Miracle-dz/UniFAR-FTUs huggingface dataset:
Exotic B-Series and S-Series: Algebraic Structures and Order Conditions for Invariant Measure Sampling

B-Series and generalizations are a powerful tool for the analysis of numerical integrators. An extension named exotic aromatic B-Series was introduced to study the order conditions for sampling the invariant measure of ergodic SDEs. Introducing a new symmetry normalization coefficient, we analyze the algebraic structures related to exotic B-Series and S-Series. Precisely, we prove the relationship between the Grossman–Larson algebras over exotic and grafted forests and the corresponding duals to the Connes–Kreimer coalgebras and use it to study the natural composition laws on exotic S-Series. Applying this algebraic framework to the derivation of order conditions for a class of stochastic Runge–Kutta methods, we present a multiplicative property that ensures some order conditions to be satisfied automatically.
Structure in the Magnetic Field of the Milky Way Disk and Halo Traced by Faraday Rotation

Magnetic fields in the ionized medium of the disk and halo of the Milky Way impose Faraday rotation on linearly polarized radio emission. We compare two surveys mapping the Galactic Faraday rotation, one showing the rotation measures of extragalactic sources seen through the Galaxy, and one showing Faraday depth of the diffuse Galactic synchrotron emission from the Global Magneto-Ionic Medium Survey. Comparing the two data sets in 5° × 10° bins shows good agreement at intermediate latitudes, 10° < ∣b∣ < 50°, and little correlation between them at lower and higher latitudes. Where they agree, both tracers show clear patterns as a function of Galactic longitude, ℓ; in the northern hemisphere a strong sin(2ℓ) pattern; and in the southern hemisphere a sin(ℓ+π) pattern. Pulsars with height above or below the plane ∣z∣ > 300 pc show similar ℓ dependence in their rotation measures. Nearby nonthermal structures show rotation measure shadows as does the Orion–Eridanus superbubble. We describe families of dynamo models that could explain the observed patterns in the two hemispheres. We suggest that a field reversal, known to cross the plane a few hundred parsecs inside the solar circle, could shift to positive z with increasing Galactic radius to explain the sin(2ℓ) pattern in the northern hemisphere. Correlation shows that rotation measures from extragalactic sources are one to two times the corresponding rotation measure of the diffuse emission, implying Faraday complexity along some lines of sight, especially in the southern hemisphere.
Structure Guided Manifolds for Discovery of Disease Characteristics

In medical image analysis, the subtle visual characteristics of many diseases are challenging to discern, particularly due to the lack of paired data. For example, in mild Alzheimer's Disease (AD), brain tissue atrophy can be difficult to observe from pure imaging data, especially without paired AD and Cognitively Normal ( CN ) data for comparison. This work presents Disease Discovery GAN ( DiDiGAN), a weakly-supervised style-based framework for discovering and visualising subtle disease features. DiDiGAN learns a disease manifold of AD and CN visual characteristics, and the style codes sampled from this manifold are imposed onto an anatomical structural"blueprint"to synthesise paired AD and CN magnetic resonance images (MRIs). To suppress non-disease-related variations between the generated AD and CN pairs, DiDiGAN leverages a structural constraint with cycle consistency and anti-aliasing to enforce anatomical correspondence. When tested on the Alzheimer's Disease Neuroimaging Initiative ( ADNI) dataset, DiDiGAN showed key AD characteristics (reduced hippocampal volume, ventricular enlargement, and atrophy of cortical structures) through synthesising paired AD and CN scans. The qualitative results were backed up by automated brain volume analysis, where systematic pair-wise reductions in brain tissue structures were also measured
A Cubic Algorithm for Computing the Hermite Normal Form of a Nonsingular Integer Matrix

A Las Vegas randomized algorithm is given to compute the Hermite normal form of a nonsingular integer matrix A of dimension n. The algorithm uses quadratic integer multiplication and cubic matrix multiplication and has running time bounded by O(n3 (log n + log ||A||)2(log n)2) bit operations, where ||A||= max ij |Aij| denotes the largest entry of A in absolute value. A variant of the algorithm that uses pseudo-linear integer multiplication is given that has running time (n3 log ||A||)1+o(1) bit operations, where the exponent “+ o(1)” captures additional factors c1 (log n)c2 (loglog||A||)c3 for positive real constants c1,c2,c3.
Sampling Complexity of Open Quantum Systems

