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A problem that plagues robotic grasping is the misalignment of the object and gripper due to difficulties in precise localization, actuation, etc. Under-actuated robotic hands with compliant mechanisms are used to adapt and compensate for these inaccuracies. However, these mechanisms come at the cost of controllability and coordination. For instance, adaptive functions that let the fingers of a two-fingered gripper adapt independently may affect the coordination necessary for grasping small objects. In this work, we develop a two-fingered robotic hand capable of grasping objects that are offset from the gripper's center, while still having the requisite coordination for grasping small objects via a novel gear-type synchronization mechanism with a magnet. This gear synchronization mechanism allows the adaptive finger's tips to be aligned enabling it to grasp objects as small as toothpicks and washers. The magnetic component allows this coordination to automatically turn off when needed, allowing for the grasping of objects that are offset/misaligned from the gripper. This equips the hand with the capability of grasping light, fragile objects (strawberries, creampuffs, etc) to heavy frying pan lids, all while maintaining their position and posture which is vital in numerous applications that require precise positioning or careful manipulation.

The parallel alternating direction method of multipliers (ADMM) algorithms have gained popularity in statistics and machine learning for their efficient handling of large sample data problems. However, the parallel structure of these algorithms is based on the consensus problem, which can lead to an excessive number of auxiliary variables for high-dimensional data. In this paper, we propose a partition-insensitive parallel framework based on the linearized ADMM (LADMM) algorithm and apply it to solve nonconvex penalized smooth quantile regression problems. Compared to existing parallel ADMM algorithms, our algorithm does not rely on the consensus problem, resulting in a significant reduction in the number of variables that need to be updated at each iteration. It is worth noting that the solution of our algorithm remains unchanged regardless of how the total sample is divided, which is also known as partition-insensitivity. Furthermore, under some mild assumptions, we prove that the iterative sequence generated by the parallel LADMM algorithm converges to a critical point of the nonconvex optimization problem. Numerical experiments on synthetic and real datasets demonstrate the feasibility and validity of the proposed algorithm.

Quantum density matrix represents all the information of the entire quantum system, and novel models of meaning employing density matrices naturally model linguistic phenomena such as hyponymy and linguistic ambiguity, among others in quantum question answering tasks. Naturally, we argue that applying the quantum density matrix into classical Question Answering (QA) tasks can show more effective performance. Specifically, we (i) design a new mechanism based on Long Short-Term Memory (LSTM) to accommodate the case when the inputs are matrixes; (ii) apply the new mechanism to QA problems with Convolutional Neural Network (CNN) and gain the LSTM-based QA model with the quantum density matrix. Experiments of our new model on TREC-QA and WIKI-QA data sets show encouraging results. Similarly, we argue that the quantum density matrix can also enhance the image feature information and the relationship between the features for the classical image classification. Thus, we (i) combine density matrices and CNN to design a new mechanism; (ii) apply the new mechanism to some representative classical image classification tasks. A series of experiments show that the application of quantum density matrix in image classification has the generalization and high efficiency on different datasets. The application of quantum density matrix both in classical question answering tasks and classical image classification tasks show more effective performance.

Accurate analytical and numerical modeling of multiscale systems is a daunting task. The need to properly resolve spatial and temporal scales spanning multiple orders of magnitude pushes the limits of both our theoretical models as well as our computational capabilities. Rigorous upscaling techniques enable efficient computation while bounding/tracking errors and helping to make informed cost-accuracy tradeoffs. The biggest challenges arise when the applicability conditions of upscaled models break down. Here, we present a non-intrusive two-way (iterative bottom-up top-down) coupled hybrid model, applied to thermal runaway in battery packs, that combines fine-scale and upscaled equations in the same numerical simulation to achieve predictive accuracy while limiting computational costs. First, we develop two methods with different orders of accuracy to enforce continuity at the coupling boundary. Then, we derive weak (i.e., variational) formulations of the fine-scale and upscaled governing equations for finite element (FE) discretization and numerical implementation in FEniCS. We demonstrate that hybrid simulations can accurately predict the average temperature fields within error bounds determined a priori by homogenization theory. Finally, we demonstrate the computational efficiency of the hybrid algorithm against fine-scale simulations.

We introduce a new discretization based on the Trefftz-DG method for solving the Stokes equations. Discrete solutions of a corresponding method fulfill the Stokes equation pointwise within each element and yield element-wise divergence-free solutions. Compared to standard DG methods, a strong reduction of the degrees of freedom is achieved, especially for higher order polynomial degrees. In addition, in contrast to many other Trefftz-DG methods, our approach allows to easily incorporate inhomogeneous right hand sides (driving forces) by using the concept of the embedded Trefftz-DG method. On top of a detailed a priori error analysis, we further compare our approach to standard discontinuous Galerkin Stokes discretizations and present numerical examples.

