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Futaki invariants of the classical moduli space of 4d N=1 supersymmetric gauge theories determine whether they have a conformal fixed point in the IR. We systematically compute the Futaki invariants for a large family of 4d N=1 supersymmetric gauge theories coming from D3-branes probing Calabi-Yau 3-fold singularities whose bases are Gorenstein Fano surfaces. In particular, we focus on the toric case where the Fano surfaces are given by the 16 reflexive convex polygons and the moduli spaces are given by the corresponding toric Calabi-Yau 3-folds. We study the distribution of and conjecture new bounds on the Futaki invariants with respect to various topological and geometric quantities. These include the minimum volume of the Sasaki-Einstein base manifolds as well as the Chern and Euler numbers of the toric Fano surfaces. Even though the moduli spaces for the family of theories studied are known to be K-stable, our work sheds new light on how the topological and geometric quantities restrict the Futaki invariants for a plethora of moduli spaces., Comment: 65 pages, 19 figures, 11 tables

We establish several fine boundary regularity results of weak solutions to non-homogeneous $s$-fractional Laplacian type equations. In particular, we prove sharp Calder\'on-Zygmund type estimates of $u/d^s$ depending on the regularity assumptions on the associated kernel coefficient including VMO, Dini continuity or the H\"older continuity, where $u$ is a weak solution to such a nonlocal problem and $d$ is the distance to the boundary function of a given domain. Our analysis is based on point-wise behaviors of maximal functions of $u/d^s$.

Large language models (LLMs) have achieved impressive results across various tasks. However, they still struggle with long-context documents. This study evaluates the performance of three leading LLMs: GPT-4o, Claude 3.5 Sonnet, and Gemini 1.5 Pro on lengthy, complex, and opinion-varying documents concerning infrastructure projects, under both zero-shot and few-shot scenarios. Our results indicate that GPT-4o excels in zero-shot scenarios for simpler, shorter documents, while Claude 3.5 Sonnet surpasses GPT-4o in handling more complex, sentiment-fluctuating opinions. In few-shot scenarios, Claude 3.5 Sonnet outperforms overall, while GPT-4o shows greater stability as the number of demonstrations increases.

This paper introduces ELMO, a real-time upsampling motion capture framework designed for a single LiDAR sensor. Modeled as a conditional autoregressive transformer-based upsampling motion generator, ELMO achieves 60 fps motion capture from a 20 fps LiDAR point cloud sequence. The key feature of ELMO is the coupling of the self-attention mechanism with thoughtfully designed embedding modules for motion and point clouds, significantly elevating the motion quality. To facilitate accurate motion capture, we develop a one-time skeleton calibration model capable of predicting user skeleton offsets from a single-frame point cloud. Additionally, we introduce a novel data augmentation technique utilizing a LiDAR simulator, which enhances global root tracking to improve environmental understanding. To demonstrate the effectiveness of our method, we compare ELMO with state-of-the-art methods in both image-based and point cloud-based motion capture. We further conduct an ablation study to validate our design principles. ELMO's fast inference time makes it well-suited for real-time applications, exemplified in our demo video featuring live streaming and interactive gaming scenarios. Furthermore, we contribute a high-quality LiDAR-mocap synchronized dataset comprising 20 different subjects performing a range of motions, which can serve as a valuable resource for future research. The dataset and evaluation code are available at {\blue \url{https://movin3d.github.io/ELMO_SIGASIA2024/}}, Comment: published at ACM Transactions on Graphics (Proc. SIGGRAPH ASIA), 2024

Atomically thin two-dimensional (2D) hexagonal boron nitride (hBN) has emerged as an essential material for the encapsulation layer in van der Waals heterostructures and efficient deep ultra-violet optoelectronics. This is primarily due to its remarkable physical properties and ultrawide bandgap (close to 6 eV, and even larger in some cases) properties. Color centers in hBN refer to intrinsic vacancies and extrinsic impurities within the 2D crystal lattice, which result in distinct optical properties in the ultraviolet (UV) to near-infrared (IR) range. Furthermore, each color center in hBN exhibits a unique emission spectrum and possesses various spin properties. These characteristics open up possibilities for the development of next-generation optoelectronics and quantum information applications, including room-temperature single-photon sources and quantum sensors. Here, we provide a comprehensive overview of the atomic configuration, optical and quantum properties, and different techniques employed for the formation of color centers in hBN. A deep understanding of color centers in hBN allows for advances in the development of next-generation UV optoelectronic applications, solid-state quantum technologies, and nanophotonics by harnessing the exceptional capabilities offered by hBN color centers.

