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We introduce sliced optimal transport dataset distance (s-OTDD), a model-agnostic, embedding-agnostic approach for dataset comparison that requires no training, is robust to variations in the number of classes, and can handle disjoint label sets. The core innovation is Moment Transform Projection (MTP), which maps a label, represented as a distribution over features, to a real number. Using MTP, we derive a data point projection that transforms datasets into one-dimensional distributions. The s-OTDD is defined as the expected Wasserstein distance between the projected distributions, with respect to random projection parameters. Leveraging the closed form solution of one-dimensional optimal transport, s-OTDD achieves (near-)linear computational complexity in the number of data points and feature dimensions and is independent of the number of classes. With its geometrically meaningful projection, s-OTDD strongly correlates with the optimal transport dataset distance while being more efficient than existing dataset discrepancy measures. Moreover, it correlates well with the performance gap in transfer learning and classification accuracy in data augmentation., Comment: 23 pages, 9 figures

The Mekong Delta Region of Vietnam faces increasing dengue risks driven by urbanization, globalization, and climate change. This study introduces a probabilistic forecasting model for predicting dengue incidence and outbreaks with one to three month lead times, integrating meteorological, sociodemographic, preventive, and epidemiological data. Seventy-two models were evaluated, and an ensemble combining top-performing spatiotemporal, supervised PCA, and semi-mechanistic hhh4 frameworks was developed. Using data from 2004-2022 for training, validation, and evaluation, the ensemble model demonstrated 69% accuracy at a 3-month horizon, outperforming a baseline model. While effective, its performance declined in years with atypical seasonality, such as 2019 and 2022. The model provides critical lead time for targeted dengue prevention and control measures, addressing a growing public health need in the region., Comment: 34 pages, 6 figures

We introduce OneDiffusion, a versatile, large-scale diffusion model that seamlessly supports bidirectional image synthesis and understanding across diverse tasks. It enables conditional generation from inputs such as text, depth, pose, layout, and semantic maps, while also handling tasks like image deblurring, upscaling, and reverse processes such as depth estimation and segmentation. Additionally, OneDiffusion allows for multi-view generation, camera pose estimation, and instant personalization using sequential image inputs. Our model takes a straightforward yet effective approach by treating all tasks as frame sequences with varying noise scales during training, allowing any frame to act as a conditioning image at inference time. Our unified training framework removes the need for specialized architectures, supports scalable multi-task training, and adapts smoothly to any resolution, enhancing both generalization and scalability. Experimental results demonstrate competitive performance across tasks in both generation and prediction such as text-to-image, multiview generation, ID preservation, depth estimation and camera pose estimation despite relatively small training dataset. Our code and checkpoint are freely available at https://github.com/lehduong/OneDiffusion, Comment: two first authors contribute equally

This paper investigates, via methods from the theory of probability on trees, critical phenomena in stochastic cascade models of Yule type, and applies these methods to the problem of uniqueness and nonuniqueness of solutions of particular mean flow equations. For linear equations, Feller's classic discovery of the relationship between critical stochastic explosion phenomena for Markov processes and uniqueness and nonuniqueness of solutions to the associated Kolmogorov equation partly illustrates the spirit of the present paper. New methods are introduced to explore the effects that stochastic critical phenomena, such as stochastic explosion, hyperexplosion, t-leaf percolation, have on their corresponding mean flow equations. These methods are illustrated in the context of two non-local differential equations that are related by linearization, the pantograph and the $\alpha$-Riccati equations. In particular, stochastic recursions, stochastic Picard iterations and transformation of solutions processes associated with these equations, are used to establish a `one-to-many principle' for their solutions. The development also includes an application of Feller's classical theory of jump Markov processes to a certain class of pantograph equations that appears to be new., Comment: 44 pages, 9 figures

Understanding the molecular-level structure and dynamics of ice surfaces is crucial for deciphering several chemical, physical, and atmospheric processes. Vibrational sum-frequency generation (SFG) spectroscopy is the most prominent tool for probing the molecular-level structure of the air--ice interface as it is a surface-specific technique, but the molecular interpretation of SFG spectra is challenging. This study utilizes a machine-learning potential, along with dipole and polarizability models trained on ab initio data, to calculate the SFG spectrum of the air--ice interface. At temperatures below ice surface premelting, our simulations support the presence of a proton-ordered arrangement at the Ice Ih surface, similar to that seen in Ice XI. Additionally, our simulations provide insight into the assignment of SFG peaks to specific molecular configurations where possible and assess the contribution of subsurface layers to the overall SFG spectrum. These insights enhance our understanding and interpretation of vibrational studies of environmental chemistry at the ice surface., Comment: 27 pages (including refs and SI) 5 main text figures

