Miracle-dz/UniFAR-FTUs huggingface dataset:
An extensible Benchmarking Graph-Mesh dataset for studying Steady-State Incompressible Navier-Stokes Equations

Recent progress in \emph{Geometric Deep Learning} (GDL) has shown its potential to provide powerful data-driven models. This gives momentum to explore new methods for learning physical systems governed by \emph{Partial Differential Equations} (PDEs) from Graph-Mesh data. However, despite the efforts and recent achievements, several research directions remain unexplored and progress is still far from satisfying the physical requirements of real-world phenomena. One of the major impediments is the absence of benchmarking datasets and common physics evaluation protocols. In this paper, we propose a 2-D graph-mesh dataset to study the airflow over airfoils at high Reynolds regime (from $10^6$ and beyond). We also introduce metrics on the stress forces over the airfoil in order to evaluate GDL models on important physical quantities. Moreover, we provide extensive GDL baselines.
Non-Precipitating Shallow Cumulus Convection is Intrinsically Unstable to Length-Scale Growth

Condensation in cumulus clouds plays a key role in structuring the mean, non-precipitating trade-wind boundary layer. Here, we summarise how this role also explains the spontaneous growth of mesoscale (> О(10) km) fluctuations in clouds and moisture around the mean state in a minimal-physics, large-eddy simulation of the undisturbed period during BOMEX on a large (О(100) km) domain. Small, spatial anomalies in latent heating in cumulus clouds, which form on top of small moisture fluctuations, give rise to circulations that transport moisture, but not heat, from dry to moist regions, and thus reinforce the latent heating anomaly. We frame this positive feedback as a linear instability in mesoscale moisture fluctuations, whose time scale depends only on i) a vertical velocity scale and ii) the mean environment’s vertical structure. In our minimal-physics setting, we show both ingredients are provided by the shallow cumulus convection itself: It is intrinsically unstable to length scale growth. The upshot is that energy released by clouds at kilometre scales may play a more profound and direct role in shaping the mesoscale trade-wind environment than is generally appreciated, motivating further research into the mechanism’s relevance.
Effective bounds on $S$-integral preperiodic points for polynomials

Given a polynomial f deﬁned over a number ﬁeld K , we make eﬀective certain special cases of a conjecture of S. Ih, on the ﬁniteness of f -preperiodic points which are S -integral with respect to a ﬁxed non-preperiodic point α . As an application, we obtain bounds on the number of S -units in the doubly indexed sequence { f n ( α ) − f m ( α ) } n>m ≥ 0 . In the case of a unicritical polynomial f c ( z ) = z 2 + c , with α ﬁxed to be the critical point 0, for parameters c outside a small region, we give an explicit bound which depends only on the number of places of bad reduction for f c . As part of the proof, we obtain novel lower bounds for the v -adically smallest preperiodic point of f c for each place v of K .
Why patient data cannot be easily forgotten?

Rights provisioned within data protection regulations, per-mit patients to request that knowledge about their information be elim-inated by data holders. With the advent of AI learned on data, one can imagine that such rights can extent to requests for forgetting knowledge of patient’s data within AI models. However, forgetting patients’ imaging data from AI models, is still an under-explored problem. In this paper, we study the inﬂuence of patient data on model performance and formulate two hypotheses for a patient’s data: either they are common and similar to other patients or form edge cases, i.e. unique and rare cases. We show that it is not possible to easily forget patient data . We propose a targeted forgetting approach to perform patient-wise forgetting. Extensive experiments on the benchmark Automated Cardiac Diagnosis Challenge dataset showcase the improved performance of the proposed targeted forgetting approach as opposed to a state-of-the-art method.
RegMixup: Mixup as a Regularizer Can Surprisingly Improve Accuracy and Out Distribution Robustness

We show that the effectiveness of the well celebrated Mixup [Zhang et al., 2018] can be further improved if instead of using it as the sole learning objective, it is utilized as an additional regularizer to the standard cross-entropy loss. This simple change not only provides much improved accuracy but also significantly improves the quality of the predictive uncertainty estimation of Mixup in most cases under various forms of covariate shifts and out-of-distribution detection experiments. In fact, we observe that Mixup yields much degraded performance on detecting out-of-distribution samples possibly, as we show empirically, because of its tendency to learn models that exhibit high-entropy throughout; making it difficult to differentiate in-distribution samples from out-distribution ones. To show the efficacy of our approach (RegMixup), we provide thorough analyses and experiments on vision datasets (ImageNet&CIFAR-10/100) and compare it with a suite of recent approaches for reliable uncertainty estimation.
A Local Continuum Model of Cell-Cell Adhesion

