The abstracts are decoded using greedy algorithm with temperature T = 0 .5 .

Optimization modeling is one of the most crucial but technical parts of operations research (OR). To automate the modeling process, existing works have leveraged large language models (LLMs), prompting them to break down tasks into steps for generating variables, constraints, and objectives. However, due to the highly complex mathematical structures inherent in OR problems, standard fixed-step decomposition often fails to achieve high performance. To address this challenge, we introduce OptiTree, a novel tree search approach designed to enhance modeling capabilities for complex problems through adaptive problem decomposition into simpler subproblems. Specifically, we develop a modeling tree that organizes a wide range of OR problems based on their hierarchical problem taxonomy and complexity, with each node representing a problem category and containing relevant high-level modeling thoughts. Given a problem to model, we recurrently search the tree to identify a series of simpler subproblems and synthesize the global modeling thoughts by adaptively integrating the hierarchical thoughts. Experiments show that OptiTree significantly improves the modeling accuracy compared to the state-of-the-art, achieving over 10\% improvements on the challenging benchmarks. The code is released at https://github.com/MIRALab-USTC/OptiTree/tree/main.

The abstracts are decoded using greedy algorithm with temperature T = 0 .5 .

HERMES (High Energy Rapid Modular Ensemble of Satellites) pathfinder is an in-orbit demonstration consisting of a constellation of six 3U nano-satellites hosting simple but innovative detectors for the monitoring of cosmic high-energy transients. The main objective of HERMES Pathfinder is to prove that accurate position of high-energy cosmic transients can be obtained using miniaturized hardware. The transient position is obtained by studying the delay time of arrival of the signal to different detectors hosted by nano-satellites on low Earth orbits. To this purpose, the goal is to achive an overall accuracy of a fraction of a micro-second. In this context, we need to develop novel tools to fully exploit the future scientific data output of HERMES Pathfinder. In this paper, we introduce a new framework to assess the background count rate of a space-born, high energy detector; a key step towards the identification of faint astrophysical transients. We employ a Neural Network (NN) to estimate the background lightcurves on different timescales. Subsequently, we employ a fast change-point and anomaly detection technique to isolate observation segments where statistically significant excesses in the observed count rate relative to the background estimate exist. We test the new software on archival data from the NASA Fermi Gamma-ray Burst Monitor (GBM), which has a collecting area and background level of the same order of magnitude to those of HERMES Pathfinder. The NN performances are discussed and analyzed over period of both high and low solar activity. We were able to confirm events in the Fermi/GBM catalog and found events, not present in Fermi/GBM database, that could be attributed to Solar Flares, Terrestrial Gamma-ray Flashes, Gamma-Ray Bursts, Galactic X-ray flash. Seven of these are selected and analyzed further, providing an estimate of localisation and a tentative classification.

Adversarial attacks on graphs have posed a major threat to the robustness of graph machine learning (GML) models. Naturally, there is an ever-escalating arms race between attackers and defenders. However, the strategies behind both sides are often not fairly compared under the same and realistic conditions. To bridge this gap, we present the Graph Robustness Benchmark (GRB) with the goal of providing a scalable, unified, modular, and reproducible evaluation for the adversarial robustness of GML models. GRB standardizes the process of attacks and defenses by 1) developing scalable and diverse datasets, 2) modularizing the attack and defense implementations, and 3) unifying the evaluation protocol in refined scenarios. By leveraging the GRB pipeline, the end-users can focus on the development of robust GML models with automated data processing and experimental evaluations. To support open and reproducible research on graph adversarial learning, GRB also hosts public leaderboards across different scenarios. As a starting point, we conduct extensive experiments to benchmark baseline techniques. GRB is open-source and welcomes contributions from the community.

In practice, real data sets may have missing values or otherwise have only partially observed records that complicate the validity and application validity of standard statistical methodology. Missingness may result from diverse causes, with an underlying mechanism of one of three types: missing completely at random (MCAR), missing at random (MAR), or not missing at random (NMAR) [16]. Under MCAR, the probability that a case (record, sample, observation) is missing feature (variable, attribute, dimension) values does not depend on either the observed or missing feature values. When the probability that a case is missing feature values may depend on the observed feature values, but not the missing feature values, the mechanism is MAR. In the more extreme and challenging case of NMAR, the probability that a case is missing feature values depends on both observed and missing feature values. Notably, if the data are MCAR, they are also MAR; if the data are not MAR, then they are NMAR. Strategies for analysis of data with missing values are often critically dependent on the missingness mechanism, and clustering is no exception. For clustering problems, the most common (and often expedient) treatment of missing values is deletion, on either a case or feature basis, or imputation [17], [18].

The $k$-means algorithm is the most popular nonparametric clustering method in use, but cannot generally be applied to data sets with missing observations. The usual practice with such data sets is to either impute the values under an assumption of a missing-at-random mechanism or to ignore the incomplete records, and then to use the desired clustering method. We develop an efficient version of the $k$-means algorithm that allows for clustering cases where not all the features have observations recorded. Our extension is called $k_m$-means and reduces to the $k$-means algorithm when all records are complete. We also provide strategies to initialize our algorithm and to estimate the number of groups in the data set. Illustrations and simulations demonstrate the efficacy of our approach in a variety of settings and patterns of missing data. Our methods are also applied to the clustering of gamma-ray bursts and to the analysis of activation images obtained from a functional Magnetic Resonance Imaging experiment.

To draw inferences about gamma-ray burst (GRB) source populations based on Swift observations, it is essential to understand the detection efficiency of the Swift burst alert telescope (BAT). This study considers the problem of modeling the Swift/BAT triggering algorithm for long GRBs, a computationally expensive procedure, and models it using machine learning algorithms. A large sample of simulated GRBs from Lien 2014 is used to train various models: random forests, boosted decision trees (with AdaBoost), support vector machines, and artificial neural networks. The best models have accuracies of $\gtrsim97\%$ ($\lesssim 3\%$ error), which is a significant improvement on a cut in GRB flux which has an accuracy of $89.6\%$ ($10.4\%$ error). These models are then used to measure the detection efficiency of Swift as a function of redshift $z$, which is used to perform Bayesian parameter estimation on the GRB rate distribution. We find a local GRB rate density of $n_0 \sim 0.48^{+0.41}_{-0.23} \ {\rm Gpc}^{-3} {\rm yr}^{-1}$ with power-law indices of $n_1 \sim 1.7^{+0.6}_{-0.5}$ and $n_2 \sim -5.9^{+5.7}_{-0.1}$ for GRBs above and below a break point of $z_1 \sim 6.8^{+2.8}_{-3.2}$. This methodology is able to improve upon earlier studies by more accurately modeling Swift detection and using this for fully Bayesian model fitting. The code used in this is analysis is publicly available online (https://github.com/PBGraff/SwiftGRB_PEanalysis).

Two classes of gamma-ray bursts (GRBs), short and long, have been determined without any doubts, and are usually ascribed to different progenitors, yet these classes overlap for a variety of descriptive parameters. A subsample of 46 long and 22 short $Fermi$ GRBs with estimated Hurst Exponents (HEs), complemented by minimum variability time-scales (MVTS) and durations ($T_{90}$) is used to perform a supervised Machine Learning (ML) and Monte Carlo (MC) simulation using a Support Vector Machine (SVM) algorithm. It is found that while $T_{90}$ itself performs very well in distinguishing short and long GRBs, the overall success ratio is higher when the training set is complemented by MVTS and HE. These results may allow to introduce a new (non-linear) parameter that might provide less ambiguous classification of GRBs.