Internet of Things (IoT) devices are deployed in the filed, there is an enormous amount of untapped potential in local computing on those IoT devices. Harnessing this potential for indoor localization, therefore, becomes an exciting research area. Conventionally, the training and deployment of indoor localization models are based on centralized servers with substantial computational resources. This centralized approach faces several challenges, including the database's inability to accommodate the dynamic and unpredictable nature of the indoor electromagnetic environment, the model retraining costs, and the susceptibility of centralized servers to security breaches. To mitigate these challenges we aim to amalgamate the offline and online phases of traditional indoor localization methods using a real-time-trainable and decentralized IoT indoor localization model based on Sparse Gaussian Process with Reduced-dimensional Inputs (SGP-RI), where the number and dimension of the input data are reduced through reference point and wireless access point filtering, respectively. The experimental results based on a multi-building and multi-floor static database as well as a single-building and single-floor dynamic database, demonstrate that the proposed SGP-RI model with less than half the training samples as inducing inputs can produce comparable localization performance to the standard Gaussian Process model with the whole training samples. The SGP-RI model enables the decentralization of indoor localization, facilitating its deployment to resource-constrained IoT devices, and thereby could provide enhanced security and privacy, reduced costs, and network dependency. Also, the model's capability of real-time training makes it possible to quickly adapt to the time-varying indoor electromagnetic environment., Comment: 10 pages, 4 figures, under review for journal publication

We argue that algebraic and combinatorial polytope mutations of Fano 3-folds can be identified with mass deformations of associated 2d (0,2) supersymmetric gauge theories realized by brane brick models. These are Type IIA brane configurations that realize a large family of 2d worldvolume theories on probe D1-branes at toric Calabi-Yau 4-folds. We show that brane brick models that are related by mass deformations associated to algebraic and combinatorial polytope mutations of Fano 3-folds have mesonic moduli spaces with the same number of generators. We show that mesonic flavor charges of these generators form convex reflexive lattice polytopes that are dual to the toric diagrams of the Fano 3-folds. The generating function of mesonic gauge invariant operators, also known as the Hilbert series of the mesonic moduli space, appears to be identical for such brane brick models under a particular refinement originating from the U(1)_R charges in the brane brick model following the mass deformation., Comment: 12 pages, 4 figures, 5 tables

Wi-Fi fingerprinting is widely applied for indoor localization due to the widespread availability of Wi-Fi devices. However, traditional methods are not ideal for multi-building and multi-floor environments due to the scalability issues. Therefore, more and more researchers have employed deep learning techniques to enable scalable indoor localization. This paper introduces a novel semi-supervised learning framework for neural networks based on wireless access point selection, noise injection, and Mean Teacher model, which leverages unlabeled fingerprints to enhance localization performance. The proposed framework can manage hybrid in/outsourcing and voluntarily contributed databases and continually expand the fingerprint database with newly submitted unlabeled fingerprints during service. The viability of the proposed framework was examined using two established deep-learning models with the UJIIndoorLoc database. The experimental results suggest that the proposed framework significantly improves localization performance compared to the supervised learning-based approach in terms of floor-level coordinate estimation using EvAAL metric. It shows enhancements up to 10.99% and 8.98% in the former scenario and 4.25% and 9.35% in the latter, respectively with additional studies highlight the importance of the essential components of the proposed framework., Comment: 12 pages, 10 figures, under preparation for a journal publication

In this paper, we present a new solution to the problem of large-scale multi-building and multi-floor indoor localization based on linked neural networks, where each neural network is dedicated to a sub-problem and trained under a hierarchical stage-wise training framework. When the measured data from sensors have a hierarchical representation as in multi-building and multi-floor indoor localization, it is important to exploit the hierarchical nature in data processing to provide a scalable solution. In this regard, the hierarchical stage-wise training framework extends the original stage-wise training framework to the case of multiple linked networks by training a lower-hierarchy network based on the prior knowledge gained from the training of higher-hierarchy networks. The experimental results with the publicly-available UJIIndoorLoc multi-building and multi-floor Wi-Fi RSSI fingerprint database demonstrate that the linked neural networks trained under the proposed hierarchical stage-wise training framework can achieve a three-dimensional localization error of 8.19 m, which, to the best of the authors' knowledge, is the most accurate result ever obtained for neural network-based models trained and evaluated with the full datasets of the UJIIndoorLoc database, and that, when applied to a model based on hierarchical convolutional neural networks, the proposed training framework can also significantly reduce the three-dimensional localization error from 11.78 m to 8.71 m., Comment: 9 pages, 5 figures, under review for journal publication

