Vehicle-to-Vehicle Charging: Model, Complexity, and Heuristics

The rapid adoption of Electric Vehicles (EVs) poses challenges for electricity grids to accommodate or mitigate peak demand. Vehicle-to-Vehicle Charging (V2VC) has been recently adopted by popular EVs, posing new opportunities and challenges to the management and operation of EVs. We present a novel V2VC model that allows decision-makers to take V2VC into account when optimizing their EV operations. We show that optimizing V2VC is NP-Complete and find that even small problem instances are computationally challenging. We propose R-V2VC, a heuristic that takes advantage of the resulting totally unimodular constraint matrix to efficiently solve problems of realistic sizes. Our results demonstrate that R-V2VC presents a linear growth in the solution time as the problem size increases, while achieving solutions of optimal or near-optimal quality. R-V2VC can be used for real-world operations and to study what-if scenarios when evaluating the costs and benefits of V2VC.

Synthesis of Through-Wall Micro-Doppler Signatures of Human Motions Using Generative Adversarial Networks

Narrowband radar micro-Doppler signatures are heavily used to identify and classify human activities. When the radar is operated in through-wall environments, the complex electromagnetic propagation phenomenology introduces considerable distortions in the micro-Doppler signatures through attenuation and multipath. The problem is particularly severe in inhomogeneous wall scenarios involving multiple wall layers, air gaps, or metal reinforcements. Through-wall radar data collection using simulations and measurements involves significant time and effort. In this paper, we propose an alternative method of synthesizing through-wall radar micro-Doppler signatures from their free space counterparts using the generative adversarial network (GAN). We train the GAN using radar micro-Doppler signatures generated from electromagnetic simulations. We generate the radar data for different human motions, along different orientations, and under diverse through-wall conditions. The synthetic radar micro-Dopplers generated from the neural networks are then evaluated for their realism using a denoising autoencoder, which shows an excellent realism score.

Convergence of coordinate ascent variational inference for log-concave measures via optimal transport

Mean field variational inference (VI) is the problem of finding the closest product (factorized) measure, in the sense of relative entropy, to a given high-dimensional probability measure $\rho$. The well known Coordinate Ascent Variational Inference (CAVI) algorithm aims to approximate this product measure by iteratively optimizing over one coordinate (factor) at a time, which can be done explicitly. Despite its popularity, the convergence of CAVI remains poorly understood. In this paper, we prove the convergence of CAVI for log-concave densities $\rho$. If additionally $\log \rho$ has Lipschitz gradient, we find a linear rate of convergence, and if also $\rho$ is strongly log-concave, we find an exponential rate. Our analysis starts from the observation that mean field VI, while notoriously non-convex in the usual sense, is in fact displacement convex in the sense of optimal transport when $\rho$ is log-concave. This allows us to adapt techniques from the optimization literature on coordinate descent algorithms in Euclidean space.

Topological Feature Search Method for Multichannel EEG: Application in ADHD classification

In recent years, the preliminary diagnosis of Attention Deficit Hyperactivity Disorder (ADHD) using electroencephalography (EEG) has garnered attention from researchers. EEG, known for its expediency and efficiency, plays a pivotal role in the diagnosis and treatment of ADHD. However, the non-stationarity of EEG signals and inter-subject variability pose challenges to the diagnostic and classification processes. Topological Data Analysis (TDA) offers a novel perspective for ADHD classification, diverging from traditional time-frequency domain features. Yet, conventional TDA models are restricted to single-channel time series and are susceptible to noise, leading to the loss of topological features in persistence diagrams.This paper presents an enhanced TDA approach applicable to multi-channel EEG in ADHD. Initially, optimal input parameters for multi-channel EEG are determined. Subsequently, each channel's EEG undergoes phase space reconstruction (PSR) followed by the utilization of k-Power Distance to Measure (k-PDTM) for approximating ideal point clouds. Then, multi-dimensional time series are re-embedded, and TDA is applied to obtain topological feature information. Gaussian function-based Multivariate Kernel Density Estimation (MKDE) is employed in the merger persistence diagram to filter out desired topological feature mappings. Finally, persistence image (PI) method is utilized to extract topological features, and the influence of various weighting functions on the results is discussed.The effectiveness of our method is evaluated using the IEEE ADHD dataset. Results demonstrate that the accuracy, sensitivity, and specificity reach 85.60%, 83.61%, and 88.33%, respectively. Compared to traditional TDA methods, our method was effectively improved and outperforms typical nonlinear descriptors. These findings indicate that our method exhibits higher precision and robustness.

A New Statistic for Testing Covariance Equality in High-Dimensional Gaussian Low-Rank Models

In this paper, we consider the problem of testing equality of the covariance matrices of L complex Gaussian multivariate time series of dimension $M$ . We study the special case where each of the L covariance matrices is modeled as a rank K perturbation of the identity matrix, corresponding to a signal plus noise model. A new test statistic based on the estimates of the eigenvalues of the different covariance matrices is proposed. In particular, we show that this statistic is consistent and with controlled type I error in the high-dimensional asymptotic regime where the sample sizes $N_1,\ldots,N_L$ of each time series and the dimension $M$ both converge to infinity at the same rate, while $K$ and $L$ are kept fixed. We also provide some simulations on synthetic and real data (SAR images) which demonstrate significant improvements over some classical methods such as the GLRT, or other alternative methods relevant for the high-dimensional regime and the low-rank model.

