Proves existence of circle patterns on surfaces with cusps.
problem Existence of circle patterns with prescribed angles on surfaces with cusps.
method Introduced combinatorial Ricci and Calabi flows to prove longtime existence and convergence.
result Existence of generalized circle patterns with prescribed angles on surfaces with cusps.
Study of combinatorial Calabi flow on ideal circle patterns.
problem Finding ideal circle patterns with prescribed curvatures.
method Combinatorial Calabi flow in hyperbolic and Euclidean geometry.
result Flow converges exponentially to ideal circle patterns.
Deep neural networks' loss surfaces contain every low-dimensional pattern.
problem Finding arbitrary low-dimensional patterns in neural network loss surfaces.
method Empirical and theoretical analysis of loss landscapes of deep neural networks.
result Deep universal approximators exhibit a property where arbitrary smooth patterns exist in their loss surfaces.
Thurston's Circle Pattern Theorem studies existence and rigidity of circle patterns of a given combinatorial type and the given non-obtuse exterior intersection angles. Using topological degree theory, variational principle, Teichmuller theory, and Sard's Theorem, this paper generalizes Circle Pattern Theorem to the ca…
The paper studies the combinatorial p-th Calabi flow for finite and infinite circle patterns.
problem Establishing convergence and long-time existence of the combinatorial p-th Calabi flow.
method Combinatorial p-th Calabi flow for finite and infinite ideal circle patterns.
result Sharp criterion for convergence in finite case and long-time existence in infinite case for p≥2. Pattern sampling has been proposed as a potential solution to the infamous pattern explosion. Instead of enumerating all patterns that satisfy the constraints, individual patterns are sampled proportional to a given quality measure. Several sampling algorithms have been proposed, but each of them has its limitations wh…
In this paper we give two different proofs of Bobenko and Springborn's theorem of circle pattern: there exists a hyperbolic (or Euclidean) circle pattern with proscribed intersection angles and cone angles on a cellular decomposed surface up to isometry (or similarity).
New method finds ideal circle patterns on spheres.
problem Finding ideal circle patterns on spheres with prescribed curvatures.
method Combinatorial Calabi flow in spherical geometry.
result Existence and convergence of the flow for ideal circle patterns.
BN^2MF identifies unknown exposure patterns in environmental mixtures.
problem Identifying unknown exposure patterns in environmental mixtures.
method Bayesian non-parametric non-negative matrix factorization (BN^2MF) with non-negative continuous priors and a non-parametric sparse prior.
result Estimates patterns of chemical exposures without specifying the number of patterns.
The paper extends circle pattern flows to hyperbolic and Euclidean geometry.
problem Extending circle pattern flows to hyperbolic and Euclidean geometry.
method Proving the existence and exponential convergence of combinatorial Calabi flows for ideal circle patterns.
result The solution to combinatorial Calabi flows converges exponentially fast to a flat cone metric.
A Delaunay cell decomposition of a surface with constant curvature gives rise to a circle pattern, consisting of the circles which are circumscribed to the facets. We treat the problem whether there exists a Delaunay cell decomposition for a given (topological) cell decomposition and given intersection angles of the ci…
Paper proves existence and uniqueness of circle patterns on surfaces with assigned geodesic curvatures.
problem Existence and uniqueness of circle patterns on surfaces with prescribed geodesic curvatures.
method Applied Perron's method and Thurston's algorithm to prove existence and convergence.
result Existence and uniqueness of circle patterns on surfaces with prescribed geodesic curvatures.
We prove that for any winding number m>0 pattern P and winding number −m pattern Q, there exist knots K such that the minimal genus of a cobordism between P(K) and Q(K) is arbitrarily large. This answers a question posed by Cochran-Harvey [CH17] and generalizes a result of Kim-Livingston [KL05].
A cornerstone of human statistical learning is the ability to extract temporal regularities / patterns from random sequences. Here we present a method of computing pattern time statistics with generating functions for first-order Markov trials and independent Bernoulli trials. We show that the pattern time statistics c…
CDPA identifies common and distinctive patterns in high-dimensional datasets.
problem Existing methods fail to capture the common pattern between coefficient matrices of shared latent factors.
method Proposes CDPA, an unsupervised learning method that incorporates both common and distinctive patterns of coefficient matrices.
result CDPA provides better characterization of common and distinctive patterns in high-dimensional datasets.
Paper solves degenerated circle pattern metric problem in spherical geometry.
problem Existence and rigidity of (degenerated) circle pattern metrics with prescribed total geodesic curvatures.
method Defined prescribed combinatorial Ricci flows and studied their convergence.
result First degenerated result for total geodesic curvatures in spherical background geometry.
New infinite-rank summand found in knot concordance group.
problem Finding an infinite-rank summand in the smooth knot concordance group.
method Using iterated satellite operations with the Mazur pattern.
result Existence of a topologically slice knot K whose iterated satellites span an infinite-rank summand. RestoreAI predicts landmine risk from patterns, improving clearance efficiency.
problem Predicting landmine risk from spatial patterns to enhance clearance efficiency.
method RestoreAI uses landmine patterns for risk prediction, implementing three deminers: linear, curved, and Bayesian.
result RestoreAI significantly boosts clearance efficiency, achieving a 14.37 percentage point increase in cleared landmines per timestep.
