Miracle-dz/UniFAR-FTUs huggingface dataset:
Local foliations by critical surfaces of the Hawking energy and small sphere limit

Local foliations of area constrained Willmore surfaces on a 3-dimensional Riemannian manifold were constructed by Lamm, Metzger and Schulze, and Ikoma, Machiodi and Mondino, the leaves of these foliations are, in particular, critical surfaces of the Hawking energy in case they are contained in a totally geodesic spacelike hypersurface. We generalize these foliations to the general case of a non-totally geodesic spacelike hypersurface, constructing a unique local foliation of area constrained critical surfaces of the Hawking energy. A discrepancy when evaluating the so called small sphere limit of the Hawking energy was found by Friedrich. He studied concentrations of area constrained critical surfaces of the Hawking energy and obtained a result that apparently differs from the well established small sphere limit of the Hawking energy of Horowitz and Schmidt, this small sphere limit in principle must be satisfied by any quasi local energy. We independently confirm the discrepancy and explain the reasons for it to happen. We also prove that these surfaces are suitable to evaluate the Hawking energy in the sense of Lamm, Metzger and Schulze, and we find an indication that these surfaces may induce an excess in the energy measured.
Good News Is Not a Sufficient Condition for Motivated Reasoning

People often receive good news that makes them feel better about the world around them, or bad news that makes them feel worse about it. This paper studies how the valence of news affects belief updating, absent functional and ego-relevant factors. Using experiments with over 1,500 participants and 5,600 observations, I test whether people engage in motivated reasoning to overly trust good news versus bad news on valence-relevant issues like cancer survival rates, others' happiness, and infant mortality. The estimate for motivated reasoning towards good news is a precisely-estimated null. Modest effects, of one-third the size of motivated reasoning in politics and performance, can be ruled out. Complementary survey evidence shows that most people expect good news to increase happiness, but to not systematically lead to motivated reasoning. These results suggest that belief-based utility is not sufficient in leading people to distort belief updating in order to favor those beliefs.
Pressure-induced transitions in FePS$_3$: Structural, magnetic and electronic properties

FePS_33 is a prototype van der Waals layered antiferromagnet and a Mott insulator under ambient conditions, which has been recently reported to go through a pressure-induced dimensionality crossover and an insulator-to-metal transition. These transitions also lead to the appearance of a novel magnetic metallic state. To further understand these emergent structural and physical properties, we have performed a first-principles study using van der Waals and Hubbard UU corrected density functional theory including a random structure search. Our computational study attempts to interpret the experimental coexistence of the low- and intermediate-pressure phases and we predict a novel high-pressure phase with distinctive dimensionality and different possible origins of metallicity.
Clifford Neural Layers for PDE Modeling

Partial differential equations (PDEs) see widespread use in sciences and engineering to describe simulation of physical processes as scalar and vector fields interacting and coevolving over time. Due to the computationally expensive nature of their standard solution methods, neural PDE surrogates have become an active research topic to accelerate these simulations. However, current methods do not explicitly take into account the relationship between different fields and their internal components, which are often correlated. Viewing the time evolution of such correlated fields through the lens of multivector fields allows us to overcome these limitations. Multivector fields consist of scalar, vector, as well as higher-order components, such as bivectors and trivectors. Their algebraic properties, such as multiplication, addition and other arithmetic operations can be described by Clifford algebras. To our knowledge, this paper presents the first usage of such multivector representations together with Clifford convolutions and Clifford Fourier transforms in the context of deep learning. The resulting Clifford neural layers are universally applicable and will find direct use in the areas of fluid dynamics, weather forecasting, and the modeling of physical systems in general. We empirically evaluate the benefit of Clifford neural layers by replacing convolution and Fourier operations in common neural PDE surrogates by their Clifford counterparts on 2D Navier-Stokes and weather modeling tasks, as well as 3D Maxwell equations. For similar parameter count, Clifford neural layers consistently improve generalization capabilities of the tested neural PDE surrogates. Source code for our PyTorch implementation is available at https://microsoft.github. io/cliffordlayers/.
Inverse-Dynamics MPC via Nullspace Resolution

