On a Conjecture of Foulkes

AbstractSuppose that Ω={1,2,…,ab} for some non-negative integers a and b. Denote by P(a,b) the set of unordered partitions of Ω into a parts of cardinality b. In this paper we study the decomposition of the permutation module CP(a,b) where C is the field of complex numbers. In particular, we show that CP(3,b) is isomorphic to a submodule of CP(b,3) for b≥3. This settles the next unproven case of a conjecture of Foulkes

Immunophenotypic Comparison of Testicular Sclerosing Sertoli Cell Tumors and Sertoli Cell Tumors Not Otherwise Specified

Testicular Sertoli cell tumors (SCTs) are rare, and most fall into the category of SCT–not otherwise specified (SCT-NOS). Only a few additional types of SCT are recognized. Sclerosing SCT (S-SCT), originally described in 1991, comprises a small fraction of SCTs and was considered a specific entity until the 2016 revision of the World Health Organization classification of non–germ cell tumors, where it was classified as a morphologic variant of SCT-NOS. In a recent study, differences in expression of PAX2/PAX8, inhibin, androgen receptor, and S100 protein between SCT-NOS and S-SCT were noted in a small number of cases. In this interinstitutional study, we compared the expression of these markers and β-catenin in 11 cases each of SCT-NOS and S-SCT to determine if differences exist that could justify keeping a separate classification of these neoplasms. PAX2/PAX8 cocktail was the only marker that was significantly overexpressed in S-SCT. Expression of androgen receptors was strong in S-SCT and variable in SCT-NOS but did not reach statistical significance. Expression of β-catenin was common in both, whereas inhibin was infrequent. The available material was insufficient for a conclusive evaluation of S100 protein expression. Overall, our results support the inclusion of S-SCT as a morphologic variant of SCT-NOS. Expression of PAX2/PAX8 in S-SCT may reflect an overactive epithelial-to-mesenchymal transition as has been shown in experimental models of acute and chronic seminiferous tubular injury and might be related to the process generating the stroma in these tumors

Prostatic stromal tumor with fatal outcome in a young man: histopathological and immunohistochemical case presentation

Stromal tumors of the prostate are rare and only a few cases have been described in the literature, including exceptional cases of stromal tumors with unknown malignant potential (STUMP) and a fatal outcome in young patients. Morphologically distinguishing a STUMP from a stromal sarcoma of the prostate (PSS) is still a challenge. We describe the histopathological and immunohistochemical findings in a 34-year-old man with a malignant specialized cell stromal tumor of the prostate that was diagnosed initially as STUMP, and he developed lung metastases within a few months. The patient attended our hospital because of lower urinary tract symptoms, after having excreted tissue through the urethra a few months before. Ultrasonography and urethrocystoscopy examinations showed a mass arising from the verumontanum, and a transurethral resection (TUR) revealed a highgrade spindle cell sarcoma reminiscent of a phyllode tumor of the breast. The tumor cells were immunoreactive for vimentin, progesterone receptor and, focally, CD34. The preliminary histological findings were subsequently confirmed after radical prostatectomy. The patient developed bilateral lung metastases and died 25 months after the initial diagnosis. Although rare in young patients, the challenging differential diagnosis of STUMP and PSS means that a prostate STUMP diagnosis made on the basis of biopsy or TUR specimens also requires urethrocystoscopic monitoring for the early detection of any progression to PSS. Radical prostatectomy should also be carefully considered

Analytic geometry of semisimple coalescent Frobenius structures

We present some results of a joint paper with Dubrovin (see references), as exposed at the Workshop "Asymptotic and Computational Aspects of Complex Differential Equations" at the CRM in Pisa, in February 2017. The analytical description of semisimple Frobenius manifolds is extended at semisimple coalescence points, namely points with some coalescing canonical coordinates although the corresponding Frobenius algebra is semisimple. After summarizing and revisiting the theory of the monodromy local invariants of semisimple Frobenius manifolds, as introduced by Dubrovin, it is shown how the definition of monodromy data can be extended also at semisimple coalescence points. Furthermore, a local Isomonodromy theorem at semisimple coalescence points is presented. Some examples of computation are taken from the quantum cohomologies of complex Grassmannians

Section Extension from Hyperbolic Geometry of Punctured Disk and Holomorphic Family of Flat Bundles

