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Indoor motion planning focuses on solving the problem of navigating an agent through a cluttered environment. To date, quite a lot of work has been done in this field, but these methods often fail to find the optimal balance between computationally inexpensive online path planning, and optimality of the path. Along with this, these works often prove optimality for single-start single-goal worlds. To address these challenges, we present a multiple waypoint path planner and controller stack for navigation in unknown indoor environments where waypoints include the goal along with the intermediary points that the robot must traverse before reaching the goal. Our approach makes use of a global planner (to find the next best waypoint at any instant), a local planner (to plan the path to a specific waypoint), and an adaptive Model Predictive Control strategy (for robust system control and faster maneuvers). We evaluate our algorithm on a set of randomly generated obstacle maps, intermediate waypoints, and start-goal pairs, with results indicating a significant reduction in computational costs, with high accuracies and robust control., Comment: Accepted at ICCR 2022

We report the observation of cluster glass-like properties in a double perovskite ruthenate Ba$_2$CoRuO$_6$ through structural (neutron and synchrotron X-ray diffraction), magnetic and transport measurements. The system exhibits classic glassy characteristics like a frequency dependence in ac Susceptibility, aging and memory effects along with persistance of short-range correlations upto room temperature. The significant ($\sim30\%$) anti-site disorder on the dimer sites, coupled with the inherent geometrical frustration, allows a variety of exchange (both antiferro- and ferromagnetic) interactions to be distributed randomly across the lattice. On cooling, locally dominant interactions cause spins to nucleate and form local, short-range ordered clusters which grow in size until a global freezing occurs at about $T_f \sim 43K$.

The lattice size of a lattice polytope is a geometric invariant which was formally introduced in the context of simplification of the defining equation of an algebraic curve, but appeared implicitly earlier in geometric combinatorics. Previous work on the lattice size was devoted to studying the lattice size in dimension 2 and 3. In this paper we establish explicit formulas for the lattice size of a family of lattice simplices in arbitrary dimension., Comment: 8 pages

This report covers our reproduction effort of the paper 'Differentiable Spatial Planning using Transformers' by Chaplot et al. . In this paper, the problem of spatial path planning in a differentiable way is considered. They show that their proposed method of using Spatial Planning Transformers outperforms prior data-driven models and leverages differentiable structures to learn mapping without a ground truth map simultaneously. We verify these claims by reproducing their experiments and testing their method on new data. We also investigate the stability of planning accuracy with maps with increased obstacle complexity. Efforts to investigate and verify the learnings of the Mapper module were met with failure stemming from a paucity of computational resources and unreachable authors.

The following paper is a reproducibility report for "Social NCE: Contrastive Learning of Socially-aware Motion Representations" {\cite{liu2020snce}} published in ICCV 2021 as part of the ML Reproducibility Challenge 2021. The original code was made available by the author \footnote{\href{https://github.com/vita-epfl/social-nce}{https://github.com/vita-epfl/social-nce}}. We attempted to verify the results claimed by the authors and reimplemented their code in PyTorch Lightning.

This work describes the automatic registration of a large network (approximately 40) of fixed, ceiling-mounted environment cameras spread over a large area (approximately 800 squared meters) using a mobile calibration robot equipped with a single upward-facing fisheye camera and a backlit ArUco marker for easy detection. The fisheye camera is used to do visual odometry (VO), and the ArUco marker facilitates easy detection of the calibration robot in the environment cameras. In addition, the fisheye camera is also able to detect the environment cameras. This two-way, bidirectional detection constrains the pose of the environment cameras to solve an optimization problem. Such an approach can be used to automatically register a large-scale multi-camera system used for surveillance, automated parking, or robotic applications. This VO based multi-camera registration method has been extensively validated using real-world experiments, and also compared against a similar approach which uses a LiDAR - an expensive, heavier and power hungry sensor.

