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We prove that the bi-invariant Einstein metric on $SU_{2n+1}$ is isolated in the moduli space of Einstein metrics, even though it admits infinitesimal deformations. This gives a non-Kähler, non-product example of this phenomenon adding to the famous example of $\mathbb{C}\mathbb{P}^{2n}\times \mathbb{C}\mathbb{P}^{1}$ found by Koiso. We apply our methods to derive similar solitonic rigidity results for the Kähler–Einstein metrics on “odd” Grassmannians. We also make explicit a connection between non-integrable deformations and the dynamical instability of metrics under Ricci flow.

INTRODUCTION Spontaneous splenic rupture without any history of trauma is a rare and under-recognized entity in patients presenting with acute abdomen. This is a life threatening condition seen in association with various haematological malignancies, medications and blood stream infections. CASE PRESENTATION We report the case of a ninety-four-year-old male who presented to a regional Australian Hospital with abdominal pain, fever and hypotension. Imaging revealed splenic rupture. Salmonella Typhi was isolated on blood and peritoneal cultures. The patient’s Salmonella exposure was likely related to frequent consumption of raw eggs. He was managed conservatively with intravenous antibiotics to treat salmonella bacteraemia. Unfortunately, the patient died prior to discharge. DISCUSSION Salmonella bacteraemia is an uncommon cause of splenic rupture. Timely diagnosis and identification of the underlying aetiology of splenic rupture is essential for targeted management of such patients. CONCLUSION Spontaneous splenic rupture is a rare and potentially life threatening disorder which should be considered in the differential diagnosis of acute abdomen, regardless of any occurrence of trauma. Early recognition of this condition is essential to prevent the associated morbidity and mortality.

We apply the Atiyah-Singer index theorem and tensor products of elliptic complexes to the cohomology of transitive Lie algebroids. We prove that the Euler characteristic of a representation of a transitive Lie algebroid $A$ over a compact manifold $M$ vanishes unless $A=TM$, and prove a general K\"{u}nneth formula. As applications we give a short proof of a vanishing result for the Euler characteristic of a principal bundle calculated using invariant differential forms, and show that the cohomology of certain Lie algebroids are exterior algebras. The latter result can be seen as a generalization of Hopf's theorem regarding the cohomology of compact Lie groups., Comment: 12 pages

Using a stability criterion due to Kr\"oncke, we show, providing ${n\neq 2k}$, the K\"ahler--Einstein metric on the Grassmannian $Gr_{k}(\mathbb{C}^{n})$ of complex $k$-planes in an $n$-dimensional complex vector space is dynamically unstable as a fixed point of the Ricci flow. This generalises the recent results of Kr\"oncke and Knopf--Sesum on the instability of the Fubini--Study metric on $\mathbb{CP}^{n}$ for $n>1$. The key to the proof is using the description of Grassmannians as certain coadjoint orbits of $SU(n)$. We are also able to prove that Kr\"oncke's method will not work on any of the other compact, irreducible, Hermitian symmetric spaces., Comment: 21 pages, v3 minor rewrites to clarify arguments, to appear in J. Geom. Anal

In this work we introduce the category of multiplicative sections of an LA -groupoid. We prove that this category carries a natural strict Lie 2-algebra structure, which is Morita invariant. As applications, we study the algebraic structure underlying multiplicative vector fields on a Lie groupoid and in particular vector fields on differentiable stacks. We also introduce the notion of geometric vector field on the quotient stack of a Lie groupoid, showing that the space of such vector fields is a Lie algebra. We describe the Lie algebra of geometric vector fields in several cases, including classifying stacks, quotient stacks of regular Lie groupoids and in particular orbifolds, and foliation groupoids.

