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Equipartition theory, beginning with the classical ham sandwich theorem, seeks the fair division of finite point sets in $\mathbb{R}^d$ by the full-dimensional regions determined by a prescribed geometric dissection of $\mathbb{R}^d$. Here we examine $\textit{equidistributions}$ of finite point sets in $\mathbb{R}^d$ by prescribed $\textit{low dimensional}$ subsets. Our main result states that if $r\geq 3$ is a prime power, then for any $m$-coloring of a sufficiently small point set $X$ in $\mathbb{R}^d$, there exists an $r$-fan in $\mathbb{R}^d$ -- that is, the union of $r$ ``half-flats'' of codimension $r-2$ centered about a common $(r-1)$-codimensional affine subspace -- which captures all the points of $X$ in such a way that each half-flat contains at most an $r$-th of the points from each color class. The number of points in $\mathbb{R}^d$ we require for this is essentially tight when $m\geq 2$. Additionally, we extend our equidistribution results to ''piercing'' distributions in a similar fashion to Dolnikov's hyperplane transversal generalization of the ham sandwich theorem. By analogy with recent work of Frick et al., our results are obtained by applying Gale duality to linear cases of topological Tverberg-type theorems. Finally, we extend our distribution results to multiple $r$-fans after establishing a multiple intersection version of a topological Tverberg-type theorem due to Sarkaria., Comment: 23 pages

One-dimensional spin chain systems have received special attention to discover the novel magnetic ground states and emergent phenomena, while the magnetic studies on rare-earth (RE)-based 1D spin chain materials are still rare. Here, we report the synthesis, structure and magnetic behaviors on a family of tetragonal tungsten-bronze structure K2RENb5O15 (RE = Ce, Pr, Nd, Sm, Gd-Ho) compounds, which consist of 1D linear spin-chain structure built by RE3+ ions along the c-axis and well spatially separated by the nonmagnetic K/Nb-O polyhedrons with large interchain distances of ~ 8.80-8.88 {\AA} in the ab-plane. The low temperature magnetic measurements reveal the absence of long-range magnetic order down to 1.8 K for all serial K2RENb5O15 compounds and the dominant ferromagnetic interactions for RE=Ce,Dy and antiferromagnetic interactions for other members. Among them, K2GdNb5O15 with spin only magnetic moment S=7/2, exhibits a long-range magnetic order with TN~0.31 K and strong spin fluctuations at low temperatures due to its low-dimension characteristics. Moreover, a large magnetocaloric effect under low field change of 0-2 T is realized at temperatures below 1 K for K2GdNb5O15, letting it as an ideal candidate for adiabatic magnetic refrigeration applications at sub-kelvin temperatures. The K2RENb5O15 become a rare family of insulting RE-based magnets to explore the novel 1D spin chain physics beyond the 3d TM-based counterparts, in terms of its combination of low dimension, strong spin-orbital coupling and the rich diversity of RE ions., Comment: 27 pages, 11 figures

Driver distraction has become a significant cause of severe traffic accidents over the past decade. Despite the growing development of vision-driven driver monitoring systems, the lack of comprehensive perception datasets restricts road safety and traffic security. In this paper, we present an AssIstive Driving pErception dataset (AIDE) that considers context information both inside and outside the vehicle in naturalistic scenarios. AIDE facilitates holistic driver monitoring through three distinctive characteristics, including multi-view settings of driver and scene, multi-modal annotations of face, body, posture, and gesture, and four pragmatic task designs for driving understanding. To thoroughly explore AIDE, we provide experimental benchmarks on three kinds of baseline frameworks via extensive methods. Moreover, two fusion strategies are introduced to give new insights into learning effective multi-stream/modal representations. We also systematically investigate the importance and rationality of the key components in AIDE and benchmarks. The project link is https://github.com/ydk122024/AIDE., Comment: Accepted by ICCV 2023

In the transportation sector, ammonia used as a power source plays a significant role in the scenario of carbon neutralization. However, the engine-out emissions correlations of ammonia-diesel dual-fuel (DF) engines are still unclear, especially the nitro-compounds of great concern and GHG. In this study, the engine-out emissions are evaluated by using a four-cylinder ammonia/diesel DF engine. Various operating conditions consisting of ammonia energy ratio (AER), engine load, and speed were carried out. Unburned NH3 increases with raising ammonia content but decreases with increasing engine load and speed. The NO+NO2 tendency shows a non-linearity trend with increasing ammonia content, while a trade-off correlation is linked to N2O. The N2O emission of ammonia engine significantly weakens the beneficial effect of GHG reduction, the 30% and 50% decarbonization targets need at least 40% and 60% ammonia energy without regard to N2O effect, while at least 65% and 80% ammonia energy respectively with considering N2O. N2O presents a parabolic-like tendency with AERs. Advanced pilot-diesel injection timing helps to reduce both NH3 and N2O, but this effect becomes insignificant as the AER is less than 0.4. A combustion strategy of the rapid heat release and ammonia-governed heat release respectively are revealed.

