Parametric UMAP Embeddings for Representation and Semisupervised Learning

UMAP is a nonparametric graph-based dimensionality reduction algorithm using applied Riemannian geometry and algebraic topology to find low-dimensional embeddings of structured data. The UMAP algorithm consists of two steps: (1) computing a graphical representation of a data set (fuzzy simplicial complex) and (2) through stochastic gradient descent, optimizing a low-dimensional embedding of the graph. Here, we extend the second step of UMAP to a parametric optimization over neural network weights, learning a parametric relationship between data and embedding. We first demonstrate that parametric UMAP performs comparably to its nonparametric counterpart while conferring the benefit of a learned parametric mapping (e.g., fast online embeddings for new data). We then explore UMAP as a regularization, constraining the latent distribution of autoencoders, parametrically varying global structure preservation, and improving classifier accuracy for semisupervised learning by capturing structure in unlabeled data.

Predicted Utility Modulates Working Memory Fidelity in the Brain

The predicted utility of information stored in working memory (WM) is hypothesized to influence the strategic allocation of WM resources. Prior work has shown that when information is prioritized, it is remembered with greater precision relative to other remembered items. However, these paradigms often complicate interpretation of the effects of predicted utility on item fidelity due to a concurrent memory load. Likewise, no fMRI studies have examined whether the predicted utility of an item modulates fidelity in the neural representation of items during the memory delay without a concurrent load. In the current study, we used fMRI to investigate whether predicted utility influences fidelity of WM representations in the brain. Using a generative model multivoxel analysis approach to estimate the quality of remembered representations across predicted utility conditions, we observed that items with greater predicted utility are maintained in memory with greater fidelity, even when they are the only item being maintained. Further, we found that this pattern follows a parametric relationship where more predicted utility corresponded to greater fidelity. These precision differences could not be accounted for based on a redistribution of resources among already-remembered items. Rather, we interpret these results in terms of a gating mechanism that allows for pre-allocation of resources based on predicted value alone. This evidence supports a theoretical distinction between resource allocation that occurs as a result of load and resource pre-allocation that occurs as a result of predicted utility.

Improving human understanding and design of complex multi-level systems with animation and parametric relationship supports

Complex systems are challenging to design, particularly when they contain multi-level organizations with non-obvious relationships among design components. Here, we investigate engineering students’ capacity to search for optimal nanoscale biosystem designs with stochastic component and system behaviors. The study aims to characterize information types that facilitate human learning and improve their complex system understanding and design proficiency. It is hypothesized that learning parametric system relationships and/or inter-level causal mechanisms improves design proficiency; these relationships and mechanisms are teachable through software interfaces. Two contrasting learning/design interfaces were developed that presented differing information types: an interface with performance charts that emphasized parametric relationship learning and an interface with agent-based animations that emphasized inter-level causality learning. Users improved on pre-/post-learning design tasks with both interfaces; users who demonstrated inter-level causal relationship understanding, which occurred primarily with the animation interface, had greater improvement. All users were then presented contrasting animations of systems with opposing emergent behaviors, resulting in many more participants demonstrating an understanding of inter-level causal behaviors. These findings reveal the difficulties in understanding and designing multi-level systems and that interactive software tools may convey crucial information that supports engineering design, particularly with respect to the development of reasoning skills for how system components relate across levels.

Finite Element Modeling of the Contact Geometry and Deformation in Biomechanics Applications1

The main contribution of this paper is to demonstrate the feasibility of using one computational environment for developing accurate geometry as well as performing the analysis of detailed biomechanics models. To this end, the finite element (FE) absolute nodal coordinate formulation (ANCF) and multibody system (MBS) algorithms are used in modeling both the contact geometry and ligaments deformations in biomechanics applications. Two ANCF approaches can be used to model the rigid contact surface geometry. In the first approach, fully parameterized ANCF volume elements are converted to surface geometry using parametric relationship that reduces the number of independent coordinate lines. This parametric relationship can be defined analytically or using a spline function representation. In the second approach, an ANCF surface that defines a gradient deficient thin plate element is used. This second approach does not require the use of parametric relations or spline function representations. These two geometric approaches shed light on the generality of and the flexibility offered by the ANCF geometry as compared to computational geometry (CG) methods such as B-splines and NURBS (Non-Uniform Rational B-Splines). Furthermore, because B-spline and NURBS representations employ a rigid recurrence structure, they are not suited as general analysis tools that capture different types of joint discontinuities. ANCF finite elements, on the other hand, lend themselves easily to geometric description and can additionally be used effectively in the analysis of ligaments, muscles, and soft tissues (LMST), as demonstrated in this paper using the knee joint as an example. In this study, ANCF finite elements are used to define the femur/tibia rigid body contact surface geometry. The same ANCF finite elements are also used to model the MCL and LCL ligament deformations. Two different contact formulations are used in this investigation to predict the femur/tibia contact forces; the elastic contact formulation which allows for penetrations and separations at the contact points, and the constraint contact formulation in which the nonconformal contact conditions are imposed as constraint equations, and as a consequence, no separations or penetrations at the contact points are allowed. For both formulations, the contact surfaces are described in a parametric form using surface parameters that enter into the ANCF finite element geometric description. A set of nonlinear algebraic equations that depend on the surface parameters is developed and used to determine the location of the contact points. These two contact formulations are implemented in a general MBS algorithm that allows for modeling rigid and flexible body dynamics.

ANCF Modeling of the Contact Geometry and Deformation in Biomechanics Applications

The purpose of this investigation is to demonstrate the use of the finite element (FE) absolute nodal coordinate formulation (ANCF) and multibody system (MBS) algorithms in modeling both the contact geometry and ligaments deformations in biomechanics applications. Two ANCF approaches can be used to model the rigid contact surface geometry. In the first approach, fully parameterized ANCF volume elements are converted to surface geometry using parametric relationship that reduces the number of independent coordinate lines. This parametric relationship can be defined analytically or using a spline function representation. In the second approach, an ANCF surface that defines a gradient deficient thin plate element is used. This second approach does not require the use of parametric relations or spline function representations. These two geometric approaches shed light on the generality of and the flexibility offered by the ANCF geometry as compared to computational geometry (CG) methods such as B-splines and NURBS (Non-Uniform Rational B-Splines). Furthermore, because B-spline and NURBS representations employ a rigid recurrence structure, they are not suited as general analysis tools that capture different types of joint discontinuities. ANCF finite elements, on the other hand, lend themselves easily to geometric description and can additionally be used effectively in the analysis of ligaments, muscles, and soft tissues (LMST), as demonstrated in this paper using the knee joint as an example. In this study, ANCF finite elements are used to define the femur/tibia rigid body contact surface geometry. The same ANCF finite elements are also used to model the MCL and LCL ligament deformations. Two different contact formulations are used in this investigation to predict the femur/tibia contact forces; the elastic contact formulation where penetrations and separations at the contact points are allowed, and the constraint contact formulation where the non-conformal contact conditions are imposed as constraint equations, and as a consequence, no separations or penetrations at the contact points are allowed. For both formulations, the contact surfaces are described in a parametric form using surface parameters that enter into the ANCF finite element geometric description. A set of nonlinear algebraic equations that depend on the surface parameters is developed and used to determine the location of the contact points. These two contact formulations are implemented in a general MBS algorithm that allows for modeling rigid and flexible body dynamics.