Pose estimation is usually tackled as either a bin classification or a regression problem. In both cases, the idea is to directly predict the pose of an object. This is a non-trivial task due to appearance variations between similar poses and similarities between dissimilar poses. Instead, we follow the key idea that comparing two poses is easier than directly predicting one. Render-and-compare approaches have been employed to that end, however, they tend to be unstable, computationally expensive, and slow for real-time applications. We propose doing category-level pose estimation by learning an alignment metric in an embedding space using a contrastive loss with a dynamic margin and a continuous pose-label space. For efficient inference, we use a simple real-time image retrieval scheme with a pre-rendered and pre-embedded reference set of renderings. To achieve robustness to real-world conditions, we employ synthetic occlusions, bounding box perturbations, and appearance augmentations. Our approach achieves state-of-the-art performance on PASCAL3D and OccludedPASCAL3D and surpasses the competing methods on KITTI3D in a cross-dataset evaluation setting. The code is currently available at https://github.com/gkouros/contrastive-pose-retrieval., Comment: 29 pages, 16 Figures, 14 tables, BMVC 2022

The Coon amplitude is the unique solution to duality constraints with logarithmic Regge trajectories. A striking feature of this solution is that it interpolates between the Veneziano amplitude and a scalar particle amplitude. However, an analytic proof of unitarity of the amplitude is not yet known. In this short note, we explicitly compute the partial wave coefficients on the leading Regge trajectory in D=4. We find that these coefficients always remain positive, even though their magnitude decreases with spin. Since the coefficients on the subleading trajectories are observed to be larger than those on the leading ones, our result indicates the positivity of the full Coon amplitude in D=4., Comment: 12 pages including appendices. Comments and suggestions are welcome

In this paper we promote the idea of quantum critical lines ({\em inter alia} surfaces) as opposed to points. A quantum critical line obtains when criticality at zero temperature is extended over a continuum in a one-dimensional line. We base our ideas on a simple but exactly solved model introduced by one of the authors involving a one-dimensional quantum transverse field Ising model with added 3-spin interaction. While many of the ideas are quite general, there are other aspects that are not. In particular, a line of criticality with continuously varying exponents is not captured. However, the exact solvability of the model gives us considerable confidence in our results. Although the pure system is analytically exactly solved, the disorder case requires numerical analyses based on exact computation of the correlation function in the Pfaffian representation. The disorder case leads to dynamic structure factor as a function of frequency and wave vector. We expect that the model is experientally realizable and perhaps many other similar models will be found to explore quantum critical lines., Comment: 11 pages, 11 figures

The following paper is a reproducibility report for "Path Planning using Neural A* Search" published in ICML2 2021 as part of the ML Reproducibility Challenge 2021. The original paper proposes the Neural A* planner, and claims it achieves an optimal balance between the reduction of node expansions and path accuracy. We verify this claim by reimplementing the model in a different framework and reproduce the data published in the original paper. We have also provided a code-flow diagram to aid comprehension of the code structure. As extensions to the original paper, we explore the effects of (1) generalizing the model by training it on a shuffled dataset, (2) introducing dropout, (3) implementing empirically chosen hyperparameters as trainable parameters in the model, (4) altering the network model to Generative Adversarial Networks (GANs) to introduce stochasticity, (5) modifying the encoder from Unet to Unet++, (6) incorporating cost maps obtained from the Neural A* module in other variations of A* search.

We compute the normalization of the D-instanton amplitudes in type 0B string theory in two dimensions and find perfect agreement with the dual matrix model result., Comment: LaTeX, 7 pages

Recent contrastive learning methods achieved state-of-the-art in low label regimes. However, the training requires large batch sizes and heavy augmentations to create multiple views of an image. With non-contrastive methods, the negatives are implicitly incorporated in the loss, allowing different images and modalities as pairs. Although the meta-information (i.e., age, sex) in medical imaging is abundant, the annotations are noisy and prone to class imbalance. In this work, we exploited already existing temporal information (different visits from a patient) in a longitudinal optical coherence tomography (OCT) dataset using temporally informed non-contrastive loss (TINC) without increasing complexity and need for negative pairs. Moreover, our novel pair-forming scheme can avoid heavy augmentations and implicitly incorporates the temporal information in the pairs. Finally, these representations learned from the pretraining are more successful in predicting disease progression where the temporal information is crucial for the downstream task. More specifically, our model outperforms existing models in predicting the risk of conversion within a time frame from intermediate age-related macular degeneration (AMD) to the late wet-AMD stage., Comment: Accepted at MICCAI 2022

