Miracle-dz/UniFAR-FTUs huggingface dataset:
The Dynamics of the Hubbard Model Through Stochastic Calculus and Girsanov Transformation

As a typical quantum many body problem, we consider the time evolution of density matrix elements in the Bose-Hubbard model. For an arbitrary initial state, these quantities can be obtained from an SDE or stochastic differential equation system. To this SDE system, a Girsanov transformation can be applied. This has the effect that all the information from the initial state moves into the drift part, into the mean field part, of the transformed system. In the large N limit with g=UN fixed, the diffusive part of the transformed system vanishes and as a result, the exact quantum dynamics is given by an ODE system which turns out to be the time dependent discrete Gross Pitaevskii equation. For the two site Bose-Hubbard model, the GP equation reduces to the mathematical pendulum and the particle imbalance is equal to the velocity of that pendulum which is either oscillatory or it can have rollovers which then corresponds to the self trapping or insulating phase. As a by-product, we also find an equivalence of the mathematical pendulum with a quartic double well potential. Collapse and revivals are a more subtle phenomenom, in order to see these the diffusive part of the SDE system or quantum corrections have to be taken into account. This can be done with an approximation and collapse and revivals can be reproduced, numerically and also through an analytic calculation. Since expectation values of Fresnel or Wiener diffusion processes, we write the density matrix elements exactly in this way, can be obtained from parabolic second order PDEs, we also obtain various exact PDE representations. The paper has been written with the goal to come up with an efficient calculation scheme for quantum many body systems and as such the formalism is generic and applies to arbitrary dimension, arbitrary hopping matrices and, with suitable adjustments, to fermionic models.
Using Deep Reinforcement Learning to solve Optimal Power Flow problem with generator failures

Deep Reinforcement Learning (DRL) is being used in many domains. One of the biggest advantages of DRL is that it enables the continuous improvement of a learning agent. Secondly, the DRL framework is robust and flexible enough to be applicable to problems of varying nature and domain. Presented work is evidence of using the DRL technique to solve an Optimal Power Flow (OPF) problem. Two classical algorithms have been presented to solve the OPF problem. The drawbacks of the vanilla DRL application are discussed, and an algorithm is suggested to improve the performance. Secondly, a reward function for the OPF problem is presented that enables the solution of inherent issues in DRL. Reasons for divergence and degeneration in DRL are discussed, and the correct strategy to deal with them with respect to OPF is presented.
Soft Metamaterials: Adaptation and Intelligence

Status. Soft metamaterials are composite structures whose collective mechanical properties go beyond those of their individual constituents [1]. For example, auxetic materials, which contract in all directions when squeezed, can be engineered via appropriate arrangements of flexible bonds. Topological metamaterials are those that use notions from topology (such as winding numbers or other topological invariants) to ensure the existence of a particular feature, typically a localized deformation mechanism or vibrational mode [1]. For instance, the lattice in Fig. 1a is rigid everywhere, except near the colored defect where there is a soft mechanical mode protected by topology. Beyond materials with fixed properties, programmable metamaterials use elastic multistability to encode specialized responses to external actuation. In Fig. 1b, a pattern (e.g. a smiley face) is programmed to appear when the metamaterial is compressed. Trainable metamaterials turn programmability into a process that emerges from a sequence of experiences [2]. For instance, the elasticity of the network in Fig. 1c is tuned through a process called directed aging, during which bonds are strengthened and weakened in response to external stress. The individual building blocks can also have an internal source of energy [3]. This is the case for the active and robotic metamaterial shown in Fig. 1d, in which a wall of motorized hinges steers the outgoing direction of a projectile. In such active media, the familiar symmetries and conservation laws of passive matter need to be revisited to write down effective elastic models [4, 5]. The concepts behind soft metamaterials, such as topology or continuum mechanics, often apply across length scales. For example, the world’s smallest origami bird in Fig. 1e is a deployable metamaterial that uses minimal actuation along with geometric constraints to guide its global shape change. One can even envision metamaterials that build themselves a possibility particularly interesting at small scales like the selfassembled colloidal structure in Fig. 1f that mimics the atomic arrangement of diamond.
Optimal thermal shortcuts for harmonically conﬁned Brownian particles

