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In this study, we explore the correlation functions of thin-shell operators, represented semiclassically by a homogeneous, thin interface of dust particles. Employing the monodromy method, we successfully compute the contribution from the Virasoro vacuum block and present the monodromy equation in a closed form without assuming the probe limit. Although an analytical solution to the monodromy equation remains difficult, we demonstrate that it is perturbatively solvable within specific limits, including the probe, the heavy-shell, and the early-time limits. Moreover, we compare our results with gravitational calculations and find precise agreement. We strengthen our findings by proving that the thermal correlation functions in gravity, after an inverse Laplace transformation, satisfy the field theory's monodromy equation. Additionally, we identify an infinite series of unphysical solutions to the monodromy equation and discuss their potential geometrical duals., Comment: 27 pages, 4 figures; minor corrections, match with published version

The capability to generate simulation-ready garment models from 3D shapes of clothed humans will significantly enhance the interpretability of captured geometry of real garments, as well as their faithful reproduction in the virtual world. This will have notable impact on fields like shape capture in social VR, and virtual try-on in the fashion industry. To align with the garment modeling process standardized by the fashion industry as well as cloth simulation softwares, it is required to recover 2D patterns. This involves an inverse garment design problem, which is the focus of our work here: Starting with an arbitrary target garment geometry, our system estimates an animatable garment model by automatically adjusting its corresponding 2D template pattern, along with the material parameters of the physics-based simulation (PBS). Built upon a differentiable cloth simulator, the optimization process is directed towards minimizing the deviation of the simulated garment shape from the target geometry. Moreover, our produced patterns meet manufacturing requirements such as left-to-right-symmetry, making them suited for reverse garment fabrication. We validate our approach on examples of different garment types, and show that our method faithfully reproduces both the draped garment shape and the sewing pattern.

Automatic assessment of impairment and disease severity is a key challenge in data-driven medicine. We propose a novel framework to address this challenge, which leverages AI models trained exclusively on healthy individuals. The COnfidence-Based chaRacterization of Anomalies (COBRA) score exploits the decrease in confidence of these models when presented with impaired or diseased patients to quantify their deviation from the healthy population. We applied the COBRA score to address a key limitation of current clinical evaluation of upper-body impairment in stroke patients. The gold-standard Fugl-Meyer Assessment (FMA) requires in-person administration by a trained assessor for 30-45 minutes, which restricts monitoring frequency and precludes physicians from adapting rehabilitation protocols to the progress of each patient. The COBRA score, computed automatically in under one minute, is shown to be strongly correlated with the FMA on an independent test cohort for two different data modalities: wearable sensors ($\rho = 0.845$, 95% CI [0.743,0.908]) and video ($\rho = 0.746$, 95% C.I [0.594, 0.847]). To demonstrate the generalizability of the approach to other conditions, the COBRA score was also applied to quantify severity of knee osteoarthritis from magnetic-resonance imaging scans, again achieving significant correlation with an independent clinical assessment ($\rho = 0.644$, 95% C.I [0.585,0.696])., Comment: 32 pages, 10 figures

The evolution of excitons from 2D to 3D is of great importance in photo-physics, yet the layer-dependent exciton polarizability has not been investigated in 2D semiconductors. Here, we determine the exciton polarizabilities for 3- to 11-layer black phosphorus-a direct bandgap semiconductor regardless of the thickness-through frequency-resolved photocurrent measurements on dual-gate devices and unveil the carrier screening effect in relatively thicker samples. By taking advantage of the broadband photocurrent spectra, we are also able to reveal the exciton response for higher-index subbands under the gate electrical field. Surprisingly, dark excitons are brightened with intensity even stronger than the allowed transitions above certain electrical field. Our study not only sheds light on the exciton evolution with sample thickness, but also paves a way for optoelectronic applications of few-layer BP in modulators, tunable photodetectors, emitters and lasers., Comment: 30 pages, 4 figures

