Miracle-dz/UniFAR-FTUs huggingface dataset:
Spectral theory of spin substitutions

<p style='text-indent:20px;'>We introduce substitutions in <inline-formula><tex-math id="M1">\begin{document}$ {\mathbb{Z}}^m $\end{document}</tex-math></inline-formula> which have non-rectangular domains based on an endomorphism <inline-formula><tex-math id="M2">\begin{document}$ Q $\end{document}</tex-math></inline-formula> of <inline-formula><tex-math id="M3">\begin{document}$ {\mathbb{Z}}^m $\end{document}</tex-math></inline-formula> and a set <inline-formula><tex-math id="M4">\begin{document}$ {\mathcal D} $\end{document}</tex-math></inline-formula> of coset representatives of <inline-formula><tex-math id="M5">\begin{document}$ {\mathbb{Z}}^m/Q{\mathbb{Z}}^m $\end{document}</tex-math></inline-formula>, which we call digit substitutions. Using a finite abelian 'spin' group we define 'spin digit substitutions' and their subshifts <inline-formula><tex-math id="M6">\begin{document}$ ({\Sigma}, {\mathbb{Z}}^m) $\end{document}</tex-math></inline-formula>. Conditions under which the subshift is measure-theoretically isomorphic to a group extension of an <inline-formula><tex-math id="M7">\begin{document}$ m $\end{document}</tex-math></inline-formula>-dimensional odometer are given, inducing a complete decomposition of the function space <inline-formula><tex-math id="M8">\begin{document}$ L^{2}({\Sigma},\mu) $\end{document}</tex-math></inline-formula>. This enables the use of group characters in <inline-formula><tex-math id="M9">\begin{document}$ {\widehat{G}} $\end{document}</tex-math></inline-formula> to derive substitutive factors and analyze the spectra of specific subspaces. We provide general sufficient criteria for the existence of pure point, absolutely continuous, and singular continuous spectral measures, together with some bounds on their spectral multiplicity. </p>
Learning explicit predictive controllers: theory and applications

In this paper, we deal with data-driven predictive control of linear time-invariant (LTI) systems. Specifically, we show for the first time how explicit predictive laws can be learnt directly from data, without needing to identify the system to control. To this aim, we resort to the Willems' fundamental lemma and we derive the explicit formulas by suitably elaborating the constrained optimization problem under investigation. The resulting optimal controller turns out to be a piecewise affine system coinciding with the solution of the original model-based problem in case of noiseless data. Such an equivalence is proven to hold asymptotically also in presence of measurement noise, thus making the proposed method a computationally efficient (but model-free) alternative to the state of the art predictive controls. The above statements are further supported by numerical simulations on three benchmark examples.
A Green's function proof of the Positive Mass Theorem

In this paper, a new proof of the Positive Mass Theorem is established through a newly discovered monotonicity formula, holding along the level sets of the Green's function of an asymptotically flat $3$-manifold. In the same context and for $1<p<3$, a Geroch-type calculation is performed along the level sets of $p$-harmonic functions, leading to a new proof of the Riemannian Penrose Inequality under favourable assumptions. A new characterisation of scalar curvature lower bounds in terms of the monotonicity formulas is also given.
On Capacity Optimality of OAMP: Beyond IID Sensing Matrices and Gaussian Signaling

This paper investigates a large unitarily invariant system (LUIS) involving a unitarily invariant sensing matrix, an arbitrarily fixed signal distribution, and forward error control (FEC) coding. A universal Gram-Schmidt orthogonalization is considered for constructing orthogonal approximate message passing (OAMP), enabling its applicability to a wide range of prototypes without the constraint of differentiability. We develop two single-input-single-output variational transfer functions for OAMP with Lipschitz continuous local estimators, facilitating an analysis of achievable rates. Furthermore, when the state evolution of OAMP has a unique fixed point, we reveal that OAMP can achieve the constrained capacity predicted by the replica method of LUIS based on matched FEC coding, regardless of the signal distribution. The replica method is rigorously validated for LUIS with Gaussian signaling and certain sub-classes of LUIS with arbitrary signal distributions. Several area properties are established based on the variational transfer functions of OAMP. Meanwhile, we present a replica constrained capacity-achieving coding principle for LUIS. This principle serves as the basis for optimizing irregular low-density parity-check (LDPC) codes specifically tailored for binary signaling in our simulation results. The performance of OAMP with these optimized codes exhibits a remarkable improvement over the unoptimized codes and even surpasses the well-known Turbo-LMMSE algorithm. For quadrature phase-shift keying (QPSK) modulation, we observe bit error rates (BER) performance near the replica constrained capacity across diverse channel conditions.
Item Response Theory -- A Statistical Framework for Educational and Psychological Measurement

