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In this paper, we investigate the problem of estimating the 4-DOF (three-dimensional position and orientation) robot-robot relative frame transformation using odometers and distance measurements between robots. Firstly, we apply a two-step estimation method based on maximum likelihood estimation. Specifically, a good initial value is obtained through unconstrained least squares and projection, followed by a more accurate estimate achieved through one-step Gauss-Newton iteration. Additionally, the optimal installation positions of Ultra-Wideband (UWB) are provided, and the minimum operating time under different quantities of UWB devices is determined. Simulation demonstrates that the two-step approach offers faster computation with guaranteed accuracy while effectively addressing the relative transformation estimation problem within limited space constraints. Furthermore, this method can be applied to real-time relative transformation estimation when a specific number of UWB devices are installed.

In this study, we propose an axiomatic system to define and quantify the precise memorization and in-context reasoning effects used by the large language model (LLM) for language generation. These effects are formulated as non-linear interactions between tokens/words encoded by the LLM. Specifically, the axiomatic system enables us to categorize the memorization effects into foundational memorization effects and chaotic memorization effects, and further classify in-context reasoning effects into enhanced inference patterns, eliminated inference patterns, and reversed inference patterns. Besides, the decomposed effects satisfy the sparsity property and the universal matching property, which mathematically guarantee that the LLM's confidence score can be faithfully decomposed into the memorization effects and in-context reasoning effects. Experiments show that the clear disentanglement of memorization effects and in-context reasoning effects enables a straightforward examination of detailed inference patterns encoded by LLMs.

This research delves into the enhancement of control mechanisms for the da Vinci Surgical System, focusing on the implementation of gravity compensation and refining the modeling of the master and patient side manipulators. Leveraging the Robot Operating System (ROS) the study aimed to fortify the precision and stability of the robots movements essential for intricate surgical procedures. Through rigorous parameter identification and the Euler Lagrange approach the team successfully derived the necessary torque equations and established a robust mathematical model. Implementation of the actual robot and simulation in Gazebo highlighted the efficacy of the developed control strategies facilitating accurate positioning and minimizing drift. Additionally, the project extended its contributions by constructing a comprehensive model for the patient side manipulator laying the groundwork for future research endeavors. This work signifies a significant advancement in the pursuit of enhanced precision and user control in robotic assisted surgeries. NOTE - This work has been submitted to the IEEE R-AL for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible.

In this work, we investigate a numerical procedure for recovering a space-dependent diffusion coefficient in a (sub)diffusion model from the given terminal data, and provide a rigorous numerical analysis of the procedure. By exploiting decay behavior of the observation in time, we establish a novel H{\"o}lder type stability estimate for a large terminal time $T$. This is achieved by novel decay estimates of the (fractional) time derivative of the solution. To numerically recover the diffusion coefficient, we employ the standard output least-squares formulation with an $H^1(\Omega)$-seminorm penalty, and discretize the regularized problem by the Galerkin finite element method with continuous piecewise linear finite elements in space and backward Euler convolution quadrature in time. Further, we provide an error analysis of discrete approximations, and prove a convergence rate that matches the stability estimate. The derived $L^2(\Omega)$ error bound depends explicitly on the noise level, regularization parameter and discretization parameter(s), which gives a useful guideline of the \textsl{a priori} choice of discretization parameters with respect to the noise level in practical implementation. The error analysis is achieved using the conditional stability argument and discrete maximum-norm resolvent estimates. Several numerical experiments are also given to illustrate and complement the theoretical analysis.

Existing debiasing methods inevitably make unreasonable or undesired predictions as they are designated and evaluated to achieve parity across different social groups but leave aside individual facts, resulting in modified existing knowledge. In this paper, we first establish a new bias mitigation benchmark BiasKE leveraging existing and additional constructed datasets, which systematically assesses debiasing performance by complementary metrics on fairness, specificity, and generalization. Meanwhile, we propose a novel debiasing method, Fairness Stamp (FAST), which enables editable fairness through fine-grained calibration on individual biased knowledge. Comprehensive experiments demonstrate that FAST surpasses state-of-the-art baselines with remarkable debiasing performance while not hampering overall model capability for knowledge preservation, highlighting the prospect of fine-grained debiasing strategies for editable fairness in LLMs.

