A MLPG4 (LBIE) Formulation in Elastostatics

Very recently, Vavourakis, Sellountos and Polyzos (2006) ({CMES: Computer Modeling in Engineering {\&} Sciences, vol. 13, pp. 171--184}) presented a comparison study on the accuracy provided by five different elastostatic Meshless Local Petrov-Galerkin (MLPG) type formulations, which are based on Local Boundary Integral Equation (LBIE) considerations. One of the main conclusions addressed in this paper is that the use of derivatives of the Moving Least Squares (MLS) shape functions decreases the solution accuracy of any MLPG(LBIE) formulation. In the present work a new, free of MLS-derivatives and non-singular MLPG(LBIE) method for solving elastic problems is demonstrated. This is accomplished by treating displacements and stresses as independent variables through the corresponding local integral equations and considering nodal points located only internally and externally and not on the global boundary of the analyzed elastic structure. The MLS approximation scheme for the interpolation of both displacements and stresses is exploited. The essential displacement and traction boundary conditions are easily satisfied via the corresponding displacement and stress local integral equations. Representative numerical examples that demonstrate the achieved accuracy of the proposed MLPG(LBIE) method are provided

A new mathematical model for the interpretation of translational research evaluating six CTLA-4 polymorphisms in high-risk melanoma patients receiving adjuvant interferon

Adjuvant therapy of stage IIB/III melanoma with interferon reduces relapse and mortality by up to 33% but is accompanied by toxicity-related complications. Polymorphisms of the CTLA-4 gene associated with autoimmune diseases could help in identifying interferon treatment benefits. We previously genotyped 286 melanoma patients and 288 healthy (unrelated) individuals for six CTLA-4 polymorphisms (SNP). Previous analyses found no significant differences between the distributions of CTLA-4 polymorphisms in the melanoma population vs. controls, no significant difference in relapse free and overall survivals among patients and no correlation between autoimmunity and specific alleles. We report new analysis of these CTLA-4 genetic profiles, using Network Phenotyping Strategy (NPS). It is graph-theory based method, analyzing the SNP patterns. Application of NPS on CTLA-4 polymorphism captures allele relationship pattern for every patient into 6-partite mathematical graph P. Graphs P are combined into weighted 6-partite graph S, which subsequently decomposed into reference relationship profiles (RRP). Finally, every individual CTLA-4 genotype pattern is characterized by the graph distances of P from eight identified RRP's. RRP's are subgraphs of S, collecting equally frequent binary allele co-occurrences in all studied loci. If S topology represents the genetic "dominant model", the RRP's and their characteristic frequencies are identical to expectation-maximization derived haplotypes and maximal likelihood estimates of their frequencies. The graphrepresentation allows showing that patient CTLA-4 haplotypes are uniquely different from the controls by absence of specific SNP combinations. New function-related insight is derived when the 6-partite graph reflects allelic state of CTLA-4. We found that we can use differences between individual P and specific RRPs to identify patient subpopulations with clearly different polymorphic patterns relatively to controls as well as to identify patients with significantly different survival. © 2014 Pancoska et al

A Boundary Element Method for Acoustic Scattering from Non-axisymmetric and Axisymmetric Elastic Shells

A Boundary Element Method (BEM), for the three-dimensional solution of both non-axisymmetric and axisymmetric coupled acoustic-elastic problems in the frequency domain, is presented. The present BEM makes use of the Burton and Miller integral equation for infinite acoustic spaces, while elastic structures are dealt with the standard boundary integral equation of elastodynamics. The axisymmetric formulation involves the use of the fast Fourier transform algorithm. Highly accurate numerical algorithms are used for the evaluation of singular integrals, while nearly singular integrals are treated, also with high accuracy, through the use of practical numerical techniques, for both the axisymmetric and non-axisymmetric cases. Two representative numerical examples are solved, that demonstrate the accuracy of the present BEM, while interesting observations are reported about its convergence properties, when arbitrarily shaped shell scatterers are under consideration

An Advanced ACA/BEM for Solving 2D Large-Scale Elastic Problems with Multi-Connected Domains

An advanced Boundary Element method (BEM) accelerated via Adaptive Cross Approximation (ACA) and Hierarchical Matrices (HM) techniques is presented for the solution of large-scale elastostatic problems with multi-connected domains like in fiber reinforced composite materials. Although the proposed ACA/ BEM is demonstrated for two-dimensional (2D) problems, it is quite general and it can be used for 3D problems. Different forms of ACA technique are employed for exploring their efficiency when they combined with a BEM code. More precisely, the fully and partially pivoted ACA with and without recompression are utilized, while the solution of the final linear system of equations is accelerated via an iterative GMRES solver. The proposed methodology is demonstrated with the solution of large scale, plane strain elastic problems dealing with the bending of unidirectional fiber composite plates with large numbers of periodically or randomly distributed cylindrical elastic fibers embedded in a matrix medium

A Meshless LBIE/LRBF Method for Solving the Nonlinear Fisher Equation: Application to Bone Healing

A simple Local Boundary Integral Equation (LBIE) method for solving the Fisher nonlinear transient diffusion equation in two dimensions (2D) is reported. The method utilizes, for its meshless implementation, randomly distributed nodal points in the interior domain and nodal points corresponding to a Boundary Element Method (BEM) mesh, at the global boundary. The interpolation of the interior and boundary potentials is accomplished using a Local Radial Basis Functions (LRBF) scheme. At the nodes of global boundary the potentials and their fluxes are treated as independent variables. On the local boundaries, potential fluxes are avoided by using the Laplacian companion solution. Potential gradients are accurately evaluated without RBFs via a LBIE, valid for gradient of potentials. Nonlinearity is treated using the Newton-Raphson scheme. The accuracy of the proposed methodology is demonstrated through representative numerical examples. Fisher equation is solved here via the LBIE/LRBF method in order to predict cell proliferation during bone healing. Cell concentrations and their gradients are numerically evaluated in a 2D model of fractured bone. The results are demonstrated and discussed

