Wide partitions, Latin tableaux, and Rota's basis conjecture

Say that mu is a ``subpartition'' of an integer partition lambda if the multiset of parts of mu is a submultiset of the parts of lambda, and define an integer partition lambda to be ``wide'' if for every subpartition mu of lambda, mu >= mu' in dominance order (where mu' denotes the conjugate or transpose of mu). Then Brian Taylor and the first author have conjectured that an integer partition lambda is wide if and only if there exists a tableau of shape lambda such that (1) for all i, the entries in the ith row of the tableau are precisely the integers from 1 to lambda_i inclusive, and (2) for all j, the entries in the jth column of the tableau are pairwise distinct. This conjecture was originally motivated by Rota's basis conjecture and, if true, yields a new class of integer multiflow problems that satisfy max-flow min-cut and integrality. Wide partitions also yield a class of graphs that satisfy ``delta-conjugacy'' (in the sense of Greene and Kleitman), and the above conjecture implies that these graphs furthermore have a completely saturated stable set partition. We present several partial results, but the conjecture remains very much open.Comment: Joined forces with Goemans and Vondrak---several new partial results; 28 pages, submitted to Adv. Appl. Mat

The power of multifolds: Folding the algebraic closure of the rational numbers

It is well known that the usual Huzita-Hatori axioms for origami enable angle trisection but not angle quintisection. Using the concept of a multifold, Lang has achieved quintisection but not arbitrary algebraic numbers. We define the n-parameter multifold and show how to use one-parameter multifolds to obtain the algebraic closure of the rational numbers.Comment: 9 pages; 4th Int'l Conf. Origami Sci. Math. Educ. (4OSME

Synergistic effects of targeted PI3K signaling inhibition and chemotherapy in liposarcoma.

While liposarcoma is the second most common soft tissue malignant tumor, the molecular pathogenesis in this malignancy is poorly understood. Our goal was therefore to expand the understanding of molecular mechanisms that drive liposarcoma and identify therapeutically-susceptible genetic alterations. We studied a cohort of high-grade liposarcomas and benign lipomas across multiple disease sites, as well as two liposarcoma cell lines, using multiplexed mutational analysis. Nucleic acids extracted from diagnostic patient tissue were simultaneously interrogated for 150 common mutations across 15 essential cancer genes using a clinically-validated platform for cancer genotyping. Western blot analysis was implemented to detect activation of downstream pathways. Liposarcoma cell lines were used to determine the effects of PI3K targeted drug treatment with or without chemotherapy. We identified mutations in the PIK3CA gene in 4 of 18 human liposarcoma patients (22%). No PIK3CA mutations were identified in benign lipomas. Western blot analysis confirmed downstream activation of AKT in both PIK3CA mutant and non-mutant liposarcoma samples. PI-103, a dual PI3K/mTOR inhibitor, effectively inhibited the activation of the PI3K/AKT in liposarcoma cell lines and induced apoptosis. Importantly, combination with PI-103 treatment strongly synergized the growth-inhibitory effects of the chemotherapy drugs doxorubicin and cisplatin in liposarcoma cells. Taken together, these findings suggest that activation of the PI3K/AKT pathway is an important cancer mechanism in liposarcoma. Targeting the PI3K/AKT/pathway with small molecule inhibitors in combination with chemotherapy could be exploited as a novel strategy in the treatment of liposarcoma