For a Lie group $G$ and a vector bundle $E$ we study those actions of the Lie group $TG$ on $E$ for which the action map $TG\times E \to E$ is a morphism of vector bundles, and call those \emph{affine actions}. We prove that the category $\mathrm{Vect}_{TG}^{\mathrm{aff}}\left(X\right)$ of such actions over a fixed $G$-manifold $X$ is equivalent to a certain slice category $\mathfrak g_X \backslash \mathrm{Vect}_G\left(X\right)$. We show that there is a monadic adjunction relating $\mathrm{Vect}_{TG}^{\mathrm{aff}}\left(X\right)$ to $\mathrm{Vect}_G\left(X\right)$, and the right adjoint of this adjunction induces an isomorphism of Grothendieck groups $K_{TG}^{\mathrm{aff}}\left(X\right) \cong KO_G\left(X\right)$. Complexification produces analogous results involving $T_\mathbb C G$ and $K_G\left(X\right)$., Comment: 26 pages

We describe a bingo-style game intended to be played at economics conferences. Early results from implementation of the game by economists at conferences suggest that fun increases more than a full standard deviation. Further study of the effects of the game are ongoing.

We reviewed bone marrow studies from 351 multiple myeloma (MM) cases, selecting 12 cases (3.4%) with predominantly small lymphocyte–like morphologic features resembling B-cell lymphoma, and correlated their genetic and clinical features. All exhibited a diffuse interstitial pattern of marrow involvement. Small lymphocyte–like plasma cells were all CD45– with bright CD38 and CD138 expression and CD20 expression in 5 cases. No case had an increase in bone marrow B lymphocytes by flow cytometry. Of 12 cases, 9 were classified as the CD-2 molecular class by gene expression profiling (GEP). The 29 CD-2 class cases with (n = 9) and without (n = 20) small lymphocyte–like features could not be discerned from one another using global GEP. Event-free, but not overall, survival was significantly better in cases with small lymphocyte–like features among those sharing the CD-2 subtype. Small lymphocyte–like MM is a rare, morphologically challenging variant distinguished from B-cell lymphoma by lack of CD45 and presence of CD138 and the clinical presentation of MM. Most cases share a common GEP signature dominated by hyperexpression of cyclin D1 or cyclin D3 genes, with increased expression of the B-cell genes CD20 and VPREB3.

Background Touch preparation cytology (TPC) has proven to be a quick and accurate intraoperative diagnostic tool for excisional breast biopsy, margins and sentinel nodes. We hypothesized that TPC of core needle biopsy (CNB) specimens can provide a same-day diagnosis in the outpatient setting. Methods Outpatients presenting with breast lesions underwent TPC of biopsy cores performed by biopsy gun or vacuum-assisted CNB. The TPC results were compared with the final diagnosis of CNB specimens. Results In all, 199 CNB and TP were performed between August 1997 and October 2002. Twenty-nine percent of lesions were malignant. Touch preparation was deferred in 21% of cases. In the remaining 157 evaluable cases, TPC had an accuracy of 89% and a false negative rate of 26%. The sensitivity, specificity, positive predictive value and negative predictive value of TPC were 74%, 97%, 93%, and 86% respectively. Conclusions Touch preparation cytology on CNB can be performed simply in the outpatient setting. Collaboration between the surgeon and pathologist allows TP to be an accurate means of same-day pathological determination.