Cell-cell adhesion is one the most fundamental mechanisms regulating collective cell migration during tissue development, homeostasis and repair, allowing cell populations to self-organize and eventually form and maintain complex tissue shapes. Cells interact with each other via the formation of protrusions or filopodia and they adhere to other cells through binding of cell surface proteins. The resulting adhesive forces are then related to cell size and shape and, often, continuum models represent them by nonlocal attractive interactions. In this paper, we present a new continuum model of cell-cell adhesion which can be derived from a general nonlocal model in the limit of short-range interactions. This new model is local, resembling a system of thin-film type equations, with the various model parameters playing the role of surface tensions between different cell populations. Numerical simulations in one and two dimensions reveal that the local model maintains the diversity of cell sorting patterns observed both in experiments and in previously used nonlocal models. In addition, it also has the advantage of having explicit stationary solutions, which provides a direct link between the model parameters and the differential adhesion hypothesis.
Multi-scale Physical Representations for Approximating PDE Solutions with Graph Neural Operators

Representing physical signals at different scales is among the most challenging problems in engineering. Several multi-scale modeling tools have been developed to describe physical systems governed by \emph{Partial Differential Equations} (PDEs). These tools are at the crossroad of principled physical models and numerical schema. Recently, data-driven models have been introduced to speed-up the approximation of PDE solutions compared to numerical solvers. Among these recent data-driven methods, neural integral operators are a class that learn a mapping between function spaces. These functions are discretized on graphs (meshes) which are appropriate for modeling interactions in physical phenomena. In this work, we study three multi-resolution schema with integral kernel operators that can be approximated with \emph{Message Passing Graph Neural Networks} (MPGNNs). To validate our study, we make extensive MPGNNs experiments with well-chosen metrics considering steady and unsteady PDEs.
Tailoring the Switching Efficiency of Magnetic Tunnel Junctions by the Fieldlike Spin-Orbit Torque

Current-induced spin-orbit torques provide a versatile tool for switching magnetic devices. In perpendicular magnets, the dampinglike component of the torque is the main driver of magnetization reversal. The degree to which the ﬁeldlike torque assists the switching is a matter of debate. Here we study the switching of magnetic tunnel junctions with a CoFeB free layer and either W or Ta underlayers, which have a ratio of ﬁeldlike to dampinglike torque of 0.3 and 1, respectively. We show that the ﬁeldlike torque can either assist or hinder the switching of CoFeB when the static in-plane magnetic ﬁeld required to deﬁne the polarity of spin-orbit torque switching has a component transverse to the current. In particular, the non-collinear alignment of the ﬁeld and current can be exploited to increase the switching efﬁciency and reliability compared to the standard collinear alignment. By probing individual switching events in real-time, we also show that the combination of transverse magnetic ﬁeld and ﬁeldlike torque can accelerate or decelerate the reversal onset. We validate our observations using micromagnetic simulations and extrapolate the results to materials with different torque ratios. Finally, we propose device geometries that leverage the ﬁeldlike torque for density increase in memory applications and synaptic weight generation.
Intrinsic Layer-Polarized Anomalous Hall Effect in Bilayer MnBi2Te4

Layer-polarized anomalous Hall effect (LP-AHE) is an attractive phenomenon in condensed-matter physics from the standpoints of both fundamental interest and device applications. The current LP-AHE research is based on the extrinsic paradigm of using external electric fields, in which the generation and control of LP-AHE are not straightforward. Here, we propose a novel mechanism that realizes intrinsic LP-AHE in bilayer lattices, through the mediation of sliding physics and Berry curvature. Moreover, this mechanism could render the LP-AHE in a controllable and reversable fashion. We analyze the symmetry requirements for a system to host such intrinsic LP-AHE. Its validity is further demonstrated in a real material of bilayer MnBi2Te4. By stacking with broken inversion symmetry, the layer-locked Berry curvature enables the intrinsic LP-AHE in bilayer MnBi2Te4, and the switchable control of its LP-AHE is achieved by sliding ferroelectricity. Our work opens a significant new direction for LP-AHE and two-dimensional (2D) materials research.
Optimization-Induced Graph Implicit Nonlinear Diffusion

Due to the over-smoothing issue, most existing graph neural networks can only capture limited dependencies with their inherently finite aggregation layers. To overcome this limitation, we propose a new kind of graph convolution, called Graph Implicit Nonlinear Diffusion (GIND), which implicitly has access to infinite hops of neighbors while adaptively aggregating features with nonlinear diffusion to prevent over-smoothing. Notably, we show that the learned representation can be formalized as the minimizer of an explicit convex optimization objective. With this property, we can theoretically characterize the equilibrium of our GIND from an optimization perspective. More interestingly, we can induce new structural variants by modifying the corresponding optimization objective. To be specific, we can embed prior properties to the equilibrium, as well as introducing skip connections to promote training stability. Extensive experiments show that GIND is good at capturing long-range dependencies, and performs well on both homophilic and heterophilic graphs with nonlinear diffusion. Moreover, we show that the optimization-induced variants of our models can boost the performance and improve training stability and efficiency as well. As a result, our GIND obtains significant improvements on both node-level and graph-level tasks.
Resolving pathology of self-interacting Proca ﬁeld: a case study of Proca star

