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This paper develops an approach to categorical deformation quantization via factorization homology. We show that a quantization of the local coefficients for factorization homology is equivalent to consistent quantizations of its value on manifolds. To formulate our results we introduce the concepts of shifted almost Poisson and BD categories. Our main example is the character stack of flat principal bundles for a reductive algebraic group $G$, where we show that applying the general framework to the Drinfeld category reproduces deformations previously introduced by Li-Bland and \v{S}evera. As a direct consequence, we can conclude a precise relation between their quantization and those introduced by Alekseev, Grosse, and Schomerus. To arrive at our results we compute factorization homology with values in a ribbon category enriched over complete $\mathbb{C}[[\hbar]]$-modules. More generally, we define enriched skein categories which compute factorization homology for ribbon categories enriched over a general closed symmetric monoidal category $\mathcal{V}$., Comment: 84 pages. First version, comments and suggestions welcome

In Monocular Keyframe Visual Simultaneous Localization and Mapping (MKVSLAM) frameworks, when incremental position tracking fails, global pose has to be recovered in a short-time window, also known as short-term relocalization. This capability is crucial for mobile robots to have reliable navigation, build accurate maps, and have precise behaviors around human collaborators. This paper focuses on the development of robust short-term relocalization capabilities for mobile robots using a monocular camera system. A novel multimodal keyframe descriptor is introduced, that contains semantic information of objects detected in the environment and the spatial information of the camera. Using this descriptor, a new Keyframe-based Place Recognition (KPR) method is proposed that is formulated as a multi-stage keyframe filtering algorithm, leading to a new relocalization pipeline for MKVSLAM systems. The proposed approach is evaluated over several indoor GPS denied datasets and demonstrates accurate pose recovery, in comparison to a bag-of-words approach., Comment: 8 pages, Keywords: VSLAM, Localization, Semantics. Presented in 2024 IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM)

Mechanistic interpretability aims to reverse engineer the computation performed by a neural network in terms of its internal components. Although there is a growing body of research on mechanistic interpretation of neural networks, the notion of a mechanistic interpretation itself is often ad-hoc. Inspired by the notion of abstract interpretation from the program analysis literature that aims to develop approximate semantics for programs, we give a set of axioms that formally characterize a mechanistic interpretation as a description that approximately captures the semantics of the neural network under analysis in a compositional manner. We use these axioms to guide the mechanistic interpretability analysis of a Transformer-based model trained to solve the well-known 2-SAT problem. We are able to reverse engineer the algorithm learned by the model -- the model first parses the input formulas and then evaluates their satisfiability via enumeration of different possible valuations of the Boolean input variables. We also present evidence to support that the mechanistic interpretation of the analyzed model indeed satisfies the stated axioms.

The first goal of this article is to investigate a refinement of previously-introduced strongly regular hyperbolic automorphisms of locally finite thick Euclidean buildings $\Delta$ of finite Coxeter system $(W,S)$. The new ones are defined for each proper subset $I \subsetneq S$ and called strongly $I$-regular hyperbolic automorphisms of $\Delta$. Generalizing previous results, we show that such elements exist in any group $G$ acting cocompactly and by automorphisms on $\Delta$. Although the dynamics of strongly $I$-regular hyperbolic elements $\gamma$ on the spherical building $\partial_\infty \Delta$ of $\Delta$ is much more complicated than for the strongly regular ones, the $\lim\limits_{n\to \infty} \gamma^{n}(\xi)$ still exists in $\partial_\infty \Delta$ for ideal points $\xi \in \partial_\infty \Delta$ that satisfy certain assumptions. An important role in this business is played by the cone topology on $\Delta \cup \partial_\infty \Delta$ and the projection of specific residues of $\partial_\infty \Delta$ on the ideal boundary of $Min(\gamma)$. All the above research is performed in order to achieve the second, and main, goal of the article. Namely, we prove that for closed groups $G$ with a type-preserving and strongly transitive action by automorphisms on $\Delta$, the Chabauty limits of certain closed subgroups of $G$ contain as a normal subgroup the entire unipotent radical of concrete parabolic subgroups of $G$.

