arXiv research

Robots learn to navigate rough terrain using reinforcement learning.

Throughout music history, theorists have identified and documented interpretable rules that capture the decisions of composers. This paper asks, "Can a machine behave like a music theorist?" It presents MUS-ROVER, a self-learning system for automatically discovering rules from symbolic music. MUS-ROVER performs feature…

Motivated by the problem of deformation quantization we introduce and study directed graph complexes with oriented loops and wheels. We develop some technique for computing cohomology of such graph complexes and apply it to several concrete examples such as wheeled completion of the operad of strongly homotopy Lie alge…

New groups constructed from tree automorphisms, proving finiteness.

New PROP structure defined for automorphism group cohomology.

New model for visual cortex border completion using bicycle wheel motions.

Unique CaTherine wheel found for LQG geodesic tree.

Optimizes variational autoencoder for detecting missing data in Mars rover transmissions.

Planetary exploration missions with Mars rovers are complicated, which generally require elaborated task planning by human experts, from the path to take to the images to capture. NASA has been using this process to acquire over 22 million images from the planet Mars. In order to improve the degree of automation and th…

A hierarchical Bayesian classifier is trained at pixel scale with spectral data from the CRISM (Compact Reconnaissance Imaging Spectrometer for Mars) imagery. Its utility in detecting rare phases is demonstrated with new geologic discoveries near the Mars-2020 rover landing site. Akaganeite is found in sediments on the…

CaTherine wheels map between diverse geometric fields.

A novel controller for wheeled robots handles joystick inputs for smooth steering.

Geometric models for Lie algebras from simple singularities.

The paper computes groups and modules for wheel graphs using Fibonacci and Chebyshev polynomials.

The purpose of this research paper it is to present a new approach in the framework of a biased roulette wheel. It is used the approach of a quantitative trading strategy, commonly used in quantitative finance, in order to assess the profitability of the strategy in the short term. The tools of backtesting and walk-for…

The model of a bicycle is a unit segment AB that can move in the plane so that it remains tangent to the trajectory of point A (the rear wheel is fixed on the bicycle frame); the same model describes the hatchet planimeter. The trajectory of the front wheel and the initial position of the bicycle uniquely determine its…

In a previous paper, we generalized the definition of the framed Kontsevich integral initially presented by Le and Murakami. We also defined an isotopy invariant $\widetilde{Z}_f$ that is well-behaved under band sum moves. Using this invariant we study the construction of the LMO invariant, the Wheeling Theorem, and th…

Using elementary equalities between various cables of the unknot and the Hopf link, we prove the Wheels and Wheeling conjectures of [Bar-Natan, Garoufalidis, Rozansky and Thurston, arXiv:q-alg/9703025] and [Deligne, letter to Bar-Natan, January 1996, http://www.ma.huji.ac.il/~drorbn/Deligne/], which give, respectively,…

We study the unwheeled rational Kontsevich integral of torus knots. We give a precise formula for these invariants up to loop degree 3 and show that they appear as colorings of simple diagrams. We show that they behave under cyclic branched coverings in a very simple way. Our proof is combinatorial: it uses the results…

Using technique of wheeled props we establish a correspondence between the homotopy theory of unimodular Lie 1-bialgebras and the famous Batalin-Vilkovisky formalism. Solutions of the so called quantum master equation satisfying certain boundary conditions are proven to be in 1-1 correspondence with representations of …

We study the rational Kontsevich integral of torus knots. We construct explicitely a series of diagrams made of circles joined together in a tree-like fashion and colored by some special rational functions. We show that this series codes exactly the unwheeled rational Kontsevich integral of torus knots, and that it beh…

We express characteristic numbers of compact hyperkähler manifolds in graph-theoretical form, considering them as a special case of the curvature invariants introduced by Rozansky and Witten. The appropriate graphs are generated by ``wheels'' and we use the recently proved Wheeling Theorem to give a formula for the L2 …

A decentralized routing framework for lunar exploration robots.

The complement of a non-separating planar graph contains a K_n minor.

