Miracle-dz/UniFAR-FTUs huggingface dataset:
Monotone comparative statics for submodular functions, with an application to aggregated deferred acceptance

We propose monotone comparative statics results for maximizers of submodular functions, as opposed to maximizers of supermodular functions as in the classical theory put forth by Veinott, Topkis, Milgrom, and Shannon among others. We introduce matrons, a natural structure that is dual to sublattices that generalizes existing structures such as matroids and polymatroids in combinatorial optimization and M-sets in discrete convex analysis. Our monotone comparative statics result is based on a natural order on matrons, which is dual in some sense to Veinott's strong set order on sublattices. As an application, we propose a deferred acceptance algorithm that operates in the case of divisible goods, and we study its convergence properties.
Decoupling by local random unitaries without simultaneous smoothing, and applications to multi-user quantum information tasks

We show that a simple telescoping sum trick, together with the triangle inequality and a tensorisation property of expected-contractive coefficients of random channels, allow us to achieve general simultaneous decoupling for multiple users via local actions. Employing both old [Dupuis et al. Commun. Math. Phys. 328:251-284 (2014)] and new methods [Dupuis, arXiv:2105.05342], we obtain bounds on the expected deviation from ideal decoupling either in the one-shot setting in terms of smooth min-entropies, or the finite block length setting in terms of R\'enyi entropies. These bounds are essentially optimal without the need to address the simultaneous smoothing conjecture, which remains unresolved. This leads to one-shot, finite block length, and asymptotic achievability results for several tasks in quantum Shannon theory, including local randomness extraction of multiple parties, multi-party assisted entanglement concentration, multi-party quantum state merging, and quantum coding for the quantum multiple access channel. Because of the one-shot nature of our protocols, we obtain achievability results without the need for time-sharing, which at the same time leads to easy proofs of the asymptotic coding theorems. We show that our one-shot decoupling bounds furthermore yield achievable rates (so far only conjectured) for all four tasks in compound settings, that is for only partially known i.i. d. source or channel, which are furthermore optimal for entanglement of assistance and state merging.
Meta-multigraph Search: Rethinking Meta-structure on Heterogeneous Information Networks

Meta-structures are widely used to define which subset of neighbors to aggregate information in heterogeneous information networks (HINs). In this work, we investigate existing meta-structures, including meta-path and meta-graph, and observe that they are initially designed manually with fixed patterns and hence are insufficient to encode various rich semantic information on diverse HINs. Through reflection on their limitation, we define a new concept called meta-multigraph as a more expressive and flexible generalization of meta-graph, and propose a stable differentiable search method to automatically optimize the meta-multigraph for specific HINs and tasks. As the flexibility of meta-multigraphs may propagate redundant messages, we further introduce a complex-to-concise (C2C) meta-multigraph that propagates messages from complex to concise along the depth of meta-multigraph. Moreover, we observe that the differentiable search typically suffers from unstable search and a significant gap between the meta-structures in search and evaluation. To this end, we propose a progressive search algorithm by implicitly narrowing the search space to improve search stability and reduce inconsistency. Extensive experiments are conducted on six medium-scale benchmark datasets and one large-scale benchmark dataset over two representative tasks, i.e., node classification and recommendation. Empirical results demonstrate that our search methods can automatically find expressive meta-multigraphs and C2C meta-multigraphs, enabling our model to outperform state-of-the-art heterogeneous graph neural networks.
Massive black holes in galactic nuclei: Theory and Simulations

Massive black holes are fundamental constituents of our cosmos, from the Big Bang to today. Understanding their formation from cosmic dawn, their growth, and the emergence of the first, rare quasars in the early Universe remains one of our greatest theoretical and observational challenges. Hydrodynamic cosmological simulations self-consistently combine the processes of structure formation at cosmological scales with the physics of smaller, galaxy scales. They capture our most realistic understanding of massive black holes and their connection to galaxy formation and have become the primary avenue for theoretical research in this field. The space-based gravitational wave interferometer, LISA, will open up new investigations into the dynamical processes involving massive black holes. Multi-messenger astrophysics brings new exciting prospects for tracing the origin, growth and merger history of massive black holes across cosmic ages.
On the Performance of a Novel Class of Linear System Solvers and Comparison with State-of-The-Art Algorithms