In cultures, and in tissues as well, Hodgkin's and Reed-Sternberg (H-RS) cells and anaplastic large cell lymphoma (ALCL) cells are known to express a variety of cytokines, including IL-1, -5, -6, -8, -9, TNF-alpha, GM-CSF, M-CSF, TGF-beta, CD70, CD80, and CD86. Various numbers of H-RS/ALCL cells may express cytokine receptors (R), such as CD30, CD40, IL-2R (CD25/CD122), IL-6R (CD126), IL-7R (CD127), TNF-R (CD120), TGF-beta-R (CD 105/endoglin), M-CSF-R (CD115), and SCF-R (CD117/c-kit receptor). All of these cytokines and cytokine receptors are implicated in the growth regulation of H-RS/ALCL cells, the histopathologic alterations in tissues, and the clinical manifestations in patients with Hodgkin's disease (HD) or ALCL. Many of these cytokines or cytokine receptors also play an important role in the pathogenesis of other types of lymphomas. In this review, we describe the cytokine or cytokine-receptor expression that is diacritic for H-RS/ALCL cells. The identification of such unique cytokine-cytokine receptor interactions is likely to explain the biologic property that distinguishes HD/ALCL from other types of lymphomas. These interactions include those of CD30L-CD30, CD40L-CD40, CD70-CD27, CD80/CD86- CD28, SCF-CD117, IL-9-IL-9R, and IL-7-IL-7R. The H-RS/ALCL cells express IL-9 and two cytokine receptors, CD30 and CD117, which are observed infrequently in NHLs. Although IL-7 expression is not restricted to H-RS/ALCL cells, the expression of IL-7 in conjunction with IL-9 and/or CD117 may be regarded as unique for HD/ALCL because of an unusual combination and a synergistic activity among these cytokines. The expression of CD70 and CD80/CD86 (as cytokines) may exert a unique effect in HD because of intimate contact between H-RS cells and CD27/CD28-positive T cells. The expression of these costimulators (CD70 and CD80/CD86) and other adhesion/constimulator molecules such as CD54 and CD58, along with the secretion of soluble cytokines such as IL-1, IL-6, IL-7, or TNFs by H-RS/ALCL cells, could result in the profound T-cell proliferation often seen in lymph nodes involved by HD and some ALCL. On the other hand, the expression of CD30L and CD40L by surrounding T cells may affect the proliferation of H-RS/ALCL cells. The cytokine-cytokine receptor interaction between H-RS cells and T cells via direct cell-cell contact is bidirectional, a situation not commonly seen in NHLs. Copyright 1995 S. Karger AG, Basel

Cytokines play important roles in the pathogenesis of lymphomas. Cytokines either can be produced or exert effects on neoplastic or reactive cells. The secretion of cytokines can provide growth advantages for tumor cells in either an autocrine or a paracrine fashion. An elevated serum or tissue level of cytokines can contribute to the clinical and histopathologic alterations associated with malignant lymphomas. The effects of cytokines on the histopathologic changes are most noticeable in Hodgkin's disease (HD). The malignant (Hodgkin's-Reed-Sternberg) cells in HD have been shown to secrete interleukin-1 (IL-1), IL-5, IL-6, IL-9, tumor necrosis factor-alpha, macrophage colony-stimulating factor, transforming growth factor-beta, and, less frequently, IL-4 and granulocyte colony-stimulating factor. These cytokines may be responsible for the increased cellular reaction and fibrosis observed in tissues involved by HD and for the immunosuppression in patients with HD. In contrast to Hodgkin's-Reed-Sternberg cells, most non-HD lymphoma cells do not produce cytokines in excess amounts. Exceptions include T-cell-rich B-cell lymphoma (IL-4), angioimmunoblastic lymphadenopathy-like T-cell lymphoma with plasmacytosis and hypergammaglobulinemia (IL-6), anaplastic large-cell lymphoma (IL-9), polymorphic immunocytoma (IL-6), and immunoblastic lymphoma (IBL) (IL-6). Some cytokines are involved in the unique cellular reactions in each of these types of lymphoma. For example, IL-4 is responsible for the T-cell reaction in T-cell-rich B-cell lymphoma, while IL-6 is accountable for the plasma cell reaction in angioimmunoblastic lymphadenopathy-type T-cell lymphoma. Others may be directly involved in the tumor cell growth or differentiation. For instance, IL-9 may be important for the autocrine proliferation of anaplastic large cell lymphoma, whereas IL-6 is essential for plasmacytoid differentiation in polymorphic immunocytoma. Further studies of the roles of cytokines in lymphomas may lead to major advances in the understanding of the molecular processes involved in the histopathogenesis of malignant lymphomas. Elucidation of the autocrine or paracrine function of cytokines also may lead to new approaches to a rational intervention in these disease processes.

