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This paper establishes a rigorous connection between circuit representations and tensor factorizations, two seemingly distinct yet fundamentally related areas. By connecting these fields, we highlight a series of opportunities that can benefit both communities. Our work generalizes popular tensor factorizations within the circuit language, and unifies various circuit learning algorithms under a single, generalized hierarchical factorization framework. Specifically, we introduce a modular "Lego block" approach to build tensorized circuit architectures. This, in turn, allows us to systematically construct and explore various circuit and tensor factorization models while maintaining tractability. This connection not only clarifies similarities and differences in existing models, but also enables the development of a comprehensive pipeline for building and optimizing new circuit/tensor factorization architectures. We show the effectiveness of our framework through extensive empirical evaluations, and highlight new research opportunities for tensor factorizations in probabilistic modeling.

Cross-modal knowledge distillation (CMKD) refers to the scenario in which a learning framework must handle training and test data that exhibit a modality mismatch, more precisely, training and test data do not cover the same set of data modalities. Traditional approaches for CMKD are based on a teacher/student paradigm where a teacher is trained on multi-modal data with the aim to successively distill knowledge from a multi-modal teacher to a single-modal student. Despite the widespread adoption of such paradigm, recent research has highlighted its inherent limitations in the context of cross-modal knowledge transfer.Taking a step beyond the teacher/student paradigm, here we introduce a new framework for cross-modal knowledge distillation, named DisCoM-KD (Disentanglement-learning based Cross-Modal Knowledge Distillation), that explicitly models different types of per-modality information with the aim to transfer knowledge from multi-modal data to a single-modal classifier. To this end, DisCoM-KD effectively combines disentanglement representation learning with adversarial domain adaptation to simultaneously extract, foreach modality, domain-invariant, domain-informative and domain-irrelevant features according to a specific downstream task. Unlike the traditional teacher/student paradigm, our framework simultaneously learns all single-modal classifiers, eliminating the need to learn each student model separately as well as the teacher classifier. We evaluated DisCoM-KD on three standard multi-modal benchmarks and compared its behaviourwith recent SOTA knowledge distillation frameworks. The findings clearly demonstrate the effectiveness of DisCoM-KD over competitors considering mismatch scenarios involving both overlapping and non-overlapping modalities. These results offer insights to reconsider the traditional paradigm for distilling information from multi-modal data to single-modal neural networks.

The Southern Photometric Local Universe Survey (S-PLUS) is a project to map $\sim9300$ sq deg of the sky using twelve bands (seven narrow and five broadbands). Observations are performed with the T80-South telescope, a robotic telescope located at the Cerro Tololo Observatory in Chile. The survey footprint consists of several large contiguous areas, including fields at high and low galactic latitudes, and towards the Magellanic Clouds. S-PLUS uses fixed exposure times to reach point source depths of about $21$ mag in the $griz$ and $20$ mag in the $u$ and the narrow filters. This paper describes the S-PLUS Data Release 4 (DR4), which includes calibrated images and derived catalogues for over 3000 sq deg, covering the aforementioned area. The catalogues provide multi-band photometry performed with the tools \texttt{DoPHOT} and \texttt{SExtractor} -- point spread function (\PSF) and aperture photometry, respectively. In addition to the characterization, we also present the scientific potential of the data. We use statistical tools to present and compare the photometry obtained through different methods. Overall we find good agreement between the different methods, with a slight systematic offset of 0.05\,mag between our \PSF and aperture photometry. We show that the astrometry accuracy is equivalent to that obtained in previous S-PLUS data releases, even in very crowded fields where photometric extraction is challenging. The depths of main survey (MS) photometry for a minimum signal-to-noise ratio $S/N = 3$ reach from $\sim19.5$ for the bluer bands to $\sim21.5$ mag on the red. The range of magnitudes over which accurate \PSF photometry is obtained is shallower, reaching $\sim19$ to $\sim20.5$ mag depending on the filter. Based on these photometric data, we provide star-galaxy-quasar classification and photometric redshift for millions of objects., Comment: 26 pages, 17 figures, 14 tables, accepted for A&A