We study the algebraic structure of the mesonic moduli spaces of bipartite field theories by computing the Hilbert series. Bipartite field theories form a large family of 4d N=1 supersymmetric gauge theories that are defined by bipartite graphs on Riemann surfaces with boundaries. By calculating the Hilbert series, we are able to identify the generators and defining generator relations of the mesonic moduli spaces of these theories. Moreover, we show that certain bipartite field theories exhibit enhanced global symmetries which can be identified through the computation of the corresponding refined Hilbert series. As part of our study, we introduce two one-parameter families of bipartite field theories defined on cylinders whose mesonic moduli spaces are all complete intersection toric Calabi-Yau 3-folds., Comment: 77 pages, 24 figures, 23 tables; v2: minor corrections

We consider nonlocal equations of the type \[ (-\Delta_{p})^{s}u = \mu \quad \text{in }\Omega, \] where $\Omega \subset \mathbb{R}^{n}$ is either a bounded domain or the whole $\mathbb{R}^{n}$, $\mu$ is a Radon measure on $\Omega$, $0

We explore statistical properties of BPS q-series for 3d N=2 strongly coupled supersymmetric theories that correspond to a particular family of 3-manifolds Y. We discover that gaps between exponents in the q-series are statistically more significant at the beginning of the q-series compared to gaps that appear in higher powers of q. Our observations are obtained by calculating saliencies of q-series features used as input data for principal component analysis, which is a standard example of an explainable machine learning technique that allows for a direct calculation and a better analysis of feature saliencies., Comment: 11 pages, 4 figures, 3 tables

Latent Diffusion Models (LDMs) have emerged as powerful generative models, known for delivering remarkable results under constrained computational resources. However, deploying LDMs on resource-limited devices remains a complex issue, presenting challenges such as memory consumption and inference speed. To address this issue, we introduce LD-Pruner, a novel performance-preserving structured pruning method for compressing LDMs. Traditional pruning methods for deep neural networks are not tailored to the unique characteristics of LDMs, such as the high computational cost of training and the absence of a fast, straightforward and task-agnostic method for evaluating model performance. Our method tackles these challenges by leveraging the latent space during the pruning process, enabling us to effectively quantify the impact of pruning on model performance, independently of the task at hand. This targeted pruning of components with minimal impact on the output allows for faster convergence during training, as the model has less information to re-learn, thereby addressing the high computational cost of training. Consequently, our approach achieves a compressed model that offers improved inference speed and reduced parameter count, while maintaining minimal performance degradation. We demonstrate the effectiveness of our approach on three different tasks: text-to-image (T2I) generation, Unconditional Image Generation (UIG) and Unconditional Audio Generation (UAG). Notably, we reduce the inference time of Stable Diffusion (SD) by 34.9% while simultaneously improving its FID by 5.2% on MS-COCO T2I benchmark. This work paves the way for more efficient pruning methods for LDMs, enhancing their applicability., Comment: 8 pages, accepted to CVPR24 First Workshop on Efficient and On-Device Generation (EDGE)

The intensive computational burden of Stable Diffusion (SD) for text-to-image generation poses a significant hurdle for its practical application. To tackle this challenge, recent research focuses on methods to reduce sampling steps, such as Latent Consistency Model (LCM), and on employing architectural optimizations, including pruning and knowledge distillation. Diverging from existing approaches, we uniquely start with a compact SD variant, BK-SDM. We observe that directly applying LCM to BK-SDM with commonly used crawled datasets yields unsatisfactory results. It leads us to develop two strategies: (1) leveraging high-quality image-text pairs from leading generative models and (2) designing an advanced distillation process tailored for LCM. Through our thorough exploration of quantization, profiling, and on-device deployment, we achieve rapid generation of photo-realistic, text-aligned images in just two steps, with latency under one second on resource-limited edge devices., Comment: 4 pages, accepted to CVPR24 First Workshop on Efficient and On-Device Generation (EDGE)

