Study circle patterns on tori, linking symplectic forms and homeomorphisms.
problem Understanding circle patterns on tori and their symplectic properties.
method Investigates the space of circle patterns on closed tori with complex projective structures, embedding it into Teichmüller spaces and analyzing symplectic forms.
result Non-degeneracy of the pulled-back Weil-Petersson symplectic form and homeomorphism between circle patterns and Teichmüller spaces.
Symplectic forms match on circle pattern space.
problem Matching symplectic forms on circle pattern space.
method Pullback of symplectic forms to circle pattern space.
result Symplectic forms on circle pattern space coincide.
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.
problem High computational complexity of exhaustive search for shapelets.
method Pattern sampling using a weighted trie to extract discriminative patterns.
result Significant reduction in computational and memory resources.
We analyze computational limits of modern Hopfield models based on pattern norms.
problem Understanding the efficiency of modern Hopfield models from a fine-grained complexity perspective.
method Fine-grained complexity analysis and upper bound criterion for pattern norms.
result Below a specific norm threshold, efficient variants of modern Hopfield models exist.
EMODM detects abnormal patterns in complex systems.
problem Detecting abnormal patterns in complex systems.
method Probabilistic models and statistical algorithms.
result EMODM detects abnormal patterns in real-time raw data.
Safe Pattern Pruning reduces pattern explosion in predictive pattern mining.
problem Exponential growth of patterns in structured data.
method Safe Pattern Pruning (SPP) method.
result Effective model building in practical data analysis.
New method computes knot Floer homology for satellite knots.
problem Computing knot Floer homology for satellite knots.
method Using immersed Heegaard diagrams and bordered Floer homology.
result Computation of knot Floer homology for satellite knots streamlined.
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.
problem Characterize circle patterns on quasi-simplicial triangulated surfaces.
method Use finite covering technique to reduce problem to simplicial case, prove characterization by KAT inequalities.
result Curvature image is characterized by KAT inequalities.
Study circle patterns and polyhedral surfaces in hyperbolic ends, proving manifold properties.
problem Understanding the space of complex projective structures on surfaces with circle patterns.
method Analyzing ideal polyhedral surfaces in hyperbolic ends, proving manifold properties and Lagrangian immersions.
result The space of complex projective structures on surfaces with circle patterns is a manifold of dimension 6g-6.
ALT improves TSC by capturing complex patterns in time series data.
problem Challenges in traditional TSC methods with time series complexity and variability.
method ALT incorporates variable-length shifted time windows to enhance LLT for better feature representation.
result ALT achieves state-of-the-art performance with few hyperparameters.
Origami patterns are classified based on their symmetry groups.
problem Classifying the symmetry groups of origami patterns.
method Iteratively compute intersection points and lines to construct mathematical origami sets, then classify them based on wallpaper groups.
result Determine which wallpaper groups can be constructed from given origami patterns.
A model predicts influential nodes in complex networks by considering indirect interactions.
problem Identifying influential nodes in complex networks using indirect interactions.
method Proposes MOGen, a multi-order generative model that considers all indirect influences up to a maximum distance.
result MOGen consistently outperforms network models and path-based approaches in predicting influential nodes.
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.
problem Defining and measuring complexity for shake-slice knots.
method Using dualizable patterns and studying knot signatures.
result Existence of n-shake-slice knots with specified complexity. New method builds complex networks from attribute interactions without normalization.
problem Improving high-level classification algorithms by capturing hidden attribute interactions.
method Proposes a new complex network building methodology based on attribute-attribute interactions, avoiding normalization.
result Demonstrates improved performance in high-level classification techniques.
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.
problem Understanding how cerebellar granular layer represents complex information.
method Constructed a model of cerebellar granular layer with gap junctions, evaluated using reservoir computing.
result Chaotic dynamics in the cerebellar granular layer produce complex and diverse output 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.
problem Incompleteness, missing information, and inaccuracies in geolocation data.
method Probabilistically ensemble similar trajectory patterns from the vicinity.
result Reconstructs missing or unreliable trajectory segments effectively.
Paper proposes efficient algorithm for recovering sparsity pattern from deterministic missing data.
problem Recovering sparsity pattern from datasets with deterministic missing structure.
method Proposes an efficient algorithm for missing value imputation using topological property of censorship filter.
result Consistently recovers the sparsity pattern with high probability in polynomial time and logarithmic sample complexity.
