Miracle-dz/UniFAR-FTUs huggingface dataset:
An immersed boundary method with subgrid resolution and improved numerical stability applied to slender bodies in Stokes flow

The immersed boundary method is a numerical and mathematical formulation for solving fluid-structure interaction problems. It relies on solving fluid equations on an Eulerian fluid grid and interpolating the resulting velocity back onto immersed structures. To resolve slender fibers, the grid spacing must be on the order of the fiber radius, and thus the number of required grid points along the filament must be of the same order as the aspect ratio. Simulations of slender bodies using the IB method can therefore be intractable. A technique is presented to address this problem in the context of Stokes flow. The velocity of the structure is split into a component coming from the underlying fluid grid, which is coarser than normally required, and a component proportional to the force (a drag term). The drag coefficient is set so that a single sphere is represented exactly on a grid of arbitrary meshwidth. Implicit treatment of the drag term removes some of the stability restrictions normally associated with the IB method. This comes at a loss of accuracy, although tests are conducted that show 1-2 digits of relative accuracy can be obtained on coarser grids. After its accuracy and stability are tested, the method is applied to two real world examples: fibers in shear flow and a suspension of fibers. These examples show that the method can reproduce existing results and make reasonable predictions about the viscosity of an aligned fiber suspension.
Convergence of Lagrange finite elements for the Maxwell Eigenvalue Problem in 2D

We consider finite element approximations of the Maxwell eigenvalue problem in two dimensions. We prove, in certain settings, convergence of the discrete eigenvalues using Lagrange finite elements. In particular, we prove convergence in three scenarios: piecewise linear elements on Powell--Sabin triangulations, piecewise quadratic elements on Clough--Tocher triangulations, and piecewise quartics (and higher) elements on general shape-regular triangulations. We provide numerical experiments that support the theoretical results. The computations also show that, on general triangulations, the eigenvalue approximations are very sensitive to nearly singular vertices, i.e., vertices that fall on exactly two "almost" straight lines.
Witnessing nonclassicality beyond quantum theory

We propose a general argument to show that if a physical system can mediate locally the generation of entanglement between two quantum systems, then it itself must be non-classical. Remarkably, we do not assume any classical or quantum formalism to describe the mediating physical system: our result follows from general information-theoretic principles, drawn from the recently proposed constructor theory of information. This argument provides the indispensable theoretical basis for recently proposed tests of non-classicality in gravity, based on witnessing gravitationally-induced entanglement in quantum probes.
Object-Based Image Coding: A Learning-Driven Revisit

The Object-Based Image Coding (OBIC) that was extensively studied about two decades ago, promised a vast application perspective for both ultra-low bitrate communication and high-level semantical content understanding, but it had rarely been used due to the inefficient compact representation of object with arbitrary shape. A fundamental issue behind is how to efficiently process the arbitrary-shaped objects at a fine granularity (e.g., feature element or pixel wise). To attack this, we have proposed to apply the element-wise masking and compression by devising an object segmentation network for image layer decomposition, and parallel convolution-based neural image compression networks to process masked foreground objects and background scene separately. All components are optimized in an end-to-end learning framework to intelligently weigh their (e.g., object and background) contributions for visually pleasant reconstruction. We have conducted comprehensive experiments to evaluate the performance on PASCAL VOC dataset at a very low bitrate scenario (e.g., $\sim \lt$0.1 bits per pixel-bpp) which have demonstrated noticeable subjective quality improvement compared with JPEG2K, HEVC-based BPG and another learned image compression method. All relevant materials are made publicly accessible at https://njuvision.github. io/Neural-ObjecE-Coding/.
$\mathcal{I}^{\prime}$-curvatures in higher dimensions and the Hirachi conjecture

We construct higher-dimensional analogues of the $\mathcal{I}^\prime$-curvature of Case and Gover in all CR dimensions $n\geq2$. Our $\mathcal{I}^\prime$-curvatures all transform by a first-order linear differential operator under a change of contact form and their total integrals are independent of the choice of pseudo-Einstein contact form on a closed CR manifold. We exhibit examples where these total integrals depend on the choice of general contact form, and thereby produce counterexamples to the Hirachi conjecture in all CR dimensions $n\geq2$.
Spontaneous symmetry breakdown of scale symmetries

We discuss spontaneous symmetry breakdown (SSB) of both global and local scale symmetries in scalar-tensor gravity with two scalar fields, one of which couples nonminimally to scalar curvature while the other is a normal scalar field. In case of a global scale symmetry, by moving from the Jordan frame to the Einstein frame, a normal scalar field becomes massive while the dilaton remains massless after the SSB. In case of a local scale symmetry, we take a gauge fixing condition for the local scale invariance, $a R + b \phi^2 = k$, which was found in our previous study of a Weyl's quadratic gravity. Together with locally scale invariant potential terms in a classical action, this gauge condition generates a Higgs potential whose vacuum expectation value (VEV) produces the Einstein-Hilbert action with an $R^2$ term in the lowest level of approximation. One interesting aspect in this model is that a massless Nambu-Goldstone boson associated with a scale invariance is absorbed into the metric tensor field and consequently an $R^2$ term is induced in the action.
Virtually RFRS Mapping Tori and Coherence