6-DoF visual localization systems utilize principled approaches rooted in 3D geometry to perform accurate camera pose estimation of images to a map. Current techniques use hierarchical pipelines and learned 2D feature extractors to improve scalability and increase performance. However, despite gains in typical recall@0.25m type metrics, these systems still have limited utility for real-world applications like autonomous vehicles because of their `worst' areas of performance - the locations where they provide insufficient recall at a certain required error tolerance. Here we investigate the utility of using `place specific configurations', where a map is segmented into a number of places, each with its own configuration for modulating the pose estimation step, in this case selecting a camera within a multi-camera system. On the Ford AV benchmark dataset, we demonstrate substantially improved worst-case localization performance compared to using off-the-shelf pipelines - minimizing the percentage of the dataset which has low recall at a certain error tolerance, as well as improved overall localization performance. Our proposed approach is particularly applicable to the crowdsharing model of autonomous vehicle deployment, where a fleet of AVs are regularly traversing a known route., Comment: 8 pages, 5 figures, To be published in RA-L 2022

We propose a novel and pragmatic framework for traffic scene perception with roadside cameras. The proposed framework covers a full-stack of roadside perception pipeline for infrastructure-assisted autonomous driving, including object detection, object localization, object tracking, and multi-camera information fusion. Unlike previous vision-based perception frameworks rely upon depth offset or 3D annotation at training, we adopt a modular decoupling design and introduce a landmark-based 3D localization method, where the detection and localization can be well decoupled so that the model can be easily trained based on only 2D annotations. The proposed framework applies to either optical or thermal cameras with pinhole or fish-eye lenses. Our framework is deployed at a two-lane roundabout located at Ellsworth Rd. and State St., Ann Arbor, MI, USA, providing 7x24 real-time traffic flow monitoring and high-precision vehicle trajectory extraction. The whole system runs efficiently on a low-power edge computing device with all-component end-to-end delay of less than 20ms., Comment: This paper is accepted and presented in ICRA 2022

Engineering design is traditionally performed by hand: an expert makes design proposals based on past experience, and these proposals are then tested for compliance with certain target specifications. Testing for compliance is performed first by computer simulation using what is called a discipline model. Such a model can be implemented by a finite element analysis, multibody systems approach, etc. Designs passing this simulation are then considered for physical prototyping. The overall process may take months, and is a significant cost in practice. We have developed a Bayesian optimization system for partially automating this process by directly optimizing compliance with the target specification with respect to the design parameters. The proposed method is a general framework for computing a generalized inverse of a high-dimensional non-linear function that does not require e.g. gradient information, which is often unavailable from discipline models. We furthermore develop a two-tier convergence criterion based on (i) convergence to a solution optimally satisfying all specified design criteria, or (ii) convergence to a minimum-norm solution. We demonstrate the proposed approach on a vehicle chassis design problem motivated by an industry setting using a state-of-the-art commercial discipline model. We show that the proposed approach is general, scalable, and efficient, and that the novel convergence criteria can be implemented straightforwardly based on existing concepts and subroutines in popular Bayesian optimization software packages., Comment: 15 pages, 16 figures

Interpolating a skewed conditional spatial random field with missing data is cumbersome in the absence of Gaussianity assumptions. Maintaining spatial homogeneity and continuity around the observed random spatial point is also challenging, especially when interpolating along a spatial surface, focusing on the boundary points as a neighborhood. Otherwise, the point far away from one may appear the closest to another. As a result, importing the hierarchical clustering concept on the spatial random field is as convenient as developing the copula with the interface of the Expectation-Maximization algorithm and concurrently utilizing the idea of the Bayesian framework. This paper introduces a spatial cluster-based C-vine copula and a modified Gaussian kernel to derive a novel spatial probability distribution. Another investigation in this paper uses an algorithm in conjunction with a different parameter estimation technique to make spatial-based copula interpolation more compatible and efficient. We apply the proposed spatial interpolation approach to the air pollution of Delhi as a crucial circumstantial study to demonstrate this newly developed novel spatial estimation technique.

