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Most datasets used for supervised machine learning consist of a single label per data point. However, in cases where more information than just the class label is available, would it be possible to train models more efficiently? We introduce two novel model architectures, which we call hybrid concept-based models, that train using both class labels and additional information in the dataset referred to as concepts. In order to thoroughly assess their performance, we introduce ConceptShapes, an open and flexible class of datasets with concept labels. We show that the hybrid concept-based models outperform standard computer vision models and previously proposed concept-based models with respect to accuracy, especially in sparse data settings. We also introduce an algorithm for performing adversarial concept attacks, where an image is perturbed in a way that does not change a concept-based model's concept predictions, but changes the class prediction. The existence of such adversarial examples raises questions about the interpretable qualities promised by concept-based models., Comment: 11 pages, 8 figures, appendix

In this paper we propose a novel approach aimed at recovering the 3D position of an UUV from UAV imagery in shallow-water environments. Through combination of UAV and UUV measurements, we show that our method can be utilized as an accurate and cost-effective alternative when compared to acoustic sensing methods, typically required to obtain ground truth information in underwater localization problems. Furthermore, our approach allows for a seamless conversion to geo-referenced coordinates which can be utilized for navigation purposes. To validate our method, we present the results with data collected through a simulation environment and field experiments, demonstrating the ability to successfully recover the UUV position with sub-meter accuracy.

We consider two nonlinear state estimation problems in a setting where an extended Kalman filter receives measurements from two sets of sensors via two channels (2C). In the stochastic-2C problem, the channels drop measurements stochastically, whereas in 2C scheduling, the estimator chooses when to read each channel. In the first problem, we generalize linear-case 2C analysis to obtain -- for a given pair of channel arrival rates -- boundedness conditions for the trace of the error covariance, as well as a worst-case upper bound. For scheduling, an optimization problem is solved to find arrival rates that balance low channel usage with low trace bounds, and channels are read deterministically with the expected periods corresponding to these arrival rates. We validate both solutions in simulations for linear and nonlinear dynamics; as well as in a real experiment with an underwater robot whose position is being intermittently found in a UAV camera image.

This document presents a summary of the 2023 Terrestrial Very-Long-Baseline Atom Interferometry Workshop hosted by CERN. The workshop brought together experts from around the world to discuss the exciting developments in large-scale atom interferometer (AI) prototypes and their potential for detecting ultralight dark matter and gravitational waves. The primary objective of the workshop was to lay the groundwork for an international TVLBAI proto-collaboration. This collaboration aims to unite researchers from different institutions to strategize and secure funding for terrestrial large-scale AI projects. The ultimate goal is to create a roadmap detailing the design and technology choices for one or more km-scale detectors, which will be operational in the mid-2030s. The key sections of this report present the physics case and technical challenges, together with a comprehensive overview of the discussions at the workshop together with the main conclusions., Comment: Summary of the Terrestrial Very-Long-Baseline Atom Interferometry Workshop held at CERN: https://indico.cern.ch/event/1208783/

The aim of this work is to improve musculoskeletal-based models of the upper-limb Wrench Feasible Set i.e. the set of achievable maximal wrenches at the hand for applications in collaborative robotics and computer aided ergonomics. In particular, a recent method performing wrench capacity evaluation called the Iterative Convex Hull Method is upgraded in order to integrate non dislocation and compression limitation constraints at the glenohumeral joint not taken into account in the available models. Their effects on the amplitude of the force capacities at the hand, glenohumeral joint reaction forces and upper-limb muscles coordination in comparison to the original iterative convex hull method are investigated in silico. The results highlight the glenohumeral potential dislocation for the majority of elements of the wrench feasible set with the original Iterative Convex Hull method and the fact that the modifications satisfy correctly stability constraints at the glenohumeral joint. Also, the induced muscles coordination pattern favors the action of stabilizing muscles, in particular the rotator-cuff muscles, and lowers that of known potential destabilizing ones according to the literature., Comment: 30 pages (double spacing), 10 figures, 2 tables

Understanding the implicit regularization imposed by neural network architectures and gradient based optimization methods is a key challenge in deep learning and AI. In this work we provide sharp results for the implicit regularization imposed by the gradient flow of Diagonal Linear Networks (DLNs) in the over-parameterized regression setting and, potentially surprisingly, link this to the phenomenon of phase transitions in generalized hardness of approximation (GHA). GHA generalizes the phenomenon of hardness of approximation from computer science to, among others, continuous and robust optimization. It is well-known that the $\ell^1$-norm of the gradient flow of DLNs with tiny initialization converges to the objective function of basis pursuit. We improve upon these results by showing that the gradient flow of DLNs with tiny initialization approximates minimizers of the basis pursuit optimization problem (as opposed to just the objective function), and we obtain new and sharp convergence bounds w.r.t.\ the initialization size. Non-sharpness of our results would imply that the GHA phenomenon would not occur for the basis pursuit optimization problem -- which is a contradiction -- thus implying sharpness. Moreover, we characterize $\textit{which}$ $\ell_1$ minimizer of the basis pursuit problem is chosen by the gradient flow whenever the minimizer is not unique. Interestingly, this depends on the depth of the DLN.

