Miracle-dz/UniFAR-FTUs huggingface dataset:
On the Trade-off between the Number of Nodes and the Number of Trees in a Random Forest

In this paper, we focus on the prediction phase of a random forest and study the problem of representing a bag of decision trees using a smaller bag of decision trees, where we only consider binary decision problems on the binary domain and simple decision trees in which an internal node is limited to querying the Boolean value of a single variable. As a main result, we show that the majority function of $n$ variables can be represented by a bag of $T$ ($<n$) decision trees each with polynomial size if $n-T$ is a constant, where $n$ and $T$ must be odd (in order to avoid the tie break). We also show that a bag of $n$ decision trees can be represented by a bag of $T$ decision trees each with polynomial size if $n-T$ is a constant and a small classification error is allowed. A related result on the $k$-out-of-$n$ functions is presented too.
StarVector: Generating Scalable Vector Graphics Code from Images

Scalable Vector Graphics (SVGs) have become integral in modern image rendering applications due to their infinite scalability in resolution, versatile usability, and editing capabilities. SVGs are particularly popular in the fields of web development and graphic design. Existing approaches for SVG modeling using deep learning often struggle with generating complex SVGs and are restricted to simpler ones that require extensive processing and simplification. This paper introduces StarVector, a multimodal SVG generation model that effectively integrates Code Generation Large Language Models (CodeLLMs) and vision models. Our approach utilizes a CLIP image encoder to extract visual representations from pixel-based images, which are then transformed into visual tokens via an adapter module. These visual tokens are pre-pended to the SVG token embeddings, and the sequence is modeled by the StarCoder model using next-token prediction, effectively learning to align the visual and code tokens. This enables StarVector to generate unrestricted SVGs that accurately represent pixel images. To evaluate StarVector's performance, we present SVG-Bench, a comprehensive benchmark for evaluating SVG methods across multiple datasets and relevant metrics. Within this benchmark, we introduce novel datasets including SVG-Stack, a large-scale dataset of real-world SVG examples, and use it to pre-train StarVector as a large foundation model for SVGs. Our results demonstrate significant enhancements in visual quality and complexity handling over current methods, marking a notable advancement in SVG generation technology. Code and models: https://github.com/joanrod/star-vector
ROSE: A reduced-order scattering emulator for optical models

A new generation of phenomenological optical potentials requires robust calibration and uncertainty quantification, motivating the use of Bayesian statistical methods. These Bayesian methods usually require calculating observables for thousands or even millions of parameter sets, making fast and accurate emulators highly desirable or even essential. Emulating scattering across different energies or with interactions such as optical potentials is challenging because of the non-affine parameter dependence, meaning the parameters do not all factorize from individual operators. Here we introduce and demonstrate the Reduced Order Scattering Emulator (ROSE) framework, a reduced basis emulator that can handle non-affine problems. ROSE is fully extensible and works within the publicly available BAND Framework software suite for calibration, model mixing, and experimental design. As a demonstration problem, we use ROSE to calibrate a realistic nucleon-target scattering model through the calculation of elastic cross sections. This problem shows the practical value of the ROSE framework for Bayesian uncertainty quantification with controlled trade-offs between emulator speed and accuracy as compared to high-fidelity solvers. Planned extensions of ROSE are discussed.
The Quantum Echo in Two-Component Bose-Einstein Condensates

The development of ultracold atom technology has enabled the precise investigations on quantum dynamics of quantum gases. Recently, inspired by experimental advancement, the $SU(1,1)$ echo, akin to the well-known $SU(2)$ spin echo, has been proposed for single-component Bose-Einstein condensate (BEC). In this paper, we investigate the possibility of quantum echo in the more intricate two-component BEC by fully exploiting its underlying symmetry, which is the Lie group $Sp(4,R)$. We demonstrate that quantum echo can occur for the two-component BEC by applying a driving protocol consisting of two steps in each period. The first step can be any Bogoliubov Hamiltonian, while the second step is a Hamiltonian with interactions turned off, which plays a similar role as the $\pi$-pulse in spin echo. We confirm our theoretical results with numerical calculations for different examples of two-component BEC. We further consider the effect of interactions between the excited boson modes on the quantum echo process and discuss the possible experiment implementation of this quantum echo.
Landscape Characteristics Comparison of Rural Settlements in China