Myelodysplastic syndrome (MDS) is a well-recognized complication of chemotherapy for multiple myeloma (MM). Serial bone marrow metaphase examinations were performed for MM restaging in 3077 patients undergoing high-dose therapy (HDT). MDS-associated cytogenetic abnormalities (MDS-CAs) were observed in 105 of 2418 patients in whom cytogenetic data were available after HDT. MDS-CAs occurred transiently in 72 patients and on 3 successive occasions (persistent MDS-CAs) in 33 patients, for 10-year estimates of 4% and 2%, respectively; only 21 patients developed overt clinical MDS and 5, acute myeloblastic leukemia (AML). MDS-CA development was linked to lower CD34 yield at collection, longer time interval from MM diagnosis to HDT, older age, and lower platelet recovery after HDT; persistent MDS-CAs were predicted by CD34 yield of less than 3 × 106/kg and need for more than 2 apheresis procedures. Applying a tertile frequency distribution over time to all 105 patients with MDS-CAs, its detection early after HDT was associated with longer time interval from diagnosis and low pre-HDT platelet count (likely resulting from pre-HDT damage), whereas late-onset MDS-CAs were noted among patients treated with Total Therapy 2 and Total Therapy 3 that applied post-HDT consolidation chemotherapy (suggesting possible post-HDT damage). While the risk of MDS-CAs was low and clinical MDS occurred infrequently, monitoring after post-HDT consolidation chemotherapy appears warranted.

Nutritional status is a primary factor in the effects of xenobiotics and may be an important consideration in development of safety standards and assessment of risk. One important xenobiotic consumed daily by millions of people worldwide is alcohol. Some adverse effects of ethanol, such as alcohol liver disease, have been linked to diet. For example, ethanol-induced hepatotoxicity in animal models requires diets that have a high percentage of the total calories as unsaturated fat. However, little attention has been given to the role of carbohydrates (or carbohydrate to fat ratio) in the effects of this important xenobiotic on liver injury. In the present study, adult male Sprague-Dawley rats (8-10/group) were infused (intragastrically) diets high in unsaturated fat (25 or 45% total calories), sufficient protein (16%) and ethanol (38%) in the presence or absence of adequate carbohydrate (21 or 2.5%) for 42-55 days (d). Animals infused ethanol-containing diets adequate in carbohydrate developed steatosis, but had no other signs of hepatic pathology. However, rats infused with the carbohydrate-deficient diet had a 4-fold increase in serum ALT levels (p < 0.05), an unexpectedly high (34-fold) induction of hepatic microsomal CYP2E1 apoprotein (p < 0.001), and focal necrosis. The strong positive association between low dietary carbohydrate, enhanced CYP2E1 induction and hepatic necrosis suggests that in the presence of low carbohydrate intake, ethanol induction of CYP2E1 is enhanced to levels sufficient to cause necrosis, possibly through reactive oxygen species and other free radicals generated by CYP2E1 metabolism of ethanol and unsaturated fatty acids.

The true identity of Hodgkin's mononuclear cells and Reed-Sternberg (H-RS) cells has been a subject of controversy for decades. Those who believe that Hodgkin's disease (HD) is a heterogeneous disease may consider it to constitute lymphomas of various origins. However, this theory seems incompatible with the finding of similar phenotypic, biologic, and immunologic properties among most HD. We believe that, in the majority of cases, HD, except for LP and some LD-type HD, is a homogeneous disease despite differences in the degree of fibrosis and/or cellular reaction. The heterogeneity in cellular reactions is a result of secretion of various cytokines by H-RS cells, which may or may not be influenced by the presence of EBV. H-RS cells, and anaplastic large cell lymphoma (ALCL) cells as well, can express a combination of cytokines and cytokine receptors that is not seen in other types of lymphomas. The unique cytokine/receptor profile (e.g. the expression of c-kit-R/CD117), along with various properties associated with H-RS/ALCL cells, leads to a hypothesis that H-RS/ALCL cells are related to similar lymphohematopoietic progenitor cells with different etiologies and somewhat limited differentiation capacity. A number of H-RS cells may differentiate with limited capacity along the B-cell pathway and may be infected by EBV, which further complicates the biologic and immunologic properties of these cells. The majority of H-RS cells may also, however, differentiate along the antigen-presenting dendritic cell pathway, as indicated by the abundant expression of restin, CD15, CD40, CD54, CD58, CD80, and CD86. The majority of ALCL cells clearly differentiate to T cells, but some may acquire B-cell or histiocyte phenotypes. The progenitor cell hypothesis may explain (1) the variable expression of CD117, CD43, and CD34 as well as the absence of CD27, CD45 and CD45RA in H-RS cells; (2) the inconsistent and irregular patterns of phenotype and genotype and the various, often very limited, degrees of differentiation among these two types of lymphoma cells; (3) the existence of secondary HD or ALCL associated with rare types of lymphomas or leukemias, or vice versa; (4) the absence of recombinase and of the B-specific transcription factors BSAP; and (5) the frequent expression of IL-7 and IL-9 in H-RS cells. Copyright 1996 S. Karger AG, Basel