Open quantum systems are ubiquitous in the physical sciences, with widespread applications in the areas of chemistry, condensed matter physics, material science, optics, and many more. Not surprisingly, there is significant interest in their efficient simulation. However, direct classical simulation quickly becomes intractable with coupling to an environment whose effective dimension grows exponentially. This raises the question: can quantum computers help model these complex dynamics? A first step in answering this question requires understanding the computational complexity of this task. Here, we map the temporal complexity of a process to the spatial complexity of a many-body state using a computational model known as the process tensor framework. With this, we are able to explore the simulation complexity of an open quantum system as a dynamic sampling problem: a system coupled to an environment can be probed at successive points in time -- accessing multi-time correlations. The complexity of multi-time sampling, which is an important and interesting problem in its own right, contains the complexity of master equations and stochastic maps as a special case. Our results show how the complexity of the underlying quantum stochastic process corresponds to the complexity of the associated family of master equations for the dynamics. We present both analytical and numerical examples whose multi-time sampling is as complex as sampling from a many-body state that is classically hard. This also implies that the corresponding family of master equations are classically hard. Our results pave the way for studying open quantum systems from a complexity-theoretic perspective, highlighting the role quantum computers will play in our understanding of quantum dynamics.
Color Recommendation for Vector Graphic Documents based on Multi-Palette Representation

Vector graphic documents present multiple visual elements, such as images, shapes, and texts. Choosing appropriate colors for multiple visual elements is challenging but crucial for amateurs and professional designers. Instead of creating a single color palette for all elements, we extract multiple color palettes from each visual element of a graphic document, and then combine them into a color sequence. We propose a masked color model for color sequence completion and recommend the specified colors based on the color context in multi-palette with high probability. We train the model and build a color recommendation system on a large-scale dataset of vector graphic documents. The proposed color recommendation method outperformed other state-of-the-art methods by quantitative and qualitative evaluations on color prediction and our color recommendation system received positive feedback from professional designers in an interview study. Our code and trained model are available at https://github.com/CyberAgentAILab/multipalette.
Active Keyword Selection to Track Evolving Topics on Twitter

How can we study social interactions on evolving topics at a mass scale? Over the past decade, researchers from diverse fields such as economics, political science, and public health have often done this by querying Twitter's public API endpoints with hand-picked topical keywords to search or stream discussions. However, despite the API's accessibility, it remains difficult to select and update keywords to collect high-quality data relevant to topics of interest. In this paper, we propose an active learning method for rapidly refining query keywords to increase both the yielded topic relevance and dataset size. We leverage a large open-source COVID-19 Twitter dataset to illustrate the applicability of our method in tracking Tweets around the key sub-topics of Vaccine, Mask, and Lockdown. Our experiments show that our method achieves an average topic-related keyword recall 2x higher than baselines. We open-source our code along with a web interface for keyword selection to make data collection from Twitter more systematic for researchers.
City deﬁnition aﬀects long-term urban scaling analyses in the United States (1900 2015)

The scaling relations between city attributes and population are emergent and ubiquitous aspects of urban growth. Quantifying these relations and understanding their theoretical foundation, however, is diﬃcult due to the challenge of deﬁning city boundaries and a lack of historical data to study city dynamics over time and space. To address this issue, we analyze scaling between city infrastructure and population across 857 United States metropolitan areas over an unprecedented 115 years using dasymetrically reﬁned historical population estimates, historical urban road network data, and multi-temporal settlement data to deﬁne dynamic city boundaries based on settlement density. We demonstrate the clearest evidence that urban scaling exponents can closely match theoretical models over a century if cities are deﬁned as dense settlement patches. In contrast, these results strongly disagree with theoretical models and vary in time if we aggregate cities into administrative-deﬁned metropolitan areas, a method used in previous analyses. Despite the close quantitative agreement with theory, the empirical scaling relations unexpectedly vary across space, a ﬁnding that is supported by global scaling analysis. Finally, our analysis of scaling coeﬃcients reveal that a city in 2015 uses more developed land and kilometers of road than a city in 1900 with a similar population, which may imply cities have become increasingly harmful to the local environment. Our results show the strengths and limitations of current theoretical models, and oﬀer a new way to study urban systems based on historical data.
A Generalist Neural Algorithmic Learner

The cornerstone of neural algorithmic reasoning is the ability to solve algorithmic tasks, especially in a way that generalises out of distribution. While recent years have seen a surge in methodological improvements in this area, they mostly focused on building specialist models. Specialist models are capable of learning to neurally execute either only one algorithm or a collection of algorithms with identical control-flow backbone. Here, instead, we focus on constructing a generalist neural algorithmic learner -- a single graph neural network processor capable of learning to execute a wide range of algorithms, such as sorting, searching, dynamic programming, path-finding and geometry. We leverage the CLRS benchmark to empirically show that, much like recent successes in the domain of perception, generalist algorithmic learners can be built by"incorporating"knowledge. That is, it is possible to effectively learn algorithms in a multi-task manner, so long as we can learn to execute them well in a single-task regime. Motivated by this, we present a series of improvements to the input representation, training regime and processor architecture over CLRS, improving average single-task performance by over 20% from prior art. We then conduct a thorough ablation of multi-task learners leveraging these improvements. Our results demonstrate a generalist learner that effectively incorporates knowledge captured by specialist models.
Spectrally shaped and pulse-by-pulse multiplexed multimode squeezed states of light

