Maximal information component analysis: a novel non-linear network analysis method.

BackgroundNetwork construction and analysis algorithms provide scientists with the ability to sift through high-throughput biological outputs, such as transcription microarrays, for small groups of genes (modules) that are relevant for further research. Most of these algorithms ignore the important role of non-linear interactions in the data, and the ability for genes to operate in multiple functional groups at once, despite clear evidence for both of these phenomena in observed biological systems.ResultsWe have created a novel co-expression network analysis algorithm that incorporates both of these principles by combining the information-theoretic association measure of the maximal information coefficient (MIC) with an Interaction Component Model. We evaluate the performance of this approach on two datasets collected from a large panel of mice, one from macrophages and the other from liver by comparing the two measures based on a measure of module entropy, Gene Ontology (GO) enrichment, and scale-free topology (SFT) fit. Our algorithm outperforms a widely used co-expression analysis method, weighted gene co-expression network analysis (WGCNA), in the macrophage data, while returning comparable results in the liver dataset when using these criteria. We demonstrate that the macrophage data has more non-linear interactions than the liver dataset, which may explain the increased performance of our method, termed Maximal Information Component Analysis (MICA) in that case.ConclusionsIn making our network algorithm more accurately reflect known biological principles, we are able to generate modules with improved relevance, particularly in networks with confounding factors such as gene by environment interactions

XFEM based fictitious domain method for linear elasticity model with crack

Reduction of computational cost of solutions is a key issue to crack identification or crack propagation problems. One of the solution is to avoid re-meshing the domain when the crack position changes or when the crack extends. To avoid re-meshing, we propose a new finite element approach for the numerical simulation of discontinuities of displacements generated by cracks inside elastic media. The approach is based on a fictitious domain method originally developed for Dirichlet conditions for the Poisson problem and for the Stokes problem, which is adapted to the Neumann boundary conditions of crack problems. The crack is represented by level-set functions. Numerical tests are made with a mixed formulation to emphasize the accuracy of the method, as well as its robustness with respect to the geometry enforced by a stabilization technique. In particular an inf-sup condition is theoretically proven for the latter. A realistic simulation with a uniformly pressurized fracture inside a volcano is given for illustrating the applicability of the method.Comment: 27 pages, 15 figure

Discontinuous Galerkin approximations in computational mechanics: hybridization, exact geometry and degree adaptivity

Discontinuous Galerkin (DG) discretizations with exact representation of the geometry and local polynomial degree adaptivity are revisited. Hybridization techniques are employed to reduce the computational cost of DG approximations and devise the hybridizable discontinuous Galerkin (HDG) method. Exact geometry described by non-uniform rational B-splines (NURBS) is integrated into HDG using the framework of the NURBS-enhanced finite element method (NEFEM). Moreover, optimal convergence and superconvergence properties of HDG-Voigt formulation in presence of symmetric second-order tensors are exploited to construct inexpensive error indicators and drive degree adaptive procedures. Applications involving the numerical simulation of problems in electrostatics, linear elasticity and incompressible viscous flows are presented. Moreover, this is done for both high-order HDG approximations and the lowest-order framework of face-centered finite volumes (FCFV).Peer ReviewedPostprint (author's final draft