We study holographic complexity for the rotating quantum BTZ black holes (quBTZ), the BTZ black holes with corrections from bulk quantum fields. Using double holography, the combined system of backreacted rotating BTZ black holes with conformal matters, can be holographically described by the rotating AdS4 C-metric with the BTZ black hole living on a codimension-1 brane. We investigate both volume complexity and action complexity of rotating quBTZ, and pay special attention to their late-time behaviors. When the mass of BTZ black hole is not very small and the rotation is not very slow, we show that the late-time rates of the volume complexity and the action complexity agree with each other up to a factor 2 and reduce to the ones of BTZ at the leading classical order, and they both receive subleading quantum corrections. For the volume complexity, the leading quantum correction comes from the backreaction of comformal matter on the geometry, similar to the static quBTZ case. For the action complexity, unlike the static case, the Wheeler-de Witt (WdW) patch in computing the action complexity for the rotating black hole does not touch the black hole singularity such that the leading order result is in good match with the one of classical BTZ. However, when the mass of BTZ black hole is small or the rotation parameter a is small, the quantum correction to the action complexity could be significant such that the late-time slope of the action complexity of quBTZ deviates very much from the one of classical BTZ. Remarkably, we notice that the nonrotating limit $a \to 0$ is singular and does not lead to the late-time slope of the action complexity for non-rotating quantum BTZ black hole. The similar phenomenon happens for higher dimensional rotating black holes., Comment: 44 pages, 16 figures

When measuring rare processes at Belle II, a huge luminosity is required, which means a large number of simulations are necessary to determine signal efficiencies and background contributions. However, this process demands high computation costs while most of the simulated data, in particular in case of background, are discarded by the event selection. Thus, filters using graph neural networks are introduced at an early stage to save the resources for the detector simulation and reconstruction of events discarded at analysis level. In our work, we improved the performance of the filters using graph attention and investigated statistical methods including sampling and reweighting to deal with the biases introduced by the filtering., Comment: to be published in ACAT 2022 proceedings in the Journal Of Physics: Conference Series

Random label noises (or observational noises) widely exist in practical machine learning settings. While previous studies primarily focus on the affects of label noises to the performance of learning, our work intends to investigate the implicit regularization effects of the label noises, under mini-batch sampling settings of stochastic gradient descent (SGD), with assumptions that label noises are unbiased. Specifically, we analyze the learning dynamics of SGD over the quadratic loss with unbiased label noises, where we model the dynamics of SGD as a stochastic differentiable equation (SDE) with two diffusion terms (namely a Doubly Stochastic Model). While the first diffusion term is caused by mini-batch sampling over the (label-noiseless) loss gradients as many other works on SGD, our model investigates the second noise term of SGD dynamics, which is caused by mini-batch sampling over the label noises, as an implicit regularizer. Our theoretical analysis finds such implicit regularizer would favor some convergence points that could stabilize model outputs against perturbation of parameters (namely inference stability). Though similar phenomenon have been investigated, our work doesn't assume SGD as an Ornstein-Uhlenbeck like process and achieve a more generalizable result with convergence of approximation proved. To validate our analysis, we design two sets of empirical studies to analyze the implicit regularizer of SGD with unbiased random label noises for deep neural networks training and linear regression., Comment: The complete manuscript of our previous submission to ICLR'21 (https://openreview.net/forum?id=g4szfsQUdy3). This manuscript was major done in 2021. We gave try to some venues but unfortunately haven't made it accepted yet