The study area is Fuping,Wuyi county in Hebei province and Qingliu,Huian county in Fujian Province.They are located in plain and mountain areas in northern and southern China respectively.The landscape data are interpreted using Landsat TM images of 2000. The landscape ecology indices are applied to study landscape structure disparity and the density,size,shape,distribution law of rural settlements in study areas.Forest and grassland are the dominant landscape in mountain area while agricultural field and human settlements are the main landscape in plain area.The rural settlements in plain area are bigger in size,even in distribution,nearer in distance;those in mountain area are smaller,uneven and far.The rural settlements are smaller less than 20 hm 2 in plain and 10 hm 2 in mountain areas.The rural settlements are Aerr apart less than 2.5km in mountain area and 0.4 km apart in plain area.The development of the cities and central villages should be encouraged to optimize the rural settlement distribution.
Efficient and Private Federated Trajectory Matching

Federated Trajectory Matching (FTM) is gaining increasing importance in big trajectory data analytics, supporting diverse applications such as public health, law enforcement, and emergency response. FTM retrieves trajectories that match with a query trajectory from a large-scale trajectory database, while safeguarding the privacy of trajectories in both the query and the database. A naive solution to FTM is to process the query through Secure Multi-Party Computation (SMC) across the entire database, which is inherently secure yet inevitably slow due to the massive secure operations. A promising acceleration strategy is to filter irrelevant trajectories from the database based on the query, thus reducing the SMC operations. However, a key challenge is how to publish the query in a way that both preserves privacy and enables efficient trajectory filtering. In this paper, we design GIST, a novel framework for efficient Federated Trajectory Matching. GIST is grounded in Geo-Indistinguishability, a privacy criterion dedicated to locations. It employs a new privacy mechanism for the query that facilitates efficient trajectory filtering. We theoretically prove the privacy guarantee of the mechanism and the accuracy of the filtering strategy of GIST. Extensive evaluations on five real datasets show that GIST is significantly faster and incurs up to 3 orders of magnitude lower communication cost than the state-of-the-arts.
Best Arm Identification with Fixed Budget: A Large Deviation Perspective

We consider the problem of identifying the best arm in stochastic Multi-Armed Bandits (MABs) using a fixed sampling budget. Characterizing the minimal instance-specific error probability for this problem constitutes one of the important remaining open problems in MABs. When arms are selected using a static sampling strategy, the error probability decays exponentially with the number of samples at a rate that can be explicitly derived via Large Deviation techniques. Analyzing the performance of algorithms with adaptive sampling strategies is however much more challenging. In this paper, we establish a connection between the Large Deviation Principle (LDP) satisfied by the empirical proportions of arm draws and that satisfied by the empirical arm rewards. This connection holds for any adaptive algorithm, and is leveraged (i) to improve error probability upper bounds of some existing algorithms, such as the celebrated \sr (Successive Rejects) algorithm \citep{audibert2010best}, and (ii) to devise and analyze new algorithms. In particular, we present \sred (Continuous Rejects), a truly adaptive algorithm that can reject arms in {\it any} round based on the observed empirical gaps between the rewards of various arms. Applying our Large Deviation results, we prove that \sred enjoys better performance guarantees than existing algorithms, including \sr. Extensive numerical experiments confirm this observation.
Harmonic motion modes in parabolic GRIN fibers

We report electromagnetic field modes solving the inhomogeneous Maxwell equations for parabolic gradient index fibers in the low refractive index contrast approximation. The first family comprises accelerating fields characterized by an intensity distribution center tracing a circular trajectory transverse to the fiber optical axis. These fields maintain an invariant shape for both their intensity and phase distributions while rotating around their center. The second family comprises breathing fields characterized by an intensity distribution center aligned with the fiber optical axis. These fields exhibit intensity distribution scaling along propagation, while their phase swirls and rotates around the optical axis without changing their intensity distribution shape and topological charge.
Glioblastoma Tumor Segmentation using an Ensemble of Vision Transformers

Glioblastoma is one of the most aggressive and deadliest types of brain cancer, with low survival rates compared to other types of cancer. Analysis of Magnetic Resonance Imaging (MRI) scans is one of the most effective methods for the diagnosis and treatment of brain cancers such as glioblastoma. Accurate tumor segmentation in MRI images is often required for treatment planning and risk assessment of treatment methods. Here, we propose a novel pipeline, Brain Radiology Aided by Intelligent Neural NETworks (BRAINNET), which leverages MaskFormer, a vision transformer model, and generates robust tumor segmentation maks. We use an ensemble of nine predictions from three models separately trained on each of the three orthogonal 2D slice directions (axial, sagittal, and coronal) of a 3D brain MRI volume. We train and test our models on the publicly available UPenn-GBM dataset, consisting of 3D multi-parametric MRI (mpMRI) scans from 611 subjects. Using Dice coefficient (DC) and 95% Hausdorff distance (HD) for evaluation, our models achieved state-of-the-art results in segmenting all three different tumor regions -- tumor core (DC = 0.894, HD = 2.308), whole tumor (DC = 0.891, HD = 3.552), and enhancing tumor (DC = 0.812, HD = 1.608).
pixelSplat: 3D Gaussian Splats from Image Pairs for Scalable Generalizable 3D Reconstruction

