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Long-period circumbinary planets appear to be as common as those orbiting single stars and have been found to frequently have orbital radii just beyond the critical distance for dynamical stability. Assessing the stability is typically done…

DARTS is a popular algorithm for neural architecture search (NAS). Despite its great advantage in search efficiency, DARTS often suffers weak stability, which reflects in the large variation among individual trials as well as the…

This paper presents a novel method for qualitative mapping of large scale spaces. The proposed framework makes use of a graphical representation of the world in order to build a map consisting of qualitative constraints on the geometric…

Adaptive Resonance Theory (ART) is considered as an effective approach for realizing continual learning thanks to its ability to handle the plasticity-stability dilemma. In general, however, the clustering performance of ART-based…

We develop necessary and sufficient conditions and a novel provably consistent and efficient algorithm for discovering topics (latent factors) from observations (documents) that are realized from a probabilistic mixture of shared latent…

Environment modeling utilizing sensor data fusion and object tracking is crucial for safe automated driving. In recent years, the classical occupancy grid map approach, which assumes a static environment, has been extended to dynamic…

The exponential increase in orbital debris and active satellites will lead to congested orbits, necessitating more frequent collision avoidance maneuvers by satellites. To minimize fuel consumption while ensuring the safety of satellites,…

We develop a stable and efficient numerical scheme for modeling the optical field evolution in a nonlinear dispersive cavity with counter propagating waves and complex, semiconductor physics gain dynamics that are expensive to evaluate. Our…

Trajectory clustering enables the discovery of common patterns in trajectory data. Current methods of trajectory clustering rely on a distance measure between two points in order to measure the dissimilarity between two trajectories. The…

Motivation: The Mapper algorithm is an essential tool to explore shape of data in topology data analysis. With a dataset as an input, the Mapper algorithm outputs a graph representing the topological features of the whole dataset. This…

Intrinsic isometric shape matching has become the standard approach for pose invariant correspondence estimation among deformable shapes. Most existing approaches assume global consistency, i.e., the metric structure of the whole manifold…

Starting from a very accurate model for density-in-cells statistics of dark matter based on large deviation theory, a bias model for the tracer density in spheres is formulated. It adopts a mean bias relation based on a quadratic bias model…

Mapper is an unsupervised machine learning algorithm generalising the notion of clustering to obtain a geometric description of a dataset. The procedure splits the data into possibly overlapping bins which are then clustered. The output of…

Kernel based methods provide a way to reconstruct potentially high-dimensional functions from meshfree samples, i.e., sampling points and corresponding target values. A crucial ingredient for this to be successful is the distribution of the…

Spectral clustering is one of the most popular clustering methods. However, how to balance the efficiency and effectiveness of the large-scale spectral clustering with limited computing resources has not been properly solved for a long…

As an alternative to the well-known methods of "chaining" and "bracketing" that have been developed in the study of random fields, a new method, which is based on a stochastic maximal inequality derived by using the Taylor expansion, is…

The stable under iterated tessellation (STIT) process is a stochastic process that produces a recursive partition of space with cut directions drawn independently from a distribution over the sphere. The case of random axis-aligned cuts is…

Grover's database search algorithm, although discovered in the context of quantum computation, can be implemented using any system that allows superposition of states. A physical realization of this algorithm is described using coupled…

Galaxy groups are essential for studying the distribution of matter on a large scale in redshift surveys and for deciphering the link between galaxy traits and their associated halos. In this work, we propose a widely applicable method for…

An influential line of recent work has focused on the generalization properties of unregularized gradient-based learning procedures applied to separable linear classification with exponentially-tailed loss functions. The ability of such…