Toward Holistic Planning and Control Optimization for Dual-Arm Rearrangement

Long-horizon task and motion planning (TAMP) is notoriously difficult to solve, let alone optimally, due to the tight coupling between the interleaved (discrete) task and (continuous) motion planning phases, where each phase on its own is frequently an NP-hard or even PSPACE-hard computational challenge. In this study, we tackle the even more challenging goal of jointly optimizing task and motion plans for a real dual-arm system in which the two arms operate in close vicinity to solve highly constrained tabletop multi-object rearrangement problems. Toward that, we construct a tightly integrated planning and control optimization pipeline, Makespan-Optimized Dual-Arm Planner (MODAP) that combines novel sampling techniques for task planning with state-of-the-art trajectory optimization techniques. Compared to previous state-of-the-art, MODAP produces task and motion plans that better coordinate a dual-arm system, delivering significantly improved execution time improvements while simultaneously ensuring that the resulting time-parameterized trajectory conforms to specified acceleration and jerk limits.

MedBN: Robust Test-Time Adaptation against Malicious Test Samples

Test-time adaptation (TTA) has emerged as a promising solution to address performance decay due to unforeseen distribution shifts between training and test data. While recent TTA methods excel in adapting to test data variations, such adaptability exposes a model to vulnerability against malicious examples, an aspect that has received limited attention. Previous studies have uncovered security vulnerabilities within TTA even when a small proportion of the test batch is maliciously manipulated. In response to the emerging threat, we propose median batch normalization (MedBN), leveraging the robustness of the median for statistics estimation within the batch normalization layer during test-time inference. Our method is algorithm-agnostic, thus allowing seamless integration with existing TTA frameworks. Our experimental results on benchmark datasets, including CIFAR10-C, CIFAR100-C and ImageNet-C, consistently demonstrate that MedBN outperforms existing approaches in maintaining robust performance across different attack scenarios, encompassing both instant and cumulative attacks. Through extensive experiments, we show that our approach sustains the performance even in the absence of attacks, achieving a practical balance between robustness and performance.

Backpropagation through space, time, and the brain

Effective learning in neuronal networks requires the adaptation of individual synapses given their relative contribution to solving a task. However, physical neuronal systems -- whether biological or artificial -- are constrained by spatio-temporal locality. How such networks can perform efficient credit assignment, remains, to a large extent, an open question. In Machine Learning, the answer is almost universally given by the error backpropagation algorithm, through both space (BP) and time (BPTT). However, BP(TT) is well-known to rely on biologically implausible assumptions, in particular with respect to spatiotemporal (non-)locality, while forward-propagation models such as real-time recurrent learning (RTRL) suffer from prohibitive memory constraints. We introduce Generalized Latent Equilibrium (GLE), a computational framework for fully local spatio-temporal credit assignment in physical, dynamical networks of neurons. We start by defining an energy based on neuron-local mismatches, from which we derive both neuronal dynamics via stationarity and parameter dynamics via gradient descent. The resulting dynamics can be interpreted as a real-time, biologically plausible approximation of BPTT in deep cortical networks with continuous-time neuronal dynamics and continuously active, local synaptic plasticity. In particular, GLE exploits the ability of biological neurons to phase-shift their output rate with respect to their membrane potential, which is essential in both directions of information propagation. For the forward computation, it enables the mapping of time-continuous inputs to neuronal space, performing an effective spatiotemporal convolution. For the backward computation, it permits the temporal inversion of feedback signals, which consequently approximate the adjoint states necessary for useful parameter updates.

Point cloud obstacle detection with the map filtration

Obstacle detection is one of the basic tasks of a robot movement in an unknown environment. The use of a LiDAR (Light Detection And Ranging) sensor allows one to obtain a point cloud in the vicinity of the sensor. After processing this data, obstacles can be found and recorded on a map. For this task, I present a pipeline capable of detecting obstacles even on a computationally limited device. The pipeline was also tested on a real robot and qualitatively evaluated on a dataset, which was collected in Brno University of Technology lab. Time consumption was recorded and compared with 3D object detectors.

MC$^2$: Multi-concept Guidance for Customized Multi-concept Generation

Customized text-to-image generation aims to synthesize instantiations of user-specified concepts and has achieved unprecedented progress in handling individual concept. However, when extending to multiple customized concepts, existing methods exhibit limitations in terms of flexibility and fidelity, only accommodating the combination of limited types of models and potentially resulting in a mix of characteristics from different concepts. In this paper, we introduce the Multi-concept guidance for Multi-concept customization, termed MC$^2$, for improved flexibility and fidelity. MC$^2$ decouples the requirements for model architecture via inference time optimization, allowing the integration of various heterogeneous single-concept customized models. It adaptively refines the attention weights between visual and textual tokens, directing image regions to focus on their associated words while diminishing the impact of irrelevant ones. Extensive experiments demonstrate that MC$^2$ even surpasses previous methods that require additional training in terms of consistency with input prompt and reference images. Moreover, MC$^2$ can be extended to elevate the compositional capabilities of text-to-image generation, yielding appealing results. Code will be publicly available at https://github.com/JIANGJiaXiu/MC-2.