Formal verification using proof assistants, such as Coq, enables the creation of high-quality software. However, the verification process requires significant expertise and manual effort to write proofs. Recent work has explored automating proof synthesis using machine learning and large language models (LLMs). This work has shown that identifying relevant premises, such as lemmas and definitions, can aid synthesis. We present Rango, a fully automated proof synthesis tool for Coq that automatically identifies relevant premises and also similar proofs from the current project and uses them during synthesis. Rango uses retrieval augmentation at every step of the proof to automatically determine which proofs and premises to include in the context of its fine-tuned LLM. In this way, Rango adapts to the project and to the evolving state of the proof. We create a new dataset, CoqStoq, of 2,226 open-source Coq projects and 196,929 theorems from GitHub, which includes both training data and a curated evaluation benchmark of well-maintained projects. On this benchmark, Rango synthesizes proofs for 32.0% of the theorems, which is 29% more theorems than the prior state-of-the-art tool Tactician. Our evaluation also shows that Rango adding relevant proofs to its context leads to a 47% increase in the number of theorems proven.

The next generation of Earth-observing spacecraft are likely to generate enormous volumes of data. A major challenge lies in the conversion of these mountains of data into information useful to researchers and other users. Hierarchical segmentation is one way to detect relationships among regions in a hyperspectral image. We implemented this algorithm on a next-generation space-capable hardware platform, and studied its performance before and after adapting it to use the platform's unique computational resources. We found that these adaptations enable an order-of-magnitude increase in performance over our initial implementation, and our detailed analysis points to areas for additional improvement.

The effectiveness of wireless sensor networks (WSNs) deployed in search and rescue, battlefield reconnaissance, surveillance, and other applications depends on inter-node interaction and maintaining network connectivity. While connectivity can be provisioned at startup, then sustained through careful coordination when nodes move, the network can be partitioned if a node suddenly fails. This paper presents recovery through inward motion (RIM), a distributed algorithm to efficiently restore network connectivity after a node failure. Instead of performing a network-wide analysis to assess the impact of the node failure and set a course of action, RIM triggers a local recovery process by relocating the neighbors of the lost node. RIM minimizes messaging overhead and reduces the distance that individual nodes travel during the recovery. Simulations validate RIM's performance.

Certain types of non-Gaussian noise sources in multicarrier communication systems behave effectively as modulating signals that control the first moment of the background Gaussian noise. The composite noise, which is the aggregate of the Gaussian and non-Gaussian noise, has a probability density function that is conditionally Gaussian with non-zero average, hence referred to as biased-Gaussian. Impulsive interferers and timing-phase error are examples of such non-Gaussian noise sources. The BER-equivalent power of a composite noise source is defined as the power of a pure Gaussian noise source that yields the same bit-error rate (BER). The BER-equivalent noise for a biased-Gaussian noise is simply the amplified version of the underlying Gaussian noise source. The amplification factor is derived from the characteristics of the non-Gaussian noise source. Any bit-loading algorithm designed for Gaussian noise sources is also applicable to biased-Gaussian noise sources provided that the BER-equivalent SNR is used in place of the measured SNR.

Impulse noise in multicarrier communication systems behaves effectively as a modulating signal that controls the first moment of the background Gaussian noise. The composite noise, which is the aggregate of the Gaussian noise and impulse noise, has a probability density function that is conditionally Gaussian with non-zero average, hence referred to as biased-Gaussian. The BER-equivalent power of the composite noise source is defined as the power of a pure Gaussian noise source that yields the same bit-error rate (BER). The BER-equivalent noise for a biased-Gaussian noise is simply the amplified version of the underlying Gaussian noise source. The amplification factor is derived from the characteristics of the impulse interference. Any bit-loading algorithm designed for Gaussian noise sources is also applicable to biased-Gaussian noise sources provided that the BER-equivalent SNR is used in place of the measured SNR.