Heat flow and calculus on metric measure spaces with Ricci curvature bounded below - the compact case

We provide a quick overview of various calculus tools and of the main results concerning the heat flow on compact metric measure spaces, with applications to spaces with lower Ricci curvature bounds. Topics include the Hopf-Lax semigroup and the Hamilton-Jacobi equation in metric spaces, a new approach to differentiation and to the theory of Sobolev spaces over metric measure spaces, the equivalence of the L^2-gradient flow of a suitably defined "Dirichlet energy" and the Wasserstein gradient flow of the relative entropy functional, a metric version of Brenier's Theorem, and a new (stronger) definition of Ricci curvature bound from below for metric measure spaces. This new notion is stable w.r.t. measured Gromov-Hausdorff convergence and it is strictly connected with the linearity of the heat flow.Comment: To the memory of Enrico Magenes, whose exemplar life, research and teaching shaped generations of mathematician

Fibroblastic polyp of the colon: clinicopathological analysis of 10 cases with emphasis on its common association with serrated crypts

: To describe the clinical and pathological features of 10 further cases of fibroblastic polyps (FP), a recently described, distinctive type of colorectal mucosal polyp. Methods and results : The patients were seven women and three men with ages ranging from 44 to 63 years. The lesions ranged in size from 2 to 4 mm. Eight of the polyps were located in the sigmoid colon. Five cases were associated with hyperplastic polyps. Histologically, FP displayed bland, plump spindle cells with oval nuclei arranged as bundles parallel to the surface or as haphazardly orientated sheets with a focal periglandular or perivascular concentric arrangement. Eight polyps represented mixed fibroblastic/hyperplastic polyps as they contained serrated (hyperplastic) crypts. Immunohistochemically, all cases were positive for vimentin and negative for desmin, smooth-muscle actin, h-caldesmon, S100 protein, c-Kit, epithelial membrane antigen, cytokeratin AE1/3, CD34, CD68, COX-2, and factor XIIIa. Ultrastructural examination supported the fibroblastic nature of the tumour cells. Conclusions : FP is a distinctive type of benign mucosal colorectal polyp characterized by its distal location, small size, frequent association with hyperplastic polyps, distinct morphological appearance and typical immunonegativity for markers of specific differentiation. FP with serrated crypts (mixed fibroblastic/hyperplastic polyp) represents a frequent variant of this lesion. Pathologists should recognize FP and discriminate it from other types of colorectal polyps.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/72181/1/j.1365-2559.2006.02357.x.pd

Eccrine porocarcinoma of the head: An important differential diagnosis in the elderly patient

Background: Eccrine porocarcinoma is a rare malignant tumor of the sweat gland, characterized by a broad spectrum of clinicopathologic presentations. Surprisingly, unlike its benign counterpart eccrine poroma, eccrine porocarcinoma is seldom found in areas with a high density of eccrine sweat glands, like the palms or soles. Instead, eccrine porocarcinoma frequently occurs on the lower extremities, trunk and abdomen, but also on the head, resembling various other skin tumors, as illustrated in the patients described herein. Observations: We report 5 cases of eccrine porocarcinoma of the head. All patients were initially diagnosed as having epidermal or melanocytic skin tumors. Only after histopathologic examination were they classified as eccrine porocarcinoma, showing features of epithelial tumors with abortive ductal differentiation. Characteristic clinical, histopathologic and immunohistochemical findings of eccrine porocarcinomas are illustrated. Conclusion: Eccrine porocarcinomas are potentially fatal adnexal malignancies, in which extensive metastatic dissemination may occur. Porocarcinomas are commonly overlooked, or misinterpreted as squamous or basal cell carcinomas as well as other common malignant and even benign skin tumors. Knowledge of the clinical pattern and histologic findings, therefore, is crucial for an early therapeutic intervention, which can reduce the risk of tumor recurrence and serious complications. Copyright (c) 2008 S. Karger AG, Basel

Static condensation optimal port/interface reduction and error estimation for structural health monitoring

Having the application in structural health monitoring in mind, we propose reduced port spaces that exhibit an exponential convergence for static condensation procedures on structures with changing geometries for instance induced by newly detected defects. Those reduced port spaces generalize the port spaces introduced in [K. Smetana and A.T. Patera, SIAM J. Sci. Comput., 2016] to geometry changes and are optimal in the sense that they minimize the approximation error among all port spaces of the same dimension. Moreover, we show numerically that we can reuse port spaces that are constructed on a certain geometry also for the static condensation approximation on a significantly different geometry, making the optimal port spaces well suited for use in structural health monitoring

Environmental toxicity, redox signaling and lung inflammation:the role of glutathione

Glutathione (γ-glutamyl-cysteinyl-glycine, GSH) is the most abundant intracellular antioxidant thiol and is central to redox defense during oxidative stress. GSH metabolism is tightly regulated and has been implicated in redox signaling and also in protection against environmental oxidant-mediated injury. Changes in the ratio of the reduced and disulfide form (GSH/GSSG) can affect signaling pathways that participate in a broad array of physiological responses from cell proliferation, autophagy and apoptosis to gene expression that involve H(2)O(2) as a second messenger. Oxidative stress due to oxidant/antioxidant imbalance and also due to environmental oxidants is an important component during inflammation and respiratory diseases such as chronic obstructive pulmonary disease, idiopathic pulmonary fibrosis, acute respiratory distress syndrome, and asthma. It is known to activate multiple stress kinase pathways and redox sensitive transcription factors such as Nrf2, NF-κB and AP-1, which differentially regulate the genes for pro-inflammatory cytokines as well as the protective antioxidant genes. Understanding the regulatory mechanisms for the induction of antioxidants, such as GSH, versus pro-inflammatory mediators at sites of oxidant-directed injuries may allow for the development of novel therapies which will allow pharmacological manipulation GSH synthesis during inflammation and oxidative injury. This article features the current knowledge about the role of GSH in redox signaling, GSH biosynthesis and particularly the regulation of transcription factor Nrf2 by GSH and downstream signaling during oxidative stress and inflammation in various pulmonary diseases. We also discussed the current therapeutic clinical trials using GSH and other thiol compounds, such as N-acetyl-L-cysteine, fudosteine, carbocysteine, erdosteine in environment-induced airways disease

