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We formulate a positivity conjecture relating the Verlinde ring associated with an untwisted affine Lie algebra at a positive integer level and a subcategory of finite-dimensional representations over the corresponding quantum affine algebra with a cluster algebra structure. Specifically, we consider a ring homomorphism from the Grothendieck ring of this representation category to the Verlinde ring and conjecture that every object in the category has a positive image under this map. We prove this conjecture in certain cases where the underlying simple Lie algebra is simply-laced with level 2 or of type $A_1$ at an arbitrary level. The proof employs the close connection between this category and cluster algebras of finite cluster type. As further evidence for the conjecture, we show that for any level, all objects have positive quantum dimensions under the assumption that some Kirillov-Reshetikhin modules have positive quantum dimensions., Comment: 46 pages

Missing values are a common problem that poses significant challenges to data analysis and machine learning. This problem necessitates the development of an effective imputation method to fill in the missing values accurately, thereby enhancing the overall quality and utility of the datasets. Existing imputation methods, however, fall short of explicitly considering the `missingness' information in the data during the embedding initialization stage and modeling the entangled feature and sample correlations during the learning process, thus leading to inferior performance. We propose M$^3$-Impute, which aims to explicitly leverage the missingness information and such correlations with novel masking schemes. M$^3$-Impute first models the data as a bipartite graph and uses a graph neural network to learn node embeddings, where the refined embedding initialization process directly incorporates the missingness information. They are then optimized through M$^3$-Impute's novel feature correlation unit (FRU) and sample correlation unit (SRU) that effectively captures feature and sample correlations for imputation. Experiment results on 25 benchmark datasets under three different missingness settings show the effectiveness of M$^3$-Impute by achieving 20 best and 4 second-best MAE scores on average.

When working with 3D facial data, improving fidelity and avoiding the uncanny valley effect is critically dependent on accurate 3D facial performance capture. Because such methods are expensive and due to the widespread availability of 2D videos, recent methods have focused on how to perform monocular 3D face tracking. However, these methods often fall short in capturing precise facial movements due to limitations in their network architecture, training, and evaluation processes. Addressing these challenges, we propose a novel face tracker, FlowFace, that introduces an innovative 2D alignment network for dense per-vertex alignment. Unlike prior work, FlowFace is trained on high-quality 3D scan annotations rather than weak supervision or synthetic data. Our 3D model fitting module jointly fits a 3D face model from one or many observations, integrating existing neutral shape priors for enhanced identity and expression disentanglement and per-vertex deformations for detailed facial feature reconstruction. Additionally, we propose a novel metric and benchmark for assessing tracking accuracy. Our method exhibits superior performance on both custom and publicly available benchmarks. We further validate the effectiveness of our tracker by generating high-quality 3D data from 2D videos, which leads to performance gains on downstream tasks., Comment: 22 pages, 25 figures, to be published in CVPR 2024

Graph neural networks have been shown successful in recent years. While different GNN architectures and training systems have been developed, GNN training on large-scale real-world graphs still remains challenging. Existing distributed systems load the entire graph in memory for graph partitioning, requiring a huge memory space to process large graphs and thus hindering GNN training on such large graphs using commodity workstations. In this paper, we propose CATGNN, a cost-efficient and scalable distributed GNN training system which focuses on scaling GNN training to billion-scale or larger graphs under limited computational resources. Among other features, it takes a stream of edges as input, instead of loading the entire graph in memory, for partitioning. We also propose a novel streaming partitioning algorithm named SPRING for distributed GNN training. We verify the correctness and effectiveness of CATGNN with SPRING on 16 open datasets. In particular, we demonstrate that CATGNN can handle the largest publicly available dataset with limited memory, which would have been infeasible without increasing the memory space. SPRING also outperforms state-of-the-art partitioning algorithms significantly, with a 50% reduction in replication factor on average.

