Subdivision Of Cells Research Articles

A novel subdivision of the bed nucleus of stria terminalis in monkey, rat, and mouse brains.

The bed nucleus of stria terminalis (BST) is a critical structure that mediates sustained vigilant responses to contextual, diffuse, and unpredictable threats. Dysfunction of the BST could lead to excessive anxiety and hypervigilance, which are often observed in posttraumatic stress disorder and anxiety disorders. Vigilance of potential future threats from the external environment is a basic brain function and probably requires rapid and/or short neural circuits, which enable both quick detection of the potential threats and fast adaptive responses. However, the BST in literature does not appear to receive spatial information directly from earlier visual or spatial processing structures. In this study, a novel subdivision of the BST is uncovered in monkey, rat, and mouse brains based on the human equivalent and is found in mouse to receive direct inputs from the ventral lateral geniculate nucleus and pretectal nucleus as well as from the spatial processing structures such as subiculum, presubiculum, and medial entorhinal cortex. This new subdivision, termed spindle-shaped small cell subdivision (BSTsc), is located between the known BST and the anterior thalamus. In addition to the unique afferent connections and cell morphology, the BSTsc also displays unique molecular signature (e.g., positive for excitatory markers) compared with other BST subdivisions, which are mostly composed of inhibitory GABAergic neurons. The BSTsc appears to have largely overlapping efferent projections with other BST subdivisions such as the projections to the amygdala, hypothalamus, nucleus accumbens, septum, and brainstem. Together, the present study suggests that the BSTsc is poised to serve as a shortcut bridge directly linking spatial information from the environment to vigilant adaptive internal responses.

3D Shape’s Approximation and Infill with Self-Supporting Lattice Structures

Aiming at the problem of 3D printing cannot manufacture lattice structure with overhanging rods or nodes, 3D shape approximation and infill algorithms with self-supporting lattice structure are proposed. Firstly, rhombic hexahedron is used as the unit cell and the function of the geometry of the unit cell and its self-supporting property is constructed, a self-supporting unit cell with minimal volume is further generated which covers the whole input 3D shape. Then the 3D shape is approximated by the iterative subdivision of the unit cells under the constraint of the shortest edge length and the number of subdivisions. Finally, to guarantee the printability of the generated lattice structure, self-supporting struts are added to support the overhanging nodes. In addition, the 3D self-supporting infill structure is generated by the subdivision of unit cells. Experimental models are selected from 3D ShapeNet, and then the algorithms are implemented and the results on VS2010 and MATLAB R2017a are visualized. The results demonstrate the effectiveness and robustness of the proposed algorithms for 3D shape approximation and infill.

Preserving consistency in geometric modeling with graph transformations

AbstractLabeled graphs are particularly well adapted to represent objects in the context of topology-based geometric modeling. Thus, graph transformation theory is used to implement modeling operations and check their consistency. This article defines a class of graph transformation rules dedicated to embedding computations. Objects are here defined as a particular subclass of labeled graphs in which arc labels encode their topological structure (i.e., cell subdivision: vertex, edge, face) and node labels encode their embedding (i.e., relevant data: vertex positions, face colors, volume density). Object consistency is defined by labeling constraints which must be preserved by modeling operations that modify topology and/or embedding. Dedicated graph transformation variables allow us to access the existing embedding from the underlying topological structure (e.g., collecting all the points of a face) in order to compute the new embedding using user-provided functions (e.g., compute the barycenter of several points). To ensure the safety of the defined operations, we provide syntactic conditions on rules that preserve the object consistency constraints.

Influence of microstructural morphology on the continuous/discontinuous yielding behavior in a medium manganese steel

The continuous and discontinuous yielding behaviors are observed in the medium Mn steels with granular and lath-typed microstructures, respectively. The continuous yielding behavior is attributed to the unique lath-typed microstructure, in which the sub-division of unit cells by laths leads to a more homogeneous distribution of GNDs and thus a higher GND density.

Space of isospectral periodic tridiagonal matrices

A periodic tridiagonal matrix is a tridiagonal matrix with additional two entries at the corners. We study the space $X_{n,\lambda}$ of Hermitian periodic tridiagonal $n\times n$-matrices with a fixed simple spectrum $\lambda$. Using the discretized Shr\"{o}dinger operator we describe all spectra $\lambda$ for which $X_{n,\lambda}$ is a topological manifold. The space $X_{n,\lambda}$ carries a natural effective action of a compact $(n-1)$-torus. We describe the topology of its orbit space and, in particular, show that whenever the isospectral space is a manifold, its orbit space is homeomorphic to $S^4\times T^{n-3}$. There is a classical dynamical system: the flow of the periodic Toda lattice, acting on $X_{n,\lambda}$. Except for the degenerate locus $X_{n,\lambda}^0$, the Toda lattice exhibits Liouville--Arnold behavior, so that the space $X_{n,\lambda}\setminus X_{n,\lambda}^0$ is fibered into tori. The degenerate locus of the Toda system is described in terms of combinatorial geometry: its structure is encoded in the special cell subdivision of a torus, which is obtained from the regular tiling of the euclidean space by permutohedra. We apply methods of commutative algebra and toric topology to describe the cohomology and equivariant cohomology modules of $X_{n,\lambda}$.

