Complexity of Coloring Reconfiguration under Recolorability Constraints

For an integer k ge 1, k-coloring reconfiguration is one of the most well-studied reconfiguration problems, defined as follows: In the problem, we are given two (vertex-)colorings of a graph using k colors, and asked to transform one into the other by recoloring only one vertex at a time, while at all times maintaining a proper coloring. The problem is known to be PSPACE-complete if k ge 4, and solvable for any graph in polynomial time if k le 3. In this paper, we introduce a recolorability constraint on the k colors, which forbids some pairs of colors to be recolored directly. The recolorability constraint is given in terms of an undirected graph R such that each node in R corresponds to a color and each edge in R represents a pair of colors that can be recolored directly. We study the hardness of the problem based on the structure of recolorability constraints R. More specifically, we prove that the problem is PSPACE-complete if R is of maximum degree at least four, or has a connected component containing more than one cycle

Algorithms for Coloring Reconfiguration Under Recolorability Constraints

Coloring reconfiguration is one of the most well-studied reconfiguration problems. In the problem, we are given two (vertex-)colorings of a graph using at most k colors, and asked to determine whether there exists a transformation between them by recoloring only a single vertex at a time, while maintaining a k-coloring throughout. It is known that this problem is solvable in linear time for any graph if k = 4. In this paper, we further investigate the problem from the viewpoint of recolorability constraints, which forbid some pairs of colors to be recolored directly. More specifically, the recolorability constraint is given in terms of an undirected graph R such that each node in R corresponds to a color, and each edge in R represents a pair of colors that can be recolored directly. In this paper, we give a linear-time algorithm to solve the problem under such a recolorability constraint if R is of maximum degree at most two. In addition, we show that the minimum number of recoloring steps required for a desired transformation can be computed in linear time for a yes-instance. We note that our results generalize the known positive ones for coloring reconfiguration

Break and sustain bifurcations of S_N-invariant equidistant economy

This paper aims at the elucidation of the bifurcation mechanism of an equidistant economy in Economic Geography. An attention is paid to the existence of invariant solutions that retain their spatial patterns when the bifurcation parameter changes. Theoretical results on symmetrybreaking bifurcation of the symmetric group SN, which describes the symmetry of this economy, is combined with the mechanism of sustain bifurcation of invariant patterns that is inherent to the economy. The stability of bifurcating branches is investigated theoretically to demonstrate that most of them are asymptotically unstable. Among a plethora of theoretically possible spatial patterns, those which actually become stable for spatial economic models are investigated numerically. The solution curves of the economy are shown to display a complicated mesh-like structure, which looks like threads of warp and weft

Break and sustain bifurcations of S_N-invariant equidistant economy

This paper aims at the elucidation of the bifurcation mechanism of an equidistant economy in Economic Geography. An attention is paid to the existence of invariant solutions that retain their spatial patterns when the bifurcation parameter changes. Theoretical results on symmetrybreaking bifurcation of the symmetric group SN, which describes the symmetry of this economy, is combined with the mechanism of sustain bifurcation of invariant patterns that is inherent to the economy. The stability of bifurcating branches is investigated theoretically to demonstrate that most of them are asymptotically unstable. Among a plethora of theoretically possible spatial patterns, those which actually become stable for spatial economic models are investigated numerically. The solution curves of the economy are shown to display a complicated mesh-like structure, which looks like threads of warp and weft

Break and sustain bifurcations of S_N-invariant equidistant economy

This paper aims at the elucidation of the bifurcation mechanism of an equidistant economy in Economic Geography. An attention is paid to the existence of invariant solutions that retain their spatial patterns when the bifurcation parameter changes. Theoretical results on symmetrybreaking bifurcation of the symmetric group SN, which describes the symmetry of this economy, is combined with the mechanism of sustain bifurcation of invariant patterns that is inherent to the economy. The stability of bifurcating branches is investigated theoretically to demonstrate that most of them are asymptotically unstable. Among a plethora of theoretically possible spatial patterns, those which actually become stable for spatial economic models are investigated numerically. The solution curves of the economy are shown to display a complicated mesh-like structure, which looks like threads of warp and weft

Factors determining maximum torque and achievement of the recommended torque for manual implant drivers: A pilot study

When fixing an oral implant superstructure with a screw, operators must be aware of the torque being applied by their fingers to prevent the transmission of excessive or insufficient torque to the implant. In this study, we identified the factors that determine individual maximum attainable torque and those that determine the achievement of the prescribed torque. We evaluated 16 dentists on their use of two types of manual implant drivers（UniGrip by Nobel Biocare and Carrier Hex by Zimmer Biomet）and measured the maximum torque（MT）generated by their fingers. The target torque was set at 15N. Measurements were taken while the participants were turning the implant screw with or without gloves in both clockwise and counterclockwise directions. The grip and finger strength of each participant were measured, and the data showed that torque values were higher among the male participants during clockwise rotation and when they were wearing gloves（p＜0.05）. Positive correlations were found between the MT and grip strength and between the MT and finger strength. These results suggest that dentists should monitor their ability to consistently achieve the recommended torque for implant drivers

Prevalence and Outcomes of Acute Hepatitis B in Okayama, Japan, 2006-2010

Hepatitis B virus (HBV) is one of the major viruses causing acute hepatitis. Recently, the incidence of acute hepatitis with genotype A has been increasing in Japan. The aim of this study was to investigate acute hepatitis B (AHB) in Okayama prefecture, with special attention to HBV genotype A. AHB patients who visited one of 12 general hospitals in Okayama prefecture between 2006 and 2010 were retrospectively analyzed. Over the course of the study period, 128 patients were diagnosed with AHB. Sexual transmission was supposed in the majority of patients (78 patients, 61%), including 59 (76%) having sex with heterosexual partners. The genotypes of HBV were assessed in 90 patients (70%), of whom 27 patients were infected with genotype A, 5 with genotype B, and 58 with genotype C. The prevalence of genotype A was significantly higher among male patients (28.7%), aged 20-29 (35.6%, p＜0.01), among men who had sex with men (100%, p＜0.005), and among patients having sex with unspecified partners (44.8%, p＜0.005). Genotype A was not a significant factor associated with delayed HBsAg disappearance. Caution should be exercised with regard to sexually transmissible diseases in order to slow the pandemic spread of AHB due to genotype A