We introduce HyperCLOVA X, a family of large language models (LLMs) tailored to the Korean language and culture, along with competitive capabilities in English, math, and coding. HyperCLOVA X was trained on a balanced mix of Korean, English, and code data, followed by instruction-tuning with high-quality human-annotated datasets while abiding by strict safety guidelines reflecting our commitment to responsible AI. The model is evaluated across various benchmarks, including comprehensive reasoning, knowledge, commonsense, factuality, coding, math, chatting, instruction-following, and harmlessness, in both Korean and English. HyperCLOVA X exhibits strong reasoning capabilities in Korean backed by a deep understanding of the language and cultural nuances. Further analysis of the inherent bilingual nature and its extension to multilingualism highlights the model's cross-lingual proficiency and strong generalization ability to untargeted languages, including machine translation between several language pairs and cross-lingual inference tasks. We believe that HyperCLOVA X can provide helpful guidance for regions or countries in developing their sovereign LLMs., Comment: 44 pages; updated authors list and fixed author names

Recent advancements in Spatial Transcriptomics (ST) technology have facilitated detailed gene expression analysis within tissue contexts. However, the high costs and methodological limitations of ST necessitate a more robust predictive model. In response, this paper introduces TRIPLEX, a novel deep learning framework designed to predict spatial gene expression from Whole Slide Images (WSIs). TRIPLEX uniquely harnesses multi-resolution features, capturing cellular morphology at individual spots, the local context around these spots, and the global tissue organization. By integrating these features through an effective fusion strategy, TRIPLEX achieves accurate gene expression prediction. Our comprehensive benchmark study, conducted on three public ST datasets and supplemented with Visium data from 10X Genomics, demonstrates that TRIPLEX outperforms current state-of-the-art models in Mean Squared Error (MSE), Mean Absolute Error (MAE), and Pearson Correlation Coefficient (PCC). The model's predictions align closely with ground truth gene expression profiles and tumor annotations, underscoring TRIPLEX's potential in advancing cancer diagnosis and treatment., Comment: Accepted to CVPR 2024

We study the incidence and spatial distribution of galaxies that are currently undergoing gravitational merging (M) or that have signs of a post merger (PM) in six galaxy clusters (A754, A2399, A2670, A3558, A3562, and A3716) within the redshift range, 0.05$\lesssim$$z$$\lesssim$0.08. To this aim, we obtained Dark Energy Camera (DECam) mosaics in $u^{\prime}$, $g^{\prime}$, and $r^{\prime}$-bands covering up to $3\times R_{200}$ of the clusters, reaching 28 mag/arcsec$^2$ surface brightness limits. We visually inspect $u^{\prime}$$g^{\prime}$$r^{\prime}$ color-composite images of volume-limited ($M_r < -20$) cluster-member galaxies to identify whether galaxies are of M or PM types. We find 4% M-type and 7% PM-type galaxies in the galaxy clusters studied. By adding spectroscopic data and studying the projected phase space diagram (PPSD) of the projected clustocentric radius and the line-of-sight velocity, we find that PM-type galaxies are more virialized than M-type galaxies, having 1--5% point higher fraction within the escape-velocity region, while the fraction of M-type was $\sim$10% point higher than PM-type in the intermediate environment. Similarly, on a substructure analysis, M types were found in the outskirt groups, while PM types populated groups in ubiquitous regions of the PPSD. Adopting literature-derived dynamical state indicator values, we observed a higher abundance of M types in dynamically relaxed clusters. This finding suggests that galaxies displaying post-merging features within clusters likely merged in low-velocity environments, including cluster outskirts and dynamically relaxed clusters., Comment: 23 pages, 15 figures, 4 tables, Published in ApJ. For photometric catalogs and associated information, see https://data.kasi.re.kr/vo/DECam_catalogs/