Treatment of eccrine porocarcinoma with metastasis to the parotid gland using intensity-modulated radiation therapy: a case report

<p>Abstract</p> <p>Introduction</p> <p>Cutaneous eccrine porocarcinomas are uncommon malignant tumors of the sweat gland.</p> <p>Case Presentation</p> <p>A 76-year-old Caucasian man presented to our hospital with a left temporal mass. We describe a case of eccrine porocarcinoma with metastasis to the parotid gland with special emphasis on the role of surgical resection and adjuvant radiation therapy.</p> <p>Conclusion</p> <p>Besides surgical resection, little is known about the role of adjuvant therapy in managing eccrine porocarcinomas. Radiation therapy should be considered within a multidisciplinary approach in patients with primary or recurrent eccrine porocarcinomas.</p

Metastatic eccrine porocarcinoma: report of a case and review of the literature

Eccrine porocarcinoma (EPC) is a rare type of skin cancer arising from the intraepidermal portion of eccrine sweat glands or acrosyringium, representing 0.005-0.01% of all cutaneous tumors. About 20% of EPC will recur and about 20% will metastasize to regional lymph nodes. There is a mortality rate of 67% in patients with lymph node metastases. Although rare, the occurrence of distant metastases has been reported

Combined parameter and model reduction of cardiovascular problems by means of active subspaces and POD-Galerkin methods

In this chapter we introduce a combined parameter and model reduction methodology and present its application to the efficient numerical estimation of a pressure drop in a set of deformed carotids. The aim is to simulate a wide range of possible occlusions after the bifurcation of the carotid. A parametric description of the admissible deformations, based on radial basis functions interpolation, is introduced. Since the parameter space may be very large, the first step in the combined reduction technique is to look for active subspaces in order to reduce the parameter space dimension. Then, we rely on model order reduction methods over the lower dimensional parameter subspace, based on a POD-Galerkin approach, to further reduce the required computational effort and enhance computational efficiency

Induction of Cytoplasmic Rods and Rings Structures by Inhibition of the CTP and GTP Synthetic Pathway in Mammalian Cells

Background: Cytoplasmic filamentous rods and rings (RR) structures were identified using human autoantibodies as probes. In the present study, the formation of these conserved structures in mammalian cells and functions linked to these structures were examined. Methodology/Principal Findings: Distinct cytoplasmic rods (,3–10 mm in length) and rings (,2–5 mm in diameter) in HEp-2 cells were initially observed in immunofluorescence using human autoantibodies. Co-localization studies revealed that, although RR had filament-like features, they were not enriched in actin, tubulin, or vimentin, and not associated with centrosomes or other known cytoplasmic structures. Further independent studies revealed that two key enzymes in the nucleotide synthetic pathway cytidine triphosphate synthase 1 (CTPS1) and inosine monophosphate dehydrogenase 2 (IMPDH2) were highly enriched in RR. CTPS1 enzyme inhibitors 6-diazo-5-oxo-L-norleucine and Acivicin as well as the IMPDH2 inhibitor Ribavirin exhibited dose-dependent induction of RR in.95 % of cells in all cancer cell lines tested as well as mouse primary cells. RR formation by lower concentration of Ribavirin was enhanced in IMPDH2-knockdown HeLa cells whereas it was inhibited in GFP-IMPDH2 overexpressed HeLa cells. Interestingly, RR were detected readily in untreated mouse embryonic stem cells (.95%); upon retinoic acid differentiation, RR disassembled in these cells but reformed when treated with Acivicin

Mast cell leukemia associated with undefined morphology and chronic basophilic leukemia

BACKGROUND: Mast cell leukemia (MCL) is rare type of neoplasia with an incidence of 1% in a large series of 342 adult patients with systemic mastocytosis (SM). Chronic basophilic leukemia (CBL) is an extremely rare type of leukemia with appearance of 7 cases in the literature. CASE PRESENTATION: A 73 year-old female patient who presented with weaknes, had a prolonged duration of hematologic remission after treatment of her CBL by hydroxyurea (HU). Evolution of SM occurring as a second neoplasia concurrently with relapse of de novo CBL was demonstrated by mast cells (MCs) infiltration in the bone marrow (BM) biopsy and smear and increase in tryptase level. Transformation to MCL with simultaneous occurrance of accelerated phase of CBL were documented by the appearance of MCs in both BM and peripheral blood (PB) smears, antigen expressions detected by flow cytometry and spesific stains. Sequence analysis of c-kit gene revealed c-kit exon 11 K550N mutation. Undefined associations of MCL with different mast cell morphology, increase in IL-6 level and accelerated phase of de novo CBL was described. CONCLUSION: Elevations in CRP and IL-6 levels occurring with increases in basophil counts to high levels revealed that febrile episodes with abdominal pain seen in our patient were induced by increase in IL-6 levels released from neoplastic basophils. Neoplastic basophils with diffuse and coarse basophilic granules possibly mimic neutrophils with toxic granules and cause wrong characterization of neoplastic basophils as neutrophils by the automated blood cell counters and misleaded physicians