Total Domishold Graphs: a Generalization of Threshold Graphs, with Connections to Threshold Hypergraphs

A total dominating set in a graph is a set of vertices such that every vertex of the graph has a neighbor in the set. We introduce and study graphs that admit non-negative real weights associated to their vertices such that a set of vertices is a total dominating set if and only if the sum of the corresponding weights exceeds a certain threshold. We show that these graphs, which we call total domishold graphs, form a non-hereditary class of graphs properly containing the classes of threshold graphs and the complements of domishold graphs, and are closely related to threshold Boolean functions and threshold hypergraphs. We present a polynomial time recognition algorithm of total domishold graphs, and characterize graphs in which the above property holds in a hereditary sense. Our characterization is obtained by studying a new family of hypergraphs, defined similarly as the Sperner hypergraphs, which may be of independent interest.Comment: 19 pages, 1 figur

Search for Λc+→ϕpπ0\Lambda_c^+\to\phi p \pi^0 and branching fraction measurement of Λc+→K−π+pπ0\Lambda_c^+\to K^-\pi^+ p \pi^0

We have searched for the Cabibbo-suppressed decay $\Lambda_c^+\to\phi p\pi^0$ in $e^+e^-$ collisions using a data sample corresponding to an integrated luminosity of 915 $\rm fb^{-1}$. The data were collected by the Belle experiment at the KEKB $e^+e^-$ asymmetric-energy collider running at or near the $\Upsilon(4S)$ and $\Upsilon(5S)$ resonances. No significant signal is observed, and we set an upper limit on the branching fraction of $\mathcal{B}(\Lambda_c^+\to \phi p\pi^0) <15.3\times10^{-5}$ at 90% confidence level. The contribution for nonresonant $\Lambda_c^+\to K^+K^- p\pi^0$ decays is found to be consistent with zero and the corresponding upper limit on its branching fraction is set to be $\mathcal{B}(\Lambda_c^+\to K^+K^-p\pi^0)_{\rm NR} <6.3\times10^{-5}$ at 90% confidence level. We also measure the branching fraction for the Cabibbo-favored decay $\Lambda_c^+\to K^-\pi^+p\pi^0$; the result is $\mathcal{B}(\Lambda_c^+\to K^-\pi^+p\pi^0)= (4.42\pm0.05\, (\rm stat.) \pm 0.12\, (\rm syst.) \pm 0.16\, (\mathcal{B}_{\rm Norm}))\%$, which is the most precise measurement to date. Finally, we have searched for an intermediate hidden-strangeness pentaquark decay $P^+_s\to\phi p$. We see no evidence for this intermediate decay and set an upper limit on the product branching fraction of ${\cal B}(\Lambda_c^+\to P^+_s \pi^0)\times {\cal B}(P^+_s\to\phi p) <8.3\times 10^{-5}$ at 90% confidence level.Comment: 8 pages, 5 figures, 1 table, minor text change in version

Decomposing 1-Sperner hypergraphs

A hypergraph is Sperner if no hyperedge contains another one. A Sperner hypergraph is equilizable (resp., threshold) if the characteristic vectors of its hyperedges are the (minimal) binary solutions to a linear equation (resp., inequality) with positive coefficients. These combinatorial notions have many applications and are motivated by the theory of Boolean functions and integer programming. We introduce in this paper the class of $1$-Sperner hypergraphs, defined by the property that for every two hyperedges the smallest of their two set differences is of size one. We characterize this class of Sperner hypergraphs by a decomposition theorem and derive several consequences from it. In particular, we obtain bounds on the size of $1$-Sperner hypergraphs and their transversal hypergraphs, show that the characteristic vectors of the hyperedges are linearly independent over the reals, and prove that $1$-Sperner hypergraphs are both threshold and equilizable. The study of $1$-Sperner hypergraphs is motivated also by their applications in graph theory, which we present in a companion paper

Study of Excited Ξc\Xi_c States Decaying into Ξc0\Xi_c^0 and Ξc+\Xi_c^+ Baryons

Using a data sample of 980 ${\rm fb}^{-1}$ of $e^+e^-$ annihilation data taken with the Belle detector operating at the KEKB asymmetric-energy $e^+e^-$ collider, we report the results of a study of excited $\Xi_c$ states that decay, via the emission of photons and/or charged pions, into $\Xi_c^0$ or $\Xi_c^+$ ground state charmed-strange baryons. We present new measurements of the masses of all members of the $\Xi_c^{\prime}$, $\Xi_c(2645)$, $\Xi_c(2790)$, $\Xi_c(2815)$, and $\Xi_c(2980)$ isodoublets, measurements of the intrinsic widths of those that decay strongly, and evidence of previously unknown transitions.Comment: Submitted to PR

Multi-rendezvous Spacecraft Trajectory Optimization with Beam P-ACO

The design of spacecraft trajectories for missions visiting multiple celestial bodies is here framed as a multi-objective bilevel optimization problem. A comparative study is performed to assess the performance of different Beam Search algorithms at tackling the combinatorial problem of finding the ideal sequence of bodies. Special focus is placed on the development of a new hybridization between Beam Search and the Population-based Ant Colony Optimization algorithm. An experimental evaluation shows all algorithms achieving exceptional performance on a hard benchmark problem. It is found that a properly tuned deterministic Beam Search always outperforms the remaining variants. Beam P-ACO, however, demonstrates lower parameter sensitivity, while offering superior worst-case performance. Being an anytime algorithm, it is then found to be the preferable choice for certain practical applications.Comment: Code available at https://github.com/lfsimoes/beam_paco__gtoc