Wi-Fi fingerprinting has emerged as the most popular approach to indoor localization. The use of ML algorithms has greatly improved the localization performance of Wi-Fi fingerprinting, but its success depends on the availability of fingerprint databases composed of a large number of RSSIs, the MAC addresses of access points, and the other measurement information. However, most fingerprint databases do not reflect well the time varying nature of electromagnetic interferences in complicated modern indoor environment. This could result in significant changes in statistical characteristics of training/validation and testing datasets, which are often constructed at different times, and even the characteristics of the testing datasets could be different from those of the data submitted by users during the operation of localization systems after their deployment. In this paper, we consider the implications of time-varying Wi-Fi fingerprints on indoor localization from a data-centric point of view and discuss the differences between static and dynamic databases. As a case study, we have constructed a dynamic database covering three floors of the IR building of XJTLU based on RSSI measurements, over 44 days, and investigated the differences between static and dynamic databases in terms of statistical characteristics and localization performance. The analyses based on variance calculations and Isolation Forest show the temporal shifts in RSSIs, which result in a noticeable trend of the increase in the localization error of a Gaussian process regression model with the maximum error of 6.65 m after 14 days of training without model adjustments. The results of the case study with the XJTLU dynamic database clearly demonstrate the limitations of static databases and the importance of the creation and adoption of dynamic databases for future indoor localization research and real-world deployment., Comment: 10 pages, 5 figures, Invited paper with Excellent Paper Award to be presented at ICAIIC 2024, Osaka, Japan, Feb. 19--22, 2023

Structured pruning of modern large language models (LLMs) has emerged as a way of decreasing their high computational needs. Width pruning reduces the size of projection weight matrices (e.g., by removing attention heads) while maintaining the number of layers. Depth pruning, in contrast, removes entire layers or blocks, while keeping the size of the remaining weights unchanged. Most current research focuses on either width-only or a blend of width and depth pruning, with little comparative analysis between the two units (width vs. depth) concerning their impact on LLM inference efficiency. In this work, we show that simple depth pruning can effectively compress LLMs while achieving comparable or superior performance to recent width pruning studies. Our pruning method boosts inference speeds, especially under memory-constrained conditions that require limited batch sizes for running LLMs, where width pruning is ineffective. In retraining pruned models for quality recovery, continued pretraining on a large corpus markedly outperforms LoRA-based tuning, particularly at severe pruning ratios. We hope this work can help build compact yet capable LLMs. Code and models can be found at: https://github.com/Nota-NetsPresso/shortened-llm, Comment: Update (arXiv-v2): continued pretraining for severe pruning ratios, compatibility with quantization, and enhanced baselines. Preliminary work (arXiv-v1) accepted at ICLR 2024 Workshop on ME-FoMo: https://openreview.net/forum?id=18VGxuOdpu

We study gradient regularity for mixed local-nonlocal problems modelled upon \[ -\Delta_p u +(-\Delta_p)^su=\mu\qquad\text{for} \quad 2-\tfrac{1}{n}

We study the counting problem of BPS D-branes wrapping holomorphic cycles of a general toric Calabi-Yau manifold. We evaluate the Jeffrey-Kirwan residues for the flavoured Witten index for the supersymmetric quiver quantum mechanics on the worldvolume of the D-branes, and find that BPS degeneracies are described by a statistical mechanical model of crystal melting. For Calabi-Yau threefolds, we reproduce the crystal melting models long known in the literature. For Calabi-Yau fourfolds, however, we find that the crystal does not contain the full information for the BPS degeneracy and we need to explicitly evaluate non-trivial weights assigned to the crystal configurations. Our discussions treat Calabi-Yau threefolds and fourfolds on equal footing, and include discussions on elliptic and rational generalizations of the BPS states counting, connections to the mathematical definition of generalized Donaldson-Thomas invariants, examples of wall crossings, and of trialities in quiver gauge theories., Comment: 53 pages; v3 minor corrections, references added

This research aims to demonstrate that AI can function not only as a tool for learning, but also as an intelligent agent with which humans can engage in collaborative learning (CL) to change epistemic practices in science classrooms. We adopted a design and development research approach, following the Analysis, Design, Development, Implementation and Evaluation (ADDIE) model, to prototype a tangible instructional system called Collaborative Learning with AI Speakers (CLAIS). The CLAIS system is designed to have 3-4 human learners join an AI speaker to form a small group, where humans and AI are considered as peers participating in the Jigsaw learning process. The development was carried out using the NUGU AI speaker platform. The CLAIS system was successfully implemented in a Science Education course session with 15 pre-service elementary science teachers. The participants evaluated the CLAIS system through mixed methods surveys as teachers, learners, peers, and users. Quantitative data showed that the participants' Intelligent-Technological, Pedagogical, And Content Knowledge was significantly increased after the CLAIS session, the perception of the CLAIS learning experience was positive, the peer assessment on AI speakers and human peers was different, and the user experience was ambivalent. Qualitative data showed that the participants anticipated future changes in the epistemic process in science classrooms, while acknowledging technical issues such as speech recognition performance and response latency. This study highlights the potential of Human-AI Collaboration for knowledge co-construction in authentic classroom settings and exemplify how AI could shape the future landscape of epistemic practices in the classroom.