Backbone‐Degradable Polymers Prepared by Chemical Vapor Deposition

Polymers prepared by chemical vapor deposition (CVD) polymerization have found broad acceptance in research and industrial applications. However, their intrinsic lack of degradability has limited wider applicability in many areas, such as biomedical devices or regenerative medicine. Herein, we demonstrate, for the first time, a backbone‐degradable polymer directly synthesized via CVD. The CVD co‐polymerization of [2.2]para‐cyclophanes with cyclic ketene acetals, specifically 5,6‐benzo‐2‐methylene‐1,3‐dioxepane (BMDO), results in well‐defined, hydrolytically degradable polymers, as confirmed by FTIR spectroscopy and ellipsometry. The degradation kinetics are dependent on the ratio of ketene acetals to [2.2]para‐cyclophanes as well as the hydrophobicity of the films. These coatings address an unmet need in the biomedical polymer field, as they provide access to a wide range of reactive polymer coatings that combine interfacial multifunctionality with degradability.Verletzliches Rückgrat: Beschichtungen aus Polymeren mit abbaubarem Rückgrat wurden durch Copolymerisation mittels chemischer Dampfabscheidung erhalten. Die Beschichtungen vereinen die Möglichkeit zur mehrfachen Funktionalisierung von Grenzflächen mit einer Abbaufähigkeit, was insbesondere für biomedizinische Anwendungen von Interesse ist.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/135566/1/ange201609307-sup-0001-misc_information.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/135566/2/ange201609307_am.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/135566/3/ange201609307.pd

Frailty in Chronic Obstructive Pulmonary Disease and Risk of Exacerbations and Hospitalizations

Background: Frailty is a complex clinical syndrome associated with vulnerability to adverse health outcomes. While frailty is thought to be common in chronic obstructive pulmonary disease (COPD), the relationship between frailty and COPD-related outcomes such as risk of acute exacerbations of COPD (AE-COPD) and hospitalizations is unclear.Purpose: To examine the association between physical frailty and risk of acute exacerbations, hospitalizations, and mortality in patients with COPD.Methods: A longitudinal analysis of data from a cohort of 280 participants was performed. Baseline frailty measures included exhaustion, weakness, low activity, slowness, and undernutrition. Outcome measures included AE-COPD, hospitalizations, and mortality over 2 years. Negative binomial regression and Cox proportional hazard modeling were used.Results: Sixty-two percent of the study population met criteria for pre-frail and 23% were frail. In adjusted analyses, the frailty syndrome was not associated with COPD exacerbations. However, among the individual components of the frailty syndrome, weakness measured by handgrip strength was associated with increased risk of COPD exacerbations (IRR 1.46, 95% CI 1.09– 1.97). The frailty phenotype was not associated with all-cause hospitalizations but was associated with increased risk of non-COPD-related hospitalizations.Conclusion: This longitudinal cohort study shows that a high proportion of patients with COPD are pre-frail or frail. The frailty phenotype was associated with an increased risk of non-COPD hospitalizations but not with all-cause hospitalizations or COPD exacerbations. Among the individual frailty components, low handgrip strength was associated with increased risk of COPD exacerbations over a 2-year period. Measuring handgrip strength may identify COPD patients who could benefit from programs to reduce COPD exacerbations

Can Extra Mixing in RGB and AGB Stars Be Attributed to Magnetic Mechanisms?

It is known that there must be some weak form of transport (called cool bottom processing, or CBP) acting in low mass RGB and AGB stars, adding nuclei, newly produced near the hydrogen-burning shell, to the convective envelope. We assume that this extra-mixing originates in a stellar dynamo operated by the differential rotation below the envelope, maintaining toroidal magnetic fields near the hydrogen-burning shell. We use a phenomenological approach to the buoyancy of magnetic flux tubes, assuming that they induce matter circulation as needed by CBP models. This establishes requirements on the fields necessary to transport material from zones where some nuclear burning takes place, through the radiative layer, and into the convective envelope. Magnetic field strengths are determined by the transport rates needed by CBP for the model stellar structure of a star of initially 1.5 solar mass, in both the AGB and RGB phases. The field required for the AGB star in the processing zone is B_0 ~ 5x10^6 G; at the base of the convective envelope this yields an intensity B_E < 10^4 G (approximately). For the RGB case, B_0 ~ 5x10^4 to 4x10^5 G, and the corresponding B_E are ~ 450 to 3500 G. These results are consistent with existing observations on AGB stars. They also hint at the basis for high field sources in some planetary nebulae and the very large fields found in some white dwarfs. It is concluded that transport by magnetic buoyancy should be considered as a possible mechanism for extra mixing through the radiative zone, as is required by both stellar observations and the extensive isotopic data on circumstellar condensates found in meteorites.Comment: 26 pages, 4 figures, accepted by Astrophysical Journa

Identification of 5,6-trans-epoxyeicosatrienoic acid in the phospholipids of red blood cells.