Let $G$ be a finitely presented group that can be written as an extension \[ 1 \longrightarrow K \longrightarrow G \longrightarrow F_2 \longrightarrow 1 \] where $K$ is either the finitely generated free group $F_n$, $n > 2$ or the fundamental group of a closed surface of genus $g > 1$. We prove that if the image of the monodromy map $\rho \colon F_2 \to \operatorname{Out(K)}$ contains an element $\varphi \in \operatorname{Out(K)}$ such that the mapping torus $K \rtimes_{\varphi} \Bbb{Z}$ is virtually residually finite rationally solvable (for instance whenever the mapping torus is hyperbolic), then $G$ is not coherent. This applies, in particular, when the image is a purely pseudo--Anosov free subgroups of the mapping class group.
Interpretable Deep Recurrent Neural Networks via Unfolding Reweighted 𝓁1-𝓁1 Minimization: Architecture Design and Generalization Analysis

Deep unfolding methods---for example, the learned iterative shrinkage thresholding algorithm (LISTA)---design deep neural networks as learned variations of optimization methods. These networks have been shown to achieve faster convergence and higher accuracy than the original optimization methods. In this line of research, this paper develops a novel deep recurrent neural network (coined reweighted-RNN) by the unfolding of a reweighted $\ell_1$-$\ell_1$ minimization algorithm and applies it to the task of sequential signal reconstruction. To the best of our knowledge, this is the first deep unfolding method that explores reweighted minimization. Due to the underlying reweighted minimization model, our RNN has a different soft-thresholding function (alias, different activation functions) for each hidden unit in each layer. Furthermore, it has higher network expressivity than existing deep unfolding RNN models due to the over-parameterizing weights. Importantly, we establish theoretical generalization error bounds for the proposed reweighted-RNN model by means of Rademacher complexity. The bounds reveal that the parameterization of the proposed reweighted-RNN ensures good generalization. We apply the proposed reweighted-RNN to the problem of video frame reconstruction from low-dimensional measurements, that is, sequential frame reconstruction. The experimental results on the moving MNIST dataset demonstrate that the proposed deep reweighted-RNN significantly outperforms existing RNN models.
Unsupervised Domain Adaptation Through Transferring both the Source-Knowledge and Target-Relatedness Simultaneously

Unsupervised domain adaptation (UDA) is an emerging research topic in the field of machine learning and pattern recognition, which aims to help the learning of unlabeled target domain by transferring knowledge from the source domain. To perform UDA, a variety of methods have been proposed, most of which concentrate on the scenario of single source and the single target domain (1S1T). However, in real applications, usually single source domain with multiple target domains are involved (1SmT), which cannot be handled directly by those 1S1T models. Unfortunately, although a few related works on 1SmT UDA have been proposed, nearly none of them model the source domain knowledge and leverage the target-relatedness jointly. To overcome these shortcomings, we herein propose a more general 1SmT UDA model through transferring both the source-knowledge and target-relatedness, UDA-SKTR for short. In this way, not only the supervision knowledge from the source domain but also the potential relatedness among the target domains are simultaneously modeled for exploitation in the process of 1SmT UDA. In addition, we construct an alternating optimization algorithm to solve the variables of the proposed model with a convergence guarantee. Finally, through extensive experiments on both benchmark and real datasets, we validate the effectiveness and superiority of the proposed method.
A Hybrid Learning Method for System Identification and Optimal Control

We present a three-step method to perform system identification and optimal control of nonlinear systems. Our approach is mainly data-driven and does not require active excitation of the system to perform system identification. In particular, it is designed for systems for which only historical data under closed-loop control are available and where historical control commands exhibit low variability. In the first step, simple simulation models of the system are built and run under various conditions. In the second step, a neural network architecture is extensively trained on the simulation outputs to learn the system physics and retrained with historical data from the real system with stopping rules. These constraints avoid overfitting that arises by fitting closed-loop controlled systems. By doing so, we obtain one (or many) system model(s), represented by this architecture, whose behavior can be chosen to match more or less the real system. Finally, state-of-the-art reinforcement learning with a variant of domain randomization and distributed learning is used for optimal control of the system. We first illustrate the model identification strategy with a simple example, the pendulum with external torque. We then apply our method to model and optimize the control of a large building facility located in Switzerland. Simulation results demonstrate that this approach generates stable functional controllers that outperform on comfort and energy benchmark rule-based controllers.
Extended Functorial Field Theories and Anomalies in Quantum Field Theories