Water caustics are commonly observed in seafloor imaging data from shallow-water areas. Traditional methods that remove caustic patterns from images often rely on 2D filtering or pre-training on an annotated dataset, hindering the performance when generalizing to real-world seafloor data with 3D structures. In this paper, we present a novel method Recurrent Gaussian Splatting (RecGS), which takes advantage of today's photorealistic 3D reconstruction technology, 3DGS, to separate caustics from seafloor imagery. With a sequence of images taken by an underwater robot, we build 3DGS recurrently and decompose the caustic with low-pass filtering in each iteration. In the experiments, we analyze and compare with different methods, including joint optimization, 2D filtering, and deep learning approaches. The results show that our method can effectively separate the caustic from the seafloor, improving the visual appearance, and can be potentially applied on more problems with inconsistent illumination., Comment: 8 pages, 9 figures

As deep neural networks (DNNs) are increasingly used in safety-critical applications, there is a growing concern for their reliability. Even highly trained, high-performant networks are not 100% accurate. However, it is very difficult to predict their behavior during deployment without ground truth. In this paper, we provide a comparative and replicability study on recent approaches that have been proposed to evaluate the reliability of DNNs in deployment. We find that it is hard to run and reproduce the results for these approaches on their replication packages and even more difficult to run them on artifacts other than their own. Further, it is difficult to compare the effectiveness of the approaches, due to the lack of clearly defined evaluation metrics. Our results indicate that more effort is needed in our research community to obtain sound techniques for evaluating the reliability of neural networks in safety-critical domains. To this end, we contribute an evaluation framework that incorporates the considered approaches and enables evaluation on common benchmarks, using common metrics.

Control systems used in Minimally Invasive Surgery (MIS) play a crucial role in ensuring preci-sion and safety throughout procedures. This paper presents a control architecture developed for a robotic system designed for MIS operations. The modular structure of the control system allows for compatibility with a range of procedures in abdominal and thoracic regions. The proposed control system, employing the master-slave concept, is presented alongside the experimental model. Functional validation is obtained by performing a Siemens NX simulation and comparing the results with several experimental runs using the experimental model of the robot. With its compact size and stiffness, the system holds promise for integration with other robotic systems. Future efforts will be dedicated to exploring and optimizing this potential collaboration to enhance the overall capabilities of robotic-assisted surgery.

The paper presents the methodology used for accuracy and repeatability measurements of the experimental model of a parallel robot developed for surgical applications. The experimental setup uses a motion tracking system (for accuracy) and a high precision measuring arm for position (for repeatability). The accuracy was obtained by comparing the trajectory data from the experimental measurement with a baseline trajectory defined with the kinematic models of the parallel robotic system. The repeatability was experi-mentally determined by moving (repeatedly) the robot platform in predefined points.

We analyze in-situ observations of imbalanced solar wind turbulence to evaluate MHD turbulence models grounded in "Critical Balance" (CB) and "Scale-Dependent Dynamic Alignment" (SDDA). At energy injection scales, both outgoing and ingoing modes exhibit a weak cascade; a simultaneous tightening of SDDA is noted. Outgoing modes persist in a weak cascade across the inertial range, while ingoing modes shift to a strong cascade at $\lambda \approx 3 \times 10^{4} d_i$, with associated spectral scalings deviating from expected behavior due to "anomalous coherence" effects. The inertial range comprises two distinct sub-inertial segments. Beyond $\lambda \gtrsim 100 d_i$, eddies adopt a field-aligned tube topology, with SDDA signatures mainly evident in high amplitude fluctuations. The scaling exponents $\zeta_{n}$ of the $n$-th order conditional structure functions, orthogonal to both the local mean field and fluctuation direction, align with the analytical models of Chandran et al. 2015 and Mallet et al. 2017, indicating "multifractal" statistics and strong intermittency; however, scaling in parallel and displacement components is more concave than predicted, possibly influenced by expansion effects. Below $\lambda \approx 100 d_i$, eddies become increasingly anisotropic, evolving into thin current sheet-like structures. Concurrently, $\zeta_{n}$ scales linearly with order, marking a shift towards "monofractal" statistics. At $\lambda \approx 8 d_i$, the increase in aspect ratio halts, and the eddies become quasi-isotropic. This change may signal tearing instability, leading to reconnection, or result from energy redirection into the ion-cyclotron wave spectrum, aligning with the "helicity barrier". Our analysis utilizes 5-point structure functions, proving more effective than the traditional 2-point method in capturing steep scaling behaviors at smaller scales.