We present a comprehensive computational study of a class of linear system solvers, called {\it Triangle Algorithm} (TA) and {\it Centering Triangle Algorithm} (CTA), developed by Kalantari \cite{kalantari23}. The algorithms compute an approximate solution or minimum-norm solution to $Ax=b$ or $A^TAx=A^Tb$, where $A$ is an $m \times n$ real matrix of arbitrary rank. The algorithms specialize when $A$ is symmetric positive semi-definite. Based on the description and theoretical properties of TA and CTA from \cite{kalantari23}, we give an implementation of the algorithms that is easy-to-use for practitioners, versatile for a wide range of problems, and robust in that our implementation does not necessitate any constraints on $A$. Next, we make computational comparisons of our implementation with the Matlab implementations of two state-of-the-art algorithms, GMRES and ``lsqminnorm". We consider square and rectangular matrices, for $m$ up to $10000$ and $n$ up to $1000000$, encompassing a variety of applications. These results indicate that our implementation outperforms GMRES and ``lsqminnorm"both in runtime and quality of residuals. Moreover, the relative residuals of CTA decrease considerably faster and more consistently than GMRES, and our implementation provides high precision approximation, faster than GMRES reports lack of convergence. With respect to ``lsqminnorm", our implementation runs faster, producing better solutions. Additionally, we present a theoretical study in the dynamics of iterations of residuals in CTA and complement it with revealing visualizations. Lastly, we extend TA for LP feasibility problems, handling non-negativity constraints. Computational results show that our implementation for this extension is on par with those of TA and CTA, suggesting applicability in linear programming and related problems.
On the Viability and Invariance of Proper Sets under Continuity Inclusions in Wasserstein Spaces

In this article, we derive necessary and sufficient conditions for the existence of solutions to state-constrained continuity inclusions in Wasserstein spaces whose right-hand sides may be discontinuous in time. These latter are based on fine investigations of the infinitesimal behaviour of the underlying reachable sets, through which we show that up to a negligible set of times, every admissible velocity of the inclusion can be approximately realised as the metric derivative of a solution of the dynamics, and vice versa. Building on these results, we are able to establish necessary and sufficient geometric conditions for the viability and invariance of stationary and time-dependent constraints, which involve a suitable notion of contingent cones in Wasserstein spaces, presented in ascending order of generality. We then close the article by exhibiting two prototypical examples of constraints sets appearing in applications for which one can compute relevant subfamilies of contingent directions.
Recall, Robustness, and Lexicographic Evaluation

Although originally developed to evaluate sets of items, recall is often used to evaluate rankings of items, including those produced by recommender, retrieval, and other machine learning systems. The application of recall without a formal evaluative motivation has led to criticism of recall as a vague or inappropriate measure. In light of this debate, we reflect on the measurement of recall in rankings from a formal perspective. Our analysis is composed of three tenets: recall, robustness, and lexicographic evaluation. First, we formally define `recall-orientation' as the sensitivity of a metric to a user interested in finding every relevant item. Second, we analyze recall-orientation from the perspective of robustness with respect to possible content consumers and providers, connecting recall to recent conversations about fair ranking. Finally, we extend this conceptual and theoretical treatment of recall by developing a practical preference-based evaluation method based on lexicographic comparison. Through extensive empirical analysis across three recommendation tasks and 17 information retrieval tasks, we establish that our new evaluation method, lexirecall, has convergent validity (i.e., it is correlated with existing recall metrics) and exhibits substantially higher sensitivity in terms of discriminative power and stability in the presence of missing labels. Our conceptual, theoretical, and empirical analysis substantially deepens our understanding of recall and motivates its adoption through connections to robustness and fairness.
DiffTraj: Generating GPS Trajectory with Diffusion Probabilistic Model

Pervasive integration of GPS-enabled devices and data acquisition technologies has led to an exponential increase in GPS trajectory data, fostering advancements in spatial-temporal data mining research. Nonetheless, GPS trajectories contain personal geolocation information, rendering serious privacy concerns when working with raw data. A promising approach to address this issue is trajectory generation, which involves replacing original data with generated, privacy-free alternatives. Despite the potential of trajectory generation, the complex nature of human behavior and its inherent stochastic characteristics pose challenges in generating high-quality trajectories. In this work, we propose a spatial-temporal diffusion probabilistic model for trajectory generation (DiffTraj). This model effectively combines the generative abilities of diffusion models with the spatial-temporal features derived from real trajectories. The core idea is to reconstruct and synthesize geographic trajectories from white noise through a reverse trajectory denoising process. Furthermore, we propose a Trajectory UNet (Traj-UNet) deep neural network to embed conditional information and accurately estimate noise levels during the reverse process. Experiments on two real-world datasets show that DiffTraj can be intuitively applied to generate high-fidelity trajectories while retaining the original distributions. Moreover, the generated results can support downstream trajectory analysis tasks and significantly outperform other methods in terms of geo-distribution evaluations.
ChatGPT: More than a Weapon of Mass Deception, Ethical challenges and responses from the Human-Centered Artificial Intelligence (HCAI) perspective