We introduce pixelSplat, a feed-forward model that learns to reconstruct 3D radiance fields parameterized by 3D Gaussian primitives from pairs of images. Our model features real-time and memory-efficient rendering for scalable training as well as fast 3D reconstruction at inference time. To overcome local minima inherent to sparse and locally supported representations, we predict a dense probability distribution over 3D and sample Gaussian means from that probability distribution. We make this sampling operation differentiable via a reparameterization trick, allowing us to back-propagate gradients through the Gaussian splatting representation. We benchmark our method on wide-baseline novel view synthesis on the real-world RealEstate10k and ACID datasets, where we outperform state-of-the-art light field transformers and accelerate rendering by 2.5 orders of magnitude while reconstructing an interpretable and editable 3D radiance field.
Transient Temperature Dynamics of Reservoirs Connected Through an Open Quantum System

The dynamics of open quantum systems connected with several reservoirs attract great attention due to its importance in quantum optics, biology, quantum thermodynamics, transport phenomena, etc. In many problems, the Born approximation is applicable which implies that the influence of the open quantum system on the reservoirs can be neglected. However, in the case of a long-time dynamics or mesoscopic reservoir, the reverse influence can be crucial. In this paper, we investigate the transient dynamics of several bosonic reservoirs connected through an open quantum system. We use an adiabatic approach to study the temporal dynamics of temperatures of the reservoirs during relaxation to thermodynamic equilibrium. We show that there are various types of temperature dynamics that strongly depend on the values of dissipative rates and initial temperatures. We demonstrate that temperatures of the reservoirs can exhibit non-monotonic behavior. Moreover, there are moments of time during which the reservoir with initially intermediate temperature becomes the hottest or coldest reservoir. The obtained results pave the way for managing energy flows in mesoscale and nanoscale systems.
A Study on Transferability of Deep Learning Models for Network Intrusion Detection

In this paper, we explore transferability in learning between different attack classes in a network intrusion detection setup. We evaluate transferability of attack classes by training a deep learning model with a specific attack class and testing it on a separate attack class. We observe the effects of real and synthetically generated data augmentation techniques on transferability. We investigate the nature of observed transferability relationships, which can be either symmetric or asymmetric. We also examine explainability of the transferability relationships using the recursive feature elimination algorithm. We study data preprocessing techniques to boost model performance. The code for this work can be found at https://github.com/ghosh64/transferability.
Dynamic Loco-manipulation on HECTOR: Humanoid for Enhanced ConTrol and Open-source Research

Despite their remarkable advancement in locomotion and manipulation, humanoid robots remain challenged by a lack of synchronized loco-manipulation control, hindering their full dynamic potential. In this work, we introduce a versatile and effective approach to controlling and generalizing dynamic locomotion and loco-manipulation on humanoid robots via a Force-and-moment-based Model Predictive Control (MPC). Specifically, we proposed a simplified rigid body dynamics (SRBD) model to take into account both humanoid and object dynamics for humanoid loco-manipulation. This linear dynamics model allows us to directly solve for ground reaction forces and moments via an MPC problem to achieve highly dynamic real-time control. Our proposed framework is highly versatile and generalizable. We introduce HECTOR (Humanoid for Enhanced ConTrol and Open-source Research) platform to demonstrate its effectiveness in hardware experiments. With the proposed framework, HECTOR can maintain exceptional balance during double-leg stance mode, even when subjected to external force disturbances to the body or foot location. In addition, it can execute 3-D dynamic walking on a variety of uneven terrains, including wet grassy surfaces, slopes, randomly placed wood slats, and stacked wood slats up to 6 cm high with the speed of 0.6 m/s. In addition, we have demonstrated dynamic humanoid loco-manipulation over uneven terrain, carrying 2.5 kg load. HECTOR simulations, along with the proposed control framework, are made available as an open-source project. (https://github.com/DRCL-USC/Hector_Simulation).
Active Preference Inference using Language Models and Probabilistic Reasoning

Actively inferring user preferences, for example by asking good questions, is important for any human-facing decision-making system. Active inference allows such systems to adapt and personalize themselves to nuanced individual preferences. To enable this ability for instruction-tuned large language models (LLMs), one may prompt them to ask users questions to infer their preferences, transforming the language models into more robust, interactive systems. However, out of the box, these models are not efficient at extracting preferences: the questions they generate are not informative, requiring a high number of user interactions and impeding the usability of the downstream system. In this work, we introduce an inference-time algorithm that helps LLMs quickly infer preferences by using more informative questions. Our algorithm uses a probabilistic model whose conditional distributions are defined by prompting an LLM, and returns questions that optimize expected entropy and expected model change. Results in a simplified interactive web shopping setting with real product items show that an LLM equipped with our entropy reduction algorithm outperforms baselines with the same underlying LLM on task performance while using fewer user interactions.
Outcomes truncated by death in RCTs: a simulation study on the survivor average causal effect