How is the irreversibility of a high-dimensional chaotic system controlled by the heterogeneity in the non-reciprocal interactions among its elements? In this paper, we address this question using a stochastic model of random recurrent neural networks that undergoes a transition from quiescence to chaos at a critical heterogeneity. In the thermodynamic limit, using dynamical mean field theory, we obtain an exact expression for the averaged entropy production rate - a measure of irreversibility - for any heterogeneity level J. We show how this quantity becomes a constant at the onset of chaos while changing its functional form upon crossing this point. The latter can be elucidated by closed-form approximations valid for below and slightly above the critical point and for large J., Comment: 13 pages, 4 figures

We present Piva (Preserving Identity with Variational Score Distillation), a novel optimization-based method for editing images and 3D models based on diffusion models. Specifically, our approach is inspired by the recently proposed method for 2D image editing - Delta Denoising Score (DDS). We pinpoint the limitations in DDS for 2D and 3D editing, which causes detail loss and over-saturation. To address this, we propose an additional score distillation term that enforces identity preservation. This results in a more stable editing process, gradually optimizing NeRF models to match target prompts while retaining crucial input characteristics. We demonstrate the effectiveness of our approach in zero-shot image and neural field editing. Our method successfully alters visual attributes, adds both subtle and substantial structural elements, translates shapes, and achieves competitive results on standard 2D and 3D editing benchmarks. Additionally, our method imposes no constraints like masking or pre-training, making it compatible with a wide range of pre-trained diffusion models. This allows for versatile editing without needing neural field-to-mesh conversion, offering a more user-friendly experience., Comment: 22 pages, 14 figures

Neural Radiance Fields (NeRFs) have emerged as powerful tools for capturing detailed 3D scenes through continuous volumetric representations. Recent NeRFs utilize feature grids to improve rendering quality and speed; however, these representations introduce significant storage overhead. This paper presents a novel method for efficiently compressing a grid-based NeRF model, addressing the storage overhead concern. Our approach is based on the non-linear transform coding paradigm, employing neural compression for compressing the model's feature grids. Due to the lack of training data involving many i.i.d scenes, we design an encoder-free, end-to-end optimized approach for individual scenes, using lightweight decoders. To leverage the spatial inhomogeneity of the latent feature grids, we introduce an importance-weighted rate-distortion objective and a sparse entropy model employing a masking mechanism. Our experimental results validate that our proposed method surpasses existing works in terms of grid-based NeRF compression efficacy and reconstruction quality., Comment: Accepted to ICML 2024

The electronic properties and optical response of ice and water are intricately shaped by their molecular structure, including the quantum mechanical nature of hydrogen atoms. In spite of numerous studies appeared over decades, a comprehensive understanding of the effect of the nuclear quantum motion on the electronic structure of water and ice at finite temperatures remains elusive. Here, we utilize molecular simulations that harness the efficiency of machine-learning potentials and many-body perturbation theory to assess the impact of nuclear quantum effects on the electronic structure of water and hexagonal ice. By comparing the results of path-integral and classical simulations, we find that including nuclear quantum effects leads to a larger renormalization of the fundamental gap of ice, compared to that of water, eventually leading to a comparable gap in the two systems, consistent with experimental estimates. Our calculations suggest that the quantum fluctuations responsible for an increased delocalization of protons in ice, relative to water, are a key factor leading to the enhancement of nuclear quantum effects on the electronic structure of ice., Comment: 16 pages, 4 figures

We derive exact equations for the spectral density of sparse networks with an arbitrary distribution of the number of single edges and triangles per node. These equations enable a systematic investigation of the effect of clustering on the spectral properties of the network adjacency matrix. In the case of heterogeneous networks, we demonstrate that the spectral density becomes more symmetric as the fluctuations in the triangle-degree sequence increase. This phenomenon is explained by the small clustering coefficient of networks with a large variance of the triangle-degree distribution. In the homogeneous case of regular clustered networks, we find that both perturbative and non-perturbative approximations fail to predict the spectral density in the high-connectivity limit. This suggests that traditional large-degree approximations may be ineffective in studying the spectral properties of networks with more complex motifs. Our theoretical results are fully confirmed by numerical diagonalizations of finite adjacency matrices., Comment: 13 pages, 7 figures