The analysis of vision-based deep neural networks (DNNs) is highly desirable but it is very challenging due to the difficulty of expressing formal specifications for vision tasks and the lack of efficient verification procedures. In this paper, we propose to leverage emerging multimodal, vision-language, foundation models (VLMs) as a lens through which we can reason about vision models. VLMs have been trained on a large body of images accompanied by their textual description, and are thus implicitly aware of high-level, human-understandable concepts describing the images. We describe a logical specification language $\texttt{Con}_{\texttt{spec}}$ designed to facilitate writing specifications in terms of these concepts. To define and formally check $\texttt{Con}_{\texttt{spec}}$ specifications, we build a map between the internal representations of a given vision model and a VLM, leading to an efficient verification procedure of natural-language properties for vision models. We demonstrate our techniques on a ResNet-based classifier trained on the RIVAL-10 dataset using CLIP as the multimodal model.

The adsorption and self-assembly of vanadyl phthalocyanine molecules on Ag(100) has been investigated using a combination of scanning tunneling microscopy and density functional theory. At sub-monolayer coverage, we observe two distinct adsorption configurations of isolated molecules, corresponding to the central O atom pointing toward (O-down) or away (O-up) from the substrate. Upon adsorption in the O-up orientation, the otherwise achiral molecules take on a windmill-like chiral appearance due to their interaction with the substrate. At monolayer coverage, we observe a self-assembled square lattice with a mixture of O-up and O-down molecules. At higher coverage we find a strong preference for bilayer formation with O-up and O-down molecules in alternating layers, suggesting stabilization by dipolar interactions. Close inspection of the multi-layer surface reveals grain boundaries separating domains of opposite organizational chirality, and long-range ordering., Comment: 15 pages, 5 figures

We introduce the notion of distributivity for implicative-orthomodular lattices, proving an analogue result of the Foulis-Holland theorem. Based on this result, we characterize the distributive implicative-orthomodular lattices. Moreover, we define the center of an implicative-orthomodular lattice as the set of all elements that commute with all other elements, and we prove that the center is an implicative-Boolean algebra. Additionally, we give new characterizations of implicative-orthomodular lattices.

The development of advanced surgical systems embedding the Master-Slave control strategy introduced the possibility of remote interaction between the surgeon and the patient, also known as teleoperation. The present paper aims to integrate innovative technologies into the teleoperation process to enhance workflow during surgeries. The proposed system incorporates a collaborative robot, Kuka IIWA LBR, and Hololens 2 (an augmented reality device), allowing the user to control the robot in an expansive environment that integrates actual (real data) with additional digital information imported via Hololens 2. Experimental data demonstrate the user's ability to control the Kuka IIWA using various gestures to position it with respect to real or digital objects. Thus, this system offers a novel solution to manipulate robots used in surgeries in a more intuitive manner, contributing to the reduction of the learning curve for surgeons. Calibration and testing in multiple scenarios demonstrate the efficiency of the system in providing seamless movements.

A better understanding of interactive pedestrian behavior in critical traffic situations is essential for the development of enhanced pedestrian safety systems. Real-world traffic observations play a decisive role in this, since they represent behavior in an unbiased way. In this work, we present an approach of how a subset of very considerable pedestrian-vehicle interactions can be derived from a camera-based observation system. For this purpose, we have examined road user trajectories automatically for establishing temporal and spatial relationships, using 110h hours of video recordings. In order to identify critical interactions, our approach combines the metric post-encroachment time with a newly introduced motion adaption metric. From more than 11,000 reconstructed pedestrian trajectories, 259 potential scenarios remained, using a post-encroachment time threshold of 2s. However, in 95% of cases, no adaptation of the pedestrian behavior was observed due to avoiding criticality. Applying the proposed motion adaption metric, only 21 critical scenarios remained. Manual investigations revealed that critical pedestrian vehicle interactions were present in 7 of those. They were further analyzed and made publicly available for developing pedestrian behavior models3. The results indicate that critical interactions in which the pedestrian perceives and reacts to the vehicle at a relatively late stage can be extracted using the proposed method., Comment: 7 pages, 8 figures, ITSC 2023 accepted

Based on implicative involutive BE algebras, we redefine the orthomodular lattices, by introducing the notion of implicative-orthomodular lattices, and we study their properties. We characterize these algebras, proving that the implicative-orthomodular lattices are quantum-Wajsberg algebras. We also define and characterize the implicative-modular algebras as a subclass of implicative-orthomodular lattices. The orthomodular softlattices and orthomodular widelattices are also redefined, by introducing the notions of implicative-orthomodular softlattices and implicative-orthomodular widelattices. Finally, we prove that the implicative-orthomodular softlattices are equivalent to implicative-orthomodular lattices and that the implicative-orthomodular widelattices are special cases of quantum-Wajsberg algebras., Comment: arXiv admin note: text overlap with arXiv:2401.04140