Item response theory (IRT) has become one of the most popular statistical models for psychometrics, a field of study concerned with the theory and techniques of psychological measurement. The IRT models are latent factor models tailored to the analysis, interpretation, and prediction of individuals’ behaviors in answering a set of measurement items that typically involve categorical response data. Many important questions of measurement are directly or indirectly answered through the use of IRT models, including scoring individuals’ test performances, validating a test scale, linking two tests, among others. This paper provides a review of item response theory, including its statistical framework and psychometric applications. We establish connections between item response theory and related topics in statistics, including empirical Bayes, nonparametric methods, matrix completion, regularized estimation, and sequential analysis. Possible future directions of IRT are discussed from the perspective of statistical learning.
Successive cohorts of Twitter users show increasing activity and shrinking content horizons

The global public sphere has changed dramatically over the past decades: A significant part of public discourse now takes place on algorithmically driven platforms. Despite its growing importance, there is scant large-scale academic research on the long-term evolution of user behaviour on these platforms. Here, we evaluate the behaviour of 600,000 individual Twitter users between 2012 and 2019 and find empirical evidence for a cohort-level acceleration of the way Twitter is used. Across time, we observe changing user-level behaviours: more tweets per time, denser interactions with others via retweets, and shorter content horizons, expressed as an individual's decaying autocorrelation of topics over time. We show that the change in usage patterns is not simply caused by a growing user base. While behaviour remains remarkably stable within each cohort over time, we relate these observations to changing compositions of new users with each new cohort containing increasingly active individuals. Our findings complement recent empirical work on social acceleration by tracking cohorts over time, controlling for cohort size, and analyzing their behavioural composition.
Gravity-Aware Monocular 3D Human-Object Reconstruction

This paper proposes GraviCap, i.e., a new approach for joint markerless 3D human motion capture and object trajectory estimation from monocular RGB videos. We focus on scenes with objects partially observed during a free flight. In contrast to existing monocular methods, we can recover scale, object trajectories as well as human bone lengths in meters and the ground plane's orientation, thanks to the awareness of the gravity constraining object motions. Our objective function is parametrised by the object's initial velocity and position, gravity direction and focal length, and jointly optimised for one or several free flight episodes. The proposed human-object interaction constraints ensure geometric consistency of the 3D reconstructions and improved physical plausibility of human poses compared to the unconstrained case. We evaluate GraviCap on a new dataset with ground-truth annotations for persons and different objects undergoing free flights. In the experiments, our approach achieves state-of-the-art accuracy in 3D human motion capture on various metrics. We urge the reader to watch our supplementary video. Both the source code and the dataset are released; see http://4dqv.mpi-inf.mpg. de/GraviCap/.
QUEACO: Borrowing Treasures from Weakly-labeled Behavior Data for Query Attribute Value Extraction

We study the problem of query attribute value extraction, which aims to identify named entities from user queries as diverse surface form attribute values and afterward transform them into formally canonical forms. Such a problem consists of two phases: named entity recognition (NER) and attribute value normalization (AVN). However, existing works only focus on the NER phase but neglect equally important AVN. To bridge this gap, this paper proposes a unified query attribute value extraction system in e-commerce search named QUEACO, which involves both two phases. Moreover, by leveraging large-scale weakly-labeled behavior data, we further improve the extraction performance with less supervision cost. Specifically, for the NER phase, QUEACO adopts a novel teacher-student network, where a teacher network that is trained on the strongly-labeled data generates pseudo-labels to refine the weakly-labeled data for training a student network. Meanwhile, the teacher network can be dynamically adapted by the feedback of the student's performance on strongly-labeled data to maximally denoise the noisy supervisions from the weak labels. For the AVN phase, we also leverage the weakly-labeled query-to-attribute behavior data to normalize surface form attribute values from queries into canonical forms from products. Extensive experiments on a real-world large-scale E-commerce dataset demonstrate the effectiveness of QUEACO.
Denoising ECG by Adaptive Filter with Empirical Mode Decomposition

Electrocardiogram (ECG) signal is an important physiological signal which contains cardiac information and is the basis to diagnosis cardiac related diseases. In this paper, several innovative and efficient methods based on adaptive filter and empirical mode decomposition (EMD) to denoise ECG signal contaminated by various kinds of noise, including baseline wander (BW), power line interference (PLI), electrode motion artifact (EM) and muscle artifact (MA), are proposed. We first present a novel method based on EMD and adaptive filter for the removal of BW and PLI in ECG signal. We then extend the method to the complex scenario where four most common noises, PLI, BW, EM and MA are present. The proposed Parallel EMD adaptive filter structure yields the best SNR improvement on the MIT-BIH arrhythmia database, corrupted by the four types of noises.
Exogeology from Polluted White Dwarfs