Optimal control (OC) using inverse dynamics provides numerical benefits, such as coarse optimization, cheaper computation of derivatives, and a high convergence rate. However, to take advantage of these benefits in model predictive control (MPC) for legged robots, it is crucial to handle efficiently its large number of equality constraints. To accomplish this, we first propose a novel approach to handle equality constraints based on nullspace parameterization. Our approach balances optimality, and both dynamics and equality-constraint feasibility appropriately, which increases the basin of attraction to high-quality local minima. To do so, we modify our feasibility-driven search by incorporating a merit function. Furthermore, we introduce a condensed formulation of inverse dynamics that considers arbitrary actuator models. We also propose a novel MPC based on inverse dynamics within a perceptive locomotion framework. Finally, we present a theoretical comparison of OC with forward and inverse dynamics and evaluate both numerically. Our approach enables the first application of inverse-dynamics MPC on hardware, resulting in the state-of-the-art dynamic climbing on the ANYmal robot. We benchmark it over a wide range of robotics problems and generate agile and complex maneuvers. We show the computational reduction of our nullspace resolution and condensed formulation (up to ${47.3}\boldsymbol{\%}$). We provide evidence of the benefits of our approach by solving coarse optimization problems with a high convergence rate (up to 10 Hz of discretization). Our algorithm is publicly available inside Crocoddyl.
Vec2Face-v2: Unveil Human Faces from their Blackbox Features via Attention-based Network in Face Recognition

In this work, we investigate the problem of face reconstruction given a facial feature representation extracted from a blackbox face recognition engine. Indeed, it is a very challenging problem in practice due to the limitations of abstracted information from the engine. We, therefore, introduce a new method named Attention-based Bijective Generative Adversarial Networks in a Distillation framework (DAB-GAN) to synthesize the faces of a subject given his/her extracted face recognition features. Given any unconstrained unseen facial features of a subject, the DAB-GAN can reconstruct his/her facial images in high definition. The DAB-GAN method includes a novel attention-based generative structure with the newly defined Bijective Metrics Learning approach. The framework starts by introducing a bijective metric so that the distance measurement and metric learning process can be directly adopted in the image domain for an image reconstruction task. The information from the blackbox face recognition engine will be optimally exploited using the global distillation process. Then an attention-based generator is presented for a highly robust generator to synthesize realistic faces with ID preservation. We have evaluated our method on the challenging face recognition databases, i.e., CelebA, LFW, CFP-FP, CP-LFW, AgeDB, CA-LFW, and consistently achieved state-of-the-art results. The advancement of DAB-GAN is also proven in both image realism and ID preservation properties.
Testing Pre-trained Language Models’ Understanding of Distributivity via Causal Mediation Analysis

To what extent do pre-trained language models grasp semantic knowledge regarding the phenomenon of distributivity? In this paper, we introduce DistNLI, a new diagnostic dataset for natural language inference that targets the semantic difference arising from distributivity, and employ the causal mediation analysis framework to quantify the model behavior and explore the underlying mechanism in this semantically-related task. We find that the extent of models’ understanding is associated with model size and vocabulary size. We also provide insights into how models encode such high-level semantic knowledge.
Deep Feature Statistics Mapping for Generalized Screen Content Image Quality Assessment

The statistical regularities of natural images, referred to as natural scene statistics, play an important role in no-reference image quality assessment. However, it has been widely acknowledged that screen content images (SCIs), which are typically computer generated, do not hold such statistics. Here we make the first attempt to learn the statistics of SCIs, based upon which the quality of SCIs can be effectively determined. The underlying mechanism of the proposed approach is based upon the wild assumption that the SCIs, which are not physically acquired, still obey certain statistics that could be understood in a learning fashion. We empirically show that the statistics deviation could be effectively leveraged in quality assessment, and the proposed method is superior when evaluated in different settings. Extensive experimental results demonstrate the Deep Feature Statistics based SCI Quality Assessment (DFSS-IQA) model delivers promising performance compared with existing NR-IQA models and shows a high generalization capability in the cross-dataset settings. The implementation of our method is publicly available at https://github.com/Baoliang93/DFSS-IQA.
Self-consistent computation of spin torques and magneto-resistance in tunnel junctions and magnetic read-heads with metallic pinhole defects

A three-dimensional self-consistent spin transport model is developed, which includes both tunnelling transport, leading to tunnelling magneto-resistance, as well as metallic transport, leading to giant magneto-resistance. An explicit solution to the drift-diffusion model is also derived, which allows analysing the effect of both the reference and free layer thickness on the spin-transfer torque polarization and field-like coefficient. It is shown the model developed here can be used to compute the signal-to-noise ratio in realistic magnetic read-heads, where spin torque-induced fluctuations and instabilities limit the maximum operating voltage. The effect of metallic pinhole defects in the insulator layer is also analysed. Increasing the area covered by pinholes results in a rapid degradation of the magneto-resistance, following an inverse dependence. Moreover, the spin torque angular dependence becomes skewed, similar to that obtained in fully metallic spin valves, and the spin-transfer torque polarization decreases. The same results are obtained when considering tunnel junctions with a single pinhole defect, but decreasing cross-sectional area, showing that even a single pinhole defect can significantly degrade the performance of tunnel junctions and magnetic read-heads below the 40 nm node.
Multifluid cosmology in f(G) gravity