The overdamped Brownian dynamics of a harmonic oscillator is a paradigmatic system in non-equilibrium statistical mechanics, which reliably models relevant stochastic systems such as colloidal particles submitted to optical conﬁnement. In this work, optimal thermal protocols are tailored to minimise the connection time between equilibrium states of overdamped d -dimensional oscillators. Application of control theory reveals that these optimal protocols are of bang-bang type, that is, the temperature of the bath has to take alternatively the minimum and maximum values allowed. Minimum connection times increase with the considered dimension d . Remarkably, this is the case even for symmetric oscillators, for example, with spherical symmetry—in which the degeneracy of the elastic constant along the d possible directions seems to imply a minimum connection time equal to that for the one-dimensional case. This surprising unavoidable price to pay when increasing dimension is thoroughly investigated and understood on a physical basis. Moreover, information theory tools such as the thermodynamic length and its divergence are analysed over the brachistochrone.
The van Est Map on Geometric Stacks

We generalize the van Est map and isomorphism theorem in three ways, and we discuss conjectured connections with homotopy theory, including a proposal of a category which unifies differentiable stacks, Lie algebroids and homotopy theory. In Part 2 of this thesis we generalize the van Est map from a comparison map between Lie groupoid cohomology and Lie algebroid cohomology to a (more conceptual) comparison map between the cohomology of a stack $\mathcal{G}$ and the cohomology of a simple foliation $\mathcal{H}\to\mathcal{G}$. In Part 1 we generalize the functions that we can take cohomology of in the context of the van Est map. Instead of using functions valued in representations, we can use functions valued in modules, eg. we can use $S^1$-valued functions and $\mathbb{Z}$-valued functions. Finally, everything we do works in both the smooth and holomorphic categories. These generalizations allow us to derive results, including classical ones, that could not be obtained with the usual van Est map, and they give a new method of computing cohomology. Part 3 of this thesis involves a proposal of a definition of Morita equivalences in the categories of Lie algebroids and LA-groupoids. What we find is that our proposed category of LA-groupoids unifies differentiable stacks, Lie algebroids and homotopy theory. In particular, there are morphisms between Lie algebroids and Lie groupoids and we show that such objects can be Morita equivalent. This gives another interpretation of the van Est map. Using this category, we argue that a classifying space for $G$ is just a space which is homotopy equivalent it. We discuss higher generalized morphisms (given by gerbes) and we conjecture the existence of a smooth version of Grothendieck's homotopy hypothesis.
Optimal Minimization of the Covariance Loss

Let <inline-formula> <tex-math notation="LaTeX">$X$ </tex-math></inline-formula> be a random vector valued in <inline-formula> <tex-math notation="LaTeX">$\mathbb {R}^{m}$ </tex-math></inline-formula> such that <inline-formula> <tex-math notation="LaTeX">$\|X\|_{2} \le 1$ </tex-math></inline-formula> almost surely. For every <inline-formula> <tex-math notation="LaTeX">$k\ge 3$ </tex-math></inline-formula>, we show that there exists a sigma algebra <inline-formula> <tex-math notation="LaTeX">$\mathcal {F}$ </tex-math></inline-formula> generated by a partition of <inline-formula> <tex-math notation="LaTeX">$\mathbb {R}^{m}$ </tex-math></inline-formula> into <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> sets such that <inline-formula> <tex-math notation="LaTeX">$\|\mathrm {Cov}(X) - \mathrm {Cov}(\mathbb {E}[X\mid \mathcal {F}]) \|_{\mathrm {F}} \lesssim \frac {1}{\sqrt {\log {k}}}$ </tex-math></inline-formula>. This is optimal up to the implicit constant and improves on a previous bound due to Boedihardjo, Strohmer, and Vershynin. Our proof provides an efficient algorithm for constructing <inline-formula> <tex-math notation="LaTeX">$\mathcal {F}$ </tex-math></inline-formula> and leads to improved accuracy guarantees for <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula>-anonymous or differentially private synthetic data. We also establish a connection between the above problem of minimizing the covariance loss and the pinning lemma from statistical physics, providing an alternate (and much simpler) algorithmic proof in the important case when <inline-formula> <tex-math notation="LaTeX">$X \in \{\pm 1\}^{m}/\sqrt {m}$ </tex-math></inline-formula> almost surely.
DeeptDCS: Deep Learning-Based Estimation of Currents Induced During Transcranial Direct Current Stimulation