We grew (Hg,Re)Ba$_2$Ca$_2$Cu$_3$O$_{8+\delta}$ ((Hg,Re)1223) single crystals with good reproducibility via the single-step flux method using monoxides as raw materials. A double-sealing method using a thick-walled quartz tube and a stainless-steel container was adopted for explosion protection. The maximum crystal size was approximately 1 mm x 1 mm in the ab plane and 0.04 mm in thickness. The crystal was square-shaped, reflecting the tetragonal crystal structure of (Hg,Re)1223. Magnetic susceptibility measurements indicated a critical temperature of 130 K. The in-plane resistivity exhibited a linear temperature dependence, indicating that the sample was close to optimal doping level. The out-of-plane resistivity was also measured, and the anisotropy parameter was 250-650 at 300 K., Comment: 21 pages, 9 figures, 2 tables

Advanced techniques using Neural Radiance Fields (NeRF), Signed Distance Fields (SDF), and Occupancy Fields have recently emerged as solutions for 3D indoor scene reconstruction. We introduce a novel two-phase learning approach, H2O-SDF, that discriminates between object and non-object regions within indoor environments. This method achieves a nuanced balance, carefully preserving the geometric integrity of room layouts while also capturing intricate surface details of specific objects. A cornerstone of our two-phase learning framework is the introduction of the Object Surface Field (OSF), a novel concept designed to mitigate the persistent vanishing gradient problem that has previously hindered the capture of high-frequency details in other methods. Our proposed approach is validated through several experiments that include ablation studies.

The Fricke-Macbeath surface is the unique Hurwitz surface of genus 7 with 504 conformal automorphisms. In this paper, we prove that the first eigenvalue of the Laplacian on the Fricke-Macbeath surface has a sevenfold multiplicity and contained in the interval $[1.23, 1.26]$. Further, we numerically identify the 7-dimensional representation of its automorphism group corresponding to the eigenspace associated to the first eigenvalue. We also determine the Dirichlet domain centered at 0 for a Fuchsian group that uniformizes the Fricke-Macbeath surface, identifying the algebraic coordinates for its vertices., Comment: 40 pages, v2: minor corrections

Text-driven localized editing of 3D objects is particularly difficult as locally mixing the original 3D object with the intended new object and style effects without distorting the object's form is not a straightforward process. To address this issue, we propose a novel NeRF-based model, Blending-NeRF, which consists of two NeRF networks: pretrained NeRF and editable NeRF. Additionally, we introduce new blending operations that allow Blending-NeRF to properly edit target regions which are localized by text. By using a pretrained vision-language aligned model, CLIP, we guide Blending-NeRF to add new objects with varying colors and densities, modify textures, and remove parts of the original object. Our extensive experiments demonstrate that Blending-NeRF produces naturally and locally edited 3D objects from various text prompts. Our project page is available at https://seokhunchoi.github.io/Blending-NeRF/, Comment: Accepted to ICCV 2023. The first two authors contributed equally to this work

In this paper, we study the problem of minimizing the spread of a viral epidemic when immunization takes a non-negligible amount of time to take into effect. Specifically, our problem is to determine which set of nodes to be vaccinated when vaccines take a random amount of time in order to maximize the total reward, which is the expected number of saved nodes. We first provide a mathematical analysis for the reward function of vaccinating an arbitrary number of nodes when there is a single source of infection. While it is infeasible to obtain the optimal solution analytically due to the combinatorial nature of the problem, we establish that the problem is a monotone submodular maximization problem and develop a greedy algorithm that achieves a $(1\!-\!1/e)$-approximation. We further extend the scenario to the ones with multiple infection sources and discuss how the greedy algorithm can be applied systematically for the multiple-source scenarios. We finally present extensive simulation results to demonstrate the superiority of our greedy algorithm over other baseline vaccination strategies., Comment: IFIP Networking 2023

For searching a new chemical material which satisfies the target characteristic value, for example emission wavelength, many cut and trial of experiments/calculations are required since the chemical space is astronomically large (organic molecules generates >10^60 candidates). Extracting feature importance is a method to reduce the chemical space, and limiting the search space to those features leads to shorter development time. Quantum computer can generate sampling data faster than classical computers, and this property is utilized to extract feature importance. In this paper, quantum annealer was used as a sampler to make data for extracting feature importance of material properties. By screening the chemical space with feature importance, it was found that the chemical space can be reduced to less than 1 percent. This result suggests that the acceleration of material research can be achievable.