We introduce Nerva, a fast neural network library under development in C++. It supports sparsity by using the sparse matrix operations of Intel's Math Kernel Library (MKL), which eliminates the need for binary masks. We show that Nerva significantly decreases training time and memory usage while reaching equivalent accuracy to PyTorch. We run static sparse experiments with an MLP on CIFAR-10. On high sparsity levels like $99\%$, the runtime is reduced by a factor of $4\times$ compared to a PyTorch model using masks. Similar to other popular frameworks such as PyTorch and Keras, Nerva offers a Python interface for users to work with., Comment: The Nerva library is available at https://github.com/wiegerw/nerva

Many-body eigenstates that are neither thermal nor many-body-localized (MBL) were numerically found in certain interacting chains with moderate quasiperiodic potentials. The energy regime consisting of these non-ergodic but extended (NEE) eigenstates has been extensively studied for being a possible many-body mobility edge between the energy-resolved MBL and thermal phases. Recently, the NEE regime was further proposed to be a prethermal phenomenon that generally occurs when different operators spread at sizably different timescales. Here, we numerically examine the mutual independence among the NEE, MBL, and thermal regimes in the lens of eigenstate entanglement spectra (ES). Given the complexity and rich information embedded in ES, we develop an unsupervised learning approach that is designed to quantify the mutual independence among general phases. Our method is first demonstrated on an illustrative toy example that uses RGB color data to represent phases, then applied to the ES of an interacting generalized Aubry Andre model from weak to strong potential strength. We find that while the MBL and thermal regimes are mutually independent, the NEE regime is dependent on the former two and smoothly appears as the potential strength decreases. We attribute our numerically finding to the fact that the ES data in the NEE regime exhibits both an MBL-like fast decay and a thermal-like long tail., Comment: 6 pages, 5 figures

Computer vision methods that explicitly detect object parts and reason on them are a step towards inherently interpretable models. Existing approaches that perform part discovery driven by a fine-grained classification task make very restrictive assumptions on the geometric properties of the discovered parts; they should be small and compact. Although this prior is useful in some cases, in this paper we show that pre-trained transformer-based vision models, such as self-supervised DINOv2 ViT, enable the relaxation of these constraints. In particular, we find that a total variation (TV) prior, which allows for multiple connected components of any size, substantially outperforms previous work. We test our approach on three fine-grained classification benchmarks: CUB, PartImageNet and Oxford Flowers, and compare our results to previously published methods as well as a re-implementation of the state-of-the-art method PDiscoNet with a transformer-based backbone. We consistently obtain substantial improvements across the board, both on part discovery metrics and the downstream classification task, showing that the strong inductive biases in self-supervised ViT models require to rethink the geometric priors that can be used for unsupervised part discovery., Comment: Accepted as a main conference paper at the European Conference of Computer Vision (ECCV) 2024

Semi-supervised domain adaptation methods leverage information from a source labelled domain with the goal of generalizing over a scarcely labelled target domain. While this setting already poses challenges due to potential distribution shifts between domains, an even more complex scenario arises when source and target data differs in modality representation (e.g. they are acquired by sensors with different characteristics). For instance, in remote sensing, images may be collected via various acquisition modes (e.g. optical or radar), different spectral characteristics (e.g. RGB or multi-spectral) and spatial resolutions. Such a setting is denoted as Semi-Supervised Heterogeneous Domain Adaptation (SSHDA) and it exhibits an even more severe distribution shift due to modality heterogeneity across domains.To cope with the challenging SSHDA setting, here we introduce SHeDD (Semi-supervised Heterogeneous Domain Adaptation via Disentanglement) an end-to-end neural framework tailored to learning a target domain classifier by leveraging both labelled and unlabelled data from heterogeneous data sources. SHeDD is designed to effectively disentangle domain-invariant representations, relevant for the downstream task, from domain-specific information, that can hinder the cross-modality transfer. Additionally, SHeDD adopts an augmentation-based consistency regularization mechanism that takes advantages of reliable pseudo-labels on the unlabelled target samples to further boost its generalization ability on the target domain. Empirical evaluations on two remote sensing benchmarks, encompassing heterogeneous data in terms of acquisition modes and spectral/spatial resolutions, demonstrate the quality of SHeDD compared to both baseline and state-of-the-art competing approaches. Our code is publicly available here: https://github.com/tanodino/SSHDA/