It has been argued that a self-interacting massive vector ﬁeld is pathological due to a dynamical formation of a singular eﬀective metric of the vector ﬁeld, which is the onset of a gradient or ghost instability. We discuss that this singularity formation is not necessarily a fundamental problem but a breakdown of the eﬀective ﬁeld theory (EFT) description of the massive vector ﬁeld. By using a model of ultraviolet (UV) completion of the massive vector ﬁeld, we demonstrate that a Proca star, a self-gravitating condensate of the vector ﬁeld, continues to exist even after the EFT suﬀers from a gradient instability without any pathology at UV, in which the EFT description is still valid and the gradient instability in EFT may be interpreted as a standard dynamical instability of a high-density boson star from the UV perspective. On the other hand, we ﬁnd that the EFT description is broken before the ghost instability appears. This suggests that a heavy degree of freedom may be spontaneously excited to cure the pathology of the EFT as the EFT dynamically tends to approach the onset of the ghost instability.
Deep learning for spin-orbit torque characterizations with a projected vector field magnet

Spin-orbit torque characterizations on magnetic heterostructures with perpendicular anisotropy are demonstrated on a projected vector field magnet via hysteresis loop shift measurement and harmonic Hall measurement with planar Hall correction. Accurate magnetic field calibration of the vector magnet is realized with the help of deep learning models, which are able to capture the nonlinear behavior between the generated magnetic field and the currents applied to the magnet. The trained models can successfully predict the applied current combinations under the circumstances of magnetic field scans, angle scans, and hysteresis loop shift measurements. The validity of the models is further verified, complemented by the comparison of the spin-orbit torque characterization results obtained from the deep-learning-trained vector magnet system with those obtained from a conventional setup comprised of two separated electromagnets. The damping-like spin-orbit torque (DL-SOT) efficiencies ( |𝜉 #$ | ) extracted from the vector magnet and the traditional measurement configuration are consistent, where |𝜉 #$ | ≈ 0.22 for amorphous W and |𝜉 #$ | ≈ 0.02 for 𝛼 -W. Our work provides an advanced method to meticulously control a vector magnet and to conveniently perform various spin-orbit torque characterizations.
MaNi: Maximizing Mutual Information for Nuclei Cross-Domain Unsupervised Segmentation

In this work, we propose a mutual information (MI) based unsupervised domain adaptation (UDA) method for the cross-domain nuclei segmentation. Nuclei vary substantially in structure and appear-ances across diﬀerent cancer types, leading to a drop in performance of deep learning models when trained on one cancer type and tested on another. This domain shift becomes even more critical as accurate segmentation and quantiﬁcation of nuclei is an essential histopathology task for the diagnosis/ prognosis of patients and annotating nuclei at the pixel level for new cancer types demands extensive eﬀort by medical experts. To address this problem, we maximize the MI between labeled source cancer type data and unlabeled target cancer type data for transferring nuclei segmentation knowledge across domains. We use the Jensen-Shanon divergence bound, requiring only one negative pair per positive pair for MI maximization. We evaluate our set-up for multiple modeling frameworks and on diﬀerent datasets comprising of over 20 cancer-type domain shifts and demonstrate competitive performance. All the recently proposed approaches consist of multiple components for improving the domain adaptation, whereas our proposed module is light and can be easily incorporated into other methods (Implementation: https://github.com/YashSharma/MaNi). gener-alizing learned knowledge from one cancer type to another. Pixel-level image
Exploring the Latent Space of Autoencoders with Interventional Assays

Autoencoders exhibit impressive abilities to embed the data manifold into a low-dimensional latent space, making them a staple of representation learning methods. However, without explicit supervision, which is often unavailable, the representation is usually uninterpretable, making analysis and principled progress challenging. We propose a framework, called latent responses, which exploits the locally contractive behavior exhibited by variational autoencoders to explore the learned manifold. More specifically, we develop tools to probe the representation using interventions in the latent space to quantify the relationships between latent variables. We extend the notion of disentanglement to take the learned generative process into account and consequently avoid the limitations of existing metrics that may rely on spurious correlations. Our analyses underscore the importance of studying the causal structure of the representation to improve performance on downstream tasks such as generation, interpolation, and inference of the factors of variation.
An Embedding Framework for the Design and Analysis of Consistent Polyhedral Surrogates