Objective: Transcranial direct current stimulation (tDCS) is a non-invasive brain stimulation technique used to generate conduction currents in the head and disrupt brain functions. To rapidly evaluate the tDCS-induced current density in near real-time, this paper proposes a deep learning-based emulator, named DeeptDCS. Methods: The emulator leverages Attention U-net taking the volume conductor models (VCMs) of head tissues as inputs and outputting the three-dimensional current density distribution across the entire head. The electrode configurations are also incorporated into VCMs without increasing the number of input channels; this enables the straightforward incorporation of the non-parametric features of electrodes (e.g., thickness, shape, size, and position) in the training and testing of the proposed emulator. Results: Attention U-net outperforms standard U-net and its other three variants (Residual U-net, Attention Residual U-net, and Multi-scale Residual U-net) in terms of accuracy. The generalization ability of DeeptDCS to non-trained electrode configurations can be greatly enhanced through fine-tuning the model. The computational time required by one emulation via DeeptDCS is a fraction of a second. Conclusion: DeeptDCS is at least two orders of magnitudes faster than a physics-based open-source simulator, while providing satisfactorily accurate results. Significance: The high computational efficiency permits the use of DeeptDCS in applications requiring its repetitive execution, such as uncertainty quantification and optimization studies of tDCS.
Deep Learning Framework for Real-time Fetal Brain Segmentation in MRI

Fetal brain segmentation is an important ﬁrst step for slice-level motion correction and slice-to-volume reconstruction in fetal MRI. Fast and accurate segmentation of the fetal brain on fetal MRI is required to achieve real-time fetal head pose estimation and motion tracking for slice re-acquisition and steering. To address this critical unmet need, in this work we analyzed the speed-accuracy performance of a variety of deep neural network models, and devised a symbolically small convolutional neural network that combines spatial details at high resolution with context features extracted at lower resolutions. We used multiple branches with skip connections to maintain high accuracy while devising a parallel combination of convolution and pooling operations as an input downsampling module to further reduce inference time. We trained our model as well as eight alternative, state-of-the-art networks with manually-labeled fetal brain MRI slices and tested on two sets of normal and challenging test cases. Experimental results show that our network achieved the highest accuracy and lowest inference time among all of the compared state-of-the-art real-time segmentation methods. We achieved average Dice scores of 97.99% and 84.04% on the normal and challenging test sets, respectively, with an inference time of 3.36 milliseconds per image on an NVIDIA GeForce RTX 2080 Ti. Code, data, and the trained models are available at this repo.
Thematic Fit Bits: Annotation Quality and Quantity Interplay for Event Participant Representation