Probabilistic integral circuits (PICs) have been recently introduced as probabilistic models enjoying the key ingredient behind expressive generative models: continuous latent variables (LVs). PICs are symbolic computational graphs defining continuous LV models as hierarchies of functions that are summed and multiplied together, or integrated over some LVs. They are tractable if LVs can be analytically integrated out, otherwise they can be approximated by tractable probabilistic circuits (PC) encoding a hierarchical numerical quadrature process, called QPCs. So far, only tree-shaped PICs have been explored, and training them via numerical quadrature requires memory-intensive processing at scale. In this paper, we address these issues, and present: (i) a pipeline for building DAG-shaped PICs out of arbitrary variable decompositions, (ii) a procedure for training PICs using tensorized circuit architectures, and (iii) neural functional sharing techniques to allow scalable training. In extensive experiments, we showcase the effectiveness of functional sharing and the superiority of QPCs over traditional PCs.

The ability to measure differences in collected data is of fundamental importance for quantitative science and machine learning, motivating the establishment of metrics grounded in physical principles. In this study, we focus on the development of such metrics for viscoelastic fluid flows governed by a large class of linear and nonlinear stress models. To do this, we introduce a kernel function corresponding to a given viscoelastic stress model that implicitly embeds flowfield snapshots into a Reproducing Kernel Hilbert Space (RKHS) whose squared norm equals the total mechanical energy. Working implicitly with lifted representations in the RKHS via the kernel function provides natural and unambiguous metrics for distances and angles between flowfields without the need for hyperparameter tuning. Additionally, we present a solution to the preimage problem for our kernels, enabling accurate reconstruction of flowfields from their RKHS representations. Through numerical experiments on an unsteady viscoelastic lid-driven cavity flow, we demonstrate the utility of our kernels for extracting energetically-dominant coherent structures in viscoelastic flows across a range of Reynolds and Weissenberg numbers. Specifically, the features extracted by Kernel Principal Component Analysis (KPCA) of flowfield snapshots using our kernel functions yield reconstructions with superior accuracy in terms of mechanical energy compared to conventional methods such as ordinary Principal Component Analysis (PCA) with na\"ively-defined state vectors or KPCA with ad-hoc choices of kernel functions. Our findings underscore the importance of principled choices of metrics in both scientific and machine learning investigations of complex fluid systems., Comment: 33 pages, 10 figures, Revised version of the publication

Timely up-to-date land use/land cover (LULC) maps play a pivotal role in supporting agricultural territory management, environmental monitoring and facilitating well-informed and sustainable decision-making. Typically, when creating a land cover (LC) map, precise ground truth data is collected through time-consuming and expensive field campaigns. This data is then utilized in conjunction with satellite image time series (SITS) through advanced machine learning algorithms to get the final map. Unfortunately, each time this process is repeated (e.g., annually over a region to estimate agricultural production or potential biodiversity loss), new ground truth data must be collected, leading to the complete disregard of previously gathered reference data despite the substantial financial and time investment they have required. How to make value of historical data, from the same or similar study sites, to enhance the current LULC mapping process constitutes a significant challenge that could enable the financial and human-resource efforts invested in previous data campaigns to be valued again. Aiming to tackle this important challenge, we here propose a deep learning framework based on recent advances in domain adaptation and generalization to combine remote sensing and reference data coming from two different domains (e.g. historical data and fresh ones) to ameliorate the current LC mapping process. Our approach, namely REFeD (data Reuse with Effective Feature Disentanglement for land cover mapping), leverages a disentanglement strategy, based on contrastive learning, where invariant and specific per-domain features are derived to recover the intrinsic information related to the downstream LC mapping task and alleviate possible distribution shifts between domains. Additionally, REFeD is equipped with an effective supervision scheme where feature disentanglement is further enforced via multiple levels of supervision at different granularities. The experimental assessment over two study areas covering extremely diverse and contrasted landscapes, namely Koumbia (located in the West-Africa region, in Burkina Faso) and Centre Val de Loire (located in centre Europe, France), underlines the quality of our framework and the obtained findings demonstrate that out-of-year information coming from the same (or similar) study site, at different periods of time, can constitute a valuable additional source of information to enhance the LC mapping process.