We write a formula for the LMO invariant of a rational homology sphere presented as a rational surgery on a link in S^3. Our main tool is a careful use of the Aarhus integral and the (now proven) "Wheels" and "Wheeling" conjectures of B-N, Garoufalidis, Rozansky and Thurston. As steps, side benefits and asides we give …

Learning to optimize - the idea that we can learn from data algorithms that optimize a numerical criterion - has recently been at the heart of a growing number of research efforts. One of the most challenging issues within this approach is to learn a policy that is able to optimize over classes of functions that are fa…

This paper explores the capability of deep neural networks to capture key characteristics of vehicle dynamics, and their ability to perform coupled longitudinal and lateral control of a vehicle. To this extent, two different artificial neural networks are trained to compute vehicle controls corresponding to a reference…

Mobile robot navigation in complex and dynamic environments is a challenging but important problem. Reinforcement learning approaches fail to solve these tasks efficiently due to reward sparsities, temporal complexities and high-dimensionality of sensorimotor spaces which are inherent in such problems. We present a nov…

We recall the construction of the Kontsevich graph orientation morphism $γ\mapsto {\rm O\vec{r}}(γ)$ which maps cocycles $γ$ in the non-oriented graph complex to infinitesimal symmetries $\dot{\mathcal{P}} = {\rm O\vec{r}}(γ)(\mathcal{P})$ of Poisson bi-vectors on affine manifolds. We reveal in particular why there alw…

Hybrid model uses LLM to build transparent Bayesian networks for trading decisions.

We propose an actor-critic, model-free, and online Reinforcement Learning (RL) framework for continuous-state continuous-action Markov Decision Processes (MDPs) when the reward is highly sparse but encompasses a high-level temporal structure. We represent this temporal structure by a finite-state machine and construct …

A spiral unibike track emerges from a mathematical construction.

This paper is part expository and part presentation of calculational results. The target space of the Kontsevich integral for knots is a space of diagrams; this space has various algebraic structures which are described here. These are utilized with Le's theorem on the behaviour of the Kontsevich integral under cabling…

As spacecraft send back increasing amounts of telemetry data, improved anomaly detection systems are needed to lessen the monitoring burden placed on operations engineers and reduce operational risk. Current spacecraft monitoring systems only target a subset of anomaly types and often require costly expert knowledge to…

We propose a neural information processing system which is obtained by re-purposing the function of a biological neural circuit model, to govern simulated and real-world control tasks. Inspired by the structure of the nervous system of the soil-worm, C. elegans, we introduce Neuronal Circuit Policies (NCPs), defined as…

Driver identification has emerged as a vital research field, where both practitioners and researchers investigate the potential of driver identification to enable a personalized driving experience. Within recent years, a selection of studies have reported that individuals could be perfectly identified based on their dr…

In this work we describe the preparation of a time series dataset of inertial measurements for determining the surface type under a wheeled robot. The data consists of over 7600 labeled time series samples, with the corresponding surface type annotation. This data was used in two public competitions with over 1500 part…

We briefly review the notion of second order constrained (continuous) system (SOCS) and then propose a discrete time counterpart of it, which we naturally call discrete second order constrained system (DSOCS). To illustrate and test numerically our model, we construct certain integrators that simulate the evolution of …

Hughes has defined a class of groups, which we call FSS (finite similarity structure) groups. Each FSS group acts on a compact ultrametric space by local similarities. The best-known example is Thompson's group V. Guided by previous work on Thompson's group V, we establish a number of new results about FSS groups. Our …

This work uses neural density estimation to analyze laser-induced breakdown spectroscopy data, enabling accurate predictions and uncertainty quantification.

We focus on the problem of teaching a robot to solve tasks presented sequentially, i.e., in a continual learning scenario. The robot should be able to solve all tasks it has encountered, without forgetting past tasks. We provide preliminary work on applying Reinforcement Learning to such setting, on 2D navigation tasks…

We study relations between vakonomically and nonholonomically constrained Lagrangian dynamics for the same set of linear constraints. The basic idea is to compare both situations at the level of variational principles, not equations of motion as has been done so far. The method seems to be quite powerful and effective.…

Study Markov staircases in symplectic embeddings of rational homology ellipsoids.

In multi-task reinforcement learning there are two main challenges: at training time, the ability to learn different policies with a single model; at test time, inferring which of those policies applying without an external signal. In the case of continual reinforcement learning a third challenge arises: learning tasks…

Space exploration missions have seen use of increasingly sophisticated robotic systems with ever more autonomy. Deep learning promises to take this even a step further, and has applications for high-level tasks, like path planning, as well as low-level tasks, like motion control, which are critical components for missi…

The paper concerns a simple model of bicycle kinematics: a bicycle is represented by an oriented segment of constant length in n-dimensional space that can move in such a way that the velocity of its rear end is aligned with the segment (the rear wheel is fixed on the bicycle frame). Starting with a closed trajectory o…

This paper characterizes Kashiwara-Vergne groups using algebraic structures of knotted tubes.

In classical reinforcement learning, when exploring an environment, agents accept arbitrary short term loss for long term gain. This is infeasible for safety critical applications, such as robotics, where even a single unsafe action may cause system failure. In this paper, we address the problem of safely exploring fin…