Wide Distribution of O157-Antigen Biosynthesis Gene Clusters in Escherichia coli

Most Escherichia coli O157-serogroup strains are classified as enterohemorrhagic E. coli (EHEC), which is known as an important food-borne pathogen for humans. They usually produce Shiga toxin (Stx) 1 and/or Stx2, and express H7-flagella antigen (or nonmotile). However, O157 strains that do not produce Stxs and express H antigens different from H7 are sometimes isolated from clinical and other sources. Multilocus sequence analysis revealed that these 21 O157:non-H7 strains tested in this study belong to multiple evolutionary lineages different from that of EHEC O157:H7 strains, suggesting a wide distribution of the gene set encoding the O157-antigen biosynthesis in multiple lineages. To gain insight into the gene organization and the sequence similarity of the O157-antigen biosynthesis gene clusters, we conducted genomic comparisons of the chromosomal regions (about 59 kb in each strain) covering the O-antigen gene cluster and its flanking regions between six O157:H7/non-H7 strains. Gene organization of the O157-antigen gene cluster was identical among O157:H7/non-H7 strains, but was divided into two distinct types at the nucleotide sequence level. Interestingly, distribution of the two types did not clearly follow the evolutionary lineages of the strains, suggesting that horizontal gene transfer of both types of O157-antigen gene clusters has occurred independently among E. coli strains. Additionally, detailed sequence comparison revealed that some positions of the repetitive extragenic palindromic (REP) sequences in the regions flanking the O-antigen gene clusters were coincident with possible recombination points. From these results, we conclude that the horizontal transfer of the O157-antigen gene clusters induced the emergence of multiple O157 lineages within E. coli and speculate that REP sequences may involve one of the driving forces for exchange and evolution of O-antigen loci

Improved detectability of small-bowel lesions via capsule endoscopy with computed virtual chromoendoscopy: A pilot study

Objective. Real-time video capsule endoscopy (CE) with flexible spectral imaging color enhancement (FICE) improves visibility of small-bowel lesions. This article aims to clarify whether CE-FICE also improves detectability of small-bowel lesions. Patients and methods. A total of 55 patients who underwent CE at Hiroshima University Hospital during the period November 2009 through March 2010 were enrolled in the study. Five patients were excluded from the study because residues and transit delays prevented sufficient evaluation. Thus, 50 patients participated. Two experienced endoscopists (each having interpreted more than 50 capsule videos) analyzed the images. One interpreted conventional capsule videos; the other, blinded to interpretation of the conventional images, interpreted CE-FICE images obtained at settings 1-3 (setting 1: red 595 nm, green 540 nm, blue 535 nm; setting 2: red 420 nm, green 520 nm, blue 530 nm; setting 3: red 595 nm, green 570 nm, blue 415 nm). Lesions were classified as angioectasia, erosion, ulceration, or tumor. Detectability was compared between the two modalities. Time taken to interpret the capsule videos was also determined. Results. Seventeen angioectasias were identified by conventional CE; 48 were detected by CE-FICE at setting 1, 45 at setting 2, and 24 at setting 3, with significant differences at settings 1 and 2 (p = 0.0003, p < 0.0001, respectively). Detection of erosion, ulceration, and tumor did not differ statistically between conventional CE and CE-FICE, nor did interpretation time (conventional CE 36 ± 6.9 min; CE-FICE setting 1, 36 ± 6.4 min; setting 2, 38 ± 5.8 min; setting 3, 35 ± 6.7 min). Conclusions. CE-FICE is superior in the lesion detection in comparison with conventional CE and improves detection of angioectasia

Short Stat5-Interacting Peptide Derived from Phospholipase C-β3 Inhibits Hematopoietic Cell Proliferation and Myeloid Differentiation

Constitutive activation of the transcription factor Stat5 in hematopoietic stem/progenitor cells leads to various hematopoietic malignancies including myeloproliferative neoplasm (MPN). Our recent study found that phospholipase C (PLC)-β3 is a novel tumor suppressor involved in MPN, lymphoma and other tumors. Stat5 activity is negatively regulated by the SH2 domain-containing protein phosphatase SHP-1 in a PLC-β3-dependent manner. PLC-β3 can form the multimolecular SPS complex together with SHP-1 and Stat5. The close physical proximity of SHP-1 and Stat5 brought about by interacting with the C-terminal segment of PLC-β3 (PLC-β3-CT) accelerates SHP-1-mediated dephosphorylation of Stat5. Here we identify the minimal sequences within PLC-β3-CT required for its tumor suppressor function. Two of the three Stat5-binding noncontiguous regions, one of which also binds SHP-1, substantially inhibited in vitro proliferation of Ba/F3 cells. Surprisingly, an 11-residue Stat5-binding peptide (residues 988-998) suppressed Stat5 activity in Ba/F3 cells and in vivo proliferation and myeloid differentiation of hematopoietic stem/progenitor cells. Therefore, this study further defines PLC-β3-CT as the Stat5- and SHP-1-binding domain by identifying minimal functional sequences of PLC-β3 for its tumor suppressor function and implies their potential utility in the control of hematopoietic malignancies