The complexity of dominating set reconfiguration

Suppose that we are given two dominating sets $D_s$ and $D_t$ of a graph $G$ whose cardinalities are at most a given threshold $k$. Then, we are asked whether there exists a sequence of dominating sets of $G$ between $D_s$ and $D_t$ such that each dominating set in the sequence is of cardinality at most $k$ and can be obtained from the previous one by either adding or deleting exactly one vertex. This problem is known to be PSPACE-complete in general. In this paper, we study the complexity of this decision problem from the viewpoint of graph classes. We first prove that the problem remains PSPACE-complete even for planar graphs, bounded bandwidth graphs, split graphs, and bipartite graphs. We then give a general scheme to construct linear-time algorithms and show that the problem can be solved in linear time for cographs, trees, and interval graphs. Furthermore, for these tractable cases, we can obtain a desired sequence such that the number of additions and deletions is bounded by $O(n)$, where $n$ is the number of vertices in the input graph

Token Jumping in minor-closed classes

Given two $k$-independent sets $I$ and $J$ of a graph $G$, one can ask if it is possible to transform the one into the other in such a way that, at any step, we replace one vertex of the current independent set by another while keeping the property of being independent. Deciding this problem, known as the Token Jumping (TJ) reconfiguration problem, is PSPACE-complete even on planar graphs. Ito et al. proved in 2014 that the problem is FPT parameterized by $k$ if the input graph is $K_{3,\ell}$-free. We prove that the result of Ito et al. can be extended to any $K_{\ell,\ell}$-free graphs. In other words, if $G$ is a $K_{\ell,\ell}$-free graph, then it is possible to decide in FPT-time if $I$ can be transformed into $J$. As a by product, the TJ-reconfiguration problem is FPT in many well-known classes of graphs such as any minor-free class

Stellar dynamics in the central arcsecond of our galaxy

We present proper motions for $>$40 stars at projected distances $\leq1.2''$ from Sagittarius A* (Sgr A*). We find evidence on a $\geq2\sigma$ level for radial anisotropy of the cluster of stars within $1''$ of Sgr A*. We find no evidence for a stationary source or variable source at the position of Sgr A*. We confirm/find accelerated motion for 6 stars, with 4 stars having passed the pericenter of their orbits during the observed time span. We calculated/constrained the orbital parameters of these stars. All orbits have moderate to high eccentricities. We discuss the possible bias in detecting preferentially orbits with high eccentricities. We find that the center of acceleration for all the orbits coincides with the radio position of Sgr A*. From the orbit of the star S2, the currently most tightly constrained one, we determine the mass of Sgr A* to be $3.3\pm0.7\times10^{6}$M$_{\odot}$ and its position to $2.0\pm2.4$ mas East and $2.7\pm4.5$ mas South of the nominal radio position. The mass estimate for the central dark mass from the orbit of S2 is fully consistent with the mass estimate of $3.4\pm0.5\times10^{6}$M$_{\odot}$ obtained from stellar proper motions within $1.2''$ of Sgr A* using a Leonard-Merritt mass estimator. We find that radio astronomical observations of the proper motion of Sgr A* in combination with its intrinsic source size place at the moment the tightest constraints on the mass density of Sgr A*, which must exceed $\rho_{\mathrm{Sgr A*}}>3\times10^{19}\mathrm{M}_{\odot}\mathrm{pc}^{-3}$.Comment: 51 pages, 16 Figures, reviewed ms submitted to ap

On the Parameterized Complexity of Simultaneous Deletion Problems

For a family of graphs F, an n-vertex graph G, and a positive integer k, the F-Deletion problem asks whether we can delete at most k vertices from G to obtain a graph in F. F-Deletion generalizes many classical graph problems such as Vertex Cover, Feedback Vertex Set, and Odd Cycle Transversal. A (multi) graph G = (V, cup_{i=1}^{alpha} E_{i}), where the edge set of G is partitioned into alpha color classes, is called an alpha-edge-colored graph. A natural extension of the F-Deletion problem to edge-colored graphs is the Simultaneous (F_1, ldots, F_alpha)-Deletion problem. In the latter problem, we are given an alpha-edge-colored graph G and the goal is to find a set S of at most k vertices such that each graph G_i - S, where G_i = (V, E_i) and 1 leq i leq alpha, is in F_i. Recently, a subset of the authors considered the aforementioned problem with F_1 = ldots = F_alpha being the family of all forests. They showed that the problem is fixed-parameter tractable when parameterized by k and alpha, and can be solved in O(2^{O(alpha k)}n^{O(1)}) time. In this work, we initiate the investigation of the complexity of Simultaneous (F_1, ldots, F_alpha)-Deletion with different families of graphs. In the process, we obtain a complete characterization of the parameterized complexity of this problem when one or more of the F_i\u27s is the class of bipartite graphs and the rest (if any) are forests. We show that if F_1 is the family of all bipartite graphs and each of F_2 = F_3 = ldots = F_alpha is the family of all forests then the problem is fixed-parameter tractable parameterized by k and alpha. However, even when F_1 and F_2 are both the family of all bipartite graphs, then the Simultaneous (F_1, F_2)-Deletion} problem itself is already W[1]-hard