The treatment of 1 + 3 covariant perturbation in a multifluid cosmology with the consideration of f (G) gravity, G being the Gauss-Bonnet term, is done in the present paper. We define a set of covariant and gauge-invariant variables to describe density, velocity and entropy perturbations for both the total matter and component fluids. We then use different techniques such as scalar decomposition, harmonic decomposition, quasi-static approximation together with the redshift transformation to get simplified perturbation equations for analysis. We then discuss number of interesting applications like the case where the universe is filled with a mixture of radiation and Gauss-Bonnet fluids as well as dust with Gauss-Bonnet fluids for both short- and long-wavelength limits. Considering polynomial f (G) model, we get numerical solutions of energy density perturbations and show that they decay with increase in redshift. This feature shows that under f (G) gravity, specifically under the considered f (G) model, one expects that the formation of the structure in the late Universe is enhanced.
Singular Levy processes and dispersive effects of generalized Schrödinger equations

We introduce new models for Schr\"odinger-type equations, which generalize standard NLS and for which different dispersion occurs depending on the directions. Our purpose is to understand dispersive properties depending on the directions of propagation, in the spirit of waveguide manifolds, but where the diffusion is of different types. We mainly consider the standard Euclidean space and the waveguide case but our arguments extend easily to other types of manifolds (like product spaces). Our approach unifies in a natural way several previous results. Those models are also generalizations of some appearing in seminal works in mathematical physics, such as relativistic strings. In particular, we prove the large data scattering on waveguide manifolds $\mathbb{R}^d \times \mathbb{T}$, $d \geq 3$. This result can be regarded as the analogue of \cite{TV2, YYZ2} in our setting and the waveguide analogue investigated in \cite{GSWZ}. A key ingredient of the proof is a Morawetz-type estimate for the setting of this model.
Linearity on ordinary Siegel moduli schemes and joint unlikely almost intersections

The goal of this paper is to study a p -adic analog of the joint of the conjectures of Andr´e–Oort and Andr´e–Pink. More precisely, on a product of ordinary Siegel formal moduli schemes, we study the distribution of points whose components are either CM points or points in Hecke orbits. We use linearity of formal subschemes of the product as the p -adic analog of geodesicness over complex numbers. Moreover, we relax the usual incidence relations by using p -adic distance. We also study a p -adic formal scheme theoretic analog of the Ax–Lindemann theorem.
Partial Observability during DRL for Robot Control

Deep Reinforcement Learning (DRL) has made tremendous advances in both simulated and real-world robot control tasks in recent years. Nevertheless, applying DRL to novel robot control tasks is still challenging, especially when researchers have to design the action and observation space and the reward function. In this paper, we investigate partial observability as a potential failure source of applying DRL to robot control tasks, which can occur when researchers are not confident whether the observation space fully represents the underlying state. We compare the performance of three common DRL algorithms, TD3, SAC and PPO under various partial observability conditions. We find that TD3 and SAC become easily stuck in local optima and underperform PPO. We propose multi-step versions of the vanilla TD3 and SAC to improve robustness to partial observability based on one-step bootstrapping.
Chromosome Segmentation Analysis Using Image Processing Techniques and Autoencoders

Chromosome analysis and identification from metaphase images is a critical part of cytogenetics based medical diagnosis. It is mainly used for identifying constitutional, prenatal and acquired abnormalities in the diagnosis of genetic diseases and disorders. The process of identification of chromosomes from metaphase is a tedious one and requires trained personnel and several hours to perform. Challenge exists especially in handling touching, overlapping and clustered chromosomes in metaphase images, which if not segmented properly would result in wrong classification. We propose a method to automate the process of detection and segmentation of chromosomes from a given metaphase image, and in using them to classify through a Deep CNN architecture to know the chromosome type. We have used two methods to handle the separation of overlapping chromosomes found in metaphases - one method involving watershed algorithm followed by autoencoders and the other a method purely based on watershed algorithm. These methods involve a combination of automation and very minimal manual effort to perform the segmentation, which produces the output. The manual effort ensures that human intuition is taken into consideration, especially in handling touching, overlapping and cluster chromosomes. Upon segmentation, individual chromosome images are then classified into their respective classes with 95.75\% accuracy using a Deep CNN model. Further, we impart a distribution strategy to classify these chromosomes from the given output (which typically could consist of 46 individual images in a normal scenario for human beings) into its individual classes with an accuracy of 98\%. Our study helps conclude that pure manual effort involved in chromosome segmentation can be automated to a very good level through image processing techniques to produce reliable and satisfying results.
Accelerated Primal-Dual Methods for Convex-Strongly-Concave Saddle Point Problems