We develop a general framework for the description of anomalies using extended functorial field theories extending previous work by Freed and Monnier. In this framework, anomalies are described by invertible field theories in one dimension higher and anomalous field theories live on their boundaries. We provide precise mathematical definitions for all concepts involved using the language of symmetric monoidal bicategories. In particular, field theories with anomalies will be described by symmetric monoidal transformations. The use of higher categorical concepts is necessary to capture the Hamiltonian picture of anomalies. The relation to the path integral and the Hamiltonian description of anomalies will be explained in detail. Furthermore, we discuss anomaly inflow in detail. We apply the general framework to the parity anomaly in fermionic systems coupled to background gauge and gravitational fields on odd-dimensional spacetimes. We use the extension of the Atiyah-Patodi-Singer index theorem to manifolds with corners due to Loya and Melrose to explicitly construct an extended invertible field theory encoding the anomaly. This allows us to compute explicitly the 2-cocycle of the projective representation of the gauge symmetry on the quantum state space, which is defined in a parity-symmetric way by suitably augmenting the standard chiral fermionic Fock spaces with Lagrangian subspaces of zero modes of the Dirac Hamiltonian that naturally appear in the index theorem. As a second application, we study discrete symmetries of Dijkgraaf-Witten theories and their gauging. Non-abelian group cohomology is used to describe discrete symmetries and we derive concrete conditions for such a symmetry to admit ’t Hooft anomalies in terms of the Lyndon-Hochschild-Serre spectral sequence. We give an explicit realization of a discrete gauge theory with ’t Hooft anomaly as a state on the boundary of a higher-dimensional Dijkgraaf-Witten theory using a relative version of the pushforward construction of Schweigert and Woike. To everyone who has sparked, encouraged or supported my interest in mathematics and natural sciences.
$R^*$: A robust MCMC convergence diagnostic with uncertainty using gradient-boosted machines

Markov chain Monte Carlo (MCMC) has transformed Bayesian model inference over the past three decades: mainly because of this, Bayesian inference is now a workhorse of applied scientists. Under general conditions, MCMC sampling converges asymptotically to the posterior distribution, but this provides no guarantees about its finite sample performance. The predominant method for monitoring convergence is to run multiple chains and monitor individual chains' characteristics and compare these to the population as a whole: if within-chain and between-chain summaries are comparable, then this is taken to indicate that the chains have converged to a common stationary distribution. Here, we introduce a new method for diagnosing convergence based on whether a machine learning classifier model can successfully discriminate the individual chains. We call this convergence measure $R^*$. In contrast to the predominant $\widehat{R}$, $R^*$ is a single statistic across all parameters that indicates lack of mixing, although individual variables' importance for this metric can also be determined. Additionally, $R^*$ is not based on any single characteristic of the sampling distribution; instead using all the information in the chain, including that given by the joint sampling distribution, which is currently largely overlooked by existing approaches. Since our choice of machine learning classifier, a gradient-boosted regression trees model (GBM), provides uncertainty in predictions, as a byproduct, we obtain uncertainty in $R^*$. The method is straightforward to implement, robust to GBM hyperparameter choice, and could be a complementary additional check on MCMC convergence for applied analyses.
Quantum mechanics is *-algebras and tensor networks.

We provide a systematic approach to quantum mechanics from an information-theoretic perspective using the language of tensor networks. Our formulation needs only a single kind of object, so-called positive *-tensors. Physical models translate experimental setups into networks of these *-tensors, and the evaluation of the resulting networks yields the probability distributions describing measurement outcomes. The idea behind our approach is similar to categorical formulations of quantum mechanics. However, our formulation is mathematically simpler and less abstract. Our presentation of the core formalism is completely self-contained and relies on minimal mathematical prerequesites. Therefore, we hope it is in principle also understandable to people without an extensive mathematical background. Additionally, we show how various types of models, like real-time evolutions or thermal systems can be translated into *-tensor networks.
Magmatic Intrusions Control Io's Crustal Thickness

Io, the most volcanically active body in the solar system, loses heat through eruptions of hot lava. Heat is supplied by tidal dissipation and is thought to be transferred through the mantle by magmatic segregation, a mode of transport that sets it apart from convecting terrestrial planets. We present a model that couples magmatic transport of tidal heat to the volcanic system in the crust, in order to determine the controls on crustal thickness, magmatic intrusions, and eruption rates. We demonstrate that magmatic intrusions are a key component of Io's crustal heat balance; around 80% of the magma delivered to the base of the crust must be emplaced and frozen as plutons to match rough estimates of crustal thickness. As magma ascends from a partially molten mantle into the crust, a decompacting boundary layer forms, which can explain possible observations of a high‐melt‐fraction region.
Common causes of vertigo and dizziness in Gujarat