A novel eicosanoid, 5,6-trans-epoxy-8Z,11Z,14Z-eicosatrienoic acid (5,6-trans-EET), was identified in rat red blood cells. Characterization of 5,6-trans-EET in the sn-2 position of the phospholipids was accomplished by hydrolysis with phospholipase A(2) followed by gas chromatography/mass spectrometry as well as electrospray ionization-tandem mass spectrometry analyses. The electron ionization spectrum of 5,6-erythro-dihydroxyeicosatrienoic acid (5,6-erythro-DHET), converted from 5,6-trans-EET in the samples, matches that of the authentic standard. Hydrogenation of the extracted 5,6-erythro-DHET with platinum(IV) oxide/hydrogen resulted in an increase of the molecular mass by 6 daltons and the same retention time shift as an authentic standard in gas chromatography, suggesting the existence of three olefins as well as the 5,6-erythro-dihydroxyl structure in the metabolite. Match of retention times by chromatography indicated identity of the stereochemistry of the red blood cell 5,6-erythro-DHET vis à vis the synthetic standard. High pressure liquid chromatography-electrospray ionization-tandem mass spectrometry analysis of the phospholipase A(2)-hydrolyzed lipid extracts from red blood cells revealed match of the mass spectrum and retention time of the compound with the authentic 5,6-trans-EET standard, providing direct evidence of the existence of 5,6-trans-EET in red blood cells. The presence of other trans-EETs was also demonstrated. The ability of both 5,6-trans-EET and its product 5,6-erythro-DHET to relax preconstricted renal interlobar arteries was significantly greater than that of 5,6-cis-EET. In contrast, 5,6-cis-EET and 5,6-trans-EET were equipotent in their capacity to inhibit collagen-induced rat platelet aggregation, whereas 5,6-erythro-DHET was without effect. We propose that the red blood cells serve as a reservoir for epoxides which on release may act in a vasoregulatory capacity

Survival Analysis of Re-resection Versus Radiofrequency Ablation for Intrahepatic Recurrence After Hepatectomy for Hepatocellular Carcinoma

Ó The Author(s) 2011. This article is published with open access at Springerlink.com Background Tumor recurrence after resection of hepatocellular carcinoma is a common phenomenon. Re-resection and radiofrequency ablation (RFA) are good options for treating recurrent HCC. This study compared the efficacy of these two modalities in the treatment of intrahepatic HCC recurrence after hepatectomy. Methods From January 2001 to December 2008, a total of 179 patients developed intrahepatic HCC recurrence after hepatectomy. To treat the recurrence, 29 patients underwent re-resection and 45 patients had RFA. Patient characteristics, clinicopathologic data, and survival outcomes were reviewed. Results Child-Pugh status, time to develop first recurrence (12.2 vs. 8.7 months), and recurrent tumor size (2.1 vs. 2.1 cm) were comparable for the two groups. Time to develop a second intrahepatic recurrence after re-resection and RFA was 5.9 and 4.0 months respectively. The 1-, 3-, and 5-year disease-free survival rates were 41.4%, 24.2%, and 24.2 % after re-resection and 32.2%, 12.4%, and 9.3% after RFA (p = 0.14). The 1-, 3-, and 5-year overall survival rates were 89.7%, 56.5%, and 35.2 % after re-resection and 83.7%, 43.1%, and 29.1 % after RFA (p = 0.48). For the second recurrence, 33.3 % of patients underwent a second round of RFA and 10.0 % underwent a third resection