Polyhedral Cells Research Articles

Retracts of Products of Chordal Graphs

In this article, we characterize the graphs G that are the retracts of Cartesian products of chordal graphs. We show that they are exactly the weakly modular graphs that do not contain K2, 3, the 4-wheel minus one spoke , and the k-wheels (for as induced subgraphs. We also show that these graphs G are exactly the cage-amalgamation graphs as introduced by Brešar and Tepeh Horvat (Cage-amalgamation graphs, a common generalization of chordal and median graphs, Eur J Combin 30 (2009), 1071–1081); this solves the open question raised by these authors. Finally, we prove that replacing all products of cliques of G by products of Euclidean simplices, we obtain a polyhedral cell complex which, endowed with an intrinsic Euclidean metric, is a CAT(0) space. This generalizes similar results about median graphs as retracts of hypercubes (products of edges) and median graphs as 1-skeletons of CAT(0) cubical complexes. © 2012 Wiley Periodicals, Inc. J. Graph Theory 73: 161–180, 2013

A case of oncocytic carcinoma arising from the submandibular gland with bilateral multiple cervical lymph node metastases

This article discusses a case of bilateral multiple cervical lymph node metastases of oncocytic carcinoma—an extremely rare neoplasm of the salivary glands—that was found in a 71-year-old Japanese female patient who presented with a painless swelling in the bilateral submandibular regions.Computed tomography demonstrated enlarged bilateral multiple lymph nodes. Multiple metastases to bilateral cervical lymph nodes were clinically suspected, and bilateral neck dissections were performed. The tumor tissue adjoined the submandibular gland with a thin fibrous connective tissue capsule. Histologically, the tumor was predominantly composed of large, round to polyhedral cells with fine granular eosinophilic cytoplasm, which were arranged in solid sheets, islands and cords.Ultrastructural analysis revealed numerous mitochondria with abnormal shapes packed in the cytoplasm of the neoplastic cells. The tumor was diagnosed as oncocytic carcinoma of the submandibular gland with bilateral multiple cervical lymph node metastases. The tumor developed neither recurrence nor distant metastasis for eight years after the operation.

Optimally dense packings for fully asymptotic Coxeter tilings by horoballs of different types

The goal of this paper to determine the optimal horoball packing arrangements and their densities for all four fully asymptotic Coxeter tilings (Coxeter honeycombs) in hyperbolic 3-space $\mathbb{H}^3$. Centers of horoballs are required to lie at vertices of the regular polyhedral cells constituting the tiling. We allow horoballs of different types at the various vertices. Our results are derived through a generalization of the projective methodology for hyperbolic spaces. The main result states that the known B\"or\"oczky--Florian density upper bound for "congruent horoball" packings of $\mathbb{H}^3$ remains valid for the class of fully asymptotic Coxeter tilings, even if packing conditions are relaxed by allowing for horoballs of different types under prescribed symmetry groups. The consequences of this remarkable result are discussed for various Coxeter tilings.

Podoplanin expression profiles characteristic of odontogenic tumor-specific tissue architectures

Podoplanin, a representative immunohistochemical marker for lymphatic endothelial cells, is also expressed in many other kinds of cancer cells, although its pathophysiological function is largely unknown. Our aim was to determine immunolocalization modes of podoplanin among odontogenic tumors to discuss possible roles of podoplanin in their characteristic tissue architecture formation. Immunohistochemical profiles of podoplanin were investigated in 40 surgical specimens from ameloblastoma (AM), adenomatoid odontogenic tumor (AOT), calcifying cystic odontogenic tumor (CCOT), and keratocystic odontogenic tumor (KCOT) in comparison with those of proliferating cell nuclear antigen (PCNA), integrin β1, fibronectin, and matrix metalloproteinase 9 (MMP-9). Podoplanin was localized in the basal cell layer or in the peripheral zone of AM foci. It was found in spindle-shaped tumor cells of AOT, in both the basal and polyhedral cells of CCOT, and in the basal and parabasal cells of KCOT linings. Podoplanin-positive (+) cells were located within areas of PCNA+ cells, and integrin β1 was localized in the cell membrane of podoplanin+ cells in the intercellular space where fibronectin and MMP-9 were deposited. In conclusion, podoplanin+ cells and areas in odontogenic tumors are in close associations with extracellular matrix signalings as well as cell proliferation.

