The main differences between these two multiplets are the way the central charge operators act and the compatibility with the Majorana reality condition on the spinors. One of the two is related to a previously studied spinning particle model. For Y=1/2, we present a multiplet composed of one even scalar, one odd vector and one even selfdual two-form, which is a truncation of a known representation of the tensor supersymmetry algebra in Euclidean spacetime. We discuss its rotation to Minkowski spacetime and provide a set of dynamical equations for it, which are however not derived from a Lagrangian. We develop a superspace formalism for vector supersymmetry with central charges and we derive our multiplets by superspace techniques. Finally, we discuss some representations with vanishing central charges.Comment: 37 page

On Embeddability of Buses in Point Sets

Set membership of points in the plane can be visualized by connecting corresponding points via graphical features, like paths, trees, polygons, ellipses. In this paper we study the \emph{bus embeddability problem} (BEP): given a set of colored points we ask whether there exists a planar realization with one horizontal straight-line segment per color, called bus, such that all points with the same color are connected with vertical line segments to their bus. We present an ILP and an FPT algorithm for the general problem. For restricted versions of this problem, such as when the relative order of buses is predefined, or when a bus must be placed above all its points, we provide efficient algorithms. We show that another restricted version of the problem can be solved using 2-stack pushall sorting. On the negative side we prove the NP-completeness of a special case of BEP.Comment: 19 pages, 9 figures, conference version at GD 201