The construction of sections of bundles with prescribed jet values plays a fundamental role in problems of algebraic and complex geometry. When the jet values are prescribed on a positive dimensional subvariety, it is handled by theorems of Ohsawa-Takegoshi type which give extension of line bundle valued square-integrable top-degree holomorphic forms from the fiber at the origin of a family of complex manifolds over the open unit 1-disk when the curvature of the metric of line bundle is semipositive. We prove here an extension result when the curvature of the line bundle is only semipositive on each fiber with negativity on the total space assumed bounded from below and the connection of the metric locally bounded, if a square-integrable extension is known to be possible over a double point at the origin. It is a Hensel-lemma-type result analogous to Artin's application of the generalized implicit function theorem to the theory of obstruction in deformation theory. The motivation is the need in the abundance conjecture to construct pluricanonical sections from flatly twisted pluricanonical sections. We also give here a new approach to the original theorem of Ohsawa-Takegoshi by using the hyperbolic geometry of the punctured open unit 1-disk to reduce the original theorem of Ohsawa-Takegoshi to a simple application of the standard method of constructing holomorphic functions by solving the d-bar equation with cut-off functions and additional blowup weight functions

Ovarian germ cell tumors with rhabdomyosarcomatous components and later development of growing teratoma syndrome: a case report

<p>Abstract</p> <p>Introduction</p> <p>Development of a sarcomatous component in a germ cell tumor is an uncommon phenomenon. Most cases reported have a grim prognosis. Growing teratoma syndrome is also an uncommon phenomenon and occurs in approximately 2% to 7% of non seminomatous germ cell tumors and should be treated surgically.</p> <p>Case presentation</p> <p>We report the case of a 12-year-old Asian girl with an ovarian mixed germ cell tumor containing a rhabdomyosarcomatous component. She was treated with a germ cell tumor chemotherapy regimen and rhabdomyosarcoma-specific chemotherapy. Towards the end of her treatment, she developed a retroperitoneal mass that was increasing in size. It was completely resected, revealing a mature teratoma, consistent with growing teratoma syndrome. She is still in complete remission approximately three years after presentation.</p> <p>Conclusion</p> <p>The presence of rhabdomyosarcoma in a germ cell tumor should be treated by a combined chemotherapy regimen (for germ cell tumor and rhabdomyosarcoma). In addition, development of a mass during or after therapy with normal serum markers should raise the possibility of growing teratoma syndrome that should be treated surgically.</p

On the Black-Hole/Qubit Correspondence

The entanglement classification of four qubits is related to the extremal black holes of the 4-dimensional STU model via a time-like reduction to three dimensions. This correspondence is generalised to the entanglement classification of a very special four-way entanglement of eight qubits and the black holes of the maximally supersymmetric N = 8 and exceptional magic N = 2 supergravity theories.Comment: 32 pages, very minor changes at the start of Sec. 4.1. Version to appear in The European Physical Journal - Plu

Hidden chromosomal abnormalities in pleuropulmonary blastomas identified by multiplex FISH

BACKGROUND: Pleuropulmonary blastoma (PPB) is a rare childhood dysontogenetic intrathoracic neoplasm associated with an unfavourable clinical behaviour. CASES PRESENTATION: We report pathological and cytogenetic findings in two cases of PPB at initial diagnosis and recurrence. Both tumors were classified as type III pneumoblastoma and histological findings were similar at diagnosis and relapse. In both cases, conventional cytogenetic techniques revealed complex numerical and structural chromosomal abnormalities. Molecular cytogenetic analysis (interphase/metaphase FISH and multicolor FISH) identified accurately chromosomal aberrations. In one case, TP53 gene deletion was detected on metaphase FISH. To date, only few cytogenetic data have been published about PPB. CONCLUSION: The PPB genetic profile remains to be established and compared to others embryonal neoplasia. Our cytogenetic data are discussed reviewing cytogenetics PPBs published cases, illustrating the contribution of multicolor FISH in order to identify pathogenetically important recurrent aberrations in PPB

Phase 1b randomized, double-blind study of namilumab, an anti-granulocyte macrophage colony-stimulating factor monoclonal antibody, in mild-to-moderate rheumatoid arthritis

Change from baseline in swollen (a) and tender (b) joint counts. *Error bars show upper SE for placebo and lower SE for namilumab. SE standard error, SJC swollen joint count, TJC tender joint count. (PDF 1292 kb