Concurrent cystic endometrial hyperplasia, ovarian luteoma and biliary cyst adenoma in an aged rabbit (Oryctolagus cuniculus): case report and literature review

A 6-year-old female nulliparous Dutch Rabbit (Oryctolagus cuniculus) was presented in shock status with a history of abdominal distention, inappetance, lethargy, polydipsia, diarrhea and weight loss since 2 weeks ago. There was no breeding history. Radiographic survey showed increased soft tissue opacity dorsal to the urinary bladder and ventral to the colon on the lateral view consistent with uteromegaly and severe intestinal distention resembling intussusceptions. Conservative treatment was failed and the animal died. In necropsy, ileocecal intussusception was noted as the main death factor. Thickened uterine endometrium in both horns was observed and the uterus was filled with mucoid fluid. Both ovaries were multilobulated and distended. On the other hand, a small cyst sized 1.5 × 2.5 cm was diagnosed on the liver surface. Several samples were obtained from lesions for histopathological evaluation. Histopathologically, dilated cystic glands of variable size lined by densely packed epithelium and hyperplasia of the endometrium resulting in irregular folds or papillar projection into the lumen were evident and the sections of ovaries revealed ovarian luteoma that composed of polyhedral cells with pale stained vacuolated cytoplasm, centrally located nuclei with distinct cytoplasmic borders and the cytoplasm of cells contain lipid droplet. The occurrence of biliary cyst adenoma was confirmed by microscopic examination of the mass that composed of multicystic space in different sizes lined by flattened to cuboidal biliary epithelium with papillary projections. These cysts were seperated by variable amount of connective tissue. The lack of postmortem investigations in aged rabbits reduced the incidence of neoplastic disease diagnosis in this species. Whereas uterine adenecarcinoma and lymphosarcoma were commonly reported in rabbits, luteoma and biliary cyst adenoma that are well described in this case report were uncommon in rabbit medicine.

Lattice Discrete Particle Model for Fiber-Reinforced Concrete. I: Theory

The lattice discrete particle model (LDPM) is a mesoscale model for heterogeneous materials. Developed for concrete, it simulates material mesostructure by modeling coarse aggregate particles and their surrounding mortar as polyhedral cells. A tetrahedralization of the particle centers generates a lattice framework where each lattice member is associated with a triangular-shaped plane of contact (facet) between two cells. Compatibility equations are formulated by describing the deformation of an assemblage of particles through rigid-body kinematics. Equilibrium equations are obtained through the force and moment equilibrium of each cell. The material behavior is assumed to be governed by a vectorial constitutive law imposed at the facets. A natural extension for this discrete model is to include the effect of dispersed fibers as discrete entities within the mesostructure. The LDPM incorporates this effect by modeling individual fibers randomly placed within the framework according to a given fiber volume fraction. The number and orientation of the fibers crossing each facet is computed and the contribution of each fiber to the facet response is formulated on the basis of a previously established micromechanical model for fiber-matrix interaction. The theory for the developed model, entitled the LDPM-F, is discussed herein. A subsequent companion paper will address model calibration and validation through the numerical simulation of experimental test results.

