Geometry problem solving (GPS) requires high-level symbolic and logical reasoning based on geometry theorem knowledge to arrive at the answer. Despite the remarkable advances achieved by Large Language Models (LLMs) in various problem-solving tasks, they still struggle to perform rigorous multi-step geometry reasoning, which is essential for GPS. In this paper, we propose a dynamic tree-based geometry problem solver named GeoTree, which combines a knowledgeable LLM with a rigorous symbolic solver to perform geometry reasoning cooperatively. Specifically, an iterative multi-step geometry reasoning process is performed dynamically based on a tree-like structure, thereby emulating divergent and deliberate human problem-solving thinking. Each geometry reasoning step is completed collaboratively through four components, consisting ofTheorem Seeker,Symbolic Solver,Evaluator, andController. First,Theorem Seekerprompts LLMs to seek out candidate theorems with their inherent geometry theorem knowledge. Subsequently,Symbolic Solverapplies the theorems on the known conditions to obtain new additional conditions. Then,Evaluatorassesses the availability of the theorems and prompts LLMs to judge the usefulness of these new conditions for the problem target, which serves as the heuristic guidance for subsequent reasoning. Finally,Controllerdetermines the termination state, which decides whether to continue invoking the other three components for further attempts. Extensive experiments on Geometry3K demonstrate the superiority of GeoTree in accuracy, efficiency, and explainability.

Multi-UAV cooperative reconnaissance for target search, localization, and tracking has attracted much attention in both civil and military applications, where strategies need to be designed for UAVs to finish the reconnaissance task cooperatively and in the time optimal manner. Different from the state-of-the-art of recent research where all the UAVs involved are equipped with homogeneous payloads, this work exploits payload diversity to enhance the time efficiency of the cooperation and proposes a fast multi-UAV cooperative reconnaissance (FMUCR) method. FMUCR groups UAVs in pairs. In each pair, one UAV is equipped with a passive positioning radar, referred to as p-UAV, while another is equipped with an active positioning radar, referred to as a-UAV. FMUCR exploits the large detection range and rough target location detection of passive radar to enable fast search and directional tracking of a target, while the precise target position calculation of active radar to enable accurate tracking of a target. Specifically, the task area is partitioned into subareas according to the number of UAV pairs. Each UAV pair conducts target search, localization, and tracking in one subarea, where the p-UAV leads searching and preliminary tracking of targets, while accurate tracking of targets are taken over by the a-UAV. Algorithms for off-line path planning and on-line path planning are designed, respectively, for target search and target tracking. The comparative simulation demonstrates that, FMUCR can greatly shorten the target discovery time with little loss in target tracking accuracy.

A multi-hop multi-AP multi-channel cooperation scheme, referred to as MHACWlan, is proposed for the purpose of improving the efficiency and performance of wireless local area network (WLAN) in dense scenarios, which is the top concern of HEW (High Efficiency WLAN), a IEEE 802.11 study group created in 2013. The proposed MHACWlan provides an effective way to solve the performance anomaly problem, interference problem, and the load imbalance problem in dense WLAN. In MHACWlan, we considers two-hop association to the APs for the wireless STAs with poor single-hop links to improve the throughput, assigning different channels for the two-hop links to reduce the interference and increase the throughput, and associating with more than one AP so as to balance the load. The mathematical analysis and simulation results demonstrate the performance benefits of MHACWlan compared to the traditional WLAN.

Channel allocation has become a significant challenge in multi-channel Ad-Hoc networks due to the fast growing of wireless applications and the limitation of spectrum resource. In this paper, we assume that the demand of each user is different and alterable, which has been known by all the others. We study the problem of demand-aware channel allocation (DaChA) from a non-cooperative strategic game theoretic view. We show that the game would converge to a Nash Equilibrium (NE), but the NE may be sub-optimal. To avoid this possible situation, we propose a novel mechanism which assigns a prior channel to each communication link. If deviating from the prior channel, we design a charging scheme which would induce players to converge to a unique NE. We analyze the Pareto-Optimality (PO) of the game and work out that the unique NE must be Pareto optimal. The simulation results demonstrate that the mechanism is efficient.

Femtocells have emerged as an effective solution to enhance indoor coverage and improve system performance in cellular networks. However, the inter-cell interference (ICI) caused by the unplanned nature of femtocells considerably leads to the degradation in throughput of users with guaranteed performance (GP). Meanwhile, the existing resource allocation algorithms bring about high complexity and large overhead. By tracking channel variation as well as arrival and departure of users, we propose a hybrid centralized/distributed resource allocation algorithm to maximize the number of GP users, with lower complexity and smaller overhead. Simulation results show that the proposed algorithm can significantly improve the system performance compared to the existing algorithms such as Q-FCRA.

The emerging Machine-to-machine (M2M) communications are posing serious challenges to cellular network systems. When a high number of M2M devices try to send data almost simultaneously, the air interface congestion would result in significant quality of service degradation in conventional Humanto- Human (H2H) communications. To solve this problem, an uplink intercell coordination admission control and scheduling scheme (ACSS) in a CDMA multicell environment is proposed in this paper, which makes the best of M2M delay tolerant feature. Delay tolerant M2M connections in the home cell and neighbor cells can be interrupted to release resource for H2H services and reestablished later. The final M2M set to be scheduled is determined by the maximum throughput criterion and residual tolerant delay criterion. Simulation results have shown that with ACSS the H2H blocking probability can be guaranteed and M2M transmission failures can be reduced, achieving better system performance and higher resource utilization.

Channel assignment is a significant challenge due to scarcity of number of channels available in multi-channel multi-radio Ad Hoc networks. Meanwhile, traffic allocation is a problem worthy of research especially in the situation that different traffic demands for different users. In this paper, we formulate the problem of joint channel and traffic assignment as a static non-cooperative game with charging scheme, taking into account the different individual demand constraints, the number of channels, and the number of radios. To some extent, the charging scheme alleviates the unfairness problem. We show the existence of Nash Equilibrium (NE) and derive the sufficient and necessary conditions to be NE. Then, the uniqueness of the Nash Equilibrium is demonstrated under reasonable conditions. Finally, we extend the algorithm to multiple collision domains. The simulation results illustrates the algorithm is efficient and has a better performance.

Density based clustering is an effective and basic clustering techniques for data with spatial attributes. Although there are many proposed algorithms and applications for density based spatial clustering, one of its widely used assumptions is that the data is distributed in a smooth space, the Euclidean space Rnfor example. On the other hand, manifolds are approximately curved spaces which are locally like smooth spaces but not smooth spaces. The purpose of this paper is to propose new density based clustering algorithms on manifolds, that is, on curved spaces. This is achieved mainly with the help of tangent spaces that are determined by manifold learning. Applications are presented for the automatic classification in creative design.