NGS 데이터를 이용한 엑손 수준 복제수변이 분석 알고리즘의 임상적 적용

학위논문(박사) -- 서울대학교대학원 : 의과대학 의학과, 2021.8. 박성섭.Introduction: Despite the importance of exonic copy number variations (CNVs) in human genetic diseases, reliable Next-generation sequencing (NGS)-based methods for detecting them are unavailable. We developed an expandable and robust exonic CNV detection tool called consistent count region (CCR)-CNV. Methods: In total, 1,000 samples of the truth set were used for validating CCR-CNV. A custom targeted gene panel containing hundreds of genes as well as exome sequencing data was included in the truth set. Results: The overall sensitivity of our method was 99.7%, which was superior to that of other CNV tools, such as DECoN, Atlas-CNV, and CNV-RF. Importantly, the false discovery rate of our method was comparable to that of other tools. CCR-CNV also showed a high concordance rate with the chromosomal microarray analysis data. Moreover, genome-wide CNV screening by using low-coverage genome sequencing showed comparable performance to that of chromosomal microarray analysis. Conclusion: Here, we present a novel diagnostic tool that allows the identification of exonic CNVs with high confidence using various reagents and clinical NGS platforms. We validated this method using the largest multiple ligation-dependent probe amplification (MLPA)-confirmed dataset, including sufficient copy-normal control data.서론: 차세대 염기서열분석 (Next-generation sequencing, NGS) 는 한 번에 수많은 유전자를 한 번에 검사하면서도 우수한 성능으로 임상현장에서 활발히 사용되고 있다. 하지만, 데이터를 활용한 복제수변이 분석에 대한 표준 알고리즘은 현재까지 부재한 상태다. 본 연구자는 NGS 데이터로부터 엑손 수준의 복제수변이를 검출하는 알고리즘을 확립하고 이를 Multiple ligation-dependent probe amplification (MLPA)로 확인된 임상검체를 이용해 검증하여 임상적용이 가능하도록 하고자 하였다. 방법: 본 연구자는 NGS 데이터로부터 엑손 수준의 복제수변이를 검출하기 위해 “Consistent Count Region”(CCR)라는 알고리즘을 고안하였다. 본 알고리즘은 대조군에서 일정하게 타겟의 리드뎁스와 정해진 범위 안에 존재하는 엑손을 CCR로 정의한다. CCR 리드뎁스 평균값으로 타겟의 리드뎁스를 나눠준 값을 이용해 복제수변이를 검출한다. 우선 CCR 알고리즘의 각 파라미터와 컷오프를 Receiver operating characteristic (ROC) 분석과 컷오프분석 (Youden Index)을 통해 최적화한다. CCR 알고리즘을 MLPA로 복제수변이의 유무가 확인된 다양한 NGS 데이터에서 임상적 효용성을 검증한다. 결과: CCR-CNV 알고리즘의 전체 민감도는 99.7%로 기존에 알려진 DECoN, Atlas-CNV, CNV-RF과 같은 알고리즘의 민감도보다 높았다. 특이도는 98.1%로 타 알고리즘과 비슷하거나 더 높은 수치를 보였다. 특히, CCR-CNV의 false discovery rate (FDR)은 기존 알고리즘과 비슷한 수준을 보였다. 결론: 본 연구자는 엑손 수준의 복제수 변이를 높은 정확도로 검출할 수 있는 알고리즘을 고안하였다. 본 알고리즘은 다양한 시약과 플랫폼에서 만들어진 NGS 데이터의 복제수 변이를 검출할 수 있음을 보였다.Introduction 1 Materials and Methods 4 Results 14 Discussion 33 References 40 국문초록 46박

A CutFEM method for Stefan-Signorini problems with application in pulsed laser ablation

In this article, we develop a cut finite element method for one-phase Stefan problems, with applications in laser manufacturing. The geometry of the workpiece is represented implicitly via a level set function. Material above the melting/vaporisation temperature is represented by a fictitious gas phase. The moving interface between the workpiece and the fictitious gas phase may cut arbitrarily through the elements of the finite element mesh, which remains fixed throughout the simulation, thereby circumventing the need for cumbersome re-meshing operations. The primal/dual formulation of the linear one-phase Stefan problem is recast into a primal non-linear formulation using a Nitsche-type approach, which avoids the difficulty of constructing inf-sup stable primal/dual pairs. Through the careful derivation of stabilisation terms, we show that the proposed Stefan-Signorini-Nitsche CutFEM method remains stable independently of the cut location. In addition, we obtain optimal convergence with respect to space and time refinement. Several 2D and 3D examples are proposed, highlighting the robustness and flexibility of the algorithm, together with its relevance to the field of micro-manufacturing