We investigate a primal-dual (PD) method for the saddle point problem (SPP) that uses a linear approximation of the primal function instead of the standard proximal step, resulting in a linearized PD (LPD) method. For convex-strongly concave SPP, we observe that the LPD method has a suboptimal dependence on the Lipschitz constant of the primal function. To fix this issue, we combine features of Accelerated Gradient Descent with the LPD method resulting in a single-loop Accelerated Linearized Primal-Dual (ALPD) method. ALPD method achieves the optimal gradient complexity when the SPP has a semi-linear coupling function. We also present an inexact ALPD method for SPPs with a general nonlinear coupling function that maintains the optimal gradient evaluations of the primal parts and significantly improves the gradient evaluations of the coupling term compared to the ALPD method. We verify our findings with numerical experiments.
Comment on `Tainted evidence: cosmological model selection versus fitting', by Eric V. Linder and Ramon Miquel (astro-ph/0702542v2)

In astro-ph/0702542v2, Linder and Miquel seek to criticize the use of Bayesian model selection for data analysis and for survey forecasting and design. Their discussion is based on three serious misunderstandings of the conceptual underpinnings and application of model-level Bayesian inference, which invalidate all their main conclusions. Their paper includes numerous further inaccuracies, including an erroneous calculation of the Bayesian Information Criterion. Here we seek to set the record straight.
Infinite-dimensional Hamilton-Jacobi equations for statistical inference on sparse graphs

We study the well-posedness of an infinite-dimensional Hamilton-Jacobi equation posed on the set of non-negative measures and with a monotonic non-linearity. Our results will be used in a companion work to propose a conjecture and prove partial results concerning the asymptotic mutual information in the assortative stochastic block model in the sparse regime. The equation we consider is naturally stated in terms of the Gateaux derivative of the solution, unlike previous works in which the derivative is usually of transport type. We introduce an approximating family of finite-dimensional Hamilton-Jacobi equations, and use the monotonicity of the non-linearity to show that no boundary condition needs to be prescribed to establish well-posedness. The solution to the infinite-dimensional Hamilton-Jacobi equation is then defined as the limit of these approximating solutions. In the special setting of a convex non-linearity, we also provide a Hopf-Lax variational representation of the solution.
A bivariate functional copula joint model for longitudinal measurements and time-to-event data

A bivariate functional copula joint model, which models the repeatedly measured longitudinal outcome at each time point with the survival data, jointly by both random effects and bivariate functional copulas, is proposed in this paper. A regular joint model normally supposes there are some subject-specific latent random effects or classes shared by the longitudinal and time-to-event processes and they are assumed to be conditionally independent given these latent random variables. Under this assumption, the joint likelihood of the two processes can be easily derived and the association between them, as well as heterogeneity among population are naturally introduced by the unobservable latent random variables. However, because of the unobservable nature of these latent variables, the conditional independence assumption is difficult to verify. Therefore, a bivariate functional copula is introduced into a regular joint model to account for the cases where there could be extra association between the two processes which cannot be captured by the latent random variables. Our proposed model includes a regular joint model as a special case when the correlation function, which is modelled continuously by B-spline basis functions as a function of time $t,$ is constant at 0 under the bivariate Gaussian copula. Simulation studies and dynamic prediction of survival probabilities are conducted to compare the performance of the proposed model with the regular joint model and a real data application on the Primary biliary cirrhosis (PBC) data is performed.
Holistic Segmentation

As panoptic segmentation provides a prediction for every pixel in input, non-standard and unseen objects systematically lead to wrong outputs. However, in safety-critical settings, robustness against out-of-distribution samples and corner cases is crucial to avoid dangerous behaviors, such as ignoring an animal or a lost cargo on the road. Since driving datasets cannot contain enough data points to properly sample the long tail of the underlying distribution, a method must deal with unknown and unseen scenarios to be deployed safely. Previous methods targeted part of this issue, by re-identifying already seen unlabeled objects. In this work, we broaden the scope proposing holistic segmentation: a task to identify and separate unseen unknown objects into instances, without learning from unknowns, while performing panoptic segmentation of known classes. We tackle this new problem with U3HS, which first finds un-knowns as highly uncertain regions, then clusters the corresponding instance-aware embeddings into individual objects. By doing so, for the first time in panoptic segmentation with unknown objects, our U3HS is not trained with unknown data, thus leaving the settings unconstrained with respect to the type of objects and allowing for a holistic scene understanding. Extensive experiments and comparisons on two public datasets, namely Cityscapes and Lost&Found as a transfer, demonstrate the effectiveness of U3HS in the challenging task of holistic segmentation, with competitive closed-set panoptic segmentation performance.