Linear smoothed finite element method for quasi-incompressible hyperelastic media

This work presents a linear smoothing scheme over high-order triangular elements within the framework of the cell-based strain smoothed finite element method for two-dimensional nonlinear problems. The main idea behind the proposed linear smoothing scheme is that it unlike the classical SFEM, it does not require the subdivision of the finite element cells into smoothing sub-cell. The other features of the classical SFEM are retained, such as: it does not require an explicit form of the derivatives of the basis functions, all the computations are done in the physical space, and the results are less sensitive to mesh distortion. A series of benchmark tests are done to demonstrate the validity and the stability of the proposed scheme. The validity and accuracy are confirmed by comparing the obtained numerical results with the standard FEM using quadratic triangular element and the exact solutions.

Adaptive Haar Type Wavelets on Manifolds

We consider embedded Haar type spaces associated with cell subdivisions of a smooth manifold. We use an adaptivity criterion connected with a nonnegative set function possessing certain monotonicity properties. We propose an algorithm for constructing embedded spaces satisfying the adaptivity criterion. To construct the wavelet decomposition, we apply the nonclassical approach and obtain the adaptive wavelet decomposition of the Haar type space on the manifold. Some model examples are given.

Mixed Uplink, Downlink Channel Allocation and Power Allocation Schemes for 5G Networks

Device-to-device (D2D) communication plays a significant role for the next generation networks i.e. (5G). The D2D communication leads to an efficient spectral utilization which results in a potential reduction in the overhead at the evolved node B side. However, without an efficient interference management scheme in place, cellular users experience a degradation in the quality of service, which makes interference mitigation a major deployment challenge. In this paper, we have put forward an efficient interference mitigation scheme in order to maximize the system throughput. This scheme comprises of three subparts. Firstly, we introduce a cell sub-division concept under which we virtually subdivide the cell into three regions, namely center, mid and outer regions. Secondly, we formulate the power allocation problem as a robust particle swarm optimization algorithm for the mid-cell region. This enables the scheme in handling the uncertainties in the allocated power, thus reaching a robust optimal solution. The third part consists of a resource allocation scheme built around a cell subdivision concept. Extensive simulations are performed under the scenarios of simultaneous uplink and downlink transmission for the center cell region and the outer cell region. We further draw the comparison of our scheme along with the schemes mentioned in the literature.

Splines of Variable Approximation Order and Their Wavelet Decompositions

We construct spline (finite element) spaces of variable approximation order and find necessary and sufficient conditions for pseudosmoothness of such splines. We study embedding of the spline spaces on embedded subdivisions and construct the corresponding wavelet decompositions. The constructions are based on the approximation relations defined on a cell subdivision of a differentiable manifold under the assumption that the multiplicity of the covering by supports of the coordinate functions is variable, which causes the variable approximation order. The spline spaces possess the adaptive approximation property. The notion of pseudosmoothness lead to new families of embedded spaces.

A penteract partition by means of the optimal subdivision of cells

Freudental's algorithm obtained way back in early forties have been traditionally used for simplicial triangulating of the hypercube. The main advantage of this algorithm is that it only generates one congruence class. Unfortunately, Freudental's algorithm is not optimal with respect to the measure of degeneracy. The multigrid methods require the degeneracy measure to be as small as possible. The minimal subdivision in the 3-dimensional case and the uniform tesseract corner subdivision in the 4-dimensional case are optimal in regards the measure of degeneracy and multigrid applications. The question about the optimal refinement strategy in more dimensional cases is still an open problem. This paper deals with a penteract subdivision with degeneracy measure much better than one obtained by the Freudental algorithm.

The Farrell–Tate and Bredon homology for [formula omitted] via cell subdivisions

We provide some new computations of Farrell–Tate and Bredon (co)homology for arithmetic groups. For calculations of Farrell–Tate or Bredon homology, one needs cell complexes where cell stabilizers fix their cells pointwise. We provide two algorithms computing an efficient subdivision of a complex to achieve this rigidity property. Applying these algorithms to available cell complexes for PSL4(Z) provides computations of Farrell–Tate cohomology for small primes as well as the Bredon homology for the classifying spaces of proper actions with coefficients in the complex representation ring.