The polycrystalline co-doped samples of Sm0.5Y0.5Fe0.58Mn0.42O3 were prepared by solid-state reaction route and its various physical properties with their correlations have been investigated. The dc magnetization measurements on the sample revealed a weak ferromagnetic (WFM) transition at TN=361 K that is followed by an incomplete spin reorientation (SR) transition at TSR1= 348 K. A first order magnetic transition (FOMT) around 292 K completes the spin reorientation transition and the material enters into a nearly collinear antiferromagnetic (AFM) state for T < 260 K. The compound exhibited magnetization reversal below the compensation temperature (Tcomp) = 92 K at low measured field of 100 Oe. At further low temperature below 71 K, the compound also exhibited Zero-field cooled memory effects confirming a reentrant spinglass state formation. Robust magnetodielectric (MD) magnetoelectric coupling has been established in the present material through field dependent dielectric and resistivity measurements. True ferroelectric transition with a considerable value of saturation polarization (= 0.06 micro C/cm2 at 15 K) have been found in the specimen below TFE= 108 K. We observed an intense spin-phonon coupling (SPC) across TSR and TN from the temperature dependent Raman spectroscopy and is responsible for the intrinsic magnetoelectric effect. This SPC also stabilizes the ferroelectric state below TFE in the material. The delicate interplay of the lattice (Phonons), charge and spins governs the observed features in the investigated physical properties of the material that makes the specimen a promising multifunctional material., Comment: 51 Pages, 17 figures. Article part 1

A large family of nonsingular rational solutions of the Kadomtsev-Petviashvili (KP) I equation are investigated. These solutions are constructed via the Gramian method and are identified as points in a complex Grassmannian. Each solution is a traveling wave moving with a uniform background velocity but have multiple peaks which evolve at a slower time scale in the co-moving frame. For large times, these peaks separate and form well-defined wave patterns in the $xy$-plane. The pattern formation are described by the roots of well-known polynomials arising in the study of rational solutions of Painlev\'e II and IV equations. This family of solutions are shown to be described by the classical Schur functions associated with partitions of integers and irreducible representations of the symmetric group of $N$ objects. It is then shown that there exists a one-to-one correspondence between the KPI rational solutions considered in this article and partitions of a positive integer $N$.

CAE engineers work with hundreds of parts spread across multiple body models. A Graph Convolutional Network (GCN) was used to develop a CAE parts classifier. As many as 866 distinct parts from a representative body model were used as training data. The parts were represented as a three-dimensional (3-D) Finite Element Analysis (FEA) mesh with values of each node in the x, y, z coordinate system. The GCN based classifier was compared to fully connected neural network and PointNet based models. Performance of the trained models was evaluated with a test set that included parts from the training data, but with additional holes, rotation, translation, mesh refinement/coarsening, variation of mesh schema, mirroring along x and y axes, variation of topographical features, and change in mesh node ordering. The trained GCN model was able to achieve 88.5% classification accuracy on the test set i.e., it was able to find the correct matching part from the dataset of 866 parts despite significant variation from the baseline part. A CAE parts classifier demonstrated in this study could be very useful for engineers to filter through CAE parts spread across several body models to find parts that meet their requirements.