Floor labels of crowdsourced RF signals are crucial for many smart-city applications, such as multi-floor indoor localization, geofencing, and robot surveillance. To build a prediction model to identify the floor number of a new RF signal upon its measurement, conventional approaches using the crowdsourced RF signals assume that at least few labeled signal samples are available on each floor. In this work, we push the envelope further and demonstrate that it is technically feasible to enable such floor identification with only one floor-labeled signal sample on the bottom floor while having the rest of signal samples unlabeled. We propose FIS-ONE, a novel floor identification system with only one labeled sample. FIS-ONE consists of two steps, namely signal clustering and cluster indexing. We first build a bipartite graph to model the RF signal samples and obtain a latent representation of each node (each signal sample) using our attention-based graph neural network model so that the RF signal samples can be clustered more accurately. Then, we tackle the problem of indexing the clusters with proper floor labels, by leveraging the observation that signals from an access point can be detected on different floors, i.e., signal spillover. Specifically, we formulate a cluster indexing problem as a combinatorial optimization problem and show that it is equivalent to solving a traveling salesman problem, whose (near-)optimal solution can be found efficiently. We have implemented FIS-ONE and validated its effectiveness on the Microsoft dataset and in three large shopping malls. Our results show that FIS-ONE outperforms other baseline algorithms significantly, with up to 23% improvement in adjusted rand index and 25% improvement in normalized mutual information using only one floor-labeled signal sample., Comment: Accepted by IEEE ICDCS 2023

To design fast neural networks, many works have been focusing on reducing the number of floating-point operations (FLOPs). We observe that such reduction in FLOPs, however, does not necessarily lead to a similar level of reduction in latency. This mainly stems from inefficiently low floating-point operations per second (FLOPS). To achieve faster networks, we revisit popular operators and demonstrate that such low FLOPS is mainly due to frequent memory access of the operators, especially the depthwise convolution. We hence propose a novel partial convolution (PConv) that extracts spatial features more efficiently, by cutting down redundant computation and memory access simultaneously. Building upon our PConv, we further propose FasterNet, a new family of neural networks, which attains substantially higher running speed than others on a wide range of devices, without compromising on accuracy for various vision tasks. For example, on ImageNet-1k, our tiny FasterNet-T0 is $2.8\times$, $3.3\times$, and $2.4\times$ faster than MobileViT-XXS on GPU, CPU, and ARM processors, respectively, while being $2.9\%$ more accurate. Our large FasterNet-L achieves impressive $83.5\%$ top-1 accuracy, on par with the emerging Swin-B, while having $36\%$ higher inference throughput on GPU, as well as saving $37\%$ compute time on CPU. Code is available at \url{https://github.com/JierunChen/FasterNet}., Comment: Accepted to CVPR 2023

Barcode magnetic nanowires typically comprise a multilayer magnetic structure in a single body with more than one segment type. Interestingly, owing to selective functionalization and novel interactions between the layers, barcode magnetic nanowires have attracted significant attention, particularly in the field of bioengineering. However, an analysis of their magnetic properties at the individual nanowire level remains challenging. With this background, herein, we investigated the characterization of magnetic nanowires at room temperature under ambient conditions based on magnetic images obtained via wide-field quantum microscopy with nitrogen-vacancy centers in diamond. Consequently, we could extract critical magnetic properties, such as the saturation magnetization and coercivity, of single nanowires by comparing the experimental results with those of micromagnetic simulations. This study opens up the possibility for a versatile characterization method suited to individual magnetic nanowires., Comment: main text (20 pages, 5 figures), supplementary materials (9 pages, 8 figures)

