arXiv research

Study circle patterns on tori, linking symplectic forms and homeomorphisms.

Symplectic forms match on circle pattern space.

We consider circle packings and, more generally, Delaunay circle patterns - arrangements of circles arising from a Delaunay decomposition of a finite set of points - on surfaces equipped with a complex projective structure. Motivated by a conjecture of Kojima, Mizushima and Tan, we prove that the forgetful map sending …

Temporal Pattern Mining (TPM) is the problem of mining predictive complex temporal patterns from multivariate time series in a supervised setting. We develop a new method called the Fast Temporal Pattern Mining with Extended Vertical Lists. This method utilizes an extension of the Apriori property which requires a more…

This paper formalizes a latent variable inference problem we call {\em supervised pattern discovery}, the goal of which is to find sets of observations that belong to a single ``pattern.'' We discuss two versions of the problem and prove uniform risk bounds for both. In the first version, collections of patterns can be…

Pattern sampling reduces time series classification complexity.

We analyze computational limits of modern Hopfield models based on pattern norms.

EMODM detects abnormal patterns in complex systems.

Safe Pattern Pruning reduces pattern explosion in predictive pattern mining.

New method computes knot Floer homology for satellite knots.

In this paper, we propose a new feature extraction technique for program execution logs. First, we automatically extract complex patterns from a program's behavior graph. Then, we embed these patterns into a continuous space by training an autoencoder. We evaluate the proposed features on a real-world malicious softwar…

Extends circle pattern theorem to quasi-simplicial triangulations.

Study circle patterns and polyhedral surfaces in hyperbolic ends, proving manifold properties.

ALT improves TSC by capturing complex patterns in time series data.

Origami patterns are classified based on their symmetry groups.

A model predicts influential nodes in complex networks by considering indirect interactions.

The understanding of geographical reality is a process of data representation and pattern discovery. Former studies mainly adopted continuous-field models to represent spatial variables and to investigate the underlying spatial continuity/heterogeneity in the regular spatial domain. In this article, we introduce a more…

New complexity measure for shake-slice knots established.

New method builds complex networks from attribute interactions without normalization.

Identifying important components or factors in large amounts of noisy data is a key problem in machine learning and data mining. Motivated by a pattern decomposition problem in materials discovery, aimed at discovering new materials for renewable energy, e.g. for fuel and solar cells, we introduce CombiFD, a framework …

An empirical study of joint bivariate probability distribution of two consecutive price increments for a set of stocks at time scales ranging from one minute to thirty minutes reveals asymmetric structures with respect to the axes y=0, y=x, x=0 and y=-x. All four asymmetry patterns remarkably resemble a four-blade mill…

Networks are a fundamental model of complex systems throughout the sciences, and network datasets are typically analyzed through lower-order connectivity patterns described at the level of individual nodes and edges. However, higher-order connectivity patterns captured by small subgraphs, also called network motifs, de…

In many complex dynamical systems, artificial or natural, one can observe self-organization of patterns emerging from local rules. Cellular automata, like the Game of Life (GOL), have been widely used as abstract models enabling the study of various aspects of self-organization and morphogenesis, such as the emergence …

Chaos in cerebellar cells enhances complexity of neural patterns.

In real-world, many problems can be formulated as the alignment between two geometric patterns. Previously, a great amount of research focus on the alignment of 2D or 3D patterns, especially in the field of computer vision. Recently, the alignment of geometric patterns in high dimension finds several novel applications…

Pattern ensembling fills in missing or inaccurate trajectory data.

For pattern knots admitting genus-one bordered Heegaard diagrams, we show the knot Floer chain complexes of the corresponding satellite knots can be computed using immersed curves. This, in particular, gives a convenient way to compute the $τ$-invariant. For patterns $P$ obtained from two-bridge links $b(p,q)$, we deri…

Paper proposes efficient algorithm for recovering sparsity pattern from deterministic missing data.

Transformers learn to integrate information from past positions incrementally, specializing heads in distinct patterns.

Deep learning applied to biological data mining.

Study detects unusual trading patterns on crypto exchanges using complexity measures.

TFPS improves time series forecasting by learning pattern-specific experts.

This research improves LSTM for monthly electricity demand forecasting using pattern-based methods.

Complex Chern-Simons theory reveals peacock patterns in perturbative series.

The edges of torn plastic sheets and growing leaves often display hierarchical buckling patterns. We show that this complex morphology (i) emerges even in zero strain configurations, and (ii) is driven by a competition between the two principal curvatures, rather than between bending and stretching. We identify the key…

Given a triangulation of a closed surface, we consider a cross ratio system that assigns a complex number to every edge satisfying certain polynomial equations per vertex. Every cross ratio system induces a complex projective structure together with a circle pattern on the closed surface. In particular, there is an ass…

A good cover in R^d is a collection of open contractible sets in R^d such that the intersection of any subcollection is either contractible or empty. Motivated by an analogy with convex sets, intersection patterns of good covers were studied intensively. Our main result is that intersection patterns of good covers are …

GraphSTONE uses topic models to capture graph structures, improving GCN performance.

Flexible Cox model for time-dependent covariates with complex sparsity patterns.

FSR efficiently discovers significant patterns with few resampled datasets.

Kernel analysis reveals rumor truth from diffusion patterns alone.

Analyzing and understanding the structure of complex relational data is important in many applications including analysis of the connectivity in the human brain. Such networks can have prominent patterns on different scales, calling for a hierarchically structured model. We propose two non-parametric Bayesian hierarchi…

Market Mill is a complex dependence pattern leading to nonlinear correlations and predictability in intraday dynamics of stock prices. The present paper puts together previous efforts to build a dynamical model reflecting the market mill asymmetries. We show that certain properties of the conditional dynamics at a sing…

Proposes a method to infer complex network topologies from multiple graphs.

TimeTrail detects financial fraud patterns through temporal correlation analysis.

Characterizing the dynamic interactive patterns of complex systems helps gain in-depth understanding of how components interrelate with each other while performing certain functions as a whole. In this study, we present a novel multimodal data fusion approach to construct a complex network, which models the interaction…

Unified framework for pattern recovery in penalized and thresholded estimation.

Acoustic Scene Classification (ASC) is a challenging task, as a single scene may involve multiple events that contain complex sound patterns. For example, a cooking scene may contain several sound sources including silverware clinking, chopping, frying, etc. What complicates ASC more is that classes of different activi…