In this work, we consider a differential description of the evolution of the state of a reaction-diffusion system under environmental fluctuations. We are interested in estimating the state of the system when only partial observations are available. To describe how observations and states are related, we combine multiplicative noise-driven dynamics with an observation model. More specifically, we ensure that the observations are subjected to error in the form of additive noise. We focus on the state estimation of a Belousov-Zhabotinskii chemical reaction. We simulate a reaction conducted in a quasi-two-dimensional physical domain, such as on the surface of a Petri dish. We aim at reconstructing the emerging chemical patterns based on noisy spectral observations. For this task, we consider a finite difference representation on the spatial domain, where nodes are chosen according to observation sites. We approximate the solution to this state estimation problem with the Block particle filter, a sequential Monte Carlo method capable of addressing the associated high-dimensionality of this state-space representation.
In the linear mixed model (LMM), the simultaneous assessment and comparison of dispersion relevance of explanatory variables associated with fixed and random effects remains an important open practical problem. Based on the restricted maximum likelihood equations in the variance components form of the LMM, we prove a proper decomposition of the sum of squares of the dependent variable into unbiased estimators of interpretable estimands of explained variation. This result leads to a natural extension of the well-known adjusted coefficient of determination to the LMM. Further, we allocate the novel unbiased estimators of explained variation to specific contributions of covariates associated with fixed and random effects within a single model fit. These parameter-wise explained variations constitute easily interpretable quantities, assessing dispersion relevance of covariates associated with both fixed and random effects on a common scale, thus allowing for a covariate ranking. For illustration, we contrast the variation explained by subjects and time in the longitudinal sleep deprivation study. By comparing the dispersion relevance of population characteristics and spatial levels, we determine literacy as a major driver of income inequality in Burkina Faso. Finally, we develop a novel relevance plot to visualize the dispersion relevance of high-dimensional genomic markers in Arabidopsis thaliana.
This paper proposes a stable sparse rapidly-exploring random trees (SST) algorithm to solve the optimal motion planning problem for hybrid systems. At each iteration, the proposed algorithm, called HySST, selects a vertex with the lowest cost among all the vertices within the neighborhood of a randomly selected sample and then extends the search tree by flow or jump, which is also chosen randomly when both regimes are possible. In addition, HySST maintains a static set of witness points such that all the vertices within the neighborhood of each witness are pruned except the vertex with the lowest cost. Through a definition of concatenation of functions defined on hybrid time domains, we show that HySST is asymptotically near optimal, namely, the probability of failing to find a motion plan such that its cost is close to the optimal cost approaches zero as the number of iterations of the algorithm increases to infinity. This property is guaranteed under mild conditions on the data defining the motion plan, which include a relaxation of the usual positive clearance assumption imposed in the literature of classical systems. The proposed algorithm is applied to an actuated bouncing ball system and a collision-resilient tensegrity multicopter system so as to highlight its generality and computational features.
Particle filtering is a common technique for six degree of freedom (6D) pose estimation due to its ability to tractably represent belief over object pose. However, the particle filter is prone to particle deprivation due to the high-dimensional nature of 6D pose. When particle deprivation occurs, it can cause mode collapse of the underlying belief distribution during importance sampling. If the region surrounding the true state suffers from mode collapse, recovering its belief is challenging since the area is no longer represented in the probability mass formed by the particles. Previous methods mitigate this problem by randomizing and resetting particles in the belief distribution, but determining the frequency of reinvigoration has relied on hand-tuning abstract heuristics. In this paper, we estimate the necessary reinvigoration rate at each time step by introducing a Counter-Hypothetical likelihood function, which is used alongside the standard likelihood. Inspired by the notions of plausibility and implausibility from Evidential Reasoning, the addition of our Counter-Hypothetical likelihood function assigns a level of doubt to each particle. The competing cumulative values of confidence and doubt across the particle set are used to estimate the level of failure within the filter, in order to determine the portion of particles to be reinvigorated. We demonstrate the effectiveness of our method on the rigid body object 6D pose tracking task.
The Transposition Distance Problem (TDP) is a classical problem in genome rearrangements which seeks to determine the minimum number of transpositions needed to transform a linear chromosome into another represented by the permutations $\pi$ and $\sigma$, respectively. This paper focuses on the equivalent problem of Sorting By Transpositions (SBT), where $\sigma$ is the identity permutation $\iota$. Specifically, we investigate palisades, a family of permutations that are "hard" to sort, as they require numerous transpositions above the celebrated lower bound devised by Bafna and Pevzner. By determining the transposition distance of palisades, we were able to provide the exact transposition diameter for $3$-permutations (TD3), a special subset of the Symmetric Group $S_n$, essential for the study of approximate solutions for SBT using the simplification technique. The exact value for TD3 has remained unknown since Elias and Hartman showed an upper bound for it. Another consequence of determining the transposition distance of palisades is that, using as lower bound the one by Bafna and Pevzner, it is impossible to guarantee approximation ratios lower than $1.375$ when approximating SBT. This finding has significant implications for the study of SBT, as this problem has been subject of intense research efforts for the past 25 years.