Morphological study of the infraorbital gland of the male barking deer, muntiacus muntjak

The morphology of the infraorbital gland of the barking deer (Muntiacus muntjak) was examined using lectin histochemistry, immunohistochemistry and scanning electron microscopy. The glands consisted of sebaceous and apocrine glands, with proportion of apocrine glands was larger than the sebaceous gland. Sebaceous glands consisted of many lobules with polyhedral cells. The apocrine glands were lined by cuboidal to columnar cells with typical apical protrusions. Seven lectins applied showed various binding intensities in the sebaceous and apocrine glands. Peanut agglutinin (PNA) and soybean agglutinin (SBA) were strongly positive in the sebaceous gland, while the others lectins showed various positive reactions from weak to strong intensities in the membrane and cytoplasm areas. In the apocrine gland portion, positive reaction with various intensities was observed for all the seven lectins. In the myoepithelial cells of the apocrine glands, positive reactions were found in moderate intensity only for SBA and dolichos biflorus agglutinin (DBA). Immunoreactivity for a-smooth muscle actin was observed in the myoepithelial cells in the basal membrane of the apocrine gland. These findings suggest that the secretion of the infraorbital gland of the barking deer contains lipid from the sebaceous gland and glycoconjugates secreted by both the sebaceous and apocrine glands. Key words: Barking deer, infraorbital gland, lectin histochemistry

Cytologic findings of a clear cell parathyroid lesion

On fine-needle aspiration (FNA) biopsy, clear cell parathyroid lesions can be misdiagnosed as thyroid neoplasms, salivary gland neoplasms, paraganglioma, or even metastatic renal cell carcinoma. We report the clinicopathological, cytologic, and histologic findings of a clear cell parathyroid tumor in a 64-year-old HIV-positive patient. A computed tomography (CT) scan with contrast showed a heterogeneous and enhancing mass at the inferolateral aspect of the left thyroid lobe. FNA showed a cellular smear with many single and loosely clustered tumor cells with finely granular and vacuolated light-purple cytoplasm and central nuclei. Occasional microfollicular structures were noted. No colloid was seen. This FNA was misdiagnosed as a follicular neoplasm of the thyroid. Sections of the excised mass showed large polyhedral cells with well-defined cell membranes and clear cytoplasm with a small amount of eosinophilic granular material. These clear cells were positive for pancytokeratin and PTH immunohistochemical stains. These results favored a diagnosis of parathyroid Water Clear Cell Adenoma. This brief report highlights the cytologic findings of clear cell parathyroid lesions and their potential diagnostic pitfalls.

Topological relationships in spatial tessellations

Tessellations of R3 that use convex polyhedral cells to fill the space can be extremely complicated. This is especially so for tessellations which are not ‘facet-to-facet’, that is, for those where the facets of a cell do not necessarily coincide with the facets of that cell's neighbours. Adjacency concepts between neighbouring cells (or between neighbouring cell elements) are not easily formulated when facets do not coincide. In this paper we make the first systematic study of these topological relationships when a tessellation of R3 is not facet-to-facet. The results derived can also be applied to the simpler facet-to-facet case. Our study deals with both random tessellations and deterministic ‘tilings’. Some new theory for planar tessellations is also given.

Cerebral Neuroblastoma and Pituitary Adenocarcinoma in Two Budgerigars (Melopsittacus undulatus)

Case 1: A tumor mass involving the rostral part of left cerebrum was found in a two-year-old female budgerigar (Melopsittacus undulatus) at necropsy. Histologically, the neoplastic cells were arranged in sheets or cords and occasionally showed nest growth patterns. These uniform tumor cells had a little cytoplasm and ovoid or round basophilic nuclei with clearly distinct cytoplasmic membranes. The tumor cells were strong diffusely immunostained with both neuron-specific enolase (NSE) and neurofilament protein and partially for synaptophysin. They lacked chromogranin A, glial fibrillary acidic protein (GFAP), vimentin, S-100, and cytokeratin antigen expression. Moreover, they had no reaction to antibodies against pituitary hormones, such as adrenocorticotrophic hormone (ACTH), growth hormone, and prolactin. The histological and immunohistochemical examination determined the tumor as neuroblastoma. Case 2: An extremely enlarged pituitary mass was found above the sella turcica of a male budgerigar. It was soft and well delineated from the adjacent structures. On histological examination, this tumor consisted of a sheet of large closely packed polyhedral cells that had scant to a large amount of pale to strongly eosinophilic cytoplasm. The pleomorphic nuclei were apparently variable in shape, from small round hyperchromatic to very large vesicular forms. The cell boundaries were not clearly distinct. The multifocal immunolabelling of neoplastic cells for NSE, synaptophysin, GFAP, and ACTH appeared, whereas a few cells reacted with vimentin and S-100 and stained negative for other markers, which were also utilized for case 1. Histological and immunohistochemical findings led to identification of corticotroph adenocarcinoma in the pituitary gland.