Spectral- and time-multiplexing are currently explored to generate large multipartite quantum states of light for quantum technologies. In the continuous variable approach, the deterministic generation of scalable entangled states requires the generation of a scalable number of squeezed modes. Here, we demonstrate the simultaneous generation of 21 squeezed spectral modes at the repetition rate of our laser, i.e., 156 MHz. We exploit the full repetition rate and the pulse shaping of a femtosecond light source to combine, for the first time, frequency- and time-multiplexing in multimode squeezing. This paves the way for the implementation of multipartite entangled states that are both scalable and fully reconfigurable.
Learning Dexterous Manipulation from Exemplar Object Trajectories and Pre-Grasps

Learning diverse dexterous manipulation behaviors with assorted objects remains an open grand challenge. While policy learning methods offer a powerful avenue to attack this problem, these approaches require extensive per-task engineering and algorithmic tuning. This paper seeks to escape these constraints, by developing a Pre-Grasp informed Dexterous Manipulation (PGDM) framework that generates diverse dexter-ous manipulation behaviors, without any task-specific reasoning or hyper-parameter tuning. At the core of PGDM is a well known robotics construct, pre-grasps (i.e. the hand-pose preparing for object interaction). This simple primitive is enough to induce efficient exploration strategies for acquiring complex dexterous manipulation behaviors. To exhaustively verify these claims, we introduce TCDM, a benchmark of 50 diverse manipulation tasks defined over multiple objects and dexterous manipulators. Tasks for TCDM are defined automatically using exemplar object trajectories from diverse sources (animators, human behaviors, etc.), without any per-task engineering and/or supervision. Our experiments validate that PGDM's exploration strategy, induced by a surprisingly simple ingredient (single pre-grasp pose), matches the performance of prior methods, which require expensive per-task feature/reward engineering, expert supervision, and hyper-parameter tuning. For animated visualizations, trained policies, and project code, please refer to https://pregrasps.github. io/.
Contrastive Learning for Time Series on Dynamic Graphs

There have been several recent efforts towards developing representations for multivariate time-series in an unsupervised learning framework. Such representations can prove beneficial in tasks such as activity recognition, health monitoring, and anomaly detection. In this paper, we consider a setting where we observe time-series at each node in a dynamic graph. We propose a framework called GraphTNC for unsupervised learning of joint representations of the graph and the time-series. Our approach employs a contrastive learning strategy. Based on an assumption that the time-series and graph evolution dynamics are piecewise smooth, we identify local windows of time where the signals exhibit approximate stationarity. We then train an encoding that allows the distribution of signals within a neighborhood to be distinguished from the distribution of non-neighboring signals. We first demonstrate the performance of our proposed framework using synthetic data, and subsequently we show that it can prove beneficial for the classification task with real-world datasets.
Unlikely Intersections with Bruhat Strata

Let A g be the moduli space of g -dimensional principally polarized abelian varieties over Z , and let T Ă A g be a closed locus, also deﬁned over Z . Motivated by unlikely intersection conjectures, we study the intersection of T F p with the Bruhat strata in A g, F p as p -varies; these are strata characterized by the existence of certain subgroup schemes inside the p -torsion of the ﬁbres. We ﬁnd that, away from a ﬁnite set of primes, positive-dimensional “unlikely” intersections of T F p with such strata are all accounted for by intersections of T with special loci inside A g . This result generalizes to all abelian-type Shimura varieties, and variations of Hodge structures equipped with certain motivic data. It moreover gives another example of how functional transcendence principles in characteristic zero can be used to study unlikely intersections in positive characteristic, building on recent work by the author.
Liesel: A Probabilistic Programming Framework for Developing Semi-Parametric Regression Models and Custom Bayesian Inference Algorithms

Liesel is a new probabilistic programming framework developed with the aim of supporting research on Bayesian inference based on Markov chain Monte Carlo (MCMC) simulations in general and semi-parametric regression specifications in particular. Its three main components are (i) an R interface (RLiesel) for the configuration of an initial semi-parametric regression model, (ii) a graph-based model building library, where the initial model graph can be manipulated to incorporate new research ideas, and (iii) an MCMC library for designing modular inference algorithms combining multiple types of well-tested and possibly customized MCMC kernels. The graph builder as well as the MCMC library are implemented in Python, relying on JAX as a numerical computing library, and can therefore benefit from the latest machine learning technology such as automatic differentiation, just-in-time (JIT) compilation, and the use of high-performance computing devices such as tensor processing units (TPUs). Liesel provides all required tools for efficient and reliable statistical research on complex models and estimation algorithms. Its modular design allows users to expand the model library and inference algorithms, offering the flexibility and customization options to tailor the software to any specific research needs.
Learning from Symmetry: Meta-Reinforcement Learning with Symmetric Data and Language Instructions

