Hard variants of stable marriage

The Stable Marriage Problem and its many variants have been widely studied in the literature (Gusfield and Irving, The Stable Marriage Problem: Structure and Algorithms, MIT Press, Cambridge, MA, 1989; Roth and Sotomayor, Two-sided matching: a study in game-theoretic modeling and analysis, Econometric Society Monographs, vol. 18, Cambridge University Press, Cambridge, 1990; Knuth, Stable Marriage and its Relation to Other Combinatorial Problems, CRM Proceedings and Lecture Notes, vol. 10, American Mathematical Society, Providence, RI, 1997), partly because of the inherent appeal of the problem, partly because of the elegance of the associated structures and algorithms, and partly because of important practical applications, such as the National Resident Matching Program (Roth, J. Political Economy 92(6) (1984) 991) and similar large-scale matching schemes. Here, we present the first comprehensive study of variants of the problem in which the preference lists of the participants are not necessarily complete and not necessarily totally ordered. We show that, under surprisingly restrictive assumptions, a number of these variants are hard, and hard to approximate. The key observation is that, in contrast to the case where preference lists are complete or strictly ordered (or both), a given problem instance may admit stable matchings of different sizes. In this setting, examples of problems that are hard are: finding a stable matching of maximum or minimum size, determining whether a given pair is stable––even if the indifference takes the form of ties on one side only, the ties are at the tails of lists, there is at most one tie per list, and each tie is of length 2; and finding, or approximating, both an `egalitarian' and a `minimum regret' stable matching. However, we give a 2-approximation algorithm for the problems of finding a stable matching of maximum or minimum size. We also discuss the significant implications of our results for practical matching schemes

ゲンパツ フメイ ガン ニオケル PET/CT ケンサ ノ ユウヨウセイ ニツイテ

We reported the utility of１８F-FDG-PET/CT examination for patients with cancer of unknownprimary origin. Twenty six patients（13 men, 13 women, aged 27-91 years, mean 71）were examined.The indication for PET/CT examination was tumor maker elevation（14 patients）, suspectedmetastatic tumor（14）and metastasis diagnosed histopathologically（3）. Patients weretold not to eat for at least four hours and a PET/CT image was obtained one hour after theadministration of 3.7MBq/kg FDG. From April to August 2006, 33 patients diagnosed with a cancerof unknown primary origin were referred to our hospital for PET/CT examination from anoutside institution. Twenty six patients could be investigated for outcomes. Seventeen patientsshowed an abnormal accumulation, with 14 of the 17 having their primary regions detected histopathologicallyor clinically. For one patient, the abnormal accumulation could not be determined toshow the origin. For 2 patients, it was difficult to diagnose if these abnormal accumulationsshowed the primary region or not, but CT examinations were helpful for a diagnosis. Seven of the9 patients who showed no abnormal accumulation were treated conservatively and the primaryregion for their cancer could not be detected during the follow up study. In 21 of 26 patients, theseresults were useful to select an appropriate therapy to be applied or a relevant examination. Weconsidered PET/CT examination, where it is possible to scan the whole body at one time, was veryuseful to get both morphologic and metabolic information. PET/CT examination showed a highersensitivity for detecting abnormal lesions than other imaging modalities

Stable marriage with incomplete lists and ties

Abstract. The original stable marriage problem requires all men and women to submit a complete and strictly ordered preference list. This is obviously often unrealistic in practice, and several relaxations have been proposed, including the following two common ones: one is to allow an incomplete list, i.e., a man is permitted to accept only a subset of the women and vice versa. The other is to allow a preference list including ties. Fortunately, it is known that both relaxed problems can still be solved in polynomial time. In this paper, we show that the situation changes substantially if we allow both relaxations (incomplete lists and ties) at the same time: the problem not only becomes NP-hard, but also the optimal cost version has no approximation algorithm achieving the approximation ratio of N 1−ɛ, where N is the instance size, unless P=NP.

RUNX1 positively regulates the ErbB2/HER2 signaling pathway through modulating SOS1 expression in gastric cancer cells

Abstract The dual function of runt-related transcriptional factor 1 (RUNX1) as an oncogene or oncosuppressor has been extensively studied in various malignancies, yet its role in gastric cancer remains elusive. Up-regulation of the ErbB2/HER2 signaling pathway is frequently-encountered in gastric cancer and contributes to the maintenance of these cancer cells. This signaling cascade is partly mediated by son of sevenless homolog (SOS) family, which function as adaptor proteins in the RTK cascades. Herein we report that RUNX1 regulates the ErbB2/HER2 signaling pathway in gastric cancer cells through transactivating SOS1 expression, rendering itself an ideal target in anti-tumor strategy toward this cancer. Mechanistically, RUNX1 interacts with the RUNX1 binding DNA sequence located in SOS1 promoter and positively regulates it. Knockdown of RUNX1 led to the decreased expression of SOS1 as well as dephosphorylation of ErbB2/HER2, subsequently suppressed the proliferation of gastric cancer cells. We also found that our novel RUNX inhibitor (Chb-M’) consistently led to the deactivation of the ErbB2/HER2 signaling pathway and was effective against several gastric cancer cell lines. Taken together, our work identified a novel interaction of RUNX1 and the ErbB2/HER2 signaling pathway in gastric cancer, which can potentially be exploited in the management of this malignancy

Comparison of alemtuzumab, anti-thymocyte globulin, and post-transplant cyclophosphamide for graft-versus-host disease and graft-versus-leukemia in murine models.

Graft-versus-host disease is a major complication after allogeneic hematopoietic stem cell transplantation for hematological malignancies. Immunosuppressive drugs, such as anti-thymocyte globulin, alemtuzumab, and post-transplant cyclophosphamide, have been used to prevent graft-versus-host disease in HLA-mismatched haploidentical hematopoietic stem cell transplantation. Here, we investigated whether these drugs could ameliorate graft-versus-host disease without diminishing the graft-versus-leukemia effect by using a xenogeneic transplanted graft-versus-host disease/graft-versus-leukemia model. Anti-thymocyte globulin treatment diminished graft-versus-host disease symptoms, completely depleted the infiltration of inflammatory cells in the liver and intestine, and led to prolonged survival. By contrast, improvement after post-transplant cyclophosphamide treatment remained minimal. Alemtuzumab treatment modestly prolonged survival despite an apparent decrease of Tregs. In the graft-versus-leukemia model, 1.5 to 2.0 mg/kg of anti-thymocyte globulin and 0.6 to 0.9 mg/kg of alemtuzumab reduced graft-versus-host disease with minimal loss of graft-versus-leukemia effect. Mice treated with 400 mg/kg of post-transplant cyclophosphamide did not develop graft-versus-host disease or leukemia, but it was difficult to evaluate the graft-versus-leukemia effect due to the sensitivity of A20 cells to cyclophosphamide. Although the current settings provide narrow optimal therapeutic windows, further studies are warranted to maximize the benefits of each immunosuppressant