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Open Access Publications from the University of California

Scholarly Works (47 results)

  • Thesis
  • Peer Reviewed
UC Irvine Electronic Theses and Dissertations (2015)

Finite element exterior calculus (FEEC) is a framework to design and understand finite element discretizations for a wide variety of systems of partial differential equations. The applications are already made to the Hodge Laplacian, Maxwell’s equations, the equations of elasticity, elliptic eigenvalue problems and etc.. In this thesis, we propose fast solvers for several numerical schemes based on the discretization of this approach and present theoretical analysis. Specifically, in the first part, we propose efficient block diagonal and block triangular preconditioners for solving the discretized linear system of the vector Laplacian by mixed finite element methods. A variable V-cycle multigrid method with the standard point-wise Gauss-Seidel smoother is proved to be a good preconditioner for the Schur complement. The major benefit of our approach is that the point-wise Gauss-Seidel smoother is more algebraic and can be easily implemented as a ‘black-box’ smoother. The multigrid solver for the Schur complement will be further used to build preconditioners for the original saddle point systems. In the second part, we propose a discretization method for the Darcy-Stokes equations under the framework of FEEC. The discretization is shown to be uniform with respect to the perturbation parameter. A preconditioner for the discrete system is also proposed and shown to be efficient. In the last part, we focus on the stochastic Stokes equations. The stochastic saddle-point linear systems are obtained by using finite element discretization under the framework of FEEC in physical space and generalized polynomial chaos expansion in random space. We prove the existence and uniqueness of the solutions to the continuous problem and its corresponding stochastic Galerkin discretization. Optimal error estimates are also derived. We construct block-diagonal/triangular preconditioners for use with the generalized minimum residual method and the bi-conjugate gradient stabilized method. An optimal multigrid solver is applied to efficiently solve the diagonal blocks that correspond to deterministic discrete Stokes systems. To demonstrate the efficiency and robustness of the discretization methods and proposed preconditioners, various numerical examples also are provided.

