We study the problem of determining whether a piece of text has been authored by a human or by a large language model (LLM). Existing state of the art logits-based detectors make use of statistics derived from the log-probability of the observed text evaluated using the distribution function of a given source LLM. However, relying solely on log probabilities can be sub-optimal. In response, we introduce AdaDetectGPT -- a novel classifier that adaptively learns a witness function from training data to enhance the performance of logits-based detectors. We provide statistical guarantees on its true positive rate, false positive rate, true negative rate and false negative rate. Extensive numerical studies show AdaDetectGPT nearly uniformly improves the state-of-the-art method in various combination of datasets and LLMs, and the improvement can reach up to 37\%. A python implementation of our method is available at https://github.com/Mamba413/AdaDetectGPT.

In this paper, a geometry-based stochastic model (GBSM) is proposed for multiple-input multiple-output (MIMO) maritime multi-user land-to-ship communication channels. The inter-link correlation between different users is modeled by spatial correlated large scale parameters (LSPs). In addition, the evaporation duct is modeled based on a twin-cluster model, and the signal propagation between two clusters is simulated by several-order reflections to obtain the delay and angle parameters of each ray. Simulations based on the proposed model focus on analyzing the statistical properties that reflect the spatial correlation between multiple users. Effects of the number of antennas, multipath components (MPCs), and different heights of evaporation duct on the correlation between users and the channel capacity are investigated and corresponding conclusions are drawn.