We present the discovery of a new H I structure in the NGC 7194 group from the observations using the Karl G. Jansky Very Large Array. NGC 7194 group is a nearby (z ~ 0.027) small galaxy group with five quiescent members. The observations reveal a 200 kpc-long H I plume that spans the entire group with a total mass of M$_{HI}$ = 3.4 x 10$^{10}$ M$_{\odot}$. The line-of-sight velocity of the H I gas gradually increases from south (7200 km s$^{-1}$) to north (8200 km $^{-1}$), and the local velocity dispersion is up to 70 km s$^{-1}$. The structure is not spatially coincident with any member galaxies but it shows close associations with a number of blue star-forming knots. Intragroup H I gas is not rare, but this particular structure is still one of the unusual cases in the sense that it does not show any clear connection with sizable galaxies in the group. We discuss the potential origins of this large-scale H I gas in the NGC 7194 group and its relation with the intergalactic star-forming knots. We propose that this HI feature could have originated from tidal interactions among group members or the infall of a late-type galaxy into the group. Alternatively, it might be leftover gas from flyby intruders., Comment: 9 pages, 3 figures

The double Cayley Grassmannian is a unique smooth equivariant completion with Picard number one of the 14-dimensional exceptional complex Lie group $G_2$, and it parametrizes eight-dimensional isotropic subalgebras of the complexified bi-octonions. We show the rigidity of the double Cayley Grassmannian under K\"{a}hler deformations. This means that for any smooth projective family of complex manifolds over a connected base of which one fiber is biholomorphic to the double Cayley Grassmannian, all other fibers are biholomorphic to the double Cayley Grassmannian., Comment: 10 pages, 2 figures. arXiv admin note: text overlap with arXiv:1905.06490

We present a collection of explicit formulas for the minimum volume of Sasaki-Einstein 5-manifolds. The cone over these 5-manifolds is a toric Calabi-Yau 3-fold. These toric Calabi-Yau 3-folds are associated with an infinite class of 4d N=1 supersymmetric gauge theories, which are realized as worldvolume theories of D3-branes probing the toric Calabi-Yau 3-folds. Under the AdS/CFT correspondence, the minimum volume of the Sasaki-Einstein base is inversely proportional to the central charge of the corresponding 4d N=1 superconformal field theories. The presented formulas for the minimum volume are in terms of geometric invariants of the toric Calabi-Yau 3-folds. These explicit results are derived by implementing machine learning regularization techniques that advance beyond previous applications of machine learning for determining the minimum volume. Moreover, the use of machine learning regularization allows us to present interpretable and explainable formulas for the minimum volume. Our work confirms that, even for extensive sets of toric Calabi-Yau 3-folds, the proposed formulas approximate the minimum volume with remarkable accuracy., Comment: 15 pages, 9 figures, 4 tables

Vanadium diselenide (VSe2) has intriguing physical properties such as unexpected ferromagnetism at the two-dimensional limit. However, the experimental results for room temperature ferromagnetism are still controversial and depend on the detailed crystal structure and stoichiometry. Here we introduce crystal truncation rod (CTR) analysis to investigate the atomic arrangement of bilayer VSe2 and bilayer graphene (BLG) hetero-structures grown on a 6H-SiC(0001) substrate. Using non-destructive CTR analysis, we were able to obtain electron density profiles and detailed crystal structure of the VSe2/BLG heterostructures. Specifically, the out-of-plane lattice parameters of each VSe2 layer were modulated by the interface compared to that of the bulk VSe2 1T phase. The atomic arrangement of the VSe2/BLG heterostructure provides deeper understanding and insight for elucidating the magnetic properties of the van der Waals heterostructure., Comment: 17 pages, 4 figures

