Coverage, Continuity and Visual Cortical Architecture

The primary visual cortex of many mammals contains a continuous representation of visual space, with a roughly repetitive aperiodic map of orientation preferences superimposed. It was recently found that orientation preference maps (OPMs) obey statistical laws which are apparently invariant among species widely separated in eutherian evolution. Here, we examine whether one of the most prominent models for the optimization of cortical maps, the elastic net (EN) model, can reproduce this common design. The EN model generates representations which optimally trade of stimulus space coverage and map continuity. While this model has been used in numerous studies, no analytical results about the precise layout of the predicted OPMs have been obtained so far. We present a mathematical approach to analytically calculate the cortical representations predicted by the EN model for the joint mapping of stimulus position and orientation. We find that in all previously studied regimes, predicted OPM layouts are perfectly periodic. An unbiased search through the EN parameter space identifies a novel regime of aperiodic OPMs with pinwheel densities lower than found in experiments. In an extreme limit, aperiodic OPMs quantitatively resembling experimental observations emerge. Stabilization of these layouts results from strong nonlocal interactions rather than from a coverage-continuity-compromise. Our results demonstrate that optimization models for stimulus representations dominated by nonlocal suppressive interactions are in principle capable of correctly predicting the common OPM design. They question that visual cortical feature representations can be explained by a coverage-continuity-compromise.Comment: 100 pages, including an Appendix, 21 + 7 figure

Estimation of diaphragm wall deflections for deep braced excavation in anisotropic clays using ensemble learning

This paper adopts the NGI-ADP soil model to carry out finite element analysis, based on which the effects of soft clay anisotropy on the diaphragm wall deflections in the braced excavation were evaluated. More than one thousand finite element cases were numerically analyzed, followed by extensive parametric studies. Surrogate models were developed via ensemble learning methods (ELMs), including the eXtreme Gradient Boosting (XGBoost), and Random Forest Regression (RFR) to predict the maximum lateral wall deformation (δhmax). Then the results of ELMs were compared with conventional soft computing methods such as Decision Tree Regression (DTR), Multilayer Perceptron Regression (MLPR), and Multivariate Adaptive Regression Splines (MARS). This study presents a cutting-edge application of ensemble learning in geotechnical engineering and a reasonable methodology that allows engineers to determine the wall deflection in a fast, alternative way

Metaheuristic design of feedforward neural networks: a review of two decades of research

Over the past two decades, the feedforward neural network (FNN) optimization has been a key interest among the researchers and practitioners of multiple disciplines. The FNN optimization is often viewed from the various perspectives: the optimization of weights, network architecture, activation nodes, learning parameters, learning environment, etc. Researchers adopted such different viewpoints mainly to improve the FNN's generalization ability. The gradient-descent algorithm such as backpropagation has been widely applied to optimize the FNNs. Its success is evident from the FNN's application to numerous real-world problems. However, due to the limitations of the gradient-based optimization methods, the metaheuristic algorithms including the evolutionary algorithms, swarm intelligence, etc., are still being widely explored by the researchers aiming to obtain generalized FNN for a given problem. This article attempts to summarize a broad spectrum of FNN optimization methodologies including conventional and metaheuristic approaches. This article also tries to connect various research directions emerged out of the FNN optimization practices, such as evolving neural network (NN), cooperative coevolution NN, complex-valued NN, deep learning, extreme learning machine, quantum NN, etc. Additionally, it provides interesting research challenges for future research to cope-up with the present information processing era

Ensemble Learning Methods for Educational Data Mining Applications

Student success efficacy studies are aimed at assessing instructional practices and learning environments by evaluating the success of and characterizing student subgroups that may benefit from such modalities. We develop an ensemble learning approach to perform these analytics tasks with specific focus on estimating individualized treatment effects (ITE). ITE are a measure from the personalized medicine literature that can, for each student, quantify the impact of the intervention strategy on student performance, even though the given student either did or did not experience this intervention (i.e., is either in the treatment group or in the control group). We illustrate our learning analytics methods in the study of a supplemental instruction component for a large enrollment introductory statistics course recognized as a curriculum bottleneck at San Diego State University. As part of this application, we show how the ensemble estimate of the ITE may be used to assess the pedagogical reform (supplemental instruction), advise students into supplemental instruction at the beginning of the course, and quantify the impact of the supplemental instruction component on at-risk subgroups. Higher Education researchers and Institutional Research practitioners struggle with the analysis of observational study data and estimation of treatment effects. Propensity score matching has widely been accepted to counteract inherent selection bias in these studies. We present an ensemble learner for propensity score estimation, and consider the use of inverse probability of treatment weighting (IPTW), variance stabilization weighting, and weight truncation to improve treatment effect estimation over propensity score matching. We run a simulation study to validate the treatment effect and propensity score estimation performance of the ensemble learner compared to logistic regression and random forest within the matching and weighting techniques. The results show that the use of the ensemble learner and variance stabilization with truncation result in the lowest mean squared error for treatment effect estimation. We contribute a new package in the statistical software environment R, matchED, that will provide educational researchers with a tool to help analyze student success study data and present actionable results. A tutorial guides the user through the use of each function and it\u27s parameters. A student success intervention is evaluated using the matchED package, and we are able to show that the intervention does help reduce an inherent equity gap between students in the intervention and their peers