In this paper we present Open Multi-Processing (OpenMP) Fortran 90/95 versions of previously published numerical programs for solving the dipolar Gross-Pitaevskii (GP) equation including the contact interaction in one, two and three spatial dimensions. The atoms are considered to be polarized along the z axis and we consider different cases, e.g., stationary and non-stationary solutions of the GP equation for a dipolar Bose-Einstein condensate (BEC) in one dimension (along x and z axes), two dimensions (in x-y and x-z planes), and three dimensions. The algorithm used is the split-step semi-implicit Crank-Nicolson scheme for imaginary- and real-time propagation to obtain stationary states and BEC dynamics, respectively, as in the previous version [R. Kishor Kumar et al., Comput. Phys. Commun. 195, 117 (2015)]. These OpenMP versions have significantly reduced execution time in multicore processors.

We prove Rogers-Ramanujan type identities for the Nahm sums associated with the tadpole Cartan matrix of rank $3$. These identities reveal the modularity of these sums, and thereby we confirm a conjecture of Penn, Calinescu and the first author in this case. We show that these Nahm sums together with some shifted sums can be combined into a vector-valued modular function on the full modular group. We also present some conjectures for a general rank., Comment: 25 pages

This paper presents an approach for approximating the reachable space of robotic manipulators based on convex polytopes. The proposed approach predicts the reachable space over a given time horizon based on the robot's actuation limits and kinematic constraints. The approach is furthermore extended to integrate the robot's environment, assuming it can be expressed in a form of linear constraints, and to account for the robot's link geometry.The accuracy of the proposed method is evaluated using simulations of robot's nonlinear dynamics and it is compared against the cartesian space limits, usually provided by manufacturers in standard datasheets.The accuracy analysis results show that the proposed method has good performance for the time horizons up to 250ms, encapsulating most of the simulated robot's reachable space while maintaining comparable volume. For a 7 dof robot, the method has an average execution time of 50ms, independent of the horizon time, potentially enabling real-time applications.

Progress in understanding quantum systems has been driven by the exploration of the geometry, topology, and dimensionality of ultracold atomic systems. The NASA Cold Atom Laboratory (CAL) aboard the International Space Station has enabled the study of ultracold atomic bubbles, a terrestrially-inaccessible topology. Proof-of-principle bubble experiments have been performed on CAL with an rf-dressing technique; an alternate technique (dual-species interaction-driven bubbles) has also been proposed. Both techniques can drive discovery in the next decade of fundamental physics research in microgravity., Comment: 17 pages, 2 figures

In this paper, a continuation of \cite{MPS}, we investigate the $S_3$-orbifold subalgebra of $(\mathcal{V}_c)^{\otimes 3}$, that is, we consider the $S_3$-fixed point vertex subalgebra of the tensor product of three copies of the universal Virasoro vertex operator algebras $\mathcal{V}_c$. Our main result is construction of a minimal, strong set of generators of this subalgebra for any generic values of $c$. More precisely, we show that this vertex algebra is of type $(2,4,6^2,8^2,9,10^2,11,12^3)$. We also investigate two prominent examples of simple $S_3$-orbifold algebras corresponding to central charges $c=\frac12$ (Ising model) and $c=-\frac{22}{5}$ (i.e. $(2,5)$-minimal model). We prove that the former is a new unitary $W$-algebra of type $(2,4,6,8)$ and the latter is isomorphic to the affine simple $W$-algebra of type $\frak{g}_2$ at non-admissible level $-\frac{19}{6}$. We also provide another version of this isomorphism using the affine $W$-algebra of type $\frak{g}_2$ coming from a subregular nilpotent element., Comment: 25 pages

This paper presents a method for aerial manipulator end-effector trajectory tracking by encompassing dynamics of the Unmanned Aerial Vehicle (UAV) and null space of the manipulator attached to it in the motion planning procedure. The proposed method runs in phases. Trajectory planning starts by not accounting for roll and pitch angles of the underactuated UAV system. Next, we propose simulating the dynamics on such a trajectory and obtaining UAV attitude through the model. The full aerial manipulator state obtained in such a manner is further utilized to account for discrepancies in planned and simulated end-effector states. Finally, the end-effector pose is corrected through the null space of the manipulator to match the desired end-effector pose obtained in trajectory planning. Furthermore, we have applied the TOPP-RA approach on the UAV by invoking the differential flatness principle. Finally, we conducted experimental tests to verify effectiveness of the planning framework.