Traffic speed is central to characterizing the fluidity of the road network. Many transportation applications rely on it, such as real-time navigation, dynamic route planning, and congestion management. Rapid advances in sensing and communication techniques make traffic speed detection easier than ever. However, due to sparse deployment of static sensors or low penetration of mobile sensors, speeds detected are incomplete and far from network-wide use. In addition, sensors are prone to error or missing data due to various kinds of reasons, speeds from these sensors can become highly noisy. These drawbacks call for effective techniques to recover credible estimates from the incomplete data. In this work, we first identify the issue as a spatiotemporal kriging problem and propose a Laplacian enhanced low-rank tensor completion (LETC) framework featuring both lowrankness and multi-dimensional correlations for large-scale traffic speed kriging under limited observations. To be specific, three types of speed correlation including temporal continuity, temporal periodicity, and spatial proximity are carefully chosen and simultaneously modeled by three different forms of graph Laplacian, named temporal graph Fourier transform, generalized temporal consistency regularization, and diffusion graph regularization. We then design an efficient solution algorithm via several effective numeric techniques to scale up the proposed model to network-wide kriging. By performing experiments on two public million-level traffic speed datasets, we finally draw the conclusion and find our proposed LETC achieves the state-of-the-art kriging performance even under low observation rates, while at the same time saving more than half computing time compared with baseline methods. Some insights into spatiotemporal traffic data modeling and kriging at the network level are provided as well.
The fundamental diagram serves as the foundation of traffic flow modeling for almost a century. With the increasing availability of road sensor data, deterministic parametric models have proved inadequate in describing the variability of real-world data, especially in congested area of the density-flow diagram. In this paper we estimate the stochastic density-flow relation introducing a nonparametric method called convex quantile regression. The proposed method does not depend on any prior functional form assumptions, but thanks to the concavity constraints, the estimated function satisfies the theoretical properties of the fundamental diagram. The second contribution is to develop the new convex quantile regression with bags (CQRb) approach to facilitate practical implementation of CQR to the real-world data. We illustrate the CQRb estimation process using the road sensor data from Finland in years 2016-2018. Our third contribution is to demonstrate the excellent out-of-sample predictive power of the proposed CQRb method in comparison to the standard parametric deterministic approach.
We introduce an approach which allows inferring causal relationships between variables for which the time evolution is available. Our method builds on the ideas of Granger Causality and Transfer Entropy, but overcomes most of their limitations. Specifically, our approach tests whether the predictability of a putative driven system Y can be improved by incorporating information from a potential driver system X, without making assumptions on the underlying dynamics and without the need to compute probability densities of the dynamic variables. Causality is assessed by a rigorous variational scheme based on the Information Imbalance of distance ranks, a recently developed statistical test capable of inferring the relative information content of different distance measures. This framework makes causality detection possible even for high-dimensional systems where only few of the variables are known or measured. Benchmark tests on coupled dynamical systems demonstrate that our approach outperforms other model-free causality detection methods, successfully handling both unidirectional and bidirectional couplings, and it is capable of detecting the arrow of time when present. We also show that the method can be used to robustly detect causality in electroencephalography data in humans.
In this paper, we propose new self-tuned robust estimators for estimating the mean of distributions with only finite variances. Our method involves introducing a new loss function that considers both the mean parameter and a robustification parameter. By simultaneously optimizing the empirical loss function with respect to both parameters, the resulting estimator for the robustification parameter can adapt to the unknown variance automatically and can achieve near-optimal finite-sample performance. Our approach outperforms previous methods in terms of both computational and asymptotic efficiency. Specifically, it does not require cross-validation or Lepski's method to tune the robustification parameter, and the variance of our estimator achieves the Cram\'er-Rao lower bound.
Simulation engines are widely adopted in robotics. However, they lack either full simulation control, ROS integration, realistic physics, or photorealism. Recently, synthetic data generation and realistic rendering has advanced tasks like target tracking and human pose estimation. However, when focusing on vision applications, there is usually a lack of information like sensor measurements or time continuity. On the other hand, simulations for most robotics tasks are performed in (semi)static environments, with specific sensors and low visual fidelity. To solve this, we introduced in our previous work a fully customizable framework for generating realistic animated dynamic environments (GRADE) [1]. We use GRADE to generate an indoor dynamic environment dataset and then compare multiple SLAM algorithms on different sequences. By doing that, we show how current research over-relies on known benchmarks, failing to generalize. Our tests with refined YOLO and Mask R-CNN models provide further evidence that additional research in dynamic SLAM is necessary. The code, results, and generated data are provided as open-source at //eliabntt.github.io/grade-rrSimulation of Dynamic Environments for SLAM
Owing to effective and flexible data acquisition, unmanned aerial vehicle (UAV) has recently become a hotspot across the fields of computer vision (CV) and remote sensing (RS). Inspired by recent success of deep learning (DL), many advanced object detection and tracking approaches have been widely applied to various UAV-related tasks, such as environmental monitoring, precision agriculture, traffic management. This paper provides a comprehensive survey on the research progress and prospects of DL-based UAV object detection and tracking methods. More specifically, we first outline the challenges, statistics of existing methods, and provide solutions from the perspectives of DL-based models in three research topics: object detection from the image, object detection from the video, and object tracking from the video. Open datasets related to UAV-dominated object detection and tracking are exhausted, and four benchmark datasets are employed for performance evaluation using some state-of-the-art methods. Finally, prospects and considerations for the future work are discussed and summarized. It is expected that this survey can facilitate those researchers who come from remote sensing field with an overview of DL-based UAV object detection and tracking methods, along with some thoughts on their further developments.