The magnetic response is a state-defining property of superconductors. The magnetic flux penetrates type-II bulk superconductors by forming quantum vortices when the enclosed magnetic flux is equal to the magnetic flux quantum. The flux quantum is the universal quantity that depends only on the ratio of fundamental constants: the electron charge and the Planck constant. This work investigates the vortex state in the hole-overdoped Ba$_{1-x}$K$_x$Fe$_2$As$_2$ by using scanning superconducting quantum interference device (SQUID) magnetometry. We observed quantum vortices that carry only a fraction of the flux quantum, which vary continuously with temperature. This finding establishes the phenomenon that superconductors support quantum vortices with non-universally quantized magnetic flux. Furthermore, the demonstrations of the mobility of the fractional vortices and the manipulability of their positions open up a route for future fluxonics applications., Comment: 19 pages, 9 figures

Theoretically, materials that break multiple symmetries allow, under certain conditions, the formation of four-fermion condensates above the superconducting critical temperature. Such states can be stabilized by phase fluctuations. Recently a fermionic quadrupling condensate that breaks the $Z_2$ time-reversal symmetry was reported in Ba$_{\rm 1-x}$K$_{\rm x}$Fe$_{2}$As$_{2}$ [V. Grinenko et al., Nat. Phys. 17, 1254 (2021)]. Evidence for the new state of matter comes from muon-spin rotation, transport, thermoelectric, and ultrasound experiments. Observing a specific heat anomaly is a very important signature of a transition to a new state of matter. However, a fluctuation-induced specific heat singularity is usually very challenging to resolve from a background of other contributions. Here, we report on detecting two anomalies in the specific heat of Ba$_{\rm 1-x}$K$_{\rm x}$Fe$_{2}$As$_{2}$ at zero magnetic field. The anomaly at the higher temperature is accompanied by the appearance of a spontaneous Nernst effect, indicating broken time-reversal ($Z_2$) symmetry. The second anomaly at the lower temperature coincides with the transition to a zero resistance state, indicating superconductivity breaking the $U(1)$ gauge symmetry. Our data provide calorimetric evidence for the $Z_2$ phase formation above the superconducting phase transition., Comment: 12 pages, 3 figures and Supplementary information

Harmonic functions are abundant in nature, appearing in limiting cases of Maxwell's, Navier-Stokes equations, the heat and the wave equation. Consequently, there are many applications of harmonic functions from industrial process optimisation to robotic path planning and the calculation of first exit times of random walks. Despite their ubiquity and relevance, there have been few attempts to incorporate inductive biases towards harmonic functions in machine learning contexts. In this work, we demonstrate effective means of representing harmonic functions in neural networks and extend such results also to quantum neural networks to demonstrate the generality of our approach. We benchmark our approaches against (quantum) physics-informed neural networks, where we show favourable performance., Comment: 12 pages (main), 7 pages (supplementary), 7 figures

Graph neural networks (GNNs) have received great attention due to their success in various graph-related learning tasks. Several GNN frameworks have then been developed for fast and easy implementation of GNN models. Despite their popularity, they are not well documented, and their implementations and system performance have not been well understood. In particular, unlike the traditional GNNs that are trained based on the entire graph in a full-batch manner, recent GNNs have been developed with different graph sampling techniques for mini-batch training of GNNs on large graphs. While they improve the scalability, their training times still depend on the implementations in the frameworks as sampling and its associated operations can introduce non-negligible overhead and computational cost. In addition, it is unknown how much the frameworks are 'eco-friendly' from a green computing perspective. In this paper, we provide an in-depth study of two mainstream GNN frameworks along with three state-of-the-art GNNs to analyze their performance in terms of runtime and power/energy consumption. We conduct extensive benchmark experiments at several different levels and present detailed analysis results and observations, which could be helpful for further improvement and optimization., Comment: Accepted by IEEE IISWC 2022

We study the problem of floor identification for radiofrequency (RF) signal samples obtained in a crowdsourced manner, where the signal samples are highly heterogeneous and most samples lack their floor labels. We propose GRAFICS, a graph embedding-based floor identification system. GRAFICS first builds a highly versatile bipartite graph model, having APs on one side and signal samples on the other. GRAFICS then learns the low-dimensional embeddings of signal samples via a novel graph embedding algorithm named E-LINE. GRAFICS finally clusters the node embeddings along with the embeddings of a few labeled samples through a proximity-based hierarchical clustering, which eases the floor identification of every new sample. We validate the effectiveness of GRAFICS based on two large-scale datasets that contain RF signal records from 204 buildings in Hangzhou, China, and five buildings in Hong Kong. Our experiment results show that GRAFICS achieves highly accurate prediction performance with only a few labeled samples (96% in both micro- and macro-F scores) and significantly outperforms several state-of-the-art algorithms (by about 45% improvement in micro-F score and 53% in macro-F score)., Comment: Accepted by IEEE ICDCS 2022