We propose GNNInfer, the first automatic property inference technique for GNNs. To tackle the challenge of varying input structures in GNNs, GNNInfer first identifies a set of representative influential structures that contribute significantly towards the prediction of a GNN. Using these structures, GNNInfer converts each pair of an influential structure and the GNN to their equivalent FNN and then leverages existing property inference techniques to effectively capture properties of the GNN that are specific to the influential structures. GNNINfer then generalizes the captured properties to any input graphs that contain the influential structures. Finally, GNNInfer improves the correctness of the inferred properties by building a model (either a decision tree or linear regression) that estimates the deviation of GNN output from the inferred properties given full input graphs. The learned model helps GNNInfer extend the inferred properties with constraints to the input and output of the GNN, obtaining stronger properties that hold on full input graphs. Our experiments show that GNNInfer is effective in inferring likely properties of popular real-world GNNs, and more importantly, these inferred properties help effectively defend against GNNs' backdoor attacks. In particular, out of the 13 ground truth properties, GNNInfer re-discovered 8 correct properties and discovered likely correct properties that approximate the remaining 5 ground truth properties. Using properties inferred by GNNInfer to defend against the state-of-the-art backdoor attack technique on GNNs, namely UGBA, experiments show that GNNInfer's defense success rate is up to 30 times better than existing baselines., Comment: 20 pages main paper, 10 pages for appendix

Starting from involutive BE algebras, we redefine the pre-MV and meta-MV algebras, by introducing the notion of pre-Wajsberg and meta-Wajsberg algebras, as generalizations of quantum-Wajsberg algebras. We characterize these algebras, we show that any pre-Wajsberg algebra is a meta-Wajsberg algebra, and we prove that an implicative-orthomodular algebra is a quantum-Wajsberg algebra if and only if it is a meta-Wajsberg algebra. It is shown that the commutative quantum-Wajsberg (implicative-orthomodular, pre-Wajsberg, meta-Wajsberg) algebras coincide with the Wajsberg algebras. We give conditions for the implicative-orthomodular, pre-Wajsberg and meta-Wajsberg algebras to be Wajsberg algebras. The commutative center of an implicative-orthomodular algebra is defined and studied, and it is proved that it is a Wajsberg subalgebra of the implicative-orthomodular algebra., Comment: arXiv admin note: text overlap with arXiv:2311.02483, arXiv:2310.13879, arXiv:2303.16481

Exploring whether Enriched Category Theory could provide the foundation of an alternative approach to Machine Learning. This paper is the first to construct and motivate a Machine Learning algorithm solely with Enriched Category Theory. In order to supplement evidence that Category Theory can be used to motivate robust and explainable algorithms, it is shown that a series of reasonable assumptions about a dataset lead to the construction of the Nearest Neighbours Algorithm. In particular, as an extension of the original dataset using profunctors in the category of Lawvere metric spaces. This leads to a definition of an Enriched Nearest Neighbours Algorithm, which consequently also produces an enriched form of the Voronoi diagram. This paper is intended to be accessible without any knowledge of Category Theory

Real-world multibody systems are often subject to phenomena like friction, joint clearances, and external events. These phenomena can significantly impact the optimal design of the system and its controller. This work addresses the gradient-based optimization methodology for multibody dynamic systems with joint friction using a direct sensitivity approach for gradient computation. After a thorough review of various friction models developed over the years, the Brown McPhee model has been found to be the most suitable for the study due to its accuracy for dynamic simulation and its compatibility with sensitivity analysis. The methodology supports co-design of the system and its controller, which is especially relevant for applications like robotics and servo-mechanical systems where the actuation and the design are highly dependent on each other. Numerical results are obtained using a new implementation of the MBSVT (Multi-Body Systems at Virginia Tech) software package; MBSVT 2.0 is reprogrammed in Julia for ease of implementation while maintaining high computational efficiency. Three case studies are provided to demonstrate the attractive properties of simultaneous optimal design and control approach for certain applications.

Statistical physics courses typically employ abstract language that describes objects too small to be seen, making the topic challenging for students to understand. In this work, we introduce a simple experiment that allows conceptualizing some of the underlying ideas of stochastic processes through direct experimentation. Students analyze stochastic trajectories of beads in a bouncing bed of smaller beads subjected to an external periodic drive. The analysis of the trajectories involves the application of a vast tool kit of statistical estimators that are useful in many fields of physics., Comment: 28 pages, 7 figures, 2 supplementary materials, accepted in American Journal of Physics