Polynomial combinatorial algorithms for skew-bisubmodular function minimization

Huber et al. (SIAM J Comput 43:1064–1084, 2014) introduced a concept of skew bisubmodularity, as a generalization of bisubmodularity, in their complexity dichotomy theorem for valued constraint satisfaction problems over the three-value domain, and Huber and Krokhin (SIAM J Discrete Math 28:1828–1837, 2014) showed the oracle tractability of minimization of skew-bisubmodular functions. Fujishige et al. (Discrete Optim 12:1–9, 2014) also showed a min–max theorem that characterizes the skew-bisubmodular function minimization, but devising a combinatorial polynomial algorithm for skew-bisubmodular function minimization was left open. In the present paper we give first combinatorial (weakly and strongly) polynomial algorithms for skew-bisubmodular function minimization

An improved bound for the rigidity of linearly constrained frameworks

We consider the problem of characterising the generic rigidity of bar-joint frameworks in Rd in which each vertex is constrained to lie in a given a ne subspace. The special case when d = 2 was previously solved by I. Streinu and L. Theran in 2010 and the case when each vertex is constrained to lie in an a ne subspace of dimension t, and d t(t 1) was solved by Cruickshank, Guler and the rst two authors in 2019. We extend the latter result by showing that the given characterisation holds whenever d 2t

A structural characterization for certifying Robinsonian matrices

A symmetric matrix is Robinsonian if its rows and columns can be simultaneously reordered in such a way that entries are monotone nondecreasing in rows and columns when moving toward the diagonal. The adjacency matrix of a graph is Robinsonian precisely when the graph is a unit interval graph, so that Robinsonian matrices form a matrix analogue of the class of unit interval graphs. Here we provide a structural characterization for Robinsonian matrices in terms of forbidden substructures, extending the notion of asteroidal triples to weighted graphs. This implies the known characterization of unit interval graphs and leads to an efficient algorithm for certifying that a matrix is not Robinsonian

Possibility of \Lambda\Lambda pairing and its dependence on background density in relativistic Hartree-Bogoliubov model

We calculate a \Lambda\Lambda pairing gap in binary mixed matter of nucleons and \Lambda hyperons within the relativistic Hartree-Bogoliubov model. Lambda hyperons to be paired up are immersed in background nucleons in a normal state. The gap is calculated with a one-boson-exchange interaction obtained from a relativistic Lagrangian. It is found that at background density \rho_{N}=2.5\rho_{0} the \Lambda\Lambda pairing gap is very small, and that denser background makes it rapidly suppressed. This result suggests a mechanism, specific to mixed matter dealt with relativistic models, of its dependence on the nucleon density. An effect of weaker \Lambda\Lambda attraction on the gap is also examined in connection with revised information of the \Lambda\Lambda interaction.Comment: 8 pages, 6 figures, REVTeX 4; substantially rewritten, emphasis is put on the LL pairing in pure neutron matte

On packing spanning arborescences with matroid constraint

Let D = (V + s, A) be a digraph with a designated root vertex S. Edmonds’ seminal result (see J. Edmonds [4]) implies that D has a packing of k spanning s-arborescences if and only if D has a packing of k (s, t)-paths for all t ∈ V, where a packing means arc-disjoint subgraphs. Let M be a matroid on the set of arcs leaving S. A packing of (s,t) -paths is called M-based if their arcs leaving S form a base of M while a packing of s-arborescences is called M -based if, for all t ∈ V, the packing of (s, t) -paths provided by the arborescences is M -based. Durand de Gevigney, Nguyen, and Szigeti proved in [3] that D has an M-based packing of s -arborescences if and only if D has an M-based packing of (s,t) -paths for all t ∈ V. Bérczi and Frank conjectured that this statement can be strengthened in the sense of Edmonds’ theorem such that each S -arborescence is required to be spanning. Specifically, they conjectured that D has an M -based packing of spanning S -arborescences if and only if D has an M -based packing of (s,t) -paths for all t ∈ V. In this paper we disprove this conjecture in its general form and we prove that the corresponding decision problem is NP-complete. We also prove that the conjecture holds for several fundamental classes of matroids, such as graphic matroids and transversal matroids. For all the results presented in this paper, the undirected counterpart also holds

Effect of self-ion irradiation on hardening and microstructure of tungsten

AbstractThe irradiation hardening and microstructures of pure W and W–3%Re for up to 5.0 dpa by self-ion irradiation were investigated in this work. The ion irradiation was conducted using 18 MeV W6+ at 500 and 800°C. A focused ion beam followed by electro-polishing was used to make thin foil specimens for transmission electron microscope observations. Dislocation loops were observed in all the irradiated samples. Voids were observed in all of the specimens except the W–3%Re irradiated to 0.2 dpa. The hardness was measured by using nanoindentation. The irradiation hardening was saturated at 1.0 dpa for pure W. In the case of W–3%Re, the irradiation hardening showed a peak at 1.0 dpa. The correlation between the microstructure and hardening was investigated