In applications such as elderly care, dementia anti-wandering and pandemic control, it is important to ensure that people are within a predefined area for their safety and well-being. We propose GEM, a practical, semi-supervised Geofencing system with network EMbedding, which is based only on ambient radio frequency (RF) signals. GEM models measured RF signal records as a weighted bipartite graph. With access points on one side and signal records on the other, it is able to precisely capture the relationships between signal records. GEM then learns node embeddings from the graph via a novel bipartite network embedding algorithm called BiSAGE, based on a Bipartite graph neural network with a novel bi-level SAmple and aggreGatE mechanism and non-uniform neighborhood sampling. Using the learned embeddings, GEM finally builds a one-class classification model via an enhanced histogram-based algorithm for in-out detection, i.e., to detect whether the user is inside the area or not. This model also keeps on improving with newly collected signal records. We demonstrate through extensive experiments in diverse environments that GEM shows state-of-the-art performance with up to 34% improvement in F-score. BiSAGE in GEM leads to a 54% improvement in F-score, as compared to the one without BiSAGE., Comment: A conference version of this paper will appear in IEEE ICDE 2023

The Explicit Congestion Notification (ECN) field has taken on new importance due to Low Latency, Low Loss, and Scalable throughput (L4S) technology designed for extremely latency-sensitive applications (such as cloud games and cloud-rendered VR/AR). ECN and L4S need to be supported by the client and server but also all devices in the network path. We have identified that "ECN bleaching", where an intermediate network device clears or "bleaches" the ECN flags, occurs and quantified how often that happens, why it happens and identified where in the network it happens. In this research, we conduct a comprehensive measurement study on end-to-end traversal of the ECN field using probes deployed on the Internet across different varied clients and servers. Using these probes, we identify and locate instances of ECN bleaching on various network paths on the Internet. In our six months of measurements, conducted in late 2021 and early 2022, we found the prevalence varied considerably from network to network. One cloud provider and two cellular providers bleach the ECN field as a matter of policy. Of the rest, we found 1,112 out of 129,252 routers, 4.17% of paths we measured showed ECN bleaching., Comment: 13 pages, 11 figures

The superconducting properties and structural parameters, including the Gr\"uneisen parameter ({\gamma}G), of the BiCh2-based (Ch: S, Se) layered superconductor LaO0.5F0.5BiS2-xSex were investigated. The superconducting transition temperature (Tc) increased with increasing Se concentration (x), and bulk superconductivity was induced by Se substitution. {\gamma}G exhibited a larger value when x greater than 0.4, where the superconducting properties were improved. These results suggest that the increase of lattice anharmonicity is preferable for superconductivity in LaO0.5F0.5BiS2-xSex. The discussion includes data for related superconductors REO0.5F0.5BiS2 (RE = Pr, Nd), where a positive correlation between {\gamma}G and Tc is revealed for Se-poor samples. In addition, specific heat analyses suggest the presence of a low-energy optical phonon mode for LaO0.5F0.5BiS2-xSex., Comment: 23 pages, 7 figures, supplemental data

We propose a novel algorithm for monocular depth estimation that decomposes a metric depth map into a normalized depth map and scale features. The proposed network is composed of a shared encoder and three decoders, called G-Net, N-Net, and M-Net, which estimate gradient maps, a normalized depth map, and a metric depth map, respectively. M-Net learns to estimate metric depths more accurately using relative depth features extracted by G-Net and N-Net. The proposed algorithm has the advantage that it can use datasets without metric depth labels to improve the performance of metric depth estimation. Experimental results on various datasets demonstrate that the proposed algorithm not only provides competitive performance to state-of-the-art algorithms but also yields acceptable results even when only a small amount of metric depth data is available for its training.