We analyze certain characters of vertex algebras that can be expressed using (generalized) q-MZVs. We consider: (i) characters of vertex algebras associated to arc spaces, (ii) characters (or indices) of $\mathcal{S}$-class vertex operator algebras in 4d $\mathcal{N}=2$ SCFT, (iii) supercharacters of the $\mathcal{U}$ family of vertex algebras. Along the way we also introduce a family of multiple $q$-zeta values associated to simple Lie algebras and present their conjectural properties., Comment: v2. 28 pages

Inspired by recent promising results in sim-to-real transfer in deep learning we built a realistic simulation environment combining a Robot Operating System (ROS)-compatible physics simulator (Gazebo) with Cycles, the realistic production rendering engine from Blender. The proposed simulator pipeline allows us to simulate near-realistic RGB-D images. To showcase the capabilities of the simulator pipeline we propose a case study that focuses on indoor robotic farming. We developed a solution for sweet pepper yield estimation task. Our approach to yield estimation starts with aerial robotics control and trajectory planning, combined with deep learning-based pepper detection, and a clustering approach for counting fruit. The results of this case study show that we can combine real time dynamic simulation with near realistic rendering capabilities to simulate complex robotic systems., Comment: Submitted to ICUAS 2022. Under review

We summarize the discussions at a virtual Community Workshop on Cold Atoms in Space concerning the status of cold atom technologies, the prospective scientific and societal opportunities offered by their deployment in space, and the developments needed before cold atoms could be operated in space. The cold atom technologies discussed include atomic clocks, quantum gravimeters and accelerometers, and atom interferometers. Prospective applications include metrology, geodesy and measurement of terrestrial mass change due to, e.g., climate change, and fundamental science experiments such as tests of the equivalence principle, searches for dark matter, measurements of gravitational waves and tests of quantum mechanics. We review the current status of cold atom technologies and outline the requirements for their space qualification, including the development paths and the corresponding technical milestones, and identifying possible pathfinder missions to pave the way for missions to exploit the full potential of cold atoms in space. Finally, we present a first draft of a possible road-map for achieving these goals, that we propose for discussion by the interested cold atom, Earth Observation, fundamental physics and other prospective scientific user communities, together with ESA and national space and research funding agencies., Comment: Summary of the Community Workshop on Cold Atoms in Space and corresponding Road-map: https://indico.cern.ch/event/1064855/

Many recent human-robot collaboration strategies, such as Assist-As-Needed (AAN), are promoting humancentered robot control, where the robot continuously adapts its assistance level based on the real-time need of its human counterpart. One of the fundamental assumptions of these approaches is the ability to measure or estimate the physical capacity of humans in real-time. In this work, we propose an algorithm for the feasibility set analysis of a generic class of linear algebra problems. This novel iterative convex-hull method is applied to the determination of the feasible Cartesian wrench polytope associated to a musculoskeletal model of the human upper limb. The method is capable of running in real-time and allows the user to define the desired estimation accuracy. The algorithm performance analysis shows that the execution time has near-linear relationship to the considered number of muscles, as opposed to the exponential relationship of the conventional methods. Finally, real-time robot control application of the algorithm is demonstrated in a Collaborative carrying experiment, where a human operator and a Franka Emika Panda robot jointly carry a 7kg object. The robot is controlled in accordance to the AAN paradigm maintaining the load carried by the human operator at 30% of its carrying capacity.

In this paper, we address the problem of autonomous exploration of unknown environments with an aerial robot equipped with a sensory set that produces large point clouds, such as LiDARs. The main goal is to gradually explore an area while planning paths and calculating information gain in short computation time, suitable for implementation on an on-board computer. To this end, we present a planner that randomly samples viewpoints in the environment map. It relies on a novel and efficient gain calculation based on the Recursive Shadowcasting algorithm. To determine the Next-Best-View (NBV), our planner uses a cuboid-based evaluation method that results in an enviably short computation time. To reduce the overall exploration time, we also use a dead end resolving strategy that allows us to quickly recover from dead ends in a challenging environment. Comparative experiments in simulation have shown that our approach outperforms the current state-of-the-art in terms of computational efficiency and total exploration time. The video of our approach can be found at https://www.youtube.com/playlist?list=PLC0C6uwoEQ8ZDhny1VdmFXLeTQOSBibQl.

We prove certain Nahm-type sum representations for the (odd modulus) Andrews-Gordon identities, the (even modulus) Andrews-Bressoud identities, and Rogers' false theta functions. These identities are motivated on one hand by a recent work of C. Jennings-Shaffer and one of us on double pole series, and, on the other hand, by C\'ordova, Gaiotto and Shao's work on defect Schur's indices.

False theta functions are functions that are closely related to classical theta functions and mock theta functions. In this paper, we study their modular properties at all ranks by forming modular completions analogous to modular completions of indefinite theta functions of any signature and thereby develop a structure parallel to the recently developed theory of higher depth mock modular forms. We then demonstrate this theoretical base on a number of examples up to depth three coming from characters of modules for the vertex algebra $W^0(p)_{A_n}$, $1 \leq n \leq 3$, and from $\hat{Z}$-invariants of $3$-manifolds associated with gauge group $\mathrm{SU}(3)$., Comment: 40 pages; v2: Brief comments and clarifications added. To appear in Communications in Contemporary Mathematics