STATISTICAL OUTLIER DETECTION METHOD FOR AIRBORNE LIDAR DATA

Abstract. Sampling the Earth’s surface using airborne LASER scanning (ALS) systems suffers from several factors inherent to the LASER system itself as well as external factors, such as the presence of particles in the atmosphere, and/or multi-path returns due to reflections. The resulting point cloud may therefore contain some outliers and removing them is an important (and difficult) step for all subsequent processes that use this kind of data as input. In the literature, there are several approaches for outlier removal, some of which require external information, such as spatial frequency characteristics or presume parametric mathematical models for surface fitting. A limitation on the height histogram filtering approach was identified from the literature review: outliers that lie within the ground elevation difference might not be detected. To overcome such a limitation, this paper proposes an adaptive alternative based on point cloud cell subdivision. Instead of computing a single histogram for the whole dataset, the method applies the filtering to smaller patches, in which the ground elevation difference can be ignored. A study area was filtered, and the results were compared quantitatively with two other methods implemented in both free and commercial software packages. The reference data was generated manually in order to provide useful quality measures. The experiment shows that none of the tested filters was able to reach a level of complete automation, therefore manual corrections by the operator are still necessary.

Adaptive refinement of hierarchical T-splines

We present an adaptive local refinement technique for isogeometric analysis based on hierarchical T-splines. An element-wise point of view is adopted, which exploits Bézier extraction, and allows adaptive refinement of standard hierarchical T-splines and truncated hierarchical T-splines in a straightforward and unified manner. No explicit basis function operations are required to build the hierarchical basis function space, as only matrix manipulations are involved. This makes the efficiency superior to that of existing implementations. In particular, the implementation of truncated hierarchical T-splines requires no explicit truncation of the basis functions. In the analysis, a multi-level T-mesh is constructed by successive cell subdivisions of an initial, coarse T-mesh. An important feature is that Bézier extraction is employed to compute the refinement operator between two successive hierarchical levels, and that, at each level, Bézier extraction is applied to obtain the stiffness matrix without, initially, considering multi-level interaction. This interaction is recovered through a subdivision operator. Numerical examples are presented for validation purposes, and to assess the convergence properties.

An hp‐adaptive unstructured finite volume solver for compressible flows

SummaryThe idea of hp‐adaptation, which has originally been developed for compact schemes (such as finite element methods), suggests an adaptation scheme using a mixture of mesh refinement and order enrichment based on the smoothness of the solution to obtain an accurate solution efficiently. In this paper, we develop an hp‐adaptation framework for unstructured finite volume methods using residual‐based and adjoint‐based error indicators. For the residual‐based error indicator, we use a higher‐order discrete operator to estimate the truncation error, whereas this estimate is weighted by the solution of the discrete adjoint problem for an output of interest to form the adaptation indicator for adjoint‐based adaptations. We perform our adaptation by local subdivision of cells with nonconforming interfaces allowed and local reconstruction of higher‐order polynomials for solution approximations. We present our results for two‐dimensional compressible flow problems including subsonic inviscid, transonic inviscid, and subsonic laminar flow around the NACA 0012 airfoil and also turbulent flow over a flat plate. Our numerical results suggest the efficiency and accuracy advantages of adjoint‐based hp‐adaptations over uniform refinement and also over residual‐based adaptation for flows with and without singularities.

Modeling of Biofilm Growth on Ager Substrate Using the Extended Finite Element Method

Various types of bacterial form adhesive aggregates on surfaces known as biofilms, which are of interest to researchers in a great variety of fields. In this paper, a continuum model based on diffusion-reaction is proposed and extended finite element method (XFEM) coupled to level set is employed to simulate the biofilm growth on ager substrate. Numerical results show the quantitative relationship between colony morphology and nutrient deletion. Comparing with experiment observation, we approve that diffusion limited regime is more appropriate than growth limited regime to describe Bacillus subtilis biofilm growth on MSgg ager substrate. Our model can be extended to investigate detailed biological process in biofilm growth such as cell subdivision and osmotic pressure induced transportation.

Adaptive hierarchical cell sub-division (AHCS) method for enhanced surface radiance temperature variability analysis

The issues with global warming and heat island effect raises the global inclination to elucidate the concerns towards the study of surface temperature variations in the urban environment. Surface radiance temperature (SRT) are considered undeniably one of the most substantial parameters to evaluate the impact of temperature variability in an urban environment. The work tried to present the thermal image processing techniques for retrieving the SRT from Landsat ETM+ data. Afterward, an innovative method namely adaptive hierarchical cell sub-division (AHCS) method in conjunction with statistical techniques were attempted to characterize the spatial variability for each of the directional attributes. These techniques also helped in detecting and quantifying the spatial variability at major and minor scales. The spatial variability through AHCS were analyzed to illustrate their native spatial distribution over urban–rural (Rurban) areas contributing to heat island. The results apparently revealed the aggregate spatial thermal configuration along Rurban areas and vice versa. The key fraction of urban landscape patches with high, sub high and low densities specified their inherent characteristics. The high-temperature type was the prevailing class in the urban core while sub medium temperature and low-temperature type were the main contributors in the rural landscape. Whereas, urban fringe exhibited very complex results of temperature variability for the various land use. The study also authenticated the approach for assimilation of spatial variability techniques with a powerful statistical approach as a reliable instrument to monitor the thermal dynamics.