We develop in this paper a multi-grade deep learning method for solving nonlinear partial differential equations (PDEs). Deep neural networks (DNNs) have received super performance in solving PDEs in addition to their outstanding success in areas such as natural language processing, computer vision, and robotics. However, training a very deep network is often a challenging task. As the number of layers of a DNN increases, solving a large-scale non-convex optimization problem that results in the DNN solution of PDEs becomes more and more difficult, which may lead to a decrease rather than an increase in predictive accuracy. To overcome this challenge, we propose a two-stage multi-grade deep learning (TS-MGDL) method that breaks down the task of learning a DNN into several neural networks stacked on top of each other in a staircase-like manner. This approach allows us to mitigate the complexity of solving the non-convex optimization problem with large number of parameters and learn residual components left over from previous grades efficiently. We prove that each grade/stage of the proposed TS-MGDL method can reduce the value of the loss function and further validate this fact through numerical experiments. Although the proposed method is applicable to general PDEs, implementation in this paper focuses only on the 1D, 2D, and 3D viscous Burgers equations. Experimental results show that the proposed two-stage multi-grade deep learning method enables efficient learning of solutions of the equations and outperforms existing single-grade deep learning methods in predictive accuracy. Specifically, the predictive errors of the single-grade deep learning are larger than those of the TS-MGDL method in 26-60, 4-31 and 3-12 times, for the 1D, 2D, and 3D equations, respectively.

At the core of the quest for a logic for PTime is a mismatch between algorithms making arbitrary choices and isomorphism-invariant logics. One approach to overcome this problem is witnessed symmetric choice. It allows for choices from definable orbits which are certified by definable witnessing automorphisms. We consider the extension of fixed-point logic with counting (IFPC) with witnessed symmetric choice (IFPC+WSC) and a further extension with an interpretation operator (IFPC+WSC+I). The latter operator evaluates a subformula in the structure defined by an interpretation. This structure possibly has other automorphisms exploitable by the WSC-operator. For similar extensions of pure fixed-point logic (IFP) it is known that IFP+WSCI simulates counting which IFP+WSC fails to do. For IFPC+WSC it is unknown whether the interpretation operator increases expressiveness and thus allows studying the relation between WSC and interpretations beyond counting. We separate IFPC+WSC from IFPC+WSCI by showing that IFPC+WSC is not closed under FO-interpretations. By the same argument, we answer an open question of Dawar and Richerby regarding non-witnessed symmetric choice in IFP. Additionally, we prove that nesting WSC-operators increases the expressiveness using the so-called CFI graphs. We show that if IFPC+WSC+I canonizes a particular class of base graphs, then it also canonizes the corresponding CFI graphs. This differs from various other logics, where CFI graphs provide difficult instances.

We propose a new framework for the sampling, compression, and analysis of distributions of point sets and other geometric objects embedded in Euclidean spaces. Our approach involves constructing a tensor called the RaySense sketch, which captures nearest neighbors from the underlying geometry of points along a set of rays. We explore various operations that can be performed on the RaySense sketch, leading to different properties and potential applications. Statistical information about the data set can be extracted from the sketch, independent of the ray set. Line integrals on point sets can be efficiently computed using the sketch. We also present several examples illustrating applications of the proposed strategy in practical scenarios.

This paper investigates the properties of Quasi Maximum Likelihood estimation of an approximate factor model for an $n$-dimensional vector of stationary time series. We prove that the factor loadings estimated by Quasi Maximum Likelihood are asymptotically equivalent, as $n\to\infty$, to those estimated via Principal Components. Both estimators are, in turn, also asymptotically equivalent, as $n\to\infty$, to the unfeasible Ordinary Least Squares estimator we would have if the factors were observed. We also show that the usual sandwich form of the asymptotic covariance matrix of the Quasi Maximum Likelihood estimator is asymptotically equivalent to the simpler asymptotic covariance matrix of the unfeasible Ordinary Least Squares. These results hold in the general case in which the idiosyncratic components are cross-sectionally heteroskedastic, as well as serially and cross-sectionally weakly correlated. This paper provides a simple solution to computing the Quasi Maximum Likelihood estimator and its asymptotic confidence intervals without the need of running any iterated algorithm, whose convergence properties are unclear, and estimating the Hessian and Fisher information matrices, whose expressions are very complex.

Due to their inherent capability in semantic alignment of aspects and their context words, attention mechanism and Convolutional Neural Networks (CNNs) are widely applied for aspect-based sentiment classification. However, these models lack a mechanism to account for relevant syntactical constraints and long-range word dependencies, and hence may mistakenly recognize syntactically irrelevant contextual words as clues for judging aspect sentiment. To tackle this problem, we propose to build a Graph Convolutional Network (GCN) over the dependency tree of a sentence to exploit syntactical information and word dependencies. Based on it, a novel aspect-specific sentiment classification framework is raised. Experiments on three benchmarking collections illustrate that our proposed model has comparable effectiveness to a range of state-of-the-art models, and further demonstrate that both syntactical information and long-range word dependencies are properly captured by the graph convolution structure.