Transformers learn to integrate information from past positions incrementally, specializing heads in distinct patterns.
problem How transformers learn to integrate information from multiple past positions with varying statistical significance.
method High-order Markov chain task, incremental learning, sparse attention patterns, simplified differential equations, stage-wise convergence, early stopping as regularizer.
result Transformers learn to specialize heads in distinct patterns, shifting from competitive to cooperative learning dynamics.
Deep learning applied to biological data mining.
problem Mining complex biological data from diverse sources.
method Artificial neural networks, deep learning architectures.
result Deep learning techniques improve pattern recognition in biological data.
Study detects unusual trading patterns on crypto exchanges using complexity measures.
problem Detecting artificial trading activity on cryptocurrency exchanges.
method Complexity and statistical-structure measures derived from high-frequency trade-level data.
result Unusual trading patterns detected on Bitget for BTC and ETH after mid-May 2025.
Satellite knots with (1,1)-patterns have their Floer homology computed using immersed curves.
problem Computing the knot Floer homology of satellite knots with specific patterns.
method Using genus-one bordered Heegaard diagrams and immersed curves to compute the knot Floer chain complexes.
result Derivation of a formula for the τ-invariant of patterns derived from two-bridge links and computation of satellite knots' τ-invariant.
TFPS improves time series forecasting by learning pattern-specific experts.
problem Challenges in forecasting time series data with varying patterns across segments.
method Dual-domain encoder, subspace clustering, pattern-specific experts.
result Significantly improved forecasting accuracy, especially in long-term forecasting.
This research improves LSTM for monthly electricity demand forecasting using pattern-based methods.
problem Forecasting mid-term monthly electricity demand with high accuracy.
method Developed a hybrid LSTM model using x-patterns and exponential smoothing.
result The hybrid model outperformed standard LSTM and classical models.
Complex Chern-Simons theory reveals peacock patterns in perturbative series.
problem Understanding the structure of partition functions in complex Chern-Simons theory.
method Analyzing the partition function as a holomorphic function and using resurgence theory.
result Perturbative series are resurgent, with trans-series involving non-perturbative variables.
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.
problem GCNs focus too much on node features and not enough on graph structures.
method GraphSTONE employs topic models of graphs to capture structural topics, which guide the aggregation of node features.
result GraphSTONE outperforms GCNs in performance, efficiency, and interpretability.
Flexible Cox model for time-dependent covariates with complex sparsity patterns.
problem Lack of flexibility in enforcing specific sparsity patterns in time-dependent Cox models.
method Proposes a flexible framework for variable selection in time-dependent Cox models, accommodating complex selection rules.
result Achieves accurate estimation with low false alarm rates for complex covariate structures.
FSR efficiently discovers significant patterns with few resampled datasets.
problem Mining significant patterns in transactional data, especially subgroups.
method FSR uses resampling to bound the supremum deviation of quality statistics, providing rigorous guarantees on false discoveries.
result FSR effectively discovers significant subgroups with a small number of resampled datasets.
Kernel analysis reveals rumor truth from diffusion patterns alone.
problem Detecting unverified rumors on Twitter using text and user identities.
method Graph kernels to extract diffusion patterns from Twitter cascade structures.
result Diffusion patterns are highly informative of rumor truth or falsehood.
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.
problem Learning multiple graph Laplacian matrices from heterogeneous graph signals with intricate topological patterns.
method Structured fusion regularization and ADMM algorithm for efficient computation.
result Establishes a non-asymptotic bound of the estimation error and reflects the effect of key factors on convergence rate.
TimeTrail detects financial fraud patterns through temporal correlation analysis.
problem Detecting and explaining complex financial fraud patterns.
method Temporal data enrichment, dynamic correlation analysis, interpretable pattern visualization.
result TimeTrail outperforms conventional methods in accuracy and interpretability.
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.
problem Pattern recovery in penalized and thresholded estimation methods.
method Defining a novel pattern notion based on subdifferentials, introducing accessibility and noiseless recovery conditions.
result Unified and extended conditions for pattern recovery in a broad class of penalized estimators.
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…