We formalize and study the natural approach of designing convex surrogate loss functions via embeddings, for problems such as classification, ranking, or structured prediction. In this approach, one embeds each of the finitely many predictions (e.g. rankings) as a point in R, assigns the original loss values to these points, and “convexifies” the loss in some way to obtain a surrogate. We establish a strong connection between this approach and polyhedral (piecewise-linear convex) surrogate losses: every discrete loss is embedded by some polyhedral loss, and every polyhedral loss embeds some discrete loss. Moreover, an embedding gives rise to a consistent link function as well as linear surrogate regret bounds. Our results are constructive, as we illustrate with several examples. In particular, our framework gives succinct proofs of consistency or inconsistency for various polyhedral surrogates in the literature, and for inconsistent surrogates, it further reveals the discrete losses for which these surrogates are consistent. We go on to show additional structure of embeddings, such as the equivalence of embedding and matching Bayes risks, and the equivalence of various notions of non-redudancy. Using these results, we establish that indirect elicitation, a necessary condition for consistency, is also sufficient when working with polyhedral surrogates.
Cold Gas Reservoirs of Low- and High-mass Central Galaxies Differ in Response to Active Galactic Nucleus Feedback

The growth of supermassive black holes, especially the associated state of active galactic nuclei (AGNs), is generally believed to be the key step in regulating star formation in massive galaxies. As the fuel of star formation, the cold gas reservoir is a direct probe of the effect of AGN feedback on their host galaxies. However, in observations, no clear connection has been found between AGN activity and the cold gas mass. In this paper, we find observational signals of the significant depletion of the total neutral hydrogen gas reservoir in optically selected Type 2 AGN-host central galaxies of stellar mass 109–1010 M ⊙. The effect of AGN feedback on the cold gas reservoir is stronger for higher star formation rates and higher AGN luminosity. But it becomes much weaker above this mass range, consistent with previous findings focusing on massive galaxies. Our result suggests that low-mass and gas-rich AGN-host central galaxies would first form dense cores before AGN feedback is triggered, removing their neutral hydrogen gas. More massive central galaxies may undergo a significantly different formation scenario by gradually building up dense cores with less effective and recurrent AGN feedback.
Molecular information theory meets protein folding

We propose an application of molecular information theory to analyze the folding of single domain proteins. We analyze results from various areas of protein science, such as sequence-based potentials, reduced amino acid alphabets, backbone configurational entropy, secondary structure content, residue burial layers, and mutational studies of protein stability changes. We found that the average information contained in the sequences of evolved proteins is very close to the average information needed to specify a fold ∼2.2 ± 0.3 bits/(site·operation). The effective alphabet size in evolved proteins equals the effective number of conformations of a residue in the compact unfolded state at around 5. We calculated an energy-to-information conversion efficiency upon folding of around 50%, lower than the theoretical limit of 70%, but much higher than human-built macroscopic machines. We propose a simple mapping between molecular information theory and energy landscape theory and explore the connections between sequence evolution, configurational entropy, and the energetics of protein folding.
Biometric Identification Systems With Both Chosen and Generated Secret Keys by Allowing Correlation

We propose a biometric identification system where the chosen- and generated-secret keys are used simultaneously, and investigate its fundamental limits from information-theoretic perspectives. The system consists of two phases: enrollment and identification phases. In the enrollment phase, for each user, the encoder uses a secret key, which is chosen independently, and the biometric identifier to generate another secret key and a helper {data}. In the identification phase, observing the biometric sequence of the identified user, the decoder estimates index, chosen- and generated-secret keys of the identified user based on the helper {data} stored in the system database. In this study, the capacity region of such a system is characterized. In the problem setting, we allow chosen- and generated-secret keys to be correlated. As a result, by permitting the correlation of the two secret keys, the sum rate of the identification, chosen- and {generated-secret key} rates can achieve a larger value compared to the case where the keys {do not correlate}. Moreover, the minimum amount of the storage rate changes in accordance with both the identification and chosen-secret key rates, but that of the privacy-leakage rate depends only on the identification rate.
Implications of the muon anomalous magnetic moment for the LHC and MUonE

We consider the anomalous magnetic moment of the muon a µ , which shows a signiﬁcant deviation from the Standard Model expectation given the recent measurements at Fermilab and BNL. We focus on Standard Model Eﬀective Field Theory (SMEFT) with the aim to identify avenues for the upcoming LHC runs and future experiments such as MUonE. To this end, we include radiative eﬀects to a µ in SMEFT to connect the muon anomaly to potentially interesting searches at the LHC, speciﬁcally Higgs decays into muon pairs and such decays with resolved photons. Our investigation shows that similar to results for concrete UV extensions of the Standard Model, the Fermilab/BNL result can indicate strong coupling within the EFT framework and a µ is increasingly sensitive to a single operator direction for high scale UV completions. In such cases, there is some complementarity between expected future experimental improvements, yet with considerable statistical challenges to match the precision provided by the recent a µ measurement.