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We investigate the motion in space of an infinitesimal particle in the gravitational field generated by three primary bodies positioned at the vertices of a fixed equilateral triangle. We assume that the distances between the primaries are small compared to their separation from the particle. By applying a Lie-Deprit normalization, we simplify the Hamiltonian, relegating both the mean anomaly and the argument of periapisis to third-order terms or higher. After reducing out the symmetries associated with the Kepler flow and the central action of the angular momentum, we examine the relative equilibria in the first and second reduced spaces. We are able to identify the conditions for the existence of circular periodic orbits and KAM tori, thus providing insight into the system's long-term stability and dynamic structure., Comment: 17 pages, 2 figures

Spatio-Temporal graph convolutional networks were originally introduced with CNNs as temporal blocks for feature extraction. Since then LSTM temporal blocks have been proposed and shown to have promising results. We propose a novel architecture combining both CNN and LSTM temporal blocks and then provide an empirical comparison between our new and the pre-existing models. We provide theoretical arguments for the different temporal blocks and use a multitude of tests across different datasets to assess our hypotheses.

Quasispecies theory provides the conceptual and theoretical bases for describing the dynamics of biological information of replicators subject to large mutation rates. This theory, initially conceived within the framework of prebiotic evolution, is also being used to investigate the evolutionary dynamics of RNA viruses and heterogeneous cancer cells populations. In this sense, efforts to approximate the initial quasispecies theory to more realistic scenarios have been made in recent decades. Despite this, how time lags in RNA synthesis and periodic fluctuations impact quasispecies dynamics remains poorly studied. In this article, we combine the theory of delayed ordinary differential equations and topological Leray-Schauder degree to investigate the classical quasispecies model in the single-peak fitness landscape considering time lags and periodic fluctuations in replication. First, we prove that the dynamics with time lags under the constant population constraint remains in the simplex in both forward and backward times. With backward mutation and periodic fluctuations, we prove the existence of periodic orbits regardless of time lags. Nevertheless, without backward mutation, neither periodic fluctuation nor the introduction of time lags leads to periodic orbits. However, in the case of periodic fluctuations, solutions converge exponentially to a periodic oscillation around the equilibria associated with a constant replication rate. We check the validity of the error catastrophe hypothesis assuming no backward mutation; we determine that the error threshold remains sound for the case of time of periodic fitness and time lags with constant fitness. Finally, our results show that the error threshold is not found with backward mutations., Comment: 18 pages and 7 figures

In the coming decade, artificial intelligence systems will continue to improve and revolutionise every industry and facet of human life. Designing effective, seamless and symbiotic communication paradigms between humans and AI agents is increasingly important. This paper reports a novel method for human-AI interaction by developing a direct brain-AI interface. We discuss a novel AI model, called MindSpeech, which enables open-vocabulary, continuous decoding for imagined speech. This study focuses on enhancing human-AI communication by utilising high-density functional near-infrared spectroscopy (fNIRS) data to develop an AI model capable of decoding imagined speech non-invasively. We discuss a new word cloud paradigm for data collection, improving the quality and variety of imagined sentences generated by participants and covering a broad semantic space. Utilising a prompt tuning-based approach, we employed the Llama2 large language model (LLM) for text generation guided by brain signals. Our results show significant improvements in key metrics, such as BLEU-1 and BERT P scores, for three out of four participants, demonstrating the method's effectiveness. Additionally, we demonstrate that combining data from multiple participants enhances the decoder performance, with statistically significant improvements in BERT scores for two participants. Furthermore, we demonstrated significantly above-chance decoding accuracy for imagined speech versus resting conditions and the identified activated brain regions during imagined speech tasks in our study are consistent with the previous studies on brain regions involved in speech encoding. This study underscores the feasibility of continuous imagined speech decoding. By integrating high-density fNIRS with advanced AI techniques, we highlight the potential for non-invasive, accurate communication systems with AI in the near future.

In the coming decade, artificial intelligence systems are set to revolutionise every industry and facet of human life. Building communication systems that enable seamless and symbiotic communication between humans and AI agents is increasingly important. This research advances the field of human-AI interaction by developing an innovative approach to decode imagined speech using non-invasive high-density functional near-infrared spectroscopy (fNIRS). Notably, this study introduces MindGPT, the first thought-to-LLM (large language model) system in the world.

Deep learning has shown remarkable results on Euclidean data (e.g. audio, images, text) however this type of data is limited in the amount of relational information it can hold. In mathematics we can model more general relational data in a graph structure while retaining Euclidean data as associated node or edge features. Due to the ubiquity of graph data, and its ability to hold multiple dimensions of information, graph deep learning has become a fast emerging field. We look at applying and optimising graph deep learning on a finance graph to produce more informed clusters of companies. Having clusters produced from multiple streams of data can be highly useful in quantitative finance; not only does it allow clusters to be tailored to the specific task but the culmination of multiple streams allows for cross source pattern recognition that would have otherwise gone unnoticed. This can provide financial institutions with an edge over competitors which is crucial in the heavily optimised world of trading. In this paper we use news co-occurrence and stock price for our data combination. We optimise our model to achieve an average testing precision of 78% and find a clear improvement in clustering capabilities when dual data sources are used; cluster purity rises from 32% for just vertex data and 42% for just edge data to 64% when both are used in comparisons to ground-truth Bloomberg clusters. The framework we provide utilises unsupervised learning which we view as key for future work due to the volume of unlabelled data in financial markets.

One hundred forty-seven students enrolled in a developmental reading program responded to a questionnaire designed to ascertain the reading attitudes and interests of middle school students. It was hypothesized that by overemphasizing basic skills instruction, schools may not be taking the necessary steps to help students develop the ability and desire to read and learn independently. Specifically the questions were designed to learn (1) what percentage of students felt the reading materials were of practical value to them, (2) what percentage found the materials of interest, (3) students' reading interests, and (4) students' perceptions of teacher choices of material for them. The results indicated that 71% felt that the materials helped them in other school subjects, but only half felt the materials helped them outside of school. Forty percent liked the reading materials; 60% did not. Sports was the subject of greatest interest, followed by animals, mystery, comics and humorous stories, and science fiction. Only half felt that teachers would select books to match their reading interests. The results seemed to indicate a lack of communication between students and teachers in the reading material selection process, and suggested a need for teachers and students to discuss the value of all activities in reading class. (The questionnaire used in the study is appended.) (HTH)