Neural networks in fluid mechanics offer an efficient approach for exploring complex flows, including multiphase and free surface flows. The recurrent neural network, particularly the Long Short-Term Memory (LSTM) model, proves attractive for learning mappings from transient inputs to dynamic outputs. This study applies LSTM to predict transient and static outputs for fluid flows under surface tension effects. Specifically, we explore two distinct droplet dynamic scenarios: droplets with diverse initial shapes impacting with solid surfaces, as well as the coalescence of two droplets following collision. Using only dimensionless numbers and geometric time series data from numerical simulations, LSTM predicts the energy budget. The marker-and-cell front-tracking methodology combined with a marker-and-cell finite-difference strategy is adopted for simulating the droplet dynamics. Using a recurrent neural network (RNN) architecture fed with time series data derived from geometrical parameters, as for example droplet diameter variation, our study shows the accuracy of our approach in predicting energy budgets, as for instance the kinetic, dissipation, and surface energy trends, across a range of Reynolds and Weber numbers in droplet dynamic problems. Finally, a two-phase sequential neural network using only geometric data, which is readily available in experimental settings, is employed to predict the energies and then use them to estimate static parameters, such as the Reynolds and Weber numbers. While our methodology has been primarily validated with simulation data, its adaptability to experimental datasets is a promising avenue for future exploration. We hope that our strategy can be useful for diverse applications, spanning from inkjet printing to combustion engines, where the prediction of energy budgets or dissipation energies is crucial.

Probabilistic Circuits (PCs) are prominent tractable probabilistic models, allowing for a range of exact inferences. This paper focuses on the main algorithm for training PCs, LearnSPN, a gold standard due to its efficiency, performance, and ease of use, in particular for tabular data. We show that LearnSPN is a greedy likelihood maximizer under mild assumptions. While inferences in PCs may use the entire circuit structure for processing queries, LearnSPN applies a hard method for learning them, propagating at each sum node a data point through one and only one of the children/edges as in a hard clustering process. We propose a new learning procedure named SoftLearn, that induces a PC using a soft clustering process. We investigate the effect of this learning-inference compatibility in PCs. Our experiments show that SoftLearn outperforms LearnSPN in many situations, yielding better likelihoods and arguably better samples. We also analyze comparable tractable models to highlight the differences between soft/hard learning and model querying.

This work addresses integrating probabilistic propositional logic constraints into the distribution encoded by a probabilistic circuit (PC). PCs are a class of tractable models that allow efficient computations (such as conditional and marginal probabilities) while achieving state-of-the-art performance in some domains. The proposed approach takes both a PC and constraints as inputs, and outputs a new PC that satisfies the constraints. This is done efficiently via convex optimization without the need to retrain the entire model. Empirical evaluations indicate that the combination of constraints and PCs can have multiple use cases, including the improvement of model performance under scarce or incomplete data, as well as the enforcement of machine learning fairness measures into the model without compromising model fitness. We believe that these ideas will open possibilities for multiple other applications involving the combination of logics and deep probabilistic models.

