STRUKTUR KOMUNITAS ECHINODERMATA DI PERAIRAN PANTAI GAPANG, DESA IBOIH, KECAMATAN SUKAKARYA, SABANG

Banda Ace

Understanding Optimization of Deep Learning via Jacobian Matrix and Lipschitz Constant

This article provides a comprehensive understanding of optimization in deep learning, with a primary focus on the challenges of gradient vanishing and gradient exploding, which normally lead to diminished model representational ability and training instability, respectively. We analyze these two challenges through several strategic measures, including the improvement of gradient flow and the imposition of constraints on a network's Lipschitz constant. To help understand the current optimization methodologies, we categorize them into two classes: explicit optimization and implicit optimization. Explicit optimization methods involve direct manipulation of optimizer parameters, including weight, gradient, learning rate, and weight decay. Implicit optimization methods, by contrast, focus on improving the overall landscape of a network by enhancing its modules, such as residual shortcuts, normalization methods, attention mechanisms, and activations. In this article, we provide an in-depth analysis of these two optimization classes and undertake a thorough examination of the Jacobian matrices and the Lipschitz constants of many widely used deep learning modules, highlighting existing issues as well as potential improvements. Moreover, we also conduct a series of analytical experiments to substantiate our theoretical discussions. This article does not aim to propose a new optimizer or network. Rather, our intention is to present a comprehensive understanding of optimization in deep learning. We hope that this article will assist readers in gaining a deeper insight in this field and encourages the development of more robust, efficient, and high-performing models.Comment: International Digital Economy Academy (IDEA

Stabilizer Approximation III: Maximum Cut

We apply the stabilizer formalism to the Maximum Cut problem, and obtain a new greedy construction heuristic. It turns out to be an elegant synthesis of the edge-contraction and differencing edge-contraction approaches. Utilizing the relation between the Maximum Cut problem and the Ising model, the approximation ratio of the heuristic is easily found to be at least $1/2$. Moreover, numerical results show that the heuristic has very nice performance for graphs with about 100 vertices.Comment: Proves that the approximation ratio is at least 1/2; greatly improves the implementation of the algorithm. 14 pages, 2 figure

Modeling Fetal Brain Development: A semi-automated platform for localization, reconstruction, and segmentation of the fetal brain on MRI

With advances in fetal magnetic resonance imaging (MRI), research in neonatal neuroscience has shifted to identify in utero brain-based biomarkers for outcome prediction in high-risk fetuses, particularly those impacted by growth restriction. Volumetric segmentation of the fetal brain can provide better understanding of the trajectories of brain development and may aid in predicting functional outcomes. The current thesis aimed to develop semi-automatic methods to target deep brain structures in the fetal brain identified on MR images in fetuses with and without growth restriction. In this study, pregnant women (35-39 weeks gestational age [n=9]) with growth appropriate (n=8) and growth restricted fetuses (n=1) were recruited. Fetal MRI was performed on 1.5 Tesla (T) and 3T MRI scanners and 2D stacks of T2-weighted images were acquired. A novel fetal whole brain segmentation algorithm developed for second trimester fetuses was applied to the T2-weighted MR images to reconstruct 2D volumes into 3D images. To segment deep brain structures, an atlas of cortical and subcortical structures was registered to the 3D reconstructed images. Linear and nonlinear registration algorithms, with two types of similarity metrics (mutual information [MI], cross-correlation [CC]), were compared to determine the optimal strategy of segmenting subcortical structures. Dice coefficients were calculated to validate the reliability of automatic methods and to compare the performance between the registration algorithms compared to manual segmentations. Comparing atlas-generated masks against manually segmented masks of the same brain structures, the median Dice-kappa coefficients for linear registration using CC performed optimally. However, post hoc analyses indicated that linear MI and CC performed comparably. Overall, this semi-automatic subcortical segmentation method for third-trimester fetal brain images provides reliable performance. This segmentation pipeline can aid in identifying early predictors of brain dysmaturation to support clinical decision making for antenatal treatment strategies and promote optimal neurodevelopment in fetuses

Constructing Voronoi diagrams in L(1) and L(infinity) metrics with two plane sweeps.

A plane-sweep method without using transformation but using two sweeps is used to construct the Voronoi diagram in L\sb1\ (L\sb\infty, respectively) metric of a set of n point sites in O(nlogn) time and O(n) space. The two sweeps advance from opposite directions and produce two symmetrical data structures called the Left-to-Right Shortest-Path-Map and Right-to-Left Shortest-Path-Map. The two maps are then tailored to produce the desired Voronoi diagram. Source: Masters Abstracts International, Volume: 34-02, page: 0796. Adviser: Y. H. Tsin. Thesis (M.Sc.)--University of Windsor (Canada), 1994