Facial expression generation is one of the most challenging and long-sought aspects of character animation, with many interesting applications. The challenging task, traditionally having relied heavily on digital craftspersons, remains yet to be explored. In this paper, we introduce a generative framework for generating 3D facial expression sequences (i.e. 4D faces) that can be conditioned on different inputs to animate an arbitrary 3D face mesh. It is composed of two tasks: (1) Learning the generative model that is trained over a set of 3D landmark sequences, and (2) Generating 3D mesh sequences of an input facial mesh driven by the generated landmark sequences. The generative model is based on a Denoising Diffusion Probabilistic Model (DDPM), which has achieved remarkable success in generative tasks of other domains. While it can be trained unconditionally, its reverse process can still be conditioned by various condition signals. This allows us to efficiently develop several downstream tasks involving various conditional generation, by using expression labels, text, partial sequences, or simply a facial geometry. To obtain the full mesh deformation, we then develop a landmark-guided encoder-decoder to apply the geometrical deformation embedded in landmarks on a given facial mesh. Experiments show that our model has learned to generate realistic, quality expressions solely from the dataset of relatively small size, improving over the state-of-the-art methods. Videos and qualitative comparisons with other methods can be found at \url{https://github.com/ZOUKaifeng/4DFM}.

We study universal properties of the torus partition function of $T\bar T$-deformed CFTs under the assumption of modular invariance, for both the original version, referred to as the double-trace version in this paper, and the single-trace version defined as the symmetric product orbifold of double-trace $T\bar T$-deformed CFTs. In the double-trace case, we specify sparseness conditions for the light states for which the partition function at low temperatures is dominated by the vacuum when the central charge of the undeformed CFT is large. Using modular invariance, this implies a universal density of high energy states, in analogy with the behavior of holographic CFTs. For the single-trace $T\bar T$ deformation, we show that modular invariance implies that the torus partition function can be written in terms of the untwisted partition function and its modular images, the latter of which can be obtained from the action of a generalized Hecke operator. The partition function and the energy of twisted states match holographic calculations in previous literature, thus providing further evidence for the conjectured holographic correspondence. In addition, we show that the single-trace partition function is universal when the central charge of the undeformed CFT is large, without needing to assume a sparse density of light states. Instead, the density of light states is shown to always saturate the sparseness condition., Comment: 26 pages; v2: added references, matches published version

A workflow describes the entirety of processing steps in an analysis, such as employed in many fields of physics. Workflow management makes the dependencies between individual steps of a workflow and their computational requirements explicit, such that entire workflows can be executed in a stand-alone manner. Though the use of workflow management is widely recommended in the interest of transparency, reproducibility and data preservation, choosing among the large variety of available workflow management tools can be overwhelming. We compare selected workflow management tools concerning all relevant criteria and make recommendations for different use cases.

Reflected entropy is a newly proposed notion in quantum information. It has important implications in holography. In this work, we study the reflected entropy in the framework of the AdS$_3$/WCFT correspondence. We determine the scaling dimensions and charges of various twist operators in non-Abelian orbifold WCFT by generalizing the uniformization map and taking into account of the charge conservation. This allows us to compute the reflected entropy, logarithmic negativity and odd entropy for two disjoint intervals in holographic WCFT. We find that the reflected entropy can be related holographically to the pre-entanglement wedge cross-section, which is given by the minimal distance between the benches in two swing surfaces., Comment: 52 pages, 11 figures

Class-imbalance is a common problem in machine learning practice. Typical Imbalanced Learning (IL) methods balance the data via intuitive class-wise resampling or reweighting. However, previous studies suggest that beyond class-imbalance, intrinsic data difficulty factors like overlapping, noise, and small disjuncts also play critical roles. To handle them, many solutions have been proposed (e.g., noise removal, borderline sampling, hard example mining) but are still confined to a specific factor and cannot generalize to broader scenarios, which raises an interesting question: how to handle both class-agnostic difficulties and the class-imbalance in a unified way? To answer this, we consider both class-imbalance and its orthogonal: intra-class imbalance, i.e., the imbalanced distribution over easy and hard samples. Such distribution naturally reflects the complex influence of class-agnostic intrinsic data difficulties thus providing a new unified view for identifying and handling these factors during learning. From this perspective, we discuss the pros and cons of existing IL solutions and further propose new balancing techniques for more robust and efficient IL. Finally, we wrap up all solutions into a generic ensemble IL framework, namely DuBE (Duple-Balanced Ensemble). It features explicit and efficient inter-\&intra-class balancing as well as easy extension with standardized APIs. Extensive experiments validate the effectiveness of DuBE. Code, examples, and documentation are available at https://github.com/AnonAuthorAI/duplebalance and https://duplebalance.readthedocs.io., Comment: 15 pages, 4 tables, 12 figures