Continuous outcome measurements truncated by death present a challenge for the estimation of unbiased treatment effects in randomized controlled trials (RCTs). One way to deal with such situations is to estimate the survivor average causal effect (SACE), but this requires making non-testable assumptions. Motivated by an ongoing RCT in very preterm infants with intraventricular hemorrhage, we performed a simulation study to compare a SACE estimator with complete case analysis (CCA, benchmark for a biased analysis) and an analysis after multiple imputation of missing outcomes. We set up 9 scenarios combining positive, negative and no treatment effect on the outcome (cognitive development) and on survival at 2 years of age. Treatment effect estimates from all methods were compared in terms of bias, mean squared error and coverage with regard to two estimands: the treatment effect on the outcome used in the simulation and the SACE, which was derived by simulation of both potential outcomes per patient. Despite targeting different estimands (principal stratum estimand, hypothetical estimand), the SACE-estimator and multiple imputation gave similar estimates of the treatment effect and efficiently reduced the bias compared to CCA. Also, both methods were relatively robust to omission of one covariate in the analysis, and thus violation of relevant assumptions. Although the SACE is not without controversy, we find it useful if mortality is inherent to the study population. Some degree of violation of the required assumptions is almost certain, but may be acceptable in practice.
Anti-de Sitter $\to$ de Sitter transition driven by Casimir forces and mitigating tensions in cosmological parameters

Over the last few years, low- and high-redshift observations set off tensions in the measurement of the present-day expansion rate $H_0$ and in the determination of the amplitude of the matter clustering in the late Universe (parameterized by $S_8$). It was recently noted that both these tensions can be resolved if the cosmological constant parametrizing the dark energy content switches its sign at a critical redshift $z_c \sim 2$. However, the anti-de Sitter (AdS) swampland conjecture suggests that the postulated switch in sign of the cosmological constant at zero temperature seems unlikely because the AdS vacua are an infinite distance appart from de Sitter (dS) vacua in moduli space. We provide an explanation for the required AdS $\to$ dS crossover transition in the vacuum energy using the Casimir forces of fields inhabiting the bulk. We then use entropy arguments to claim that any AdS $\to$ dS transition between metastable vacua must be accompanied by a reduction of the species scale where gravity becomes strong. We provide a few examples supporting this AdS $\to$ dS uplift conjecture.
An arithmetic count of osculating lines

We say that a line in $\mathbb P^{n+1}_k$ is osculating to a hypersurface $Y$ if they meet with contact order $n+1$. When $k=\mathbb C$, it is known that through a fixed point of $Y$, there are exactly $n! $ of such lines. Under some parity condition on $n$ and $\mathrm{deg}(Y)$, we define a quadratically enriched count of these lines over any perfect field $k$. The count takes values in the Grothendieck-Witt ring of quadratic forms over $k$ and depends linearly on $\mathrm{deg}(Y)$.
An exact divergence-free spectral method for incompressible and resistive magneto-hydrodynamic equations in two and three dimensions

In this paper, we present exact divergence-free spectral method for solving the incompressible and resistive magneto-hydrodynamic (MHD) equations in two and three dimensions, as well as the efficient solution algorithm and unconditionally energy-stable fully-discretized numerical schemes. We introduce new ideas of constructing two families of exact divergence-free vectorial spectral basis functions on domains diffeomorphic to squares or cubes. These bases are obtained with the help of orthogonality and derivative relation of generalised Jacobi polynomials, several de Rham complexes, as well as the property of contravariant Piola transformation. They are well-suited for discretizing the velocity and magnetic fields, respectively, thereby ensuring point-wise preservation of the incompressibility condition and the magnetic Gauss's law. With the aid of these bases, we propose a family of exact divergence-free implicit-explicit $k$-step backward differentiation formula (DF-BDF-$k$) fully-discretized schemes for the MHD system. These schemes naturally decouple the pressure field from the velocity field. Consequently, the stability of the space-time fully-discretized numerical schemes based on these bases are significantly enhanced. These schemes exhibit unconditional stability for $k=1,2$, and demonstrate exceptional stability and accuracy for $k=3,4$, verified with extensive numerical results for long time simulations using large time step sizes. Furthermore, we present efficient solution algorithms for these two decoupled equations for the velocity and magnetic fields, respectively, by exploiting the sparsity and structure of the resultant linear algebraic systems. Ample numerical examples in two and three dimensions are provided to demonstrate the distinctive accuracy, efficiency and stability of our proposed method.