It is difficult to study the interiors of terrestrial planets in the Solar System and the problem is magnified for distant exoplanets. However, sometimes nature is helpful. Some planetary bodies are torn to fragments and consumed by the strong gravity close to the descendants of Sun-like stars, white dwarfs. We can deduce the general composition of the planet when we observe the spectroscopic signature of the white dwarf. Most planetary fragments that fall into white dwarfs appear to be rocky with a variable fraction of associated ice and carbon. These white dwarf planetary systems provide a unique opportunity to study the geology of exoplanetary systems.
Learning Anchored Unsigned Distance Functions with Gradient Direction Alignment for Single-view Garment Reconstruction

While single-view 3D reconstruction has made significant progress benefiting from deep shape representations in recent years, garment reconstruction is still not solved well due to open surfaces, diverse topologies and complex geometric details. In this paper, we propose a novel learn-able Anchored Unsigned Distance Function (AnchorUDF) representation for 3D garment reconstruction from a single image. AnchorUDF represents 3D shapes by predicting unsigned distance fields (UDFs) to enable open garment surface modeling at arbitrary resolution. To capture diverse garment topologies, AnchorUDF not only computes pixel-aligned local image features of query points, but also leverages a set of anchor points located around the surface to enrich 3D position features for query points, which provides stronger 3D space context for the distance function. Furthermore, in order to obtain more accurate point projection direction at inference, we explicitly align the spatial gradient direction of AnchorUDF with the ground-truth direction to the surface during training. Extensive experiments on two public 3D garment datasets, i.e., MGN and Deep Fashion3D, demonstrate that AnchorUDF achieves the state-of-the-art performance on single-view garment reconstruction. Code is available at https://github.com/zhaofang0627/AnchorUDF.
Anomalous singularity of the solution of the vector Dyson equation in the critical case

We consider the solution of the vector Dyson equation −1/m = z + Sm in the case when S has a block staircase structure with (n− 1) different critical zero blocks below the strictly positive anti-diagonal and all elements right above the anti-diagonal are strictly positive. We prove that the components of m behave as fractional powers of z in the neighbourhood of zero and show that the self-consistent density of states ρ(E) behaves as |E|− n−1 n+1 as E tends to zero, where n is a number of blocks. Both constant block and non-constant block cases are considered. In the non-constant case uniform estimates for the components of m are obtained. AMS Subject Classification (2010): 60B20.
Energy dependence of underlying-event observables from RHIC to LHC energies

A study of the charged-particle density (number density) in the transverse region of the dihadron correlations exploiting the existing pp and pp̄ data from RHIC to LHC energies is reported. This region has contributions from the Underlying Event (UE) as well as from Initialand FinalState Radiation (ISR-FSR). Based on the data, a two-component model is built. This has the functional form ∝ s+β log(s), where the logarithmic ((β = 0.140±0.007)) and the power-law (α = 0.270±0.005) terms describe the components more sensitive to the ISR-FSR and UE contributions, respectively. The model describes the data from RHIC to LHC energies, the extrapolation to higher energies indicates that at around √ s ≈ 100 TeV the number density associated to UE will match that from ISR-FSR. Although this behaviour is not predicted by PYTHIA 8.244, the powerlaw behaviour of the UE contribution is consistent with the energy dependence of the parameter that regulates Multiparton Interactions. Using simulations, KNO-like scaling properties of the multiplicity distributions in the regions sensitive to either UE or ISR-FSR are also discussed. The results presented here can be helpful to constrain QCD-inspired Monte Carlo models at the Future Circular Collider energies, as well as to characterize the UE-based event classifiers which are currently used at the LHC.
CP-violating transport theory for electroweak baryogenesis with thermal corrections

We derive CP-violating transport equations for fermions for electroweak baryogenesis from the CTP-formalism including thermal corrections at the one-loop level. We consider both the VEV-insertion approximation (VIA) and the semiclassical (SC) formalism. We show that the VIA-method is based on an assumption that leads to an ill-defined source term containing a pinch singularity, whose regularisation by thermal effects leads to ambiguities including spurious ultraviolet and infrared divergences. We then carefully review the derivation of the semiclassical formalism and extend it to include thermal corrections. We present the semiclassical Boltzmann equations for thermal WKB-quasiparticles with source terms up to the second order in gradients that contain both dispersive and finite width corrections. We also show that the SC-method reproduces the current divergence equations and that a correct implementation of the Fick's law captures the semiclassical source term even with conserved total current ∂μ j μ = 0. Our results show that the VIA-source term is not just ambiguous, but that it does not exist. Finally, we show that the collisional source terms reported earlier in the semiclassical literature are also spurious, and vanish in a consistent calculation.
Do Vision Transformers See Like Convolutional Neural Networks?