Topological relationships in spatial tessellations

Tessellations of R 3 that use convex polyhedral cells to fill the space can be extremely complicated. This is especially so for tessellations which are not ‘facet-to-facet’, that is, for those where the facets of a cell do not necessarily coincide with the facets of that cell's neighbours. Adjacency concepts between neighbouring cells (or between neighbouring cell elements) are not easily formulated when facets do not coincide. In this paper we make the first systematic study of these topological relationships when a tessellation of R 3 is not facet-to-facet. The results derived can also be applied to the simpler facet-to-facet case. Our study deals with both random tessellations and deterministic ‘tilings’. Some new theory for planar tessellations is also given.

Numerical simulations of highly nonlinear steady and unsteady free surface flows

A numerical simulation model based on an open source Computational Fluid Dynamics (CFD) package-Open Field Operation and Manipulation (OpenFOAM) has been developed to study highly nonlinear steady and unsteady free surface flows. A two-fluid formulation is used in this model and the free surface is captured using the classical Volume Of Fluid (VOF) method. The incompressible Euler/Navier-Stokes equations are solved using a finite volume method on unstructured polyhedral cells. Both steady and unsteady free surface flows are simulated, which include: (1) a submerged NACA0012 2-D hydrofoil moving at a constant speed, (2) the Wigley hull moving at a constant speed, (3) numerical wave tank, (4) green water overtopping a fixed 2-D deck, (5) green water impact on a fixed 3-D body without or with a vertical wall on the deck. The numerical results obtained have been compared with the experimental measurements and other CFD results, and the agreements are satisfactory. The present numerical model can thus be used to simulate highly nonlinear steady and unsteady free surface flows.

Large eddy simulations of jet flow interaction within staggered rod bundles

This work is a numerical investigation of experimental work on dual isothermal jet injection into a staggered rod bundle, mimicking phenomena present in the lower plenum of the very high temperature gas cooled reactor. Large eddy simulations were used to model the unsteady flow of the experimental conditions. As a basis, steady state simulations as well as time averaged comparisons were made with the standard and realizable k–ɛ formulations. Grid sensitivity studies were performed over six grids with the most refined grid comprised of roughly 26.5 million semi-structured polyhedral cells. The continuous wavelet transform was used for instantaneous signal decomposition of results taken within the domain in an effort to devise a better approach to validating CFD predictions of the complex flows in the lower plenum of the VHTR.

Computing Abstractions of Nonlinear Systems

Sufficiently accurate finite state models, also called symbolic models or discrete abstractions, allow one to apply fully automated methods, originally developed for purely discrete systems, to formally reason about continuous and hybrid systems, and to design finite state controllers that provably enforce predefined specifications. We present a novel algorithm to compute such finite state models for nonlinear discrete-time and sampled systems which depends on quantizing the state space using polyhedral cells, embedding these cells into suitable supersets whose attainable sets are convex, and over-approximating attainable sets by intersections of supporting half-spaces. We prove a novel recursive description of these half-spaces and propose an iterative procedure to compute them efficiently. We also provide new sufficient conditions for the convexity of attainable sets which imply the existence of the aforementioned embeddings of quantizer cells. Our method yields highly accurate abstractions and applies to nonlinear systems under mild assumptions, which reduce to sufficient smoothness in the case of sampled systems. Its practicability in the design of discrete controllers for nonlinear continuous plants under state and control constraints is demonstrated by an example.