Long-term treatment of osteoporosis: safety and efficacy appraisal of denosumab

Denosumab is a fully human monoclonal antibody to the receptor activator of nuclear factor-κB ligand (RANKL), a member of the tumor necrosis factor receptor superfamily essential for osteoclastogenesis. Denosumab treatment is associated with a rapid, sustained, and reversible reduction in bone turnover markers, a continuous marked increase in bone mineral density at all sites, and a marked decrease in the risk of vertebral, hip, and nonvertebral fractures in women with postmenopausal osteoporosis. Therefore, it could be considered as an effective alternative to previous bisphosphonate treatment as well as first-line treatment of severe osteoporosis. Cost-effectiveness studies support this suggestion. In addition, denosumab seems to be the safest treatment option in patients with impaired renal function. Denosumab is characterized by reversibility of its effect after treatment discontinuation, in contrast with bisphosphonates. Large-scale clinical trials, including the extension of FREEDOM trial for up to 5 years, are reassuring for its safety. However, given its brief post-market period, vigilance regarding adverse events related to putative RANKL inhibition in tissues other than bone, as well as those related to bone turnover oversuppression, is advised

FastSVD-ML-ROM\textit{FastSVD-ML-ROM}: A Reduced-Order Modeling Framework based on Machine Learning for Real-Time Applications

Digital twins have emerged as a key technology for optimizing the performance of engineering products and systems. High-fidelity numerical simulations constitute the backbone of engineering design, providing an accurate insight into the performance of complex systems. However, large-scale, dynamic, non-linear models require significant computational resources and are prohibitive for real-time digital twin applications. To this end, reduced order models (ROMs) are employed, to approximate the high-fidelity solutions while accurately capturing the dominant aspects of the physical behavior. The present work proposes a new machine learning (ML) platform for the development of ROMs, to handle large-scale numerical problems dealing with transient nonlinear partial differential equations. Our framework, mentioned as $\textit{FastSVD-ML-ROM}$, utilizes $\textit{(i)}$ a singular value decomposition (SVD) update methodology, to compute a linear subspace of the multi-fidelity solutions during the simulation process, $\textit{(ii)}$ convolutional autoencoders for nonlinear dimensionality reduction, $\textit{(iii)}$ feed-forward neural networks to map the input parameters to the latent spaces, and $\textit{(iv)}$ long short-term memory networks to predict and forecast the dynamics of parametric solutions. The efficiency of the $\textit{FastSVD-ML-ROM}$ framework is demonstrated for a 2D linear convection-diffusion equation, the problem of fluid around a cylinder, and the 3D blood flow inside an arterial segment. The accuracy of the reconstructed results demonstrates the robustness and assesses the efficiency of the proposed approach.Comment: 35 pages, 22 figure

Chronic p53-independent p21 expression causes genomic instability by deregulating replication licensing

The cyclin-dependent kinase inhibitor p21WAF1/CIP1 (p21) is a cell-cycle checkpoint effector and inducer of senescence, regulated by p53. Yet, evidence suggests that p21 could also be oncogenic, through a mechanism that has so far remained obscure. We report that a subset of atypical cancerous cells strongly expressing p21 showed proliferation features. This occurred predominantly in p53-mutant human cancers, suggesting p53-independent upregulation of p21 selectively in more aggressive tumour cells. Multifaceted phenotypic and genomic analyses of p21-inducible, p53-null, cancerous and near-normal cellular models showed that after an initial senescence-like phase, a subpopulation of p21-expressing proliferating cells emerged, featuring increased genomic instability, aggressiveness and chemoresistance. Mechanistically, sustained p21 accumulation inhibited mainly the CRL4–CDT2 ubiquitin ligase, leading to deregulated origin licensing and replication stress. Collectively, our data reveal the tumour-promoting ability of p21 through deregulation of DNA replication licensing machinery—an unorthodox role to be considered in cancer treatment, since p21 responds to various stimuli including some chemotherapy drugs

Prognostic significance of the sequential detection of circulating melanoma cells by RT–PCR in high-risk melanoma patients receiving adjuvant interferon

The purpose of this study was to address the prognostic significance of circulating melanoma cells by reverse transcriptase-polymerase chain reaction in the peripheral blood of stage IIB and III melanoma patients on high-dose adjuvant interferon at multiple sequential time points from initiation of treatment. Tyrosinase mRNA in peripheral blood from these patients was assayed by reverse transcriptase polymerase chain reaction prior to initiation of adjuvant interferon, at completion of 1 month of intravenous interferon and at 3 monthly intervals until progression. Four hundred and eighteen blood samples from 60 melanoma patients were analysed. The median follow-up time calculated from the time of inclusion in the study was 23 months (range 2–38 months). Tyrosinase mRNA in blood was detected in 42 (70%) of 60 patients: 16 (76%) of 21 stage IIB patients and 26 (66%) of 39 stage III patients. The presence of tyrosinase mRNA in blood was correlated with a shorter disease-free survival (P : 0.03) and in multivariante analysis was an indepent prognostic factor for relapse. Patients who seroconverted to a negative reverse-transcriptase-polymerase chain reaction after induction treatment had a significantly lower probability of recurrence. The presence of circulating melanoma cells is a marker of a high relapse risk and shorter disease-free survival whether detected postoperatively or during follow-up. Tyrosinase mRNA amplification by reverse-transcriptase-polymerase chain reaction may be a useful tool for monitoring the efficacy of adjuvant treatment in stage IIB and III melanoma patients