Purpose: To achieve automatic hyperparameter estimation for the joint recovery of quantitative MR images, we propose a Bayesian formulation of the reconstruction problem that incorporates the signal model. Additionally, we investigate the use of complementary undersampling patterns to determine optimal undersampling schemes for quantitative MRI. Theory: We introduce a novel nonlinear approximate message passing framework, referred to as ``AMP-PE'', that enables the simultaneous recovery of distribution parameters and quantitative maps. Methods: We employed the variable flip angle multi-echo (VFA-ME) method to acquire measurements. Both retrospective and prospective undersampling approaches were utilized to obtain Fourier measurements using variable-density and Poisson-disk patterns. Furthermore, we extensively explored various undersampling schemes, incorporating complementary patterns across different flip angles and/or echo times. Results: AMP-PE adopts a model-based joint recovery strategy, it outperforms the $l_1$-norm minimization approach that follows a decoupled recovery strategy. A comparison with an existing joint-recovery approach further demonstrates the advantageous outcomes of AMP-PE. For quantitative $T_1$ mapping using VFA-ME, employing identical k-space sampling patterns across different echo times produced the best performance. Whereas for $T_2^*$ and proton density mappings, using complementary sampling patterns across different flip angles yielded the best performance. Conclusion: AMP-PE is equipped with built-in parameter estimation, and works naturally in clinical settings with varying acquisition protocols and scanners. It also achieves improved performance by combining information from the MR signal model and the sparse prior on images.

Context-Aware Emotion Recognition (CAER) is a crucial and challenging task that aims to perceive the emotional states of the target person with contextual information. Recent approaches invariably focus on designing sophisticated architectures or mechanisms to extract seemingly meaningful representations from subjects and contexts. However, a long-overlooked issue is that a context bias in existing datasets leads to a significantly unbalanced distribution of emotional states among different context scenarios. Concretely, the harmful bias is a confounder that misleads existing models to learn spurious correlations based on conventional likelihood estimation, significantly limiting the models' performance. To tackle the issue, this paper provides a causality-based perspective to disentangle the models from the impact of such bias, and formulate the causalities among variables in the CAER task via a tailored causal graph. Then, we propose a Contextual Causal Intervention Module (CCIM) based on the backdoor adjustment to de-confound the confounder and exploit the true causal effect for model training. CCIM is plug-in and model-agnostic, which improves diverse state-of-the-art approaches by considerable margins. Extensive experiments on three benchmark datasets demonstrate the effectiveness of our CCIM and the significance of causal insight., Comment: Accepted by CVPR 2023. CCIM is available at https://github.com/ydk122024/CCIM

In wearable sensing applications, data is inevitable to be irregularly sampled or partially missing, which pose challenges for any downstream application. An unique aspect of wearable data is that it is time-series data and each channel can be correlated to another one, such as x, y, z axis of accelerometer. We argue that traditional methods have rarely made use of both times-series dynamics of the data as well as the relatedness of the features from different sensors. We propose a model, termed as DynImp, to handle different time point's missingness with nearest neighbors along feature axis and then feeding the data into a LSTM-based denoising autoencoder which can reconstruct missingness along the time axis. We experiment the model on the extreme missingness scenario ($>50\%$ missing rate) which has not been widely tested in wearable data. Our experiments on activity recognition show that the method can exploit the multi-modality features from related sensors and also learn from history time-series dynamics to reconstruct the data under extreme missingness., Comment: 5 pages, 2 figures, accepted in ICASSP'2022

Purpose: For quantitative susceptibility mapping (QSM), the lack of ground-truth in clinical settings makes it challenging to determine suitable parameters for the dipole inversion. We propose a probabilistic Bayesian approach for QSM with built-in parameter estimation, and incorporate the nonlinear formulation of the dipole inversion to achieve a robust recovery of the susceptibility maps. Theory: From a Bayesian perspective, the image wavelet coefficients are approximately sparse and modelled by the Laplace distribution. The measurement noise is modelled by a Gaussian-mixture distribution with two components, where the second component is used to model the noise outliers. Through probabilistic inference, the susceptibility map and distribution parameters can be jointly recovered using approximate message passing (AMP). Methods: We compare our proposed AMP with built-in parameter estimation (AMP-PE) to the state-of-the-art L1-QSM, FANSI and MEDI approaches on the simulated and in vivo datasets, and perform experiments to explore the optimal settings of AMP-PE. Reproducible code is available at https://github.com/EmoryCN2L/QSM_AMP_PE Results: On the simulated Sim2Snr1 dataset, AMP-PE achieved the lowest NRMSE, DFCM and the highest SSIM, while MEDI achieved the lowest HFEN. On the in vivo datasets, AMP-PE is robust and successfully recovers the susceptibility maps using the estimated parameters, whereas L1-QSM, FANSI and MEDI typically require additional visual fine-tuning to select or double-check working parameters. Conclusion: AMP-PE provides automatic and adaptive parameter estimation for QSM and avoids the subjectivity from the visual fine-tuning step, making it an excellent choice for the clinical setting., Comment: Keywords: Approximate message passing, Compressive sensing, Outlier modelling, Parameter estimation, Quantitative susceptibility mapping