This article explores the ethical problems arising from the use of ChatGPT as a kind of generative AI and suggests responses based on the Human-Centered Artificial Intelligence (HCAI) framework. The HCAI framework is appropriate because it understands technology above all as a tool to empower, augment, and enhance human agency while referring to human wellbeing as a grand challenge, thus perfectly aligning itself with ethics, the science of human flourishing. Further, HCAI provides objectives, principles, procedures, and structures for reliable, safe, and trustworthy AI which we apply to our ChatGPT assessments. The main danger ChatGPT presents is the propensity to be used as a weapon of mass deception (WMD) and an enabler of criminal activities involving deceit. We review technical specifications to better comprehend its potentials and limitations. We then suggest both technical (watermarking, styleme, detectors, and fact-checkers) and non-technical measures (terms of use, transparency, educator considerations, HITL) to mitigate ChatGPT misuse or abuse and recommend best uses (creative writing, non-creative writing, teaching and learning). We conclude with considerations regarding the role of humans in ensuring the proper use of ChatGPT for individual and social wellbeing.
Towards Effective and Interpretable Human-Agent Collaboration in MOBA Games: A Communication Perspective

MOBA games, e.g., Dota2 and Honor of Kings, have been actively used as the testbed for the recent AI research on games, and various AI systems have been developed at the human level so far. However, these AI systems mainly focus on how to compete with humans, less on exploring how to collaborate with humans. To this end, this paper makes the first attempt to investigate human-agent collaboration in MOBA games. In this paper, we propose to enable humans and agents to collaborate through explicit communication by designing an efficient and interpretable Meta-Command Communication-based framework, dubbed MCC, for accomplishing effective human-agent collaboration in MOBA games. The MCC framework consists of two pivotal modules: 1) an interpretable communication protocol, i.e., the Meta-Command, to bridge the communication gap between humans and agents; 2) a meta-command value estimator, i.e., the Meta-Command Selector, to select a valuable meta-command for each agent to achieve effective human-agent collaboration. Experimental results in Honor of Kings demonstrate that MCC agents can collaborate reasonably well with human teammates and even generalize to collaborate with different levels and numbers of human teammates. Videos are available at https://sites.google. com/view/mcc-demo.
Unified quantum state tomography and Hamiltonian learning: A language-translation-like approach for quantum systems

Schr\"odinger's equation serves as a fundamental component in characterizing quantum systems, wherein both quantum state tomography and Hamiltonian learning are instrumental in comprehending and interpreting quantum systems. While numerous techniques exist for carrying out state tomography and learning Hamiltonians individually, no method has been developed to combine these two aspects. In this study, we introduce a new approach that employs the attention mechanism in transformer models to effectively merge quantum state tomography and Hamiltonian learning. By carefully choosing and preparing the training data, our method integrates both tasks without altering the model's architecture, allowing the model to effectively learn the intricate relationships between quantum states and Hamiltonian. We also demonstrate the effectiveness of our approach across various quantum systems, ranging from simple 2-qubit cases to more involved 2D antiferromagnetic Heisenberg structures. The data collection process is streamlined, as it only necessitates a one-way generation process beginning with state tomography. Furthermore, the scalability and few-shot learning capabilities of our method could potentially minimize the resources required for characterizing and optimizing quantum systems. Our research provides valuable insights into the relationship between Hamiltonian structure and quantum system behavior, fostering opportunities for additional studies on quantum systems and the advancement of quantum computation and associated technologies.
Coulomb collisions in the Boltzmann equation for electrons in low-temperature gas discharge plasmas

This paper investigates the effects of electron-electron and electron-ion Coulomb collisions on the electron distribution function and transport coefficients obtained from the Boltzmann equation for simple dc gas discharge conditions. Expressions are provided for the full Coulomb collision terms acting on both the isotropic and anisotropic parts of the electron distribution function, which are then incorporated in the freeware Boltzmann equation solver BOLSIG+. Different Coulomb collision effects are demonstrated and discussed on the basis of BOLSIG+ results for argon gas. It is shown that the anisotropic part of the electron-electron collision term, neglected in previous work, can in certain cases have a large effect on the electron mobility and is essential when describing the transition towards the Coulomb-collision dominated regime characterized by Spitzer transport coefficients. Finally, a brief overview is presented of the discharge conditions for which different Coulomb collision effects occur in different gases.
Dense network motifs enhance dynamical stability

Network motifs are the building blocks of complex networks and are significantly involved in the network dynamics such as information processing and local operations in the brain, biological marks for drug targets, identifying and predicting protein complexes in PPI networks, as well as echo chambers in social networks. Here we show that dense motifs such as cliques have different stable states than the network itself. These stable states enhance the dynamical stability of the network and can even turn local stable states into global ones. Moreover, we show how cliques create polarization phenomena and global opinion changes.
Urban GeoBIM Construction by Integrating Semantic LiDAR Point Clouds With as-Designed BIM Models

