An Optimal Algorithm for the Maximum-Density Segment Problem

We address a fundamental problem arising from analysis of biomolecular sequences. The input consists of two numbers $w_{\min}$ and $w_{\max}$ and a sequence $S$ of $n$ number pairs $(a_i,w_i)$ with $w_i>0$. Let {\em segment} $S(i,j)$ of $S$ be the consecutive subsequence of $S$ between indices $i$ and $j$. The {\em density} of $S(i,j)$ is $d(i,j)=(a_i+a_{i+1}+...+a_j)/(w_i+w_{i+1}+...+w_j)$. The {\em maximum-density segment problem} is to find a maximum-density segment over all segments $S(i,j)$ with $w_{\min}\leq w_i+w_{i+1}+...+w_j \leq w_{\max}$. The best previously known algorithm for the problem, due to Goldwasser, Kao, and Lu, runs in $O(n\log(w_{\max}-w_{\min}+1))$ time. In the present paper, we solve the problem in O(n) time. Our approach bypasses the complicated {\em right-skew decomposition}, introduced by Lin, Jiang, and Chao. As a result, our algorithm has the capability to process the input sequence in an online manner, which is an important feature for dealing with genome-scale sequences. Moreover, for a type of input sequences $S$ representable in $O(m)$ space, we show how to exploit the sparsity of $S$ and solve the maximum-density segment problem for $S$ in $O(m)$ time.Comment: 15 pages, 12 figures, an early version of this paper was presented at 11th Annual European Symposium on Algorithms (ESA 2003), Budapest, Hungary, September 15-20, 200

"An Econometric Analysis of SARS and Avian Flu on International Tourist Arrivals to Asia"

This paper compares the impacts of SARS and human deaths arising from Avian Flu on international tourist arrivals to Asia. The effects of SARS and human deaths from Avian Flu will be compared directly according to human deaths. The nature of the short run and long run relationship is examined empirically by estimating a static line fixed effect model and a difference transformation dynamic model, respectively. Empirical results from the static fixed effect and difference transformation dynamic models are consistent, and indicate that both the short run and long run SARS effect have a more significant impact on international tourist arrivals than does Avian Flu. In addition, the effects of deaths arising from both SARS and Avian Flu suggest that SARS is more important to international tourist arrivals than is Avian Flu. Thus, while Avian Flu is here to stay, its effect is currently not as significant as that of SARS.

Quantum Critical Spin-2 Chain with Emergent SU(3) Symmetry

We study the quantum critical phase of a SU(2) symmetric spin-2 chain obtained from spin-2 bosons in a one-dimensional lattice. We obtain the scaling of the entanglement entropy and finite-size energies by exact diagonalization and density-matrix renormalization group methods. From the numerical results of the energy spectrum, central charge, and scaling dimension we identify the conformal field theory describing the whole critical phase to be the SU(3)$_1$ Wess-Zumino-Witten model. We find that while in the whole critical phase the Hamiltonian is only SU(2) invariant, there is an emergent SU(3) symmetry in the thermodynamic limit

Iterative Scale-Up ExpansionIoU and Deep Features Association for Multi-Object Tracking in Sports

Multi-object tracking algorithms have made significant advancements due to the recent developments in object detection. However, most existing methods primarily focus on tracking pedestrians or vehicles, which exhibit relatively simple and regular motion patterns. Consequently, there is a scarcity of algorithms that address the tracking of targets with irregular or non-linear motion, such as multi-athlete tracking. Furthermore, popular tracking algorithms often rely on the Kalman filter for object motion modeling, which fails to track objects when their motion contradicts the linear motion assumption of the Kalman filter. Due to this reason, we proposed a novel online and robust multi-object tracking approach, named Iterative Scale-Up ExpansionIoU and Deep Features for multi-object tracking. Unlike conventional methods, we abandon the use of the Kalman filter and propose utilizing the iterative scale-up expansion IoU. This approach achieves superior tracking performance without requiring additional training data or adopting a more robust detector, all while maintaining a lower computational cost compared to other appearance-based methods. Our proposed method demonstrates remarkable effectiveness in tracking irregular motion objects, achieving a score of 75.3% in HOTA. It outperforms all state-of-the-art online tracking algorithms on the SportsMOT dataset, covering various kinds of sport scenarios

BIOMECHANICAL ANALYSIS DURING COUNTERMOVEMENT JUMP IN CHILDREN AND ADULTS

This study was to examine the biomechanical characteristics of children and adults during countermovement jump. Seven children and seven adult males were recruited to the study. A Peak high-speed camera (120Hz) synchronized with a force plate (600Hz) were used to record vertical jumping action. The kinetic parameters were calculated by using inverse dynamic method. Results showed that the children had both immature joint function prior to propulsion and inadequate knee and ankle joints function during propulsion. It is concluded that a lack of form in jumping strategy was performed during vertical jumpings in the children's group in terms of the kinetic methods was performed. This information may be used in following studies about countermovement jump, avoiding some important information needed only by kinematic analysis, it will be more complete to apply kinetic analysis for children movement researches