Medical events of interest, such as mortality, often happen at a low rate in electronic medical records, as most admitted patients survive. Training models with this imbalance rate (class density discrepancy) may lead to suboptimal prediction. Traditionally this problem is addressed through ad-hoc methods such as resampling or reweighting but performance in many cases is still limited. We propose a framework for training models for this imbalance issue: 1) we first decouple the feature extraction and classification process, adjusting training batches separately for each component to mitigate bias caused by class density discrepancy; 2) we train the network with both a density-aware loss and a learnable cost matrix for misclassifications. We demonstrate our model's improved performance in real-world medical datasets (TOPCAT and MIMIC-III) to show improved AUC-ROC, AUC-PRC, Brier Skill Score compared with the baselines in the domain.

Unknown-view tomography (UVT) reconstructs a 3D density map from its 2D projections at unknown, random orientations. A line of work starting with Kam (1980) employs the method of moments (MoM) with rotation-invariant Fourier features to solve UVT in the frequency domain, assuming that the orientations are uniformly distributed. This line of work includes the recent orthogonal matrix retrieval (OMR) approaches based on matrix factorization, which, while elegant, either require side information about the density that is not available, or fail to be sufficiently robust. For OMR to break free from those restrictions, we propose to jointly recover the density map and the orthogonal matrices by requiring that they be mutually consistent. We regularize the resulting non-convex optimization problem by a denoised reference projection and a nonnegativity constraint. This is enabled by the new closed-form expressions for spatial autocorrelation features. Further, we design an easy-to-compute initial density map which effectively mitigates the non-convexity of the reconstruction problem. Experimental results show that the proposed OMR with spatial consensus is more robust and performs significantly better than the previous state-of-the-art OMR approach in the typical low-SNR scenario of 3D UVT., Comment: Keywords: unknown view tomography, single-particle cryo-electron microscopy, method of moments, autocorrelation, spherical harmonics

Designing efficient sparse recovery algorithms that could handle noisy quantized measurements is important in a variety of applications -- from radar to source localization, spectrum sensing and wireless networking. We take advantage of the approximate message passing (AMP) framework to achieve this goal given its high computational efficiency and state-of-the-art performance. In AMP, the signal of interest is assumed to follow certain prior distribution with unknown parameters. Previous works focused on finding the parameters that maximize the measurement likelihood via expectation maximization -- an increasingly difficult problem to solve in cases involving complicated probability models. In this paper, we treat the parameters as unknown variables and compute their posteriors via AMP. The parameters and signal of interest can then be jointly recovered. Compared to previous methods, the proposed approach leads to a simple and elegant parameter estimation scheme, allowing us to directly work with 1-bit quantization noise model. We then further extend our approach to general multi-bit quantization noise model. Experimental results show that the proposed framework provides significant improvement over state-of-the-art methods across a wide range of sparsity and noise levels., Comment: arXiv admin note: text overlap with arXiv:2007.07679

In many machine learning tasks, input features with varying degrees of predictive capability are acquired at varying costs. In order to optimize the performance-cost trade-off, one would select features to observe a priori. However, given the changing context with previous observations, the subset of predictive features to select may change dynamically. Therefore, we face the challenging new problem of foresight dynamic selection (FDS): finding a dynamic and light-weight policy to decide which features to observe next, before actually observing them, for overall performance-cost trade-offs. To tackle FDS, this paper proposes a Bayesian learning framework of Variational Foresight Dynamic Selection (VFDS). VFDS learns a policy that selects the next feature subset to observe, by optimizing a variational Bayesian objective that characterizes the trade-off between model performance and feature cost. At its core is an implicit variational distribution on binary gates that are dependent on previous observations, which will select the next subset of features to observe. We apply VFDS on the Human Activity Recognition (HAR) task where the performance-cost trade-off is critical in its practice. Extensive results demonstrate that VFDS selects different features under changing contexts, notably saving sensory costs while maintaining or improving the HAR accuracy. Moreover, the features that VFDS dynamically select are shown to be interpretable and associated with the different activity types. We will release the code.