We use a recent Pantheon+SH0ES compilation of Type Ia Supernova distance measurements at low-redshift, i.e., $0.01 \leq z \leq 0.10$, in order to investigate the directional dependency of the deceleration parameter ($q_0$) in different patches ($60^{\circ}$ size) across the sky, as a probe of the statistical isotropy of the Universe. We adopt a cosmographic approach to compute the cosmological distances, fixing $H_0$ and $M_B$ to reference values provided by the collaboration. By looking at 500 different patches randomly taken across the sky, we find a maximum $\sim 3\sigma$ CL anisotropy level for $q_0$, whose direction points orthogonally to the cosmic microwave background (CMB) dipole axis, i.e., $(RA^{\rm SN},DEC^{\rm SN}) = (267^{\circ},6^{\circ})$ vs $(RA^{\rm CMB},DEC^{\rm CMB}) = (167^{\circ},-7^{\circ})$. We assessed the statistical significance of those results, finding that such a signal is expected due to the limitations of the observational sample. These results support that there is no significant evidence for a departure from the cosmic isotropy assumption, one of the pillars of the standard cosmological model., Comment: Matches published version in PRD

In photon upconverting core-shell nanoparticles, structure strongly dictates performance. Conventional imaging in scanning transmission electron microscopy has sufficient resolution to probe the atomic structure of these nanoparticles, but contrast, dose, and projection limitations make conventional imaging modes insufficient for fully characterizing these structures. Phase retrieval methods provide a promising alternative imaging mode, and in particular, multislice electron ptychography can recover depth-dependent information. Here, we study beam-sensitive photon upconverting core-shell nanoparticles with a multislice ptychography approach using a low electron dose to avoid damage. Large strain fields arise in these heterostructures due to the mismatch in lattice parameter between the core and the shell. We reconstruct both a nanoparticle that appears defect-free and one that has a large break in the side and map the distribution of strain in 3D by computing distortion fields from high-resolution potential images of each slice. In the defect-free nanoparticle, we observe twisting of the shell, while in the broken nanoparticle we measure the 3D position of the crack, the core, and dislocations. These results highlight the advantage of multislice electron ptychography to recover 3D information from a single scan, even under strict electron dose requirements from beam-sensitive samples., Comment: 6 pages, 4 figures

Lip segmentation is crucial in computer vision, especially for lip reading. Despite extensive face segmentation research, lip segmentation has received limited attention. The aim of this study is to compare state-of-the-art lip segmentation models using a standardized setting and a publicly available dataset. Five techniques, namely EHANet, Mask2Former, BiSeNet V2, PIDNet, and STDC1, are qualitatively selected based on their reported performance, inference time, code availability, recency, and popularity. The CelebAMask-HQ dataset, comprising manually annotated face images, is used to fairly assess the lip segmentation performance of the selected models. Inference experiments are conducted on a Raspberry Pi4 to emulate limited computational resources. The results show that Mask2Former and EHANet have the best performances in terms of mIoU score. BiSeNet V2 demonstrate competitive performance, while PIDNet excels in recall but has lower precision. Most models present inference time ranging from 1000 to around 3000 milliseconds on a Raspberry Pi4, with PIDNet having the lowest mean inference time. This study provides a comprehensive evaluation of lip segmentation models, highlighting their performance and inference times. The findings contribute to the development of lightweight techniques and establish benchmarks for future advances in lip segmentation, especially in IoT and edge computing scenarios.

Continuous latent variables (LVs) are a key ingredient of many generative models, as they allow modelling expressive mixtures with an uncountable number of components. In contrast, probabilistic circuits (PCs) are hierarchical discrete mixtures represented as computational graphs composed of input, sum and product units. Unlike continuous LV models, PCs provide tractable inference but are limited to discrete LVs with categorical (i.e. unordered) states. We bridge these model classes by introducing probabilistic integral circuits (PICs), a new language of computational graphs that extends PCs with integral units representing continuous LVs. In the first place, PICs are symbolic computational graphs and are fully tractable in simple cases where analytical integration is possible. In practice, we parameterise PICs with light-weight neural nets delivering an intractable hierarchical continuous mixture that can be approximated arbitrarily well with large PCs using numerical quadrature. On several distribution estimation benchmarks, we show that such PIC-approximating PCs systematically outperform PCs commonly learned via expectation-maximization or SGD.