Reliable probability estimation is of crucial importance in many real-world applications where there is inherent (aleatoric) uncertainty. Probability-estimation models are trained on observed outcomes (e.g. whether it has rained or not, or whether a patient has died or not), because the ground-truth probabilities of the events of interest are typically unknown. The problem is therefore analogous to binary classification, with the difference that the objective is to estimate probabilities rather than predicting the specific outcome. This work investigates probability estimation from high-dimensional data using deep neural networks. There exist several methods to improve the probabilities generated by these models but they mostly focus on model (epistemic) uncertainty. For problems with inherent uncertainty, it is challenging to evaluate performance without access to ground-truth probabilities. To address this, we build a synthetic dataset to study and compare different computable metrics. We evaluate existing methods on the synthetic data as well as on three real-world probability estimation tasks, all of which involve inherent uncertainty: precipitation forecasting from radar images, predicting cancer patient survival from histopathology images, and predicting car crashes from dashcam videos. We also give a theoretical analysis of a model for high-dimensional probability estimation which reproduces several of the phenomena evinced in our experiments. Finally, we propose a new method for probability estimation using neural networks, which modifies the training process to promote output probabilities that are consistent with empirical probabilities computed from the data. The method outperforms existing approaches on most metrics on the simulated as well as real-world data., Comment: SL, AK, WZ, ML, SM contributed equally to this work; 36 pages, 17 figures, 12 tables

We revisit the spectrum of linear axisymmetric gravitational perturbations of the (near-)extreme Kerr black hole. Our aim is to characterise those perturbations that are responsible for the deviations away from extremality, and to contrast them with the linearized perturbations treated in the Newman-Penrose formalism. For the near horizon region of the (near-)extreme Kerr solution, i.e. the (near-)NHEK background, we provide a complete characterisation of axisymmetric modes. This involves an infinite tower of propagating modes together with the much subtler low-lying mode sectors that contain the deformations driving the black hole away from extremality. Our analysis includes their effects on the line element, their contributions to Iyer-Wald charges around the NHEK geometry, and how to reconstitute them as gravitational perturbations on Kerr. We present in detail how regularity conditions along the angular variables modify the dynamical properties of the low-lying sector, and in particular their role in the new developments of nearly-AdS$_2$ holography., Comment: 73 pages, 1 figure; v2: minor typos corrected; v3: matches published version

We provide a non conformal generalization of the Comp\`ere-Song-Strominger (CSS) boundary conditions for AdS$_3$ gravity that breaks the $\widehat u(1)$ Kac-Moody-Virasoro symmetry to two $u(1)$s. The holographic dual specified by the new boundary conditions can be understood as an irrelevant deformation of a warped conformal field theory (WCFT). Upon consistent reduction to two dimensions, AdS$_3$ gravity results in a deformed Jackiw-Teitelboim dilaton gravity model coupled to a Maxwell field. We show that near extremality the boundary conditions inherited from generalized CSS boundary conditions in three dimensions give rise to an effective action exhibiting the same symmetry breaking pattern as the complex Sachdev-Ye-Kitaev models. Besides the Schwarzian term reflecting the breaking of conformal symmetry, the effective action contains an additional term that captures the breaking of the $\widehat u(1)$ Kac-Moody symmetry., Comment: 49 pages, 1 figure; v2 minor corrections and additions. Version to appear in JHEP

We discuss the connections between the complex SYK model at the conformal limit and warped conformal field theories. Both theories have an $SL(2,R) \times U(1)$ global symmetry. We present comparisons on symmetries, correlation functions, the effective action and the entropy formula. We also use modular covariance to reinterpret results in the complex SYK model., Comment: 27 pages