Convolutional neural networks (CNNs) have so far been the de-facto model for visual data. Recent work has shown that (Vision) Transformer models (ViT) can achieve comparable or even superior performance on image classification tasks. This raises a central question: how are Vision Transformers solving these tasks? Are they acting like convolutional networks, or learning entirely different visual representations? Analyzing the internal representation structure of ViTs and CNNs on image classification benchmarks, we find striking differences between the two architectures, such as ViT having more uniform representations across all layers. We explore how these differences arise, finding crucial roles played by self-attention, which enables early aggregation of global information, and ViT residual connections, which strongly propagate features from lower to higher layers. We study the ramifications for spatial localization, demonstrating ViTs successfully preserve input spatial information, with noticeable effects from different classification methods. Finally, we study the effect of (pretraining) dataset scale on intermediate features and transfer learning, and conclude with a discussion on connections to new architectures such as the MLP-Mixer.
RePOSE: Fast 6D Object Pose Refinement via Deep Texture Rendering

We present RePOSE, a fast iterative refinement method for 6D object pose estimation. Prior methods perform refinement by feeding zoomed-in input and rendered RGB images into a CNN and directly regressing an update of a refined pose. Their runtime is slow due to the computational cost of CNN, which is especially prominent in multiple-object pose refinement. To overcome this problem, RePOSE leverages image rendering for fast feature extraction using a 3D model with a learnable texture. We call this deep texture rendering, which uses a shallow multilayer perceptron to directly regress a view-invariant image representation of an object. Furthermore, we utilize differentiable Levenberg-Marquardt (LM) optimization to refine a pose fast and accurately by minimizing the distance between the input and rendered image representations without the need of zooming in. These image representations are trained such that differentiable LM optimization converges within few iterations. Consequently, RePOSE runs at 92 FPS and achieves state-of-the-art accuracy of 51.6% on the Occlusion LineMOD dataset - a 4.1% absolute improvement over the prior art, and comparable result on the YCB-Video dataset with a much faster runtime. The code is available at https://github.com/sh8/repose.
Decentralized Federated Learning for UAV Networks: Architecture, Challenges, and Opportunities

Unmanned aerial vehicles (UAVs), or drones, are envisioned to support extensive applications in next-generation wireless networks in both civil and military fields. Empowering UAV networks' intelligence with artificial intelligence, especially machine learning (ML), techniques, is inevitable and appealing to enable the aforementioned applications. To solve the problems of traditional cloud-centric ML for UAV networks such as privacy concerns, unacceptable latency, and resource burden, a distributed ML technique, federated learning (FL), recently has been proposed to enable multiple UAVs to collaboratively train an ML model without letting out raw data. However, almost all existing FL paradigms are still centralized (i.e., a central entity is in charge of ML model aggregation and fusion over the whole network), which could result in the issue of a single point of failure and are inappropriate to UAV networks with both unreliable nodes and links. Thus motivated, in this article, we propose a novel architecture called Decentralized Federated Learning for UAV Networks (DFL-UN), which enables FL within UAV networks without a central entity. We also conduct a preliminary simulation study to validate the feasibility and effectiveness of the DFLUN architecture. Finally, we discuss the main challenges and potential research directions in the DFL-UN.
Enhancing Few-Shot Image Classification with Unlabelled Examples

We develop a transductive meta-learning method that uses unlabelled instances to improve few-shot image classification performance. Our approach combines a regularized Mahalanobis-distance-based soft k-means clustering procedure with a modified state of the art neural adaptive feature extractor to achieve improved test-time classification accuracy using unlabelled data. We evaluate our method on transductive few-shot learning tasks, in which the goal is to jointly predict labels for query (test) examples given a set of support (training) examples. We achieve state of the art performance on the Meta-Dataset, mini-ImageNet and tiered-ImageNet benchmarks. All trained models and code have been made publicly available1.
Prediction of moisture transfer parameters for convective drying of shrimp at different pretreatments

By the analytical model proposed by Dincer and Dost, the mass transfer parameters (moisture transfer coefficient and moisture diffusivity) of shrimp samples were determined. Three sets of drying experiments were performed with three samples of shrimpI: without boiling (WB), boiled in salt solution (SB) and boiled in salt solution and subjected to liquid smoking process (SBS). The experiments were performed under controlled conditions of drying air at temperature of 60°C and velocity of 1.5 m/s. Experimental dimensionless moisture content data were used to calculate the drying coefficients and lag factors, which were then incorporated into the analytical model for slab and cylinder shapes. The results showed an adequate fit between the experimental data and the values predicted from the correlation. The boiling is the most recommended pretreatment, because provided a shorter drying time, with high values of moisture transfer coefficient and moisture diffusivity.