A high-order flux reconstruction method with adaptive mesh refinement and artificial diffusivity on unstructured moving/deforming mesh for shock capturing

This article presents new progress of shock capturing on unstructured dynamic grids by using adaptive mesh refinement (AMR) method in conjunction with artificial diffusivity (AD) under the framework of flux reconstruction (FR)/correction procedure via reconstruction (CPR) method. The proposed AMR algorithm is applicable even when the grid undergoes dynamic motion. It features an innovative data structure that is capable of direct addressing in managing the system of cells on multiple levels of refinement. A conservative mortar method is used to handle non-conforming interfaces resulted from cell subdivision. The AD is added in regions of strong dilatation to counter the Gibbs oscillation that is disruptive to high-order solutions when shock discontinuities exist. Several test cases are used to verify that this FR-AMR-AD framework can achieve high-order accuracy for smooth flows, and obtain stable solution with the presence of shock discontinuity. By further limiting the shock within subdivided adjacent cells, a sharp shock solution can be obtained with reduced amount of AD addition, hence errors from adding dissipation, on dynamically refined grids.

On the Usage of Tetrahedral Background Cells in Nodal Integration of RPIM for 3D Elasto-Static Problems

In this paper, tetrahedral background cells are used in nodal integration of radial point interpolation method (RPIM). The nodal integration is based on Taylor series terms and it is originally applied for the solutions of 2D problems in literature. Therefore, in this study, it is attempted that the tetrahedral integration cells are used in the solution of 3D elasto-static problems. The accuracy is seriously affected by order of Taylor series terms and it is investigated up to fifth order. A methodology is developed for prevention of negative volumes and calculation problems in subdivision of integration cells for each node. Three different case studies are solved with different support domain sizes and shape parameters. The best accuracy is achieved with fourth-order Taylor terms in nodal integration radial point interpolation method (NI-RPIM). [Formula: see text]-value of 3.00 and [Formula: see text] value of 1.03 in radial basis functions give good results in all cases.

Various contact approaches for the finite cell method

The finite cell method (FCM) provides a method for the computation of structures which can be described as a mixture of high-order FEM and a special integration technique. The method is one of the novel computational methods and is highly developed within the last decade. One of the major problems of FCM is the description of boundary conditions inside cells as well as in sub-cells. And a completely open problem is the description of contact. Therefore, the motivation of the current work is to develop a set of computational contact mechanics approaches which will be effective for the finite element cell method. Thus, for the FCM method we are developing and testing hereby focusing on the Hertz problem the following algorithms: direct integration in the cell method, allowing the fastest implementation, but suffering from numerical artifacts such as the "stamp effect"; the most efficient scheme concerning approximation properties the cell-surface-to-analytical-surface contact element designed for contact with rigid bodies leading to cell-wisely contact elements; and finally the discrete-cell-to-cell contact approach based on the finite discrete method. All developed methods are carefully verified with the analytical Hertz solution. The cell subdivisions, the order of the shape functions as well as the selection of the classes for shape functions are investigated for all developed contact approaches. This analysis allows to choose the most robust approach depending on the needs of the user such as correct representation of the stresses, or only satisfaction of geometrical non-penetration conditions.

A General Algorithm for Evaluating Domain Integrals in 2D Boundary Element Method for Transient Heat Conduction

A time-dependent boundary integral equation method named as pseudo-initial condition method is widely used to solve the transient heat conduction problems. Accurate evaluation of the domain integrals in the pseudo-initial condition formulation is of crucial importance for its successful implementation. As the time-dependent kernel in the domain integral is close to singular when small time step is used, a straightforward computation using Gaussian quadrature may produce large errors, and thus lead to instability of the analysis. To improve the computational accuracy of the domain integral, a coordinate transformation coupled with a domain cell subdivision technique is presented in this paper for 2D boundary element method. The coordinate transformation is denoted as (α, β) transformation, while the cell subdivision technique considers the position of the source point, the shape of the integration cell and the relations between the size of the cell and the time step. With the cell subdivision technique, more Gaussian points are shifted towards the source point, thus more accurate results can be obtained. Numerical examples have demonstrated the accuracy and efficiency of the proposed method.