Transforming neutral, characterless input motions to embody the distinct style of a notable character in real time is highly compelling for character animation. This paper introduces MOCHA, a novel online motion characterization framework that transfers both motion styles and body proportions from a target character to an input source motion. MOCHA begins by encoding the input motion into a motion feature that structures the body part topology and captures motion dependencies for effective characterization. Central to our framework is the Neural Context Matcher, which generates a motion feature for the target character with the most similar context to the input motion feature. The conditioned autoregressive model of the Neural Context Matcher can produce temporally coherent character features in each time frame. To generate the final characterized pose, our Characterizer network incorporates the characteristic aspects of the target motion feature into the input motion feature while preserving its context. This is achieved through a transformer model that introduces the adaptive instance normalization and context mapping-based cross-attention, effectively injecting the character feature into the source feature. We validate the performance of our framework through comparisons with prior work and an ablation study. Our framework can easily accommodate various applications, including characterization with only sparse input and real-time characterization. Additionally, we contribute a high-quality motion dataset comprising six different characters performing a range of motions, which can serve as a valuable resource for future research., Comment: presented at Siggraph Asia 2023

We investigate elliptic irregular obstacle problems with $p$-growth involving measure data. Emphasis is on the strongly singular case $1 < p \le 2-1/n$, and we obtain several new comparison estimates to prove gradient potential estimates in an intrinsic form. Our approach can be also applied to derive zero-order potential estimates.

Recent advancements in technology have brought forth new forms of interactive applications, such as the social metaverse, where end users interact with each other through their virtual avatars. In such applications, precise full-body tracking is essential for an immersive experience and a sense of embodiment with the virtual avatar. However, current motion capture systems are not easily accessible to end users due to their high cost, the requirement for special skills to operate them, or the discomfort associated with wearable devices. In this paper, we present MOVIN, the data-driven generative method for real-time motion capture with global tracking, using a single LiDAR sensor. Our autoregressive conditional variational autoencoder (CVAE) model learns the distribution of pose variations conditioned on the given 3D point cloud from LiDAR.As a central factor for high-accuracy motion capture, we propose a novel feature encoder to learn the correlation between the historical 3D point cloud data and global, local pose features, resulting in effective learning of the pose prior. Global pose features include root translation, rotation, and foot contacts, while local features comprise joint positions and rotations. Subsequently, a pose generator takes into account the sampled latent variable along with the features from the previous frame to generate a plausible current pose. Our framework accurately predicts the performer's 3D global information and local joint details while effectively considering temporally coherent movements across frames. We demonstrate the effectiveness of our architecture through quantitative and qualitative evaluations, comparing it against state-of-the-art methods. Additionally, we implement a real-time application to showcase our method in real-world scenarios. MOVIN dataset is available at \url{https://movin3d.github.io/movin_pg2023/}.

We introduce unsupervised machine learning techniques in order to identify toric phases of 4d N=1 supersymmetric gauge theories corresponding to the same toric Calabi-Yau 3-fold. These 4d N=1 supersymmetric gauge theories are worldvolume theories of a D3-brane probing a toric Calabi-Yau 3-fold and are realized in terms of a Type IIB brane configuration known as a brane tiling. It corresponds to the skeleton graph of the coamoeba projection of the mirror curve associated to the toric Calabi-Yau 3-fold. When we vary the complex structure moduli of the mirror Calabi-Yau 3-fold, the coamoeba and the corresponding brane tilings change their shape, giving rise to different toric phases related by Seiberg duality. We illustrate that by employing techniques such as principal component analysis (PCA) and t-distributed stochastic neighbor embedding (t-SNE), we can project the space of coamoeba labelled by complex structure moduli down to a lower dimensional phase space with phase boundaries corresponding to Seiberg duality. In this work, we illustrate this technique by obtaining a 2-dimensional phase diagram for brane tilings corresponding to the cone over the zeroth Hirzebruch surface F0., Comment: 15 pages, 10 figures, 2 tables

Deep spiking neural networks (SNNs) are promising neural networks for their model capacity from deep neural network architecture and energy efficiency from SNNs' operations. To train deep SNNs, recently, spatio-temporal backpropagation (STBP) with surrogate gradient was proposed. Although deep SNNs have been successfully trained with STBP, they cannot fully utilize spike information. In this work, we proposed gradient scaling with local spike information, which is the relation between pre- and post-synaptic spikes. Considering the causality between spikes, we could enhance the training performance of deep SNNs. According to our experiments, we could achieve higher accuracy with lower spikes by adopting the gradient scaling on image classification tasks, such as CIFAR10 and CIFAR100., Comment: ICML-23 Localized Learning Workshop: Decentralized Model Updates via Non-Global Objectives