In this work, we demonstrate the formation and electronic influence of lateral heterointerfaces in FeSn containing Kagome and honeycomb layers. Lateral heterostructures offer spatially resolved property control, enabling the integration of dissimilar materials and promoting phenomena not typically observed in vertical heterostructures. Using the molecular beam epitaxy technique, we achieve a controllable synthesis of lateral heterostructures in the Kagome metal FeSn. With scanning tunneling microscopy/spectroscopy in conjunction with first-principles calculations, we provide a comprehensive understanding of the bonding motif connecting the Fe3Sn-terminated Kagome and Sn2-terminated honeycomb surfaces. More importantly, we reveal a distance-dependent evolution of the electronic states in the vicinity of the heterointerfaces. This evolution is significantly influenced by the orbital character of the flat bands. Our findings suggest an approach to modulate the electronic properties of the Kagome lattice, which should be beneficial for the development of future quantum devices., Comment: To appear ACS Nano

In this work, we have proposed an approach for improving the GCN for predicting ratings in social networks. Our model is expanded from the standard model with several layers of transformer architecture. The main focus of the paper is on the encoder architecture for node embedding in the network. Using the embedding layer from the graph-based convolution layer, the attention mechanism could rearrange the feature space to get a more efficient embedding for the downstream task. The experiments showed that our proposed architecture achieves better performance than GCN on the traditional link prediction task.

The ability to rapidly develop materials with desired properties has a transformative impact on a broad range of emerging technologies. In this work, we introduce a new framework based on the diffusion model, a recent generative machine learning method to predict 3D structures of disordered materials from a target property. For demonstration, we apply the model to identify the atomic structures of amorphous carbons ($a$-C) as a representative material system from the target X-ray absorption near edge structure (XANES) spectra--a common experimental technique to probe atomic structures of materials. We show that conditional generation guided by XANES spectra reproduces key features of the target structures. Furthermore, we show that our model can steer the generative process to tailor atomic arrangements for a specific XANES spectrum. Finally, our generative model exhibits a remarkable scale-agnostic property, thereby enabling generation of realistic, large-scale structures through learning from a small-scale dataset (i.e., with small unit cells). Our work represents a significant stride in bridging the gap between materials characterization and atomic structure determination; in addition, it can be leveraged for materials discovery in exploring various material properties as targeted.

Accurate simulation of detector responses to hadrons is paramount for all physics programs at the Large Hadron Collider (LHC). Central to this simulation is the modeling of hadronic interactions. Unfortunately, the absence of first-principle theoretical guidance has made this a formidable challenge. The state-of-the-art simulation tool, \textsc{Geant4}, currently relies on phenomenology-inspired parametric models. Each model is designed to simulate hadronic interactions within specific energy ranges and for particular types of hadrons. Despite dedicated tuning efforts, these models sometimes fail to describe the data in certain physics processes accurately. Furthermore, fine-tuning these models with new measurements is laborious. Our research endeavors to leverage generative models to simulate hadronic interactions. While our ultimate goal is to train a generative model using experimental data, we have taken a crucial step by training conditional normalizing flow models with \textsc{Geant4} simulation data. Our work marks a significant stride toward developing a fully differentiable and data-driven model for hadronic interactions in High Energy and Nuclear Physics., Comment: 7 pages, 5 figures, Proceeding of 26th International Conference On Computing High Energy & Nuclear Physics (CHEP 2023)

Neuroscience research has evolved to generate increasingly large and complex experimental data sets, and advanced data science tools are taking on central roles in neuroscience research. Neurodata Without Borders (NWB), a standard language for neurophysiology data, has recently emerged as a powerful solution for data management, analysis, and sharing. We here discuss our efforts to implement NWB data science pipelines. We describe general principles and specific use cases that illustrate successes, challenges, and non-trivial decisions in software engineering. We hope that our experience can provide guidance for the neuroscience community and help bridge the gap between experimental neuroscience and data science., Comment: 32 pages, 9 figures

Machine learning interatomic potentials (MLIPs) enable the accurate simulation of materials at larger sizes and time scales, and play increasingly important roles in the computational understanding and design of materials. However, MLIPs are only as accurate and robust as the data they are trained on. In this work, we present DImensionality-Reduced Encoded Clusters with sTratified (DIRECT) sampling as an approach to select a robust training set of structures from a large and complex configuration space. By applying DIRECT sampling on the Materials Project relaxation trajectories dataset with over one million structures and 89 elements, we develop an improved materials 3-body graph network (M3GNet) universal potential that extrapolate more reliably to unseen structures. We further show that molecular dynamics (MD) simulations with universal potentials such as M3GNet can be used in place of expensive \textit{ab initio} MD to rapidly create a large configuration space for target materials systems. Combined with DIRECT sampling, we develop a highly reliable moment tensor potential for Ti-H system without the need for iterative optimization. This work paves the way towards robust high throughput development of MLIPs across any compositional complexity.

