PI control of discrete linear repetitive processes

Repetitive processes are a distinct class of 2D systems (i.e. information propagation in two independent directions) of both systems theoretic and applications interest. They cannot be controlled by direct extension of existing techniques from either standard (termed 1D here) or 2D systems theory. In this paper, we exploit their unique physical structure to show how two term, i.e. proportional plus integral (or PI) action, can be used to control these processes to produce desired behavior (as opposed to just stability).     

Galanin Receptors (GalR1, GalR2, and GalR3) Expression in Colorectal Cancer Tissue and Correlations to the Overall Survival and Poor Prognosis of CRC Patients

Colorectal cancer (CRC) is the second most common cause of cancer in women and the third in men. The postoperative pathomorphological evaluation of patients with CRC is extremely important for future therapeutic decisions. Although our previous studies demonstrated high galanin (GAL) presence within tumor tissue and an elevated concentration of GAL in the serum of CRC patients, to date, there is a lack of data regarding GAL receptor (GalR) protein expression in CRC cells. Therefore, the aim of this study was to evaluate the presence of all three types of GalRs (GalR1, GalR2 and GalR3) within epithelial cells of the human colon and CRC tissue with the use of the immunohistochemical method and to correlate the results with the clinical-pathological data. We found stronger immunoreactivity of GalR1 and GalR3 in CRC cells compared to epithelial cells of the unchanged mucosa of the large intestine. No differences in the GalR2 protein immunoreactivity between the studied tissues were noted. We also found that the increased immunoexpression of the GalR3 in CRC tissue correlated with the better prognosis and longer survival (p < 0.0079) of CRC patients (n = 55). The obtained results suggest that GalR3 may play the role of a prognostic factor for CRC patients. Based on data from the TCGA-COAD project deposited in the GDC Data Portal, we also found that GalR mRNA in cancer samples and the adjacent normal tissue did not correlate with immunoexpression of the GalR proteins in CRC cells and epithelial cells of the unchanged mucosa.     

Atomically Precise Prediction of 2D Self‐Assembly of Weakly Bonded Nanostructures: STM Insight into Concentration‐Dependent Architectures

A joint experimental and computational study is reported on the concentration‐dependant self‐assembly of a flat C₃‐symmetric molecule on a graphite surface. As a model system a tripodal molecule, 1,3,5‐tris(pyridin‐3‐ylethynyl)benzene, has been chosen, which can adopt either C_3h or C_s symmetry when planar, as a result of pyridyl rotation along the alkynyl spacers. Density functional theory (DFT) simulations of 2D nanopatterns with different surface coverage reveal that the molecule can generate different types of self‐assembled motifs. The stability of fourteen 2D patterns and the influence of concentration are analyzed. It is found that ordered, densely packed monolayers and 2D porous networks are obtained at high and low concentrations, respectively. A concentration‐dependent scanning tunneling microscopy (STM) investigation of this molecular self‐assembly system at a solution/graphite interface reveals four supramolecular motifs, which are in perfect agreement with those predicted by simulations. Therefore, this DFT method represents a key step forward toward the atomically precise prediction of molecular self‐assembly on surfaces and at interfaces.     

Plane Problem for Layered Composites with Periodic Array of Interfacial Cracks Under Compressive Static Loading

The current paper addresses the problem of 2-D modelling of the onset of failure process in a layered composite with periodic array of interfacial cracks under static compression along layers. The statement of the problem is based on the most accurate approach, the model of piecewise-homogenous medium. The condition of plane strain state is considered. The shear and the extensional buckling modes are examined. The laminae are modelled by transversally isotropic material (a matrix reinforced by continuous parallel fibres). The complex non-classical failure mechanics problem is solved utilizing finite element analysis. It is found that the 0°-plies volume fraction, the crack length and the mutual position of cracks influence the critical strain in the composite.     

A hybrid continuous-discrete approach to large discrete structural optimization problems

Many optimum structural designs are based on searching for the best of all combinations, arising from the number of structural members, and parameters of listed rolled profiles. Even, in a relatively simple design, the number of such combinations is of an order higher than ten. All known methods of finding discrete minimum of structural weight require very large number of analyses often of an order of four. In this study, a relatively simple method of solving such problems is presented. It is based on a tree graph, representing discrete values of the structural volume. The structure can be subjected to multi static loadings with constraints imposed on displacements and stresses. The number of analyses, in the proposed algorithm, is limited to the order of two. The knowledge needed to apply the method is limited to FEM and graph representation. The paper is illustrated with two examples with numbers of combinations up to 42³⁸.