    Cover page: Fast Solvers for Numerical Schemes Based On Finite Element Exterior Calculus
    • Article
    • Peer Reviewed
    UC Irvine Previously Published Works (2017)
    Visual perceptual learning through practice or training can significantly improve performance on visual tasks. Originally seen as a manifestation of plasticity in the primary visual cortex, perceptual learning is more readily understood as improvements in the function of brain networks that integrate processes, including sensory representations, decision, attention, and reward, and balance plasticity with system stability. This review considers the primary phenomena of perceptual learning, theories of perceptual learning, and perceptual learning's effect on signal and noise in visual processing and decision. Models, especially computational models, play a key role in behavioral and physiological investigations of the mechanisms of perceptual learning and for understanding, predicting, and optimizing human perceptual processes, learning, and performance. Performance improvements resulting from reweighting or readout of sensory inputs to decision provide a strong theoretical framework for interpreting perceptual learning and transfer that may prove useful in optimizing learning in real-world applications.
      Cover page: Visual Perceptual Learning and Models
      • Article
      • Peer Reviewed
      UC Irvine Previously Published Works (2023)
      The external noise paradigm and perceptual template model (PTM) have successfully been applied to characterize observer properties and mechanisms of observer state changes (e.g. attention and perceptual learning) in several research domains, focusing on individual level analysis. In this study, we developed a new hierarchical Bayesian perceptual template model (HBPTM) to model the trial-by-trial data from all individuals and conditions in a published spatial cuing study within a single structure and compared its performance to that of a Bayesian Inference Procedure (BIP), which separately infers the posterior distributions of the model parameters for each individual subject without the hierarchical structure. The HBPTM allowed us to compute the joint posterior distribution of the hyperparameters and parameters at the population, observer, and experiment levels and make statistical inferences at all these levels. In addition, we ran a large simulation study that varied the number of observers and number of trials in each condition and demonstrated the advantage of the HBPTM over the BIP across all the simulated datasets. Although it is developed in the context of spatial attention, the HBPTM and its extensions can be used to model data from the external noise paradigm in other domains and enable predictions of human performance at both the population and individual levels.
        Cover page: Hierarchical Bayesian perceptual template modeling of mechanisms of spatial attention in central and peripheral cuing
        • Article
        • Peer Reviewed
        UC Irvine Previously Published Works (2014)
        Feedback has been shown to play a complex role in visual perceptual learning. It is necessary for performance improvement in some conditions while not others. Different forms of feedback, such as trial-by-trial feedback or block feedback, may both facilitate learning, but with different mechanisms. False feedback can abolish learning. We account for all these results with the Augmented Hebbian Reweight Model (AHRM). Specifically, three major factors in the model advance performance improvement: the external trial-by-trial feedback when available, the self-generated output as an internal feedback when no external feedback is available, and the adaptive criterion control based on the block feedback. Through simulating a comprehensive feedback study (Herzog & Fahle, 1997), we show that the model predictions account for the pattern of learning in seven major feedback conditions. The AHRM can fully explain the complex empirical results on the role of feedback in visual perceptual learning.
          Cover page: Modeling trial by trial and block feedback in perceptual learning
          • Article
          • Peer Reviewed
          UC Irvine Previously Published Works (2023)
          Perceptual learning, the improvement of perceptual judgments with practice, occurs in many visual tasks. There are, however, relatively fewer studies examining perceptual learning in spatial frequency judgments. In addition, perceptual learning has generally been studied in two-alternative tasks, occasionally in n-alternative tasks, and infrequently in identification. Recently, perceptual learning was found in an orientation identification task (eight-alternatives) and was well accounted for by a new identification integrated reweighting theory (I-IRT) (Liu et al., submitted). Here, we examined perceptual learning in a similar eight-alternative spatial frequency absolute identification task in two different training protocols, finding learning in the majority but not all observers. We fit the I-IRT to the spatial frequency learning data and discuss possible model explanations for variations in learning.
            Cover page: Learning spatial frequency identification through reweighted decoding.
            • Article
            • Peer Reviewed
            UC Irvine Previously Published Works (2022)
            The visual expertise of adult humans is jointly determined by evolution, visual development, and visual perceptual learning. Perceptual learning refers to performance improvements in perceptual tasks after practice or training in the task. It occurs in almost all visual tasks, ranging from simple feature detection to complex scene analysis. In this Review, we focus on key behavioral aspects of visual perceptual learning. We begin by describing visual perceptual learning tasks and manipulations that influence the magnitude of learning, and then discuss specificity of learning. Next, we present theories and computational models of learning and specificity. We then review applications of visual perceptual learning in visual rehabilitation. Finally, we summarize the general principles of visual perceptual learning, discuss the tension between plasticity and stability, and conclude with new research directions.
              Cover page: Current directions in visual perceptual learning.
              • Article
              • Peer Reviewed
              UC Irvine Previously Published Works (2015)
              In this paper, we consider the use of H(div) elements in the velocity-pressure formulation to discretize Stokes equations in two dimensions. We address the error estimate of the element pair RT0-P0, which is known to be suboptimal, and render the error estimate optimal by the symmetry of the grids and by the superconvergence result of Lagrange inter-polant. By enlarging RT0 such that it becomes a modified BDM-type element, we develop a new discretization [Formula: see text]. We, therefore, generalize the classical MAC scheme on rectangular grids to triangular grids and retain all the desirable properties of the MAC scheme: exact divergence-free, solver-friendly, and local conservation of physical quantities. Further, we prove that the proposed discretization [Formula: see text] achieves the optimal convergence rate for both velocity and pressure on general quasi-uniform grids, and one and half order convergence rate for the vorticity and a recovered pressure. We demonstrate the validity of theories developed here by numerical experiments.
                Cover page: Convergence Analysis of Triangular MAC Schemes for Two Dimensional Stokes Equations
                • Article
                • Peer Reviewed
                UC Irvine Previously Published Works (2024)
                A large body of literature has examined specificity and transfer of perceptual learning, suggesting a complex picture. Here, we distinguish between transfer over variations in a task-relevant feature (e.g., transfer of a learned orientation task to a different reference orientation) and transfer over a task-irrelevant feature (e.g., transfer of a learned orientation task to a different retinal location or different spatial frequency), and we focus on the mechanism for the latter. Experimentally, we assessed whether learning a judgment of one feature (such as orientation) using one value of an irrelevant feature (e.g., spatial frequency) transfers to another value of the irrelevant feature. Experiment 1 examined whether learning in eight-alternative orientation identification with one or multiple spatial frequencies transfers to stimuli at five different spatial frequencies. Experiment 2 paralleled Experiment 1, examining whether learning in eight-alternative spatial-frequency identification at one or multiple orientations transfers to stimuli with five different orientations. Training the orientation task with a single spatial frequency transferred widely to all other spatial frequencies, with a tendency to specificity when training with the highest spatial frequency. Training the spatial frequency task fully transferred across all orientations. Computationally, we extended the identification integrated reweighting theory (I-IRT) to account for the transfer data (Dosher, Liu, & Lu, 2023; Liu, Dosher, & Lu, 2023). Just as location-invariant representations in the original IRT explain transfer over retinal locations, incorporating feature-invariant representations effectively accounted for the observed transfer. Taken together, we suggest that feature-invariant representations can account for transfer of learning over a task-irrelevant feature.
                  Cover page: Transfer of visual perceptual learning over a task-irrelevant feature through feature-invariant representations: Behavioral experiments and model simulations.
                  • Article
                  • Peer Reviewed
                  Proceedings of the Annual Meeting of the Cognitive Science Society, Volume 35 (2013)
                    Cover page: Adaptive Estimation of Psychometric Slope and Threshold with Differential Evolution
                    • Article
                    • Peer Reviewed
                    UC Irvine Previously Published Works (2015)
                    In this article we develop an extension to the signal detection theory framework to separately estimate internal noise arising from representational and decision processes. Our approach constrains signal detection theory models with decision noise by combining a multipass external noise paradigm with confidence rating responses. In a simulation study we present evidence that representation and decision noise can be separately estimated over a range of representative underlying representational and decision noise level configurations. These results also hold across a number of decision rules and show resilience to rule miss-specification. The new theoretical framework is applied to a visual detection confidence-rating task with 3 and 5 response categories. This study compliments and extends the recent efforts of researchers (Benjamin, Diaz, & Wee, 2009; Mueller & Weidemann, 2008; Rosner & Kochanski, 2009; Kellen, Klauer, & Singmann, 2012) to separate and quantify underlying sources of response variability in signal detection tasks.
                      Cover page: Separating Decision and Encoding Noise in Signal Detection Tasks
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