Human hepatocytes and endothelial cells in organotypic membrane systems

The realization of organotypic liver model that exhibits stable phenotype is a major challenge in the field of liver tissue engineering. In this study we developed liver organotypic co-culture systems by using synthetic and biodegradable membranes with primary human hepatocytes and human umbilical vein endothelial cells (HUVEC). Synthetic membranes prepared by a polymeric blend constituted of modified polyetheretherketone (PEEK-WC) and polyurethane (PU) and biodegradable chitosan membranes were developed by phase inversion technique and used in homotypic and organotypic culture systems. The morphological and functional characteristics of cells in the organotypic co-culture membrane systems were evaluated in comparison with homotypic cultures and traditional systems. Hepatocytes in the organotypic co-culture systems exhibit compact polyhedral cells with round nuclei and well demarcated cell–cell borders like in vivo, as a result of heterotypic interaction with HUVECs. In addition HUVECs formed tube-like structures directly through the interactions with the membranes and hepatocytes and indirectly through the secretion of ECM proteins which secretion improved in the organotypic co-culture membrane systems. The heterotypic cell–cell contacts have beneficial effect on the hepatocyte albumin production, urea synthesis and drug biotransformation. The developed organotypic co-culture membrane systems elicit liver specific functions in vitro and could be applied for the realization of engineered liver tissues to be used in tissue engineering, drug metabolism studies and bioartificial liver devices.

Open-source MATLAB implementation of consistent discretisations on complex grids

Accurate geological modelling of features such as faults, fractures or erosion requires grids that are flexible with respect to geometry. Such grids generally contain polyhedral cells and complex grid-cell connectivities. The grid representation for polyhedral grids in turn affects the efficient implementation of numerical methods for subsurface flow simulations. It is well known that conventional two-point flux-approximation methods are only consistent for K-orthogonal grids and will, therefore, not converge in the general case. In recent years, there has been significant research into consistent and convergent methods, including mixed, multipoint and mimetic discretisation methods. Likewise, the so-called multiscale methods based upon hierarchically coarsened grids have received a lot of attention. The paper does not propose novel mathematical methods but instead presents an open-source Matlab® toolkit that can be used as an efficient test platform for (new) discretisation and solution methods in reservoir simulation. The aim of the toolkit is to support reproducible research and simplify the development, verification and validation and testing and comparison of new discretisation and solution methods on general unstructured grids, including in particular corner point and 2.5D PEBI grids. The toolkit consists of a set of data structures and routines for creating, manipulating and visualising petrophysical data, fluid models and (unstructured) grids, including support for industry standard input formats, as well as routines for computing single and multiphase (incompressible) flow. We review key features of the toolkit and discuss a generic mimetic formulation that includes many known discretisation methods, including both the standard two-point method as well as consistent and convergent multipoint and mimetic methods. Apart from the core routines and data structures, the toolkit contains add-on modules that implement more advanced solvers and functionality. Herein, we show examples of multiscale methods and adjoint methods for use in optimisation of rates and placement of wells.

Implementation of an iterative solution procedure for multi-fluid gas–particle flow models on unstructured grids

An iterative procedure for the solution of multi-fluid equations for gas–particle flows, with kinetic theory closures and frictional stress models for the description of the particle phase is presented and was implemented in the fully unstructured open source code OpenFOAM ®, capable of using arbitrarily-shaped polyhedral cells. Improved interpolation practices have been adopted to ensure the smoothness of the solution in situations where the phase effective density presents steep gradients, aiming at reproducing the discretisation typical of the staggered grid arrangement. This was achieved including the strongly varying source terms of the momentum equation in the momentum interpolation procedure. Phase coupling was implemented using the partial elimination algorithm, which was incorporated in the improved interpolation practice. An implicit treatment for the particle pressure was implemented to ensure the robustness of the algorithm whenever the particle phase approaches the packed condition, where strong and rapidly changing stresses as a function of the dispersed phase volume fraction are present. The implemented code was tested against a number of test cases, including a bubbling fluidised bed, and results were verified against the solution provided by another solver (MFIX), or against published numerical solutions.