Castleman’s disease (CD) is a rare, non-clonal lymphoproliferative disorder featuring histologically hyaline-vascular (HV), plasmacytic (PC) or a mixed variant. Clinically, CD presents with localized lymphadenopathy (unicentric CD: UCD) or generalized lymphadenopathy often associated with constitutional symptoms (multicentric CD: MCD). The etiology of CD in HIV negative patients is not known, but elevated serum levels of IL6 are closely linked to the gravity of systemic manifestations of MCD. We present data on the largest CD series thus far reported with various treatment modalities, including anti-IL6 strategies. Between 1989 and 2004, 37 patients were referred to our institution with HIV-negative CD. None of the patients tested had evidence of HHV8 infection by serology or PCR. Eleven patients had UCD. The median age in UCD was 43 years (range 29–62) with a preponderance of non-white patients (ratio 4.5:1). All patients had HV disease except one who had PC variant. One patient did not receive any specific treatment and is lost to follow up. The other 10 patients all underwent complete surgical resection. Three patients were de-bulked prior to surgery with steroids, rituxan ±cytoxan (n=2) or radiotherapy (n=1). None of these patients has evidence of disease with a median follow up of 43 mths (range 12–140 mths). Twenty-six patients had MCD. The median age was 44 years (range: 19–87) with no racial preponderance. All presented with constitutional symptoms including fatigue, anorexia or low grade fever. MCD was equal distributed amongst histological types (HV versus PC/mixed disease) and was frequently associated with peripheral neuropathy (n=5). Bronchiolitis obliterans and pemphigus, amyloidosis and myeloma were each present in 1 respective patient. The OS in MCD was 8.8 yrs with no significant difference between HVD and PC/mixed variants. A group of 12 MCD patients was treated with steroids, chemotherapy and/or anti-CD20 ab had an OS of 42 months (range: 2–111). Four patients died, whilst 4 are alive and disease free at 48, 50, 96 and 111 months. A group of 5 MCD patients was treated with the anti-trypazonomiasis agent suramin, which has anti-IL6 properties, and 4 died. The fifth patient is a long-term survivor (108 mths) after rescue with anti-IL6 based ab therapy. Nine additional MCD patients received anti-IL6 based ab therapy; 2 died. The median OS survival in this group was 74 months (range: 10–168) with 4 patients in CR at 16, 84, 108 and 168 mths. Anti-IL6 based ab therapy was very effective in abrogating debilitating constitutional symptoms. In recent patients, FDG-PET scanning showed that involved lymph nodes visible by CT scan had differential metabolic activity. PET showed response to therapy earlier than on CT or could demonstrate residual activity in normal nodes. We conclude that 1) MCD often has HV type histology, 2) anti-IL6 based ab therapies hold considerable promise in the management of symptomatic MCD, and 3) PET-scanning is helpful in monitoring disease response and activity. Figure Figure

State and national standards call for teaching evolution concepts as early as kindergarten, which provides motivation to continue developing science instruction and curriculum for young learners. The importance of addressing students’ folk theories regarding science justifies teaching evolution early in K-12 education. In this project, we developed, implemented, and researched standards-based lessons to teach elements of evolution (speciation and adaption) to kindergarteners and second graders. Our lessons attended to the students’ prior knowledge, and utilized inquiry and modeling to teach and assess their ability to recognize patterns of similarity and differences among organisms. Using their products and comments as evidence, it was apparent the students were able to communicate recognition of patterns and effectively apply their knowledge in near transfer activities, indicating they achieved our learning objectives. This provides support for teaching evolution concepts in the early grades and evidence of the ability for young children to effectively engage in supported inquiry and modeling for learning science.