Background: Dizziness is one of the most common complaints in medicine just second to headache. It frightens not only the patient but also frustrates the physicians. There is a long list of causes of dizziness but the common causes vary from place to place. The aim of this study was to know the common causes of dizziness and vertigo in Gujarat to generate the awareness among the doctors who get the patients with this common ailment so that they can better manage dizzy patients. Methods: This prospective study included thirty-five patients with dizziness and vertigo that came to the Department of ENT for their management. Results: Patients were divided into three categories. The first group of patients was having associated cochlear symptoms. Second group patients had isolated vertigo. Third group patients had associated CNS or medical conditions. The largest was the second group (37.5%) of isolated vertigo patients. The commonest diagnosis (18.75%) in this group was benign paroxysmal positional vertigo, followed by acute vestibular neuritis. Meniere’s disease and migraine and its variant were the most common causes in first and third group respectively. Conclusions: The overall scenario of causes of dizziness and vertigo in our study follow the international trend. Benign paroxysmal positional vertigo, acute vestibular neuronitis, Menieres disease and migraine were found the most common causes of vertigo.
Will Online Digital Footprints Reveal Your Relationship Status?

With the increasing social acceptance and openness, more and more sexual-minority men (SMM) have succeeded in creating and sustaining steady relationships in recent years. Maintaining steady relationships is beneficial to the wellbeing of SMM both mentally and physically. However, the relationship maintaining for them is also challenging due to the much less supports compared to the heterosexual couples, so that it is important to identify those SMM in steady relationship and provide corresponding personalized assistance. Furthermore, knowing SMM's relationship and the correlations with other visible features is also beneficial for optimizing the social applications' functionalities in terms of privacy preserving and friends recommendation. With the prevalence of SMM-oriented social apps (called SMMSA for short), this paper investigates the relationship status of SMM from a new perspective, that is, by introducing the SMM's online digital footprints left on SMMSA (e.g., presented profile, social interactions, expressions, sentiment, and mobility trajectories). Specifically, using a filtered dataset containing 2,359 active SMMSA users with their self-reported relationship status and publicly available app usage data, we explore the correlations between SMM's relationship status and their online digital footprints on SMMSA and present a set of interesting findings. Moreover, we demonstrate that by utilizing such correlations, it has the potential to construct machine-learning-based models for relationship status inference. Finally, we elaborate on the implications of our findings from the perspective of better understanding the SMM community and improving their social welfare.
A Multi-perspective Analysis of Social Context and Personal Factors in Office Settings for the Design of an Effective Mobile Notification System

In this study, we investigate the effects of social context, personal and mobile phone usage on the inference of work engagement/challenge levels of knowledge workers and their responsiveness to well-being related notifications. Our results show that mobile application usage is associated to the responsiveness and work engagement/challenge levels of knowledge workers. We also developed multi-level (within- and between-subjects) models for the inference of attentional states and engagement/challenge levels with mobile application usage indicators as inputs, such as the number of applications used prior to notifications, the number of switches between applications, and application category usage. The results of our analysis show that the following features are effective for the inference of attentional states and engagement/challenge levels: the number of switches between mobile applications in the last 45 minutes and the duration of application usage in the last 5 minutes before users' response to ESM messages.
Using Sonar for Liveness Detection to Protect Smart Speakers against Remote Attackers

Smart speakers, which wait for voice commands and complete tasks for users, are becoming part of common households. While voice commands came with basic functionalities in the earlier days, as the market grew, various commands with critical functionalities were developed; e.g., access banking services, send money, open front door. Such voice commands can cause serious consequences once smart speakers are attacked. Recent research shows that smart speakers are vulnerable to malicious voice commands sent from other speakers (e.g., TV, baby monitor, radio) in the same area. In this work, we propose the Speaker-Sonar, a sonar-based liveness detection system for smart speakers. Our approach aims to protect the smart speakers from remote attackers that leverage network-connected speakers to send malicious commands. The key idea of our approach is to make sure that the voice command is indeed coming from the user. For this purpose, the Speaker-Sonar emits an inaudible sound and tracks the user's direction to compare it with the direction of the received voice command. The Speaker-Sonar does not require additional action from the user and works through an automatic consistency check. We built the Speaker-Sonar on a raspberry pi 3b, a circular microphone array, and a commodity speaker by imitating the Amazon Echo. Our evaluation shows that the Speaker-Sonar can reject remote voice attacks with an average accuracy of 95.5% in 2 meters, which significantly raises the bar for remote attackers. To the best of our knowledge, our defense is able to defend against known remote voice attack techniques.