Fine-grained classification often requires recognizing specific object parts, such as beak shape and wing patterns for birds. Encouraging a fine-grained classification model to first detect such parts and then using them to infer the class could help us gauge whether the model is indeed looking at the right details better than with interpretability methods that provide a single attribution map. We propose PDiscoNet to discover object parts by using only image-level class labels along with priors encouraging the parts to be: discriminative, compact, distinct from each other, equivariant to rigid transforms, and active in at least some of the images. In addition to using the appropriate losses to encode these priors, we propose to use part-dropout, where full part feature vectors are dropped at once to prevent a single part from dominating in the classification, and part feature vector modulation, which makes the information coming from each part distinct from the perspective of the classifier. Our results on CUB, CelebA, and PartImageNet show that the proposed method provides substantially better part discovery performance than previous methods while not requiring any additional hyper-parameter tuning and without penalizing the classification performance. The code is available at https://github.com/robertdvdk/part_detection., Comment: 9 pages, 8 figures, ICCV

This work presents a framework for billiards in convex domains on two dimensional Riemannian manifolds. These domains are contained in connected, simply connected open subsets which are totally normal. In this context, some basic properties that have long been known for billiards on the plane are established. We prove the twist property and investigate conditions on the billiard for the existence and non existence of rotational invariant curves., Comment: We changed the title, from "The Twist Property and the Existence of Invariant Curves for Convex Billiards on Surfaces" to "On the role of the surface geometry in convex billiards"

Models for fine-grained image classification tasks, where the difference between some classes can be extremely subtle and the number of samples per class tends to be low, are particularly prone to picking up background-related biases and demand robust methods to handle potential examples with out-of-distribution (OOD) backgrounds. To gain deeper insights into this critical problem, our research investigates the impact of background-induced bias on fine-grained image classification, evaluating standard backbone models such as Convolutional Neural Network (CNN) and Vision Transformers (ViT). We explore two masking strategies to mitigate background-induced bias: Early masking, which removes background information at the (input) image level, and late masking, which selectively masks high-level spatial features corresponding to the background. Extensive experiments assess the behavior of CNN and ViT models under different masking strategies, with a focus on their generalization to OOD backgrounds. The obtained findings demonstrate that both proposed strategies enhance OOD performance compared to the baseline models, with early masking consistently exhibiting the best OOD performance. Notably, a ViT variant employing GAP-Pooled Patch token-based classification combined with early masking achieves the highest OOD robustness., Comment: Accepted at the 2023 IEEE/CVF International Conference on Computer Vision Workshop (ICCVW) on Out Of Distribution Generalization in Computer Vision (OOD-CV)

Reduced-order models have been widely adopted in fluid mechanics, particularly in the context of Newtonian fluid flows. These models offer the ability to predict complex dynamics, such as instabilities and oscillations, at a considerably reduced computational cost. In contrast, the reduced-order modeling of non-Newtonian viscoelastic fluid flows remains relatively unexplored. This work leverages the sparse identification of nonlinear dynamics algorithm to develop interpretable reduced-order models for viscoelastic flows. In particular, we explore a benchmark oscillatory viscoelastic flow on the four-roll mill geometry using the classical Oldroyd-B fluid. This flow exemplifies many canonical challenges associated with non-Newtonian flows, including transitions, asymmetries, instabilities, and bifurcations arising from the interplay of viscous and elastic forces, all of which require expensive computations in order to resolve the fast timescales and long transients characteristic of such flows. First, we demonstrate the effectiveness of our data-driven surrogate model to predict the transient evolution and accurately reconstruct the spatial flow field for fixed flow parameters. We then develop a fully parametric, nonlinear model capable of capturing the dynamic variations as a function of the Weissenberg number. While the training data is predominantly concentrated on a limit cycle regime for moderate Wi, we show that the parameterized model can be used to extrapolate, accurately predicting the dominant dynamics in the case of high Weissenberg numbers. The proposed methodology represents an initial step in the field of reduced-order modeling for viscoelastic flows with the potential to be further refined and enhanced for the design, optimization, and control of a wide range of non-Newtonian fluid flows using machine learning and reduced-order modeling techniques.