Modeling thematic fit (a verb-argument compositional semantics task) currently requires a very large burden of labeled data. We take a linguistically machine-annotated large corpus and replace corpus layers with output from higher-quality, more modern taggers. We compare the old and new corpus versions’ impact on a verb-argument fit modeling task, using a high-performing neural approach. We discover that higher annotation quality dramatically reduces our data requirement while demonstrating better supervised predicate-argument classification. But in applying the model to psycholinguistic tasks outside the training objective, we see clear gains at scale, but only in one of two thematic fit estimation tasks, and no clear gains on the other. We also see that quality improves with training size, but perhaps plateauing or even declining in one task. Last, we tested the effect of role set size. All this suggests that the quality/quantity interplay is not all you need. We replicate previous studies while modifying certain role representation details and set a new state-of-the-art in event modeling, using a fraction of the data. We make the new corpus version public.
Wavelet neural operator: a neural operator for parametric partial differential equations

With massive advancements in sensor technologies and Internet-of-things, we now have access to terabytes of historical data; however, there is a lack of clarity in how to best exploit the data to predict future events. One possible alternative in this context is to utilize operator learning algorithm that directly learn nonlinear mapping between two functional spaces; this facilitates real-time prediction of naturally arising complex evolutionary dynamics. In this work, we introduce a novel operator learning algorithm referred to as the Wavelet Neural Operator (WNO) that blends integral kernel with wavelet transformation. WNO harnesses the superiority of the wavelets in time-frequency localization of the functions and enables accurate tracking of patterns in spatial domain and effective learning of the functional mappings. Since the wavelets are localized in both time/space and frequency, WNO can provide high spatial and frequency resolution. This offers learning of the finer details of the parametric dependencies in the solution for complex problems. The efficacy and robustness of the proposed WNO are illustrated on a wide array of problems involving Burger's equation, Darcy flow, Navier-Stokes equation, Allen-Cahn equation, and Wave advection equation. Comparative study with respect to existing operator learning frameworks are presented. Finally, the proposed approach is used to build a digital twin capable of predicting Earth's air temperature based on available historical data.
Wasserstein Adversarial Learning based Temporal Knowledge Graph Embedding

Research on knowledge graph embedding (KGE) has emerged as an active field in which most existing KGE approaches mainly focus on static structural data and ignore the influence of temporal variation involved in time-aware triples. In order to deal with this issue, several temporal knowledge graph embedding (TKGE) approaches have been proposed to integrate temporal and structural information in recent years. However, these methods only employ a uniformly random sampling to construct negative facts. As a consequence, the corrupted samples are often too simplistic for training an effective model. In this paper, we propose a new temporal knowledge graph embedding framework by introducing adversarial learning to further refine the performance of traditional TKGE models. In our framework, a generator is utilized to construct high-quality plausible quadruples and a discriminator learns to obtain the embeddings of entities and relations based on both positive and negative samples. Meanwhile, we also apply a Gumbel-Softmax relaxation and the Wasserstein distance to prevent vanishing gradient problems on discrete data; an inherent flaw in traditional generative adversarial networks. Through comprehensive experimentation on temporal datasets, the results indicate that our proposed framework can attain significant improvements based on benchmark models and also demonstrate the effectiveness and applicability of our framework.
Performance of a five-axis machine tool as a coordinate measuring machine (CMM)

The use of machine tools for on-machine coordinate measurement on the workpiece is becoming commonplace. However, numerous errors can adversely affect the measurement accuracy. For instance, the inter-axis parameters are major contributors to the overall machine tool’s inaccuracy hence estimation and compensation of such errors are prerequisite to fully exploit the machine’s measurement capability. This paper presents a scheme to assess the accuracy of coordinate measurement by probing a precision sphere mounted on the machine table for different rotary axes indexations. Only the sphericity of the reference sphere is assumed and neither its size nor position. All individual probing data from all indexations are used for the assessment of the apparent out of sphericity of the reference sphere. Machine readings are processed either directly, using the machine nominal model, or using a compensated model. This provides a fast method to validate on-machine measurement before and after compensation with the exception of isotropic scale effects.
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- mode oscillations of neutr

