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

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

On the Origin of HD149026b

The high density of the close-in extrasolar planet HD149026b suggests the presence of a huge core in the planet, which challenges planet formation theory. We first derive constraints on the amount of heavy elements and hydrogen/helium present in the planet: We find that preferred values of the core mass are between 50 and 80 M_E. We then investigate the possibility of subcritical core accretion as envisioned for Uranus and Neptune and find that the subcritical accretion scenario is unlikely in the case of HD149026b for at least two reasons: (i) Subcritical planets are such that the ratio of their core mass to their total mass is above ~0.7, in contradiction with constraints for all but the most extreme interior models of HD149026b; (ii) High accretion rates and large isolation mass required for the formation of a subcritical core of 30 M_E are possible only at specific orbital distances in a disk with a surface density of dust equal to at least 10 times that of the minimum mass solar nebula. This value climbs to 30 when considering a 50 M_E core. These facts point toward two main routes for the formation of this planet: (i) Gas accretion that is limited by a slow viscous inflow of gas in an evaporating disk; (ii) A significant modification of the composition of the planet after as accretion has stopped. These two routes are not mutually exclusive. Illustrating the second route, we show that for a wide range of impact parameters, giant impacts lead to a loss of the gas component of the planet and thus may lead to planets that are highly enriched in heavy elements. In the giant impact scenario, we expect an outer giant planet to be present. Observational studies by imaging, astrometry and long term interferometry of this system are needed to better narrow down the ensemble of possibilities.Comment: 29 pages, 8 figures, to appear in the 10 October 2006 issue of Ap

Age-Dependent Decline in β-Cell Proliferation Restricts the Capacity of β-Cell Regeneration in Mice

ObjectiveThe aim of this study was to elucidate whether age plays a role in the expansion or regeneration of beta-cell mass.Research design and methodsWe analyzed the capacity of beta-cell expansion in 1.5- and 8-month-old mice in response to a high-fat diet, after short-term treatment with the glucagon-like peptide 1 (GLP-1) analog exendin-4, or after streptozotocin (STZ) administration.ResultsYoung mice responded to high-fat diet by increasing beta-cell mass and beta-cell proliferation and maintaining normoglycemia. Old mice, by contrast, did not display any increases in beta-cell mass or beta-cell proliferation in response to high-fat diet and became diabetic. To further assess the plasticity of beta-cell mass with respect to age, young and old mice were injected with a single dose of STZ, and beta-cell proliferation was analyzed to assess the regeneration of beta-cells. We observed a fourfold increase in beta-cell proliferation in young mice after STZ administration, whereas no changes in beta-cell proliferation were observed in older mice. The capacity to expand beta-cell mass in response to short-term treatment with the GLP-1 analog exendin-4 also declined with age. The ability of beta-cell mass to expand was correlated with higher levels of Bmi1, a polycomb group protein that is known to regulate the Ink4a locus, and decreased levels of p16(Ink4a)expression in the beta-cells. Young Bmi1(-/-) mice that prematurely upregulate p16(Ink4a)failed to expand beta-cell mass in response to exendin-4, indicating that p16(Ink4a)levels are a critical determinant of beta-cell mass expansion.Conclusionsbeta-Cell proliferation and the capacity of beta-cells to regenerate declines with age and is regulated by the Bmi1/p16(Ink4a)pathway

Frequent loss of RUNX3 gene expression in remnant stomach cancer and adjacent mucosa with special reference to topography

Our previous studies suggest that a lack of RUNX3 function is causally related to the genesis and progression of human gastric cancer. This study was conducted to determine whether alteration of RUNX3 gene expression could be detected in the normal-looking gastric remnant mucosa, and to ascertain any difference in the potential of gastric carcinogenesis between the anastomotic site and other areas in the remnant stomach after distal gastrectomy for peptic ulcer (RB group) or gastric cancer (RM group), by analysing RUNX3 expression with special reference to topography. A total of 89 patients underwent distal gastrectomy for gastric cancer from the intact stomach (GCI group) and 58 patients underwent resection of the remnant stomach for gastric cancer (RB group: 34 cases, RM group: 24 cases). We detected RUNX3 and gene promoter methylation by in situ hybridisation, quantitative reverse transcriptase–polymerase chain reaction (RT–PCR), and methylation-specific PCR. The interval between the initial surgery and surgery for remnant gastric cancer (interval time) was 10.4 years in the RM group, and 27.5 years in the RB group. Cancers in the RB group were significantly more predominant in the anastomosis area (P<0.05). Within the tumour, downregulation of RUNX3 expression ranged from 74.7 to 85.7% in the three groups. The rate of downregulation of RUNX3 of adjacent mucosa was 39.2% (11 in 28 cases) in RB and 47.6% (10 in 21 cases) in RM, which are significantly higher than that of the GCI group (19.5%, 17 in 87 cases). In noncancerous mucosa of the remnant stomach in the RB group, RUNX3 expression decreased more near the anastomosis area. In the RM group, however, there were no significant differences in RUNX3 expression by sampling location. Based on RUNX3 downregulation and clinical features, residual stomach mucosa of the RM group would have a higher potential of gastric carcinogenesis compared to the RB or GCI group. Gastric stump mucosa of the RB group has higher potential especially than other areas of residual stomach mucosa. Measurement of RUNX3 expression and detection of RUNX3 methylation in remnant gastric mucosa may estimate the forward risk of carcinogenesis in the remnant stomach

Functional Analysis and Molecular Dynamics Simulation of LOX-1 K167N Polymorphism Reveal Alteration of Receptor Activity

The human lectin-like oxidized low density lipoprotein receptor 1 LOX-1, encoded by the ORL1 gene, is the major scavenger receptor for oxidized low density lipoprotein in endothelial cells. Here we report on the functional effects of a coding SNP, c.501G>C, which produces a single amino acid change (K>N at codon 167). Our study was aimed at elucidating whether the c.501G>C polymorphism changes the binding affinity of LOX-1 receptor altering its function. The presence of p.K167N mutation reduces ox-LDL binding and uptake. Ox-LDL activated extracellular signal-regulated kinases 1 and 2 (ERK 1/2) is inhibited. Furthermore, ox-LDL induced biosynthesis of LOX-1 receptors is dependent on the p.K167N variation. In human macrophages, derived from c.501G>C heterozygous individuals, the ox-LDL induced LOX-1 46 kDa band is markedly lower than in induced macrophages derived from c.501G>C controls. Investigation of p.K167N mutation through molecular dynamics simulation and electrostatic analysis suggests that the ox-LDL binding may be attributed to the coupling between the electrostatic potential distribution and the asymmetric flexibility of the basic spine residues. The N/N-LOX-1 mutant has either interrupted electrostatic potential and asymmetric fluctuations of the basic spine arginines