Developments in 3-D real worlds promote the integration of geoinformation and building information models (BIMs) known as GeoBIM. Light detection and ranging (LiDAR) integrated with global navigation satellite systems (GNSSs) can provide geo-referenced information at the urban scale. However, constructing detailed urban GeoBIM poses challenges in terms of LiDAR data quality. BIM models designed from software are fine on geometrical information but are often located in local coordinates and limited at an individual building level. In this study, we propose a complementary strategy to solve the contradiction between fine and large-scale construction of GeoBIM in urban scenes. A deep learning framework and graph theory are combined for LiDAR point cloud segmentation. Then, a coarse-to-fine matching program is developed to integrate building point clouds with corresponding BIM models. Results show that the overall segmentation accuracy of LiDAR datasets reaches up to 90%, and average positioning accuracies of building BIM models are 0.156 m, demonstrating the effectiveness of the method in segmentation and matching processes. This work offers a practical solution for rapid and accurate urban GeoBIM construction.
Sweet division problems: from chocolate bars to honeycomb strips and back

We consider two division problems on narrow strips of square and hexagonal lattices. In both cases we compute the bivariate enumerating sequences and the corresponding generating functions, which allowed us to determine the asymptotic behavior of the total number of such subdivisions and the expected number of parts. For the square lattice we extend results of two recent references by establishing polynomiality of enumerating sequences forming columns and diagonals of the triangular enumerating sequence. In the hexagonal case, we find a number of new combinatorial interpretations of the Fibonacci numbers and find combinatorial proofs of some Fibonacci related identities. We also show how both cases could be treated via the transfer matrix method and discuss some directions for future research.
Missing Values and Imputation in Healthcare Data: Can Interpretable Machine Learning Help?

Missing values are a fundamental problem in data science. Many datasets have missing values that must be properly handled because the way missing values are treated can have large impact on the resulting machine learning model. In medical applications, the consequences may affect healthcare decisions. There are many methods in the literature for dealing with missing values, including state-of-the-art methods which often depend on black-box models for imputation. In this work, we show how recent advances in interpretable machine learning provide a new perspective for understanding and tackling the missing value problem. We propose methods based on high-accuracy glass-box Explainable Boosting Machines (EBMs) that can help users (1) gain new insights on missingness mechanisms and better understand the causes of missingness, and (2) detect -- or even alleviate -- potential risks introduced by imputation algorithms. Experiments on real-world medical datasets illustrate the effectiveness of the proposed methods.
An Asynchronous Decentralized Algorithm for Wasserstein Barycenter Problem

Wasserstein Barycenter Problem (WBP) has recently received much attention in the field of artificial intelligence. In this paper, we focus on the decentralized setting for WBP and propose an asynchronous decentralized algorithm (A$^2$DWB). A$^2$DWB is induced by a novel stochastic block coordinate descent method to optimize the dual of entropy regularized WBP. To our knowledge, A$^2$DWB is the first asynchronous decentralized algorithm for WBP. Unlike its synchronous counterpart, it updates local variables in a manner that only relies on the stale neighbor information, which effectively alleviate the waiting overhead, and thus substantially improve the time efficiency. Empirical results validate its superior performance compared to the latest synchronous algorithm.
End-to-End Feasible Optimization Proxies for Large-Scale Economic Dispatch

The article proposes a novel End-to-End Learning and Repair (E2ELR) architecture for training optimization proxies for economic dispatch problems. E2ELR combines deep neural networks with closed-form, differentiable repair layers, thereby integrating learning and feasibility in an end-to-end fashion. E2ELR is also trained with self-supervised learning, removing the need for labeled data and the solving of numerous optimization problems offline. E2ELR is evaluated on industry-size power grids with tens of thousands of buses using an economic dispatch that co-optimizes energy and reserves. The results demonstrate that the self-supervised E2ELR achieves state-of-the-art performance, with optimality gaps that outperform other baselines by at least an order of magnitude.
Conformational landscape of long semiflexible linear and ring polymers near attractive surfaces

Conformations of a crowded neutral semiflexible polymer under confinement near an attractive wall are studied via coarse-grained simulations. We study the effects of the interplay of the length of the polymer, bending rigidity, and the repulsive crowder density on such equilibrium semiflexible polymer conformations. The length of the polymer dictates the number of distinct conformations of the adsorbed semiflexible polymer, suggesting that previous studies of short polymers are limited. The crowder density is shown to effectively reduce the bending rigidity of the polymers and at the highest crowder density considered, a crumpled wall-adsorbed polymer conformation is seen regardless of the semiflexibility. In addition, we study the role of the topology of the semiflexible polymer by comparing the results of linear semiflexible polymers with those of ring polymers. The conformational landscape of crowded ring polymers shows less diversity than that of a linear polymer and crowders are seen to affect the ring polymers differently than their linear counterparts.