There is an urgent need to control global warming caused by humans to achieve a sustainable future. $CO_2$ levels are rising steadily and while countries worldwide are actively moving toward the sustainability goals proposed during the Paris Agreement in 2015, we are still a long way to go from achieving a sustainable mode of global operation. The increased popularity of cryptocurrencies since the introduction of Bitcoin in 2009 has been accompanied by an increasing trend in greenhouse gas emissions and high electrical energy consumption. Popular energy tracking studies (e.g., Digiconomist and the Cambridge Bitcoin Energy Consumption Index (CBECI)) have estimated energy consumption ranges of 29.96 TWh to 135.12 TWh and 26.41 TWh to 176.98 TWh respectively for Bitcoin as of July 2021, which are equivalent to the energy consumption of countries such as Sweden and Thailand. The latest estimate by Digiconomist on carbon footprints shows a 64.18 Mt$CO_2$ emission by Bitcoin as of July 2021, close to the emissions by Greece and Oman. This review compiles estimates made by various studies from 2018 to 2021. We compare with the energy consumption and carbon footprints of these cryptocurrencies with countries around the world, and centralized transaction methods such as Visa. We identify the problems associated with cryptocurrencies, and propose solutions that can help reduce their energy usage and carbon footprints. Finally, we present case studies on cryptocurrency networks namely, Ethereum 2.0 and Pi Network, with a discussion on how they solve some of the challenges we have identified.

Compiler correctness is an old problem, but with the emergence of smart contracts on blockchains that problem presents itself in a new light. Smart contracts are self-contained pieces of software that control assets, which are often of high financial value, in an adversarial environment and, once committed to the blockchain, they cannot be changed anymore. Smart contracts are typically developed in a high-level contract language and compiled to low-level virtual machine code before being committed to the blockchain. For a smart contract user to trust a given piece of low-level code on the blockchain, they must convince themselves that (a) they are in possession of the matching source code and (b) that the compiler faithfully translated the source code's semantics. Classic approaches to compiler correctness tackle the second point. We argue that translation certification also addresses the first. We describe the proof architecture of a novel translation certification framework, implemented in Coq, for a functional smart contract language. We demonstrate that we can model the compilation pipeline as a sequence of translation relations that facilitate a modular proof approach and are robust in the face of an evolving compiler implementation.

A family of nonsingular rational solutions of the Kadomtsev-Petviashvili (KP) I equation are investigated. These solutions have multiple peaks whose heights are time-dependent and the peak trajectories in the $xy$-plane are altered after collision. Thus they differ from the standard multi-peaked KPI simple $n$-lump solutions whose peak heights as well as peak trajectories remain unchanged after interaction.The anomalous scattering occurs due to a non-trivial internal dynamics among the peaks in a slow time scale. This phenomena is explained by relating the peak locations to the roots of complex heat polynomials. It follows from the long time asymptotics of the solutions that the peak trajectories separate as $O(\sqrt{|t|})$ as $|t| \to \infty$, and all the peak heights approach the same constant value corresponding to that of the simple 1-lump solution. Consequently, a multi-peaked $n$-lump solution evolves to a superposition of $n$ 1-lump solutions asymptotically as $|t| \to \infty$., Comment: 24 pages, 26 images, accepted for publication in Journal of Physics A: Mathematical and Theoretical

Uncertainty pervades through the modern robotic autonomy stack, with nearly every component (e.g., sensors, detection, classification, tracking, behavior prediction) producing continuous or discrete probabilistic distributions. Trajectory forecasting, in particular, is surrounded by uncertainty as its inputs are produced by (noisy) upstream perception and its outputs are predictions that are often probabilistic for use in downstream planning. However, most trajectory forecasting methods do not account for upstream uncertainty, instead taking only the most-likely values. As a result, perceptual uncertainties are not propagated through forecasting and predictions are frequently overconfident. To address this, we present a novel method for incorporating perceptual state uncertainty in trajectory forecasting, a key component of which is a new statistical distance-based loss function which encourages predicting uncertainties that better match upstream perception. We evaluate our approach both in illustrative simulations and on large-scale, real-world data, demonstrating its efficacy in propagating perceptual state uncertainty through prediction and producing more calibrated predictions., Comment: IEEE International Conference on Robotics and Automation (ICRA) 2022 -- 8 pages, 6 figures, 4 tables