Paper classifies pillow box isometric deformations preserving crease patterns.
problem Classifying pillow box isometric deformations preserving crease patterns.
method Continuous isometric deformations from pillow boxes to double rectangles, preserving crease patterns.
result Such deformations necessarily change pillow box topology.
Unique circle patterns on spheres found for spherical conical metrics.
problem Non-uniqueness in circle packing for spherical metrics.
method Prescribed geodesic total curvature instead of cone angles.
result Unique existence of circle patterns for spherical conical metrics.
We present a novel algorithm, Westfall-Young light, for detecting patterns, such as itemsets and subgraphs, which are statistically significantly enriched in one of two classes. Our method corrects rigorously for multiple hypothesis testing and correlations between patterns through the Westfall-Young permutation proced…
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…
In this paper we study predictive pattern mining problems where the goal is to construct a predictive model based on a subset of predictive patterns in the database. Our main contribution is to introduce a novel method called safe pattern pruning (SPP) for a class of predictive pattern mining problems. The SPP method a…
A streaming GNN model tackles continual learning for updating node representations in real-time.
problem Learning new patterns in streaming graph data while maintaining existing patterns.
method Designing an approximation algorithm for pattern detection, combining data replaying and model regularization.
result Our model efficiently updates model parameters and achieves comparable performance to model retraining.
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.
Recent sequential pattern mining methods have used the minimum description length (MDL) principle to define an encoding scheme which describes an algorithm for mining the most compressing patterns in a database. We present a novel subsequence interleaving model based on a probabilistic model of the sequence database, w…
Proposes tPARAFAC2 for tracking evolving patterns in time-evolving data.
problem Lack of temporal regularization in tensor factorizations for capturing evolving patterns.
method Temporal PARAFAC2 (tPARAFAC2) with temporal regularization.
result tPARAFAC2 accurately captures evolving patterns better than existing methods.
New patterns on spheres and hyperbolic planes described by integrable systems.
problem Integrable systems and variational principles for spherical and hyperbolic ring patterns.
method Discrete integrable system, variational principles, elliptic dilogarithm function.
result Existence and uniqueness of ring patterns for Dirichlet and Neumann problems.
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.
The paper explores the existence of multiple curved foldings with a common crease pattern.
problem Determining the number of distinct curved foldings with a given crease and crease pattern.
method Analyzing origami maps and their singular sets, focusing on the crease and crease pattern.
result For a non-closed simple arc crease, there are exactly 4 distinct non-congruent curved foldings.
Paper proposes TRA to learn multiple stock trading patterns.
problem Inconsistent i.i.d. assumption limits stock prediction performance.
method TRA architecture with Optimal Transport for pattern assignment.
result Improves information coefficient (IC) by 0.04-0.06 compared to baselines.
With the help of hyper-ideal circle pattern theory, we have developed a discrete version of the classical uniformization theorems for surfaces represented as finite branched covers over the Riemann sphere as well as compact polyhedral surfaces with non-positive curvature. We show that in the case of such surfaces discr…
In the field of exploratory data mining, local structure in data can be described by patterns and discovered by mining algorithms. Although many solutions have been proposed to address the redundancy problems in pattern mining, most of them either provide succinct pattern sets or take the interests of the user into acc…
The existence of forbidden patterns, i.e., certain missing sequences in a given time series, is a recently proposed instrument of potential application in the study of time series. Forbidden patterns are related to the permutation entropy, which has the basic properties of classic chaos indicators, thus allowing to sep…
Fine-tunes GNNs by preserving generative patterns to improve transferability.
problem Vanilla fine-tuning fails due to structural divergence between pre-training and downstream graphs.
method G-Tuning, which reconstructs the generative patterns of the downstream graph using graphon bases.
result G-Tuning achieves an average improvement of 0.5% and 2.6% on in-domain and out-of-domain transfer learning experiments.
New criteria for ideal circle patterns on surfaces.
problem Determining when a surface supports ideal circle patterns.
method Introducing a character L(D,Φ) and using combinatorial Ricci flows. result Simpler and more easily verifiable criteria for ideal circle patterns.
New method reduces state redundancy in HSMM for driving patterns.
problem Overestimation of states in HSMM models.
method Robust HDP-HSMM (rHDP-HSMM) method to reduce redundant states.
result Improved consistency and accurate inference of driving maneuvers.
We prove existence and uniqueness results for patterns of circles with prescribed intersection angles in constant curvature surfaces. Our method is based on two new functionals--one for the Euclidean and one for the hyperbolic case. We show how Colin de Verdi`ere's, Br"agger's and Rivin's functionals can be derived fro…
Proposes a new voice conversion model that preserves pitch patterns.
problem Preserving pitch patterns while changing speaker identity.
method Variational-autoencoder-based model with an auxiliary network.
result Ensures the conversion result correctly reflects specified F0/timbre