OXYPHILIC ADENOMA INVOLVING FLOOR OF THE MOUTH: A CASE REPORT

Oxyphilic adenomas are unusual neoplasm of the head and neck region affecting the glandular epithelial tissue. They were first called as oncocytoma, which is composed of oncocytes and were first described by Schaffer and Hamperl. Oncocytes are polyhedral cells and contain abundant cytoplasm filled with eosinophilic granules. Oxyphilic adenomas are benign neoplasm and represent approximately less than 1% of all salivary gland tumors. They are found generally in the parotid gland, affecting parotid gland region extraorally and rarely encountered in various other sites. Involvement of floor of the mouth is very rare. Presented in this article is a case report of patient suffering from neoplasm, which was histopathologically diagnosed as oxyphilic adenoma.

Characteristics of Anterior Uveal Melanocytomas in 17 Cases

To evaluate a case series of anterior uveal melanocytomas (AUMs) for their distinct clinical, histopathologic, and high-frequency ultrasound (UBM) characteristics. Retrospective single-center case series. Seventeen consecutive patients with AUMs. Retrospective review of patient, tumor, UBM, histopathologic, and follow-up characteristics. Follow-up data included change in visual acuity, growth, secondary glaucoma, extrascleral extension, or malignant transformation. Tumor, high-frequency ultrasound, histopathologic, and follow-up characteristics. Seventeen patients had a median follow-up of 20 months (range, 1-130). Tumor was darkly pigmented with nodular configuration in 100% of patients, irregular surface in 82% of patients, characteristic cobblestone surface appearance in 59% of patients, and feathery or fimbriated margins in 88% of patients. Intrinsic vascularity, ectropion uveae, episcleral sentinel vessel, sector cataract, or heterochromia was not seen. High-frequency ultrasound showed high (71%) or moderately high (12%) internal reflectivity in the majority of tumors. Thirteen tumors (76%) involved the iris, 47% of tumors were club-shaped, and 100% of tumors showed no intrinsic vascularity. Mean tumor thickness was 1 mm (standard deviation [SD] ± 0.5, median 0.9, range 0.3-2.1 mm). Mean largest basal dimension was 3.1 mm (SD ± 2.3, median 2.3, range 0.5-9.4 mm) (n=14). Three pathologic evaluations revealed plump polyhedral cells with abundant cytoplasm, small round to oval nuclei, inconspicuous nucleoli, and finely dispersed chromatin. Two tumors had extrascleral extension, 2 tumors were documented to grow, and 1 tumor caused medically controlled glaucoma. Anterior uveal melanocytomas are uncommon benign melanocytic tumors with characteristic clinical features. High-frequency ultrasound imaging offers excellent views of obscure posterior extent and allows precise tumor measurement and monitoring for growth. It is an invaluable adjunct to digital slit-lamp photography for evaluating tumor stability or growth. This study presents and correlates unique clinical, high-frequency ultrasound and histopathologic characteristics.

Aortic body chemodectoma in a cow: clinical, morphopathological, and immunohistochemical study

A 3-year-old Holstein cow with a history of severe weakness, dyspnea, pale mucous membranes, increased respiratory rate associated with marked abdominal respiration, severe arrhythmia, and tachycardia was referred to a slaughterhouse by the referring veterinarian due to poor prognosis. After slaughter, a large, firm, white, multilobulated mass about 5 cm in diameter was located at the base of the heart that extended to the right atrium and obliterated partially the right atrial lumen. Microscopically, tumor cells were aligned along and around the capillaries and were discrete, cuboidal to polyhedral cells with little cytoplasm arranged in distinct packets surrounded by thin fibrous septa. The nuclei were round to oval and were placed centrally in the cells. Immunoreactivity for S100 protein was positive multifocally, mostly in the peripherally located sustentacular cells, but NSE and CrA were negative. On the basis of the clinicopathological and immunohistochemical findings, the tumor was diagnosed as aortic body chemodectoma.