Zeolites are inorganic materials known for their diversity of applications, synthesis conditions, and resulting polymorphs. Although their synthesis is controlled both by inorganic and organic synthesis conditions, computational studies of zeolite synthesis have focused mostly on organic template design. In this work, we use a strong distance metric between crystal structures and machine learning (ML) to create inorganic synthesis maps in zeolites. Starting with 253 known zeolites, we show how the continuous distances between frameworks reproduce inorganic synthesis conditions from the literature without using labels such as building units. An unsupervised learning analysis shows that neighboring zeolites according to our metric often share similar inorganic synthesis conditions, even in template-based routes. In combination with ML classifiers, we find synthesis-structure relationships for 14 common inorganic conditions in zeolites, namely Al, B, Be, Ca, Co, F, Ga, Ge, K, Mg, Na, P, Si, and Zn. By explaining the model predictions, we demonstrate how (dis)similarities towards known structures can be used as features for the synthesis space. Finally, we show how these methods can be used to predict inorganic synthesis conditions for unrealized frameworks in hypothetical databases and interpret the outcomes by extracting local structural patterns from zeolites. In combination with template design, this work can accelerate the exploration of the space of synthesis conditions for zeolites.

The use of social robots as instruments for social mediation has been gaining traction in the field of Human-Robot Interaction (HRI). So far, the design of such robots and their behaviors is often driven by technological platforms and experimental setups in controlled laboratory environments. To address complex social relationships in the real world, it is crucial to consider the actual needs and consequences of the situations found therein. This includes understanding when a mediator is necessary, what specific role such a robot could play, and how it moderates human social dynamics. In this paper, we discuss six relevant roles for robotic mediators that we identified by investigating a collection of videos showing realistic group situations. We further discuss mediation behaviors and target measures to evaluate the success of such interventions. We hope that our findings can inspire future research on robot-assisted social mediation by highlighting a wider set of mediation applications than those found in prior studies. Specifically, we aim to inform the categorization and selection of interaction scenarios that reflect real situations, where a mediation robot can have a positive and meaningful impact on group dynamics.

The study of adaptive dynamics, involving many degrees of freedom on two separated timescales, one for fast changes of state variables and another for the slow adaptation of parameters controlling the former's dynamics is crucial for understanding feedback mechanisms underlying evolution and learning. We present a path-integral approach \`a la Martin-Siggia-Rose-De Dominicis-Janssen (MSRDJ) to analyse nonequilibrium phase transitions in such dynamical systems. As an illustration, we apply our framework to the adaptation of gene-regulatory networks under a dynamic genotype-phenotype map: phenotypic variations are shaped by the fast stochastic gene-expression dynamics and are coupled to the slowly evolving distribution of genotypes, each encoded by a network structure. We establish that under this map, genotypes corresponding to reciprocal networks of coherent feedback loops are selected within an intermediate range of environmental noise, leading to phenotypic robustness., Comment: 30 pages and 2 figures

Given a random sample from a multivariate normal distribution whose covariance matrix is a Toeplitz matrix, we study the largest off-diagonal entry of the sample correlation matrix. Assuming the multivariate normal distribution has the covariance structure of an auto-regressive sequence, we establish a phase transition in the limiting distribution of the largest off-diagonal entry. We show that the limiting distributions are of Gumbel-type (with different parameters) depending on how large or small the parameter of the autoregressive sequence is. At the critical case, we obtain that the limiting distribution is the maximum of two independent random variables of Gumbel distributions. This phase transition establishes the exact threshold at which the auto-regressive covariance structure behaves differently than its counterpart with the covariance matrix equal to the identity. Assuming the covariance matrix is a general Toeplitz matrix, we obtain the limiting distribution of the largest entry under the ultra-high dimensional settings: it is a weighted sum of two independent random variables, one normal and the other following a Gumbel-type law. The counterpart of the non-Gaussian case is also discussed. As an application, we study a high-dimensional covariance testing problem.

An error occurs in a part of the statement and proof of Proposition 2.2 in Jour. Math. Anal. and Appl., 476, (2019), 53-85 that is corrected in this erratum. The revised result reveals a new and unexpected critical phenomenon, having further implications for non-uniqueness of solutions to a nonlinear differential equation of the Riccati type.

