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Large language models (LLMs) have achieved remarkable success in natural language processing (NLP), demonstrating significant capabilities in processing and understanding text data. However, recent studies have identified limitations in LLMs’ ability to manipulate, program, and reason about structured data, especially graphs. We introduce GraphEval36K1 , the first comprehensive graph dataset, comprising 40 graph coding problems and 36,900 test cases to evaluate the ability of LLMs on graph problem solving. Our dataset is categorized into eight primary and four sub-categories to ensure a thorough evaluation across different types of graphs. We benchmark ten LLMs, finding that private models outperform open-source ones, though the gap is narrowing. We also analyze the performance of LLMs across directed vs undirected graphs, different kinds of graph concepts, and network models. Furthermore, to improve the usability of our evaluation framework, we propose Structured Symbolic Decomposition (SSD), an instruction-based method designed to enhance LLM performance on complex graph tasks. Results show that SSD improves the average passing rate of GPT-4, GPT4o, Gemini-Pro and Claude-3-Sonnet by 8.38%, 6.78%, 29.28% and 25.28%, respectively. 

Abstract Plasma irregularities in the ionosphere induce scintillation of radio signals. Radio occultation (RO) observations of the Global Navigation Satellite Systems (GNSS) signals from low Earth orbit (LEO) allow monitoring of the ionospheric scintillation. Under certain conditions, it is possible to localize (geolocate) plasma irregularities along the line‐of‐sight between the GNSS and LEO satellites. While several techniques have been considered for the localization, in this study we use the back propagation (BP) of complex RO signals (phase and amplitude) measured at a high rate (HR), 50–100 Hz. Our method is based on a numerical solution of the wave equation, originally proposed for geolocation in 2002, with some modifications. We consider theoretical aspects of the BP technique, including assumptions, approximations and limitations, and perform numerical modeling of radio wave propagation. We investigate geolocation by BP for two regions with aligned and mis‐aligned irregularities and explain multi‐valued geolocations. We focus on the equatorial F region, consistent with the COSMIC‐2 observation sampling and use the IGRF‐13 model of the Earth's magnetic field to define the orientation of plasma irregularities. We use our method for processing of COSMIC‐2 HR scintillation data collected from the precise orbit determination antennas for 2 years: 2021 and 2023 (years with low and high solar activity). The results, represented by gridded monthly maps of geolocations, show clear seasonal and interannual variations. Additionally, we present comparison of the geolocations obtained independently from L1 and L2 signals for a 2‐month period. 

Abstract The paper presents the effects of the storm‐time prompt penetration electric fields (PPEF) and traveling atmospheric disturbances (TADs) on the total electron content (TEC), foF2 and hmF2 in the American sector (north and south) during the geomagnetic storm on 23–24 April 2023. The data show a poleward shift of the Equatorial Ionization Anomaly (EIA) crests to 18°N and 20°S in the evening of 23 April (attributed to eastward PPEF) and the EIA crests remaining almost in the same latitudes after the PPEF reversed westward. The thermospheric neutral wind velocity, foF2, hmF2, and TEC variations show that TADs from the northern and southern high latitudes propagating equatorward and crossing the equator after midnight on 23 April. The meridional keograms of ΔTEC show the TAD structures in the north/south propagated with phase velocity 470/485 m/s, wave length 4,095/4,016 km and period 2.42/2.30 hr, respectively. The interactions of the TADs also appear to modify the wind velocities in low latitudes. The eastward PPEF and equatorward TADs also favored the development of a clear/not so clear F3 layer in northern/southern regions of the equator.