—Meta-reinforcement learning (meta-RL) is a promising approach that enables the agent to learn new tasks quickly. However, most meta-RL algorithms show poor generalization in multiple-task scenarios due to the insufﬁ-cient task information provided only by rewards. Language-conditioned meta-RL improves the generalization by matching language instructions and the agent’s behaviors. Learning from symmetry is an important form of human learning, therefore, combining symmetry and language instructions into meta-RL can help improve the algorithm’s generalization and learning efﬁciency. We thus propose a dual-MDP meta-reinforcement learning method that enables learning new tasks efﬁciently with symmetric data and language instructions. We evaluate our method in multiple challenging manipulation tasks, and experimental results show our method can greatly improve the generalization and efﬁciency of meta-reinforcement learning.
Isospectral connections, ergodicity of frame flows, and polynomial maps between spheres

We show that on closed negatively curved Riemannian manifolds with simple length spectrum, the spectrum of the Bochner Laplacian determines both the isomorphism class of the vector bundle and the connection up to gauge under a low-rank assumption. We also show that flows of frames on low-rank frame bundles extending the geodesic flow in negative curvature are ergodic whenever the bundle admits no holonomy reduction. This is achieved by exhibiting a link between these problems and the classification of polynomial maps between spheres in real algebraic geometry.
Combined Unbalanced Distribution System State and Line Impedance Matrix Estimation

To address the challenges that the decarbonization of the energy sector is bringing about, advanced distribution network management and operation strategies are being developed. Many of these strategies require accurate network models to work effectively. However, distribution network data are known to contain errors, and attention has been given to techniques that allow to derive improved network information. This paper presents a novel method to derive line impedance values from smart meter measurement time series, with realistic assumptions in terms of meter accuracy, resolution and penetration. The method is based on unbalanced state estimation and is cast as a non-convex quadratically constrained optimization problem. Both line lengths and impedance matrix models can be estimated based on an exact nonlinear formulation of the steady-state three-phase network physics. The method is evaluated on the IEEE European Low Voltage feeder (906 buses) and shows promising results.
Decentralized Distributed Expert Assisted Learning (D2EAL) approach for cooperative target-tracking

This paper addresses the problem of cooperative target tracking using a heterogeneous multi-robot system, where the robots are communicating over a dynamic communication network, and heterogeneity is in terms of different types of sensors and prediction algorithms installed in the robots. The problem is cast into a distributed learning framework, where robots are considered as 'agents' connected over a dynamic communication network. Their prediction algorithms are considered as 'experts' giving their look-ahead predictions of the target's trajectory. In this paper, a novel Decentralized Distributed Expert-Assisted Learning (D2EAL) algorithm is proposed, which improves the overall tracking performance by enabling each robot to improve its look-ahead prediction of the target's trajectory by its information sharing, and running a weighted information fusion process combined with online learning of weights based on a prediction loss metric. Theoretical analysis of D2EAL is carried out, which involves the analysis of worst-case bounds on cumulative prediction loss, and weights convergence analysis. Simulation studies show that in adverse scenarios involving large dynamic bias or drift in the expert predictions, D2EAL outperforms well-known covariance-based estimate/prediction fusion methods, both in terms of prediction performance and scalability.
To Fix or Not to Fix: A Critical Study of Crypto-misuses in the Wild

Recent studies have revealed that 87 % to 96 % of the Android apps using cryptographic APIs have a misuse which may cause security vulnerabilities. As previous studies did not conduct a qualitative examination of the validity and severity of the findings, our objective was to understand the findings in more depth. We analyzed a set of 936 open-source Java applications for cryptographic misuses. Our study reveals that 88.10 % of the analyzed applications fail to use cryptographic APIs securely. Through our manual analysis of a random sample, we gained new insights into effective false positives. For example, every fourth misuse of the frequently misused JCA class MessageDigest is an effective false positive due to its occurrence in a non-security context. As we wanted to gain deeper insights into the security implications of these misuses, we created an extensive vulnerability model for cryptographic API misuses. Our model includes previously undiscussed attacks in the context of cryptographic APIs such as DoS attacks. This model reveals that nearly half of the misuses are of high severity, e.g., hard-coded credentials and potential Man-in-the-Middle attacks.