We introduce a novel variant of GNN for particle tracking called Hierarchical Graph Neural Network (HGNN). The architecture creates a set of higher-level representations which correspond to tracks and assigns spacepoints to these tracks, allowing disconnected spacepoints to be assigned to the same track, as well as multiple tracks to share the same spacepoint. We propose a novel learnable pooling algorithm called GMPool to generate these higher-level representations called "super-nodes", as well as a new loss function designed for tracking problems and HGNN specifically. On a standard tracking problem, we show that, compared with previous ML-based tracking algorithms, the HGNN has better tracking efficiency performance, better robustness against inefficient input graphs, and better convergence compared with traditional GNNs., Comment: 7 pages, 5 figures, submitted to the 21st International Workshop on Advanced Computing and Analysis Techniques in Physics Research

The relationship between genotype and phenotype plays a crucial role in determining the function and robustness of biological systems. Here the evolution progresses through the change in genotype, whereas the selection is based on the phenotype, and genotype-phenotype relation also evolves. Theory for such phenotypic evolution remains poorly-developed, in contrast to evolution under the fitness landscape determined by genotypes. Here we provide statistical-physics formulation of this problem by introducing replicas for genotype and phenotype. We apply it to an evolution model, in which phenotypes are given by spin configurations; genotypes are interaction matrix for spins to give the Hamiltonian, and the fitness depends only on the configuration of a subset of spins called target. We describe the interplay between the genetic variations and phenotypic variances by noise in this model by our new approach that extends the replica theory for spin-glasses to include spin-replica for phenotypes and coupling-replica for genotypes. Within this framework we obtain a phase diagram of the evolved phenotypes against the noise and selection pressure, where each phase is distinguished by the fitness and overlaps for genotypes and phenotypes. Among the phases, robust fitted phase, relevant to biological evolution, is achieved under the intermediate level of noise (temperature), where robustness to noise and to genetic mutation are correlated, as a result of replica symmetry. We also find a trade-off between maintaining a high fitness level of phenotype and acquiring a robust pattern of genes as well as the dependence of this trade-off on the ratio between the size of the functional (target) part to that of the remaining non-functional (non-target) one. The selection pressure needed to achieve high fitness increases with the fraction of target spins., Comment: 15 pages, 7 figures

Homophily, the tendency of humans to attract each other when sharing similar features, traits, or opinions has been identified as one of the main driving forces behind the formation of structured societies. Here we ask to what extent homophily can explain the formation of social groups, particularly their size distribution. We propose a spin-glass-inspired framework of self-assembly, where opinions are represented as multidimensional spins that dynamically self-assemble into groups; individuals within a group tend to share similar opinions (intra-group homophily), and opinions between individuals belonging to different groups tend to be different (inter-group heterophily). We compute the associated non-trivial phase diagram by solving a self-consistency equation for 'magnetization' (combined average opinion). Below a critical temperature, there exist two stable phases: one ordered with non-zero magnetization and large clusters, the other disordered with zero magnetization and no clusters. The system exhibits a first-order transition to the disordered phase. We analytically derive the group-size distribution that successfully matches empirical group-size distributions from online communities., Comment: 6 pages, 5 pages of SI, to appear in Phys. Rev. Lett

In one-dimensional (1D) systems, electronic interactions lead to a breakdown of Fermi liquid theory and the formation of a Tomonaga-Luttinger Liquid (TLL). The strength of its many-body correlations can be quantified by a single dimensionless parameter, the Luttinger parameter $K$, characterising the competition between the electrons' kinetic and electrostatic energies. Recently, signatures of a TLL have been reported for the topological edge states of quantum spin Hall (QSH) insulators, strictly 1D electronic structures with linear (Dirac) dispersion and spin-momentum locking. Here we show that the many-body interactions in such helical Luttinger Liquid can be effectively controlled by the edge state's dielectric environment. This is reflected in a tunability of the Luttinger parameter $K$, distinct on different edges of the crystal, and extracted to high accuracy from the statistics of tunnelling spectra at tens of tunneling points. The interplay of topology and many-body correlations in 1D helical systems has been suggested as a potential avenue towards realising non-Abelian parafermions.

We use a comprehensive longitudinal dataset on criminal acts over five years in a European country to study specialization in criminal careers. We cluster crime categories by their relative co-occurrence within criminal careers, deriving a natural, data-based taxonomy of criminal specialization. Defining specialists as active criminals who stay within one category of offending behavior, we study their socio-demographic attributes, geographic range, and positions in their collaboration networks, relative to their generalist counterparts. In comparison to generalists, specialists tend to be older, more likely to be female, operate within a smaller geographic range, and collaborate in smaller, more tightly-knit local networks. We observe that specialists are more intensely embedded in criminal networks and find evidence that specialization indeed reflects division of labor and organization.