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A symbolic analysis of observed time series data requires making a discrete partition of a continuous state space containing observations of the dynamics. A particular kind of partition, called ``generating'', preserves all dynamical…
Dynamic maps that allow continuous map rotations, e.g., on mobile devices, encounter new issues unseen in static map labeling before. We study the following dynamic map labeling problem: The input is a static, labeled map, i.e., a set P of…
Embedding large graphs in low dimensional spaces has recently attracted significant interest due to its wide applications such as graph visualization, link prediction and node classification. Existing methods focus on computing the…
Persistent homology is a powerful mathematical tool that summarizes useful information about the shape of data allowing one to detect persistent topological features while one adjusts the resolution. However, the computation of such…
An accurate depth map of the environment is critical to the safe operation of autonomous robots and vehicles. Currently, either light detection and ranging (LIDAR) or stereo matching algorithms are used to acquire such depth information.…
Medical imaging quantitative features had once disputable usefulness in clinical studies. Nowadays, advancements in analysis techniques, for instance through machine learning, have enabled quantitative features to be progressively useful in…
A contiguous area cartogram is a geographic map in which the area of each region is proportional to numerical data (e.g., population size) while keeping neighboring regions connected. In this study, we investigated whether value-to-area…
This paper proposes a stable volume and a stable volume variant, referred to as a stable sub-volume, for more reliable data analysis using persistent homology. In prior research, an optimal cycle and similar ideas have been proposed to…
We consider the degree-Rips construction from topological data analysis, which provides a density-sensitive, multiparameter hierarchical clustering algorithm. We analyze its stability to perturbations of the input data using the…
Assessing the boundedness and stability of vector nonlinear systems with variable delays and coefficients remains a challenging problem with broad applications in science and engineering. Existing methods tend to produce overly conservative…
This paper is concerned with the matching stability problem across different decoder layers in DEtection TRansformers (DETR). We point out that the unstable matching in DETR is caused by a multi-optimization path problem, which is…
Existing methods rarely capture the temporal evolution of solution norms in vector nonlinear DDEs with variable delays and coefficients, often leading to overly conservative boundedness and stability criteria. We develop a framework that…
We introduce a generalized version of the famous Stable Marriage problem, now based on multi-modal preference lists. The central twist herein is to allow each agent to rank its potentially matching counterparts based on more than one…
By varying a parameter of a one-dimensional piecewise smooth map, stable periodic orbits are observed. In this paper, complete analytic characterization of these stable periodic orbits is obtained. An interesting relationship between the…
Exchangeable graph models (ExGM) subsume a number of popular network models. The mathematical object that characterizes an ExGM is termed a graphon. Finding scalable estimators of graphons, provably consistent, remains an open issue. In…
A graph with convex quadratic stability number is a graph for which the stability number is determined by solving a convex quadratic program. Since the very beginning, where a convex quadratic programming upper bound on the stability number…
We extend and improve the existing characterization of the dynamics of general quadratic real polynomial maps with coefficients that depend on a single parameter $\lambda$, and generalize this characterization to cubic real polynomial maps,…
Motivation: Radiomics refers to the high-throughput mining of quantitative features from radiographic images. It is a promising field in that it may provide a non-invasive solution for screening and classification. Standard machine learning…
Continuous attractor networks (CANs) are widely used to model how the brain temporarily retains continuous behavioural variables via persistent recurrent activity, such as an animal's position in an environment. However, this memory…
This paper presents a novel methodology for evaluating the boundedness, stability, and instability of some vector nonlinear systems with multiple time-varying delays and variable coefficients. The proposed technique develops two scalar…