In this paper, we propose an optimal sequential procedure for the early detection of potential side effects resulting from the administration of some treatment (e.g. a vaccine, say). The results presented here extend previous results obtained in Wang and Boukai (2024) who study the single side effect case to the case of two (or more) side effects. While the sequential procedure we employ, simultaneously monitors several of the treatment's side effects, the $(\alpha, \beta)$-optimal test we propose does not require any information about the inter-correlation between these potential side effects. However, in all of the subsequent analyses, including the derivations of the exact expressions of the Average Sample Number (ASN), the Power function, and the properties of the post-test (or post-detection) estimators, we accounted specifically, for the correlation between the potential side effects. In the real-life application (such as post-marketing surveillance), the number of available observations is large enough to justify asymptotic analyses of the sequential procedure (testing and post-detection estimation) properties. Accordingly, we also derive the consistency and asymptotic normality of our post-test estimators; results which enable us to also provide (asymptotic, post-detection) confidence intervals for the probabilities of various side-effects. Moreover, to compare two specific side effects, their relative risk plays an important role. We derive the distribution of the estimated relative risk in the asymptotic framework to provide appropriate inference. To illustrate the theoretical results presented, we provide two detailed examples based on the data of side effects on COVID-19 vaccine collected in Nigeria (see Nigeria (see Ilori et al. (2022)).

When studying political communication, combining the information from text, audio, and video signals promises to reflect the richness of human communication more comprehensively than confining it to individual modalities alone. However, when modeling such multimodal data, its heterogeneity, connectedness, and interaction are challenging to address. We argue that aligning the respective modalities can be an essential step in entirely using the potential of multimodal data because it informs the model with human understanding. Exploring aligned modalities unlocks promising analytical leverage. First, it allows us to make the most of information in the data, which inter alia opens the door to better quality predictions. Second, it is possible to answer research questions that span multiple modalities with cross-modal queries. Finally, alignment addresses concerns about model interpretability. We illustrate the utility of this approach by analyzing how German MPs address members of the far-right AfD in their speeches, and predicting the tone of video advertising in the context of the 2020 US presidential race. Our paper offers important insights to all keen to analyze multimodal data effectively.

In this study, we further investigate the robustness and generalization ability of an neural network (NN) based force estimation method, using the da Vinci Research Kit Si (dVRK-Si). To evaluate our method's performance, we compare the force estimation accuracy with several baseline methods. We conduct comparative studies between the dVRK classic and dVRK-Si systems to benchmark the effectiveness of these approaches. We conclude that the NN-based method provides comparable force estimation accuracy across the two systems, as the average root mean square error (RMSE) over the average range of force ratio is approximately 3.07% for the dVRK classic, and 5.27% for the dVRK-Si. On the dVRK-Si, the force estimation RMSEs for all the baseline methods are 2 to 4 times larger than the NN-based method in all directions. One possible reason is, we made assumptions in the baseline methods that static forces remain the same or dynamics is time-invariant. These assumptions may hold for the dVRK Classic, as it has pre-loaded weight and maintains horizontal self balance. Since the dVRK-Si configuration does not have this property, assumptions do not hold anymore, therefore the NN-based method significantly outperforms.

Recently, graph neural networks have been gaining a lot of attention to simulate dynamical systems due to their inductive nature leading to zero-shot generalizability. Similarly, physics-informed inductive biases in deep-learning frameworks have been shown to give superior performance in learning the dynamics of physical systems. There is a growing volume of literature that attempts to combine these two approaches. Here, we evaluate the performance of thirteen different graph neural networks, namely, Hamiltonian and Lagrangian graph neural networks, graph neural ODE, and their variants with explicit constraints and different architectures. We briefly explain the theoretical formulation highlighting the similarities and differences in the inductive biases and graph architecture of these systems. We evaluate these models on spring, pendulum, gravitational, and 3D deformable solid systems to compare the performance in terms of rollout error, conserved quantities such as energy and momentum, and generalizability to unseen system sizes. Our study demonstrates that GNNs with additional inductive biases, such as explicit constraints and decoupling of kinetic and potential energies, exhibit significantly enhanced performance. Further, all the physics-informed GNNs exhibit zero-shot generalizability to system sizes an order of magnitude larger than the training system, thus providing a promising route to simulate large-scale realistic systems.