Arising from: Mankowitz, D.J., Michi, A., Zhernov, A. et al. Faster sorting algorithms discovered using deep reinforcement learning.Nature 618, 257-263 (2023). doi.org/10.1038/s41586-023-06004-9. The article cited above presents new implementations of sorting algorithms found through deep reinforcement learning that work on a small number of numeric inputs. For 3 numbers, the published implementation contains 17 assembly instructions, and the authors state that no shorter program exists. This note presents two counterexamples for this claim and a straightforward C/C++ implementation that is faster than theirs.

Adaptive networks (ANs) are effective real time techniques to process and track events observed by sensor networks and, more recently, to equip Internet of Things (IoT) applications. ANs operate over nodes equipped with collaborative adaptive filters that solve distributively an estimation problem common to the whole network. However, they do not guarantee that nodes do not lose from cooperation, as compared to its non-cooperative operation; that poor nodes are rejected and exceptional nodes estimates reach the entire network; and that performance is uniform over all nodes. In order to enforce such properties, this work introduces the concept of distributed universal estimation, which encompasses the new concepts of local universality, global universality and universality with respect to the non-cooperative operation. We then construct a new cooperation protocol that is proven to be distributively universal, outperforming direct competitors from the literature, as shown by several simulations. Mean and mean-square analytical models are developed, with good agreement between theory and simulations.

We study the spreading of elastoviscoplastic (EVP) droplets under surface tension effects. The non- Newtonian material flows like a viscoelastic liquid above the yield stress and behaves like a viscoelastic solid below it. Hence, the droplet initially flows under surface tension forces but eventually reaches a final equilibrium shape when the stress everywhere inside the droplet falls below the resisting rheological stresses. We use numerical simulations and combine Volume-of-Fluid (VOF) method and an EVP constitutive model to systematically study the dynamics of spreading and the final shape of the droplets. The spreading process examined in this study finds applications in coating, droplet-based inkjet printing, and 3D printing, where complex fluids such as paints, thermoplastic filaments, or bio-inks are deposited onto surfaces. Additionally, the computational framework enables the study of a wide range of multiphase interfacial phenomena, from elastocapillarity to plastocapillarity., Comment: 15 pages, 14 figures

Multi-dimensional classification (MDC) can be employed in a range of applications where one needs to predict multiple class variables for each given instance. Many existing MDC methods suffer from at least one of inaccuracy, scalability, limited use to certain types of data, hardness of interpretation or lack of probabilistic (uncertainty) estimations. This paper is an attempt to address all these disadvantages simultaneously. We propose a formal framework for probabilistic MDC in which learning an optimal multi-dimensional classifier can be decomposed, without loss of generality, into learning a set of (smaller) single-variable multi-class probabilistic classifiers and a directed acyclic graph. Current and future developments of both probabilistic classification and graphical model learning can directly enhance our framework, which is flexible and provably optimal. A collection of experiments is conducted to highlight the usefulness of this MDC framework., Comment: Accepted for the 39th Conference on Uncertainty in Artificial Intelligence (UAI 2023)

We describe the development, operation, and application of the 4D Camera -- a 576 by 576 pixel active pixel sensor for scanning/transmission electron microscopy which operates at 87,000 Hz. The detector generates data at approximately 480 Gbit/s which is captured by dedicated receiver computers with a parallelized software infrastructure that has been implemented to process the resulting 10 - 700 Gigabyte-sized raw datasets. The back illuminated detector provides the ability to detect single electron events at accelerating voltages from 30 - 300 keV. Through electron counting, the resulting sparse data sets are reduced in size by 10 - 300x compared to the raw data, and open-source sparsity-based processing algorithms offer rapid data analysis. The high frame rate allows for large and complex 4D-STEM experiments to be accomplished with typical STEM scanning parameters.