Dust Embedded Sources at the Galactic Center. 2 to 4μ\mum imaging and spectroscopy in the central parsec

We present the first L-band spectroscopic observations for a dozen stellar sources in the central 0.5 pc of the GC stellar cluster that are bright in the 2-4 micron wavelength domain. With the aid of additional K-band spectroscopic data, we derive optical depth spectra of the sources after fitting their continuum emission with a single reddened blackbody continuum. We also derive intrinsic source spectra by correcting the line of sight extinction via the optical depth spectrum of a late type star that is most likely not affected by local dust emission or extinction at the Galactic Center. The good agreement between the two approaches shows that the overall variation of the line-of-sight extinction across the central 0.5 pc is $\Delta A_{\mathrm{K}}\leq0.5$ mag. The extinction corrected spectra of the hot He-stars are in good agreement with pure Rayleigh Jeans continuum spectra. The intrinsic spectra of all other sources are in agreement with continuum emission and absorption features due to the dust in which they are embedded. We interprete both facts as evidence that a significant amount of the absorption takes place within the central parsec of the Galactic Center and is most likely associated with the individual sources there. We find absorption features at 3.0 micron, 3.4 micron, and 3.48 micron wavelength. Correlations between all three features show that they are very likely to arise in the ISM of the central 0.5 pc. Spectroscopy of high MIR-excess sources 0.5'' north of the IRS 13 complex is largely consistent with them being YSOs. However, a bow-shock nature of these sources cannot be excluded.Comment: 19 pages. 19 figures. 6 tables. Accepted in A&

Reconfiguration of Cliques in a Graph

We study reconfiguration problems for cliques in a graph, which determine whether there exists a sequence of cliques that transforms a given clique into another one in a step-by-step fashion. As one step of a transformation, we consider three different types of rules, which are defined and studied in reconfiguration problems for independent sets. We first prove that all the three rules are equivalent in cliques. We then show that the problems are PSPACE-complete for perfect graphs, while we give polynomial-time algorithms for several classes of graphs, such as even-hole-free graphs and cographs. In particular, the shortest variant, which computes the shortest length of a desired sequence, can be solved in polynomial time for chordal graphs, bipartite graphs, planar graphs, and bounded treewidth graphs

Role of the Subunits Interactions in the Conformational Transitions in Adult Human Hemoglobin: an Explicit Solvent Molecular Dynamics Study

Hemoglobin exhibits allosteric structural changes upon ligand binding due to the dynamic interactions between the ligand binding sites, the amino acids residues and some other solutes present under physiological conditions. In the present study, the dynamical and quaternary structural changes occurring in two unligated (deoxy-) T structures, and two fully ligated (oxy-) R, R2 structures of adult human hemoglobin were investigated with molecular dynamics. It is shown that, in the sub-microsecond time scale, there is no marked difference in the global dynamics of the amino acids residues in both the oxy- and the deoxy- forms of the individual structures. In addition, the R, R2 are relatively stable and do not present quaternary conformational changes within the time scale of our simulations while the T structure is dynamically more flexible and exhibited the T\rightarrow R quaternary conformational transition, which is propagated by the relative rotation of the residues at the {\alpha}1{\beta}2 and {\alpha}2{\beta}1 interface.Comment: Reprinted (adapted) with permission from J. Phys. Chem. B DOI:10.1021/jp3022908. Copyright (2012) American Chemical Societ

A thermal cycling reliability study of ultrasonically bonded copper wires

In this work we report on a reliability investigation regarding heavy copper wires ultrasonically bonded onto active braze copper substrates. The results obtained from both a non-destructive approach using 3D X-ray tomography and shear tests showed no discernible degradation or wear out from initial conditions to 2900 passive thermal cycles from − 55 to 125 °C. Instead, an apparent increase in shear strength is observed as the number of thermal cycles increases. Nanoindentation hardness investigations suggest the occurrence of cyclic hardening. Microstructural investigations of the interfacial morphologies before and after cycling and after shear testing are also presented and discussed