We investigate the impact of the neutron-star matter equation of state on the $f$- and $p_1$-mode oscillations of neutron stars obtained within the Cowling approximation and linearized general relativity. The $f$- and $p_1$-mode oscillation frequencies, and their damping times are calculated using representative sets of Skyrme Hartree-Fock and relativistic mean-field models, all of which reproduce nuclear systematics and support $2M_\odot$ neutron stars. Our study shows strong correlations between the frequencies of $f$- and $p_1$-modes and their damping times with the pressure of $\beta$-equilibrated matter at densities equal to or slightly higher than the nuclear saturation density $\rho_0$. Such correlations are found to be almost independent of the composition of the stars. The frequency of the $p_1$-mode of $1. 4M_\odot$ star is strongly correlated with the slope of the symmetry energy $L_0$ and $\beta$-equilibrated pressure at density $\rho_0$. Compared to GR calculations, the error in the Cowling approximation for the $f$-mode is about 30\% for neutron stars of low mass, whereas it decreases with increasing mass. The accuracy of the $p_1$-mode is better than 15\% for neutron stars of maximum mass, and improves for lower masses and higher number of radial nodes.
Optimizing One-pixel Black-box Adversarial Attacks

The output of Deep Neural Networks (DNN) can be altered by a small perturbation of the input in a black box setting by making multiple calls to the DNN. However, the high computation and time required makes the existing approaches unusable. This work seeks to improve the One-pixel (few-pixel) black-box adversarial attacks to reduce the number of calls to the network under attack. The One-pixel attack uses a non-gradient optimization algorithm to ﬁnd pixel-level perturbations under the constraint of a ﬁxed number of pixels, which causes the network to predict the wrong label for a given image. We show through experimental results how the choice of the optimization algorithm and initial positions to search can reduce function calls and increase attack success signiﬁcantly, making the attack more practical in real-world settings.
Vehicle Noise: Comparison of Loudness Ratings in the Field and the Laboratory

Objective: Distorted loudness perception is one of the main complaints of hearing aid users. Measuring loudness perception in the clinic as experienced in everyday listening situations is important for loudness-based hearing aid fitting. Little research has been done comparing loudness perception in the field and in the laboratory.Design: Participants rated the loudness in the field and in the laboratory of 36 driving actions. The field measurements were recorded with a 360° camera and a tetrahedral microphone. The recorded stimuli, which are openly accessible, were presented in three conditions in the laboratory: 360° video recordings with a head-mounted display, video recordings with a desktop monitor and audio-only.Study samples: Thirteen normal-hearing participants and 18 hearing-impaired participants with hearing aids.Results: The driving actions were rated as louder in the laboratory than in the field for the condition with a desktop monitor and for the audio-only condition. The less realistic a laboratory condition was, the more likely it was for a participant to rate a driving action as louder. The field-laboratory loudness differences were bigger for louder sounds.Conclusion: The results of this experiment indicate the importance of increasing realism and immersion when measuring loudness in the clinic.
Learning Multi-dimensional Edge Feature-based AU Relation Graph for Facial Action Unit Recognition

The activations of Facial Action Units (AUs) mutually influence one another. While the relationship between a pair of AUs can be complex and unique, existing approaches fail to specifically and explicitly represent such cues for each pair of AUs in each facial display. This paper proposes an AU relationship modelling approach that deep learns a unique graph to explicitly describe the relationship between each pair of AUs of the target facial display. Our approach first encodes each AU's activation status and its association with other AUs into a node feature. Then, it learns a pair of multi-dimensional edge features to describe multiple task-specific relationship cues between each pair of AUs. During both node and edge feature learning, our approach also considers the influence of the unique facial display on AUs' relationship by taking the full face representation as an input. Experimental results on BP4D and DISFA datasets show that both node and edge feature learning modules provide large performance improvements for CNN and transformer-based backbones, with our best systems achieving the state-of-the-art AU recognition results. Our approach not only has a strong capability in modelling relationship cues for AU recognition but also can be easily incorporated into various backbones. Our PyTorch code is made available at https://github.com/CVI-SZU/ME-GraphAU.