Stock trend prediction, the task of forecasting future trends of stocks from their historical feature sequences, remains highly challenging due to the complex and dynamic nature of financial markets. In reality, stocks form diverse relationships that transcend traditional sector boundaries as market conditions evolve, i.e., stocks within the same sector may display different trends, while those in different sectors often exhibit similar movements. However, most existing stock prediction methods rely on predefined static relationships, lacking flexibility to adapt to changing market dynamics. Furthermore, objectives widely adopted in prior work have limitations in capturing complex patterns and relationships in stock market data. To address these limitations, we propose DYCOR, a novel stock trend prediction method that integrates two key innovations: (i) dynamic stock clustering, which captures market characteristics without relying on predefined relationship data by adaptively discovering hidden stock relationships; and (ii) correlation-aware training, which aligns predicted and ground-truth stock trends by reflecting their correlations in a fine-grained manner. We evaluate DYCOR on three datasets NASDAQ, NYSE, and S&P 500 widely used in existing research, and this method demonstrates superior performance across correlation-based and retrieval-based metrics compared to state-of-the-art baseline methods, while maintaining competitive runtime efficiency.

Given four congruent balls A,B,C,D in Rδ that have disjoint interior and admit a line that intersects them in the order ABCD, we show that the distance between the centers of consecutive balls is smaller than the distance between the centers of A and D. This allows us to give a new short proof that n interior-disjoint congruent balls admit at most three geometric permutations, two if n⩾7. We also make a conjecture that would imply that n⩾4 such balls admit at most two geometric permutations, and show that if the conjecture is false, then there is a counter-example that is algebraically highly degenerate.

We study the problem of maintaining the contour tree T of a terrain Sigma, represented as a triangulated xy-monotone surface, as the heights of its vertices vary continuously with time. We characterize the combinatorial changes in T and how they relate to topological changes in Sigma. We present a kinetic data structure (KDS) for maintaining T efficiently. It maintains certificates that fail, i.e., an event occurs, only when the heights of two adjacent vertices become equal or two saddle vertices appear on the same contour. Assuming that the heights of two vertices of Sigma become equal only O(1) times and these instances can be computed in O(1) time, the KDS processes O(kappa + n) events, where n is the number of vertices in Sigma and kappa is the number of events at which the combinatorial structure of T changes, and processes each event in O(log n) time. The KDS can be extended to maintain an augmented contour tree and a join/split tree.

We present the first I/O-and practically-efficient algorithm for simplifying a planar subdivision, such that no point is moved more than a given distance ε xy and such that neighbor relations between faces (homotopy) are preserved.Under some practically realistic assumptions, our algorithm uses O(SORT(N )) I/Os, where N is the size of the decomposition and SORT(N ) is the number of I/Os need to sort in the standard externalmemory model of computation.Previously, such an algorithm was only known for the special case of contour map simplification.Our algorithm is simple enough to be of practical interest.In fact, although more general, it is significantly simpler than the previous contour map simplification algorithm.We have implemented our algorithm and present results of experimenting with it on massive reallife data.The experiments confirm that the algorithm is efficient in practice.For example, for the contour map simplification problem it is significantly faster than the previous algorithm, while obtaining approximately the same simplification factor.