Shortest Reconfiguration of Perfect Matchings via Alternating Cycles

Motivated by adjacency in perfect matching polytopes, we study the shortest reconfiguration problem of perfect matchings via alternating cycles. Namely, we want to find a shortest sequence of perfect matchings which transforms one given perfect matching to another given perfect matching such that the symmetric difference of each pair of consecutive perfect matchings is a single cycle. The problem is equivalent to the combinatorial shortest path problem in perfect matching polytopes. We prove that the problem is NP-hard even when a given graph is planar or bipartite, but it can be solved in polynomial time when the graph is outerplanar

Studies on the Relationship between Pulmonary Tuberculous Cavities and Draining Bronchi, by Injecting Acrylic Resin

この論文は国立情報学研究所の学術雑誌公開支援事業により電子化されました。We have studied 83 tuberculosis lungs removed at operation or at autopsy, three-dimensionally, pathologically, and histologically by means of the plasticinjected casts, and further investigated the relationship between cavities and draining bronchi and have reached the following conclusions. 1). The 7th to 9th bronchi in each lobe are big enough to play the role of draining bronchi, thus it may be said that the caseated foci larger than a lobule are facing directly to these bronchi. This is why these foci are always threatened by the danger of cavitation. 2). It is extremely difficult for a cavity to be cut off from the trachea by connective tissues obstruction of its draining bronchus; indeed this kind of obstruction has not been found at all in our studies. 3). There is a parallel relation between the state of a cavity and the tuberculous lesion of its draining bronchus, but in many cases there is a difference in the extent of the disease. Accordingly it is necessary to keep in mind the state of the draining bronchus at the time of treatment of the cavity. 4). The modes of opening of a cavity into its draining bronchus are; (1) a cavity opening into the end of a bronchus at its top (pattern I), and (2) a cavity opening into the lateral wall of a bronchus. According to the different stages of the developing cavity, the patterns seem to alter as follows⟶pattern I⟶pattern II⟶pattern I. 5). A cavity, less than 1.5cm in diameter, has usually one draining bronchus, while a bigger cavity than the above has generally two or more bronchi, and a cavity larger than the above two kinds of cavities has several draining bronchi, but seldom more than four. The drainidg bronchi from megacavities are fewer in number but manytimes larger in size than those of the above cavities. This is apparently due to the fact that the other small draining bronchi were obliterated during the course of the development of the disease. 6) A cavitation is not necessarly limited to a single pulmonary segment, but the draining bronchus of a cavity, which is 1.5cm. in diameter, communicates with the two neighboring segments, especially those of megacavities sometimes communicate with many segments. The intersegmental partitions, which consist of connective tissue and branches of pulmonary veins, are not firm enough to check caseation and cavitation of the intersegmental connective tissue during the development and fusion of the tuberculous focus. 7). Morphological changes in draining bronchi such as stenosis, obstruction, partial dilatation, and single or multiple flexions are observable. Partial stenosis is distinctly observable at the opening of the bronchi into cavities, and in other parts, a partial stenosis and a partial dilatation of the draining bronchus occur alternatly and the extent of the lesions gradually decreases in degree towards the pulmonary hilum. The morphological changes of draining bronchi parallel the degree of the tuberculous lesion around the cavity or the caseated focus. 8). With pneumothorax the bronchi take the form of stratification roughly parallel to the axis of a lobe, and the bronchial bending and obstruction are not recognized. Even in highly collapsed lungs of perfect pneumothorax, bronchial obstruction is not recognizable, but only the shortening narrowing of bronchi. 9). One form of direct treatment of tuberculosis, the incision treatment, aims at cleaning the cavity and cicatrized healing by means of draining the contents of cavity through the body wall, and not through a draining bronchus. But unfortunately this treatment is not very through when we consider the relationship between a cavity and the bronchial tuberculous lesion. From this point of view resection seems to be the more thorough treatment, but indications for this treatment are limited to cases in the early stage, if we consider bronchial lesions and disseminated foci. Therefore, those caseated foci which seems to tend towards softening and dec

A parameterized view to the robust recoverable base problem of matroids under structural uncertainty

We study a robust recoverable version of the matroid base problem where the uncertainty is imposed on combinatorial structures rather than on weights as studied in the literature. We prove that the problem is NP-hard even when a given matroid is uniform or graphic. On the other hand, we prove that the problem is fixed-parameter tractable with respect to the number of scenarios

Shortest Reconfiguration of Perfect Matchings via Alternating Cycles

Motivated by adjacency in perfect matching polytopes, we study the shortest reconfiguration problem of perfect matchings via alternating cycles. Namely, we want to find a shortest sequence of perfect matchings which transforms one given perfect matching to another given perfect matching such that the symmetric difference of each pair of consecutive perfect matchings is a single cycle. The problem is equivalent to the combinatorial shortest path problem in perfect matching polytopes. We prove that the problem is NP-hard even when a given graph is planar or bipartite, but it can be solved in polynomial time when the graph is outerplanar

Structural and Electronic Properties of a Triangular Lattice Magnet NaPrTe2_2 Compared with NaNdTe2_2 and NaTbTe2_2

NaPrTe2, NaNdTe2, and NaTbTe2 are found to be triangular lattice magnets with the alpha-NaFeO2 structure, where lanthanoid atoms with 4f electrons form a triangular lattice, based on the structural analysis and physical property measurements of synthesized polycrystalline samples. The alpha-NaFeO2 structure is a new polymorph of NaPrTe2, which has been reported to crystallize in the cubic LiTiO2 structure. Polytypism in NaPrTe2 was discussed based on the structural parameters determined by the Rietveld analysis. NaPrTe2 is suggested to be in the proximity of the phase boundary between the LiTiO2 and alpha-NaFeO2 types, as compared to NaNdTe2 and NaTbTe2, indicating that this compound might be interesting from the perspectives of the dimensional control of geometrically frustrated lattices. The magnetic susceptibility and heat capacity data indicated that NaPrTe2 do not show long-range magnetic order or a spin-glass transition above 2 K.Comment: 6 pages, 7 figure

Hardness of Finding Combinatorial Shortest Paths on Graph Associahedra

We prove that the computation of a combinatorial shortest path between two vertices of a graph associahedron, introduced by Carr and Devadoss, is NP-hard. This resolves an open problem raised by Cardinal. A graph associahedron is a generalization of the well-known associahedron. The associahedron is obtained as the graph associahedron of a path. It is a tantalizing and important open problem in theoretical computer science whether the computation of a combinatorial shortest path between two vertices of the associahedron can be done in polynomial time, which is identical to the computation of the flip distance between two triangulations of a convex polygon, and the rotation distance between two rooted binary trees. Our result shows that a certain generalized approach to tackling this open problem is not promising. As a corollary of our theorem, we prove that the computation of a combinatorial shortest path between two vertices of a polymatroid base polytope cannot be done in polynomial time unless P = NP. Since a combinatorial shortest path on the matroid base polytope can be computed in polynomial time, our result reveals an unexpected contrast between matroids and polymatroids

The Combination of D-dimer and Glasgow Prognostic Score Can Be Useful in Predicting VTE in Patients with Stage IIIC and IVA Ovarian Cancer

Cancer patients have increased risk of venous thromboembolism (VTE) that must be assessed before treatment. This study aimed to determine effective VTE biomarkers in gynecologic cancer (GC). We investigated the correlation between D-dimer levels, Khorana risk score (KRS), Glasgow prognostic score (GPS), and VTE in 1499 GC patients (583 cervical cancer (CC), 621 endometrial cancer (EC), and 295 ovarian cancer (OC) patients) treated at our institution between January 2008 and December 2019. χ2 and Mann–Whitney U-tests were used to determine statistical significance. We used receiver operating characteristic-curve analysis to evaluate the discriminatory ability of each parameter. D-dimer levels were significantly correlated with KRS and GPS in patients with GC. VTE was diagnosed in 11 CC (1.9%), 27 EC (4.3%), and 39 OC patients (13.2%). Optimal D-dimer cut-off values for VTE were 3.1, 3.2, and 3.9 μg/ml in CC, EC and OC patients, respectively. D-dimer could significantly predict VTE in all GC patients. Furthermore, D-dimer combined with GPS was more accurate in predicting VTE than other VTE biomarkers in stage IIIC and IVA OC (AUC: 0.846; p<0.001). This study demonstrates that combined D-dimer and GPS are useful in predicting VTE in patients with OC

Crystallization characteristics of amorphous trehalose dried from alcohol

Trehalose forms a glass that can be used to preserve labile substances under desiccation. The crystallization characteristics, namely crystallization temperature (Tcry) and isothermal crystallization behavior of amorphous trehalose, dried from alcohol (methanol, ethanol), was analyzed and the results were compared with those for the amorphous trehalose freeze-dried from water. The use of alcohol as a solvent lowered the Tcry from 184 ± 6 °C for the case of an aqueous solvent to 103 ± 5 °C/methanol and 120 ± 8 °C/ethanol. The formation of multiple forms of crystals and partial melting were suggested by the thermal analysis. Isothermal crystallization experiments showed that the alcohol-originated amorphous trehalose was eventually exclusively converted into β-form crystals. The induction period (tind) before the start of isothermal crystallization was markedly shortened when alcohol was used as the solvent compared to water. The tind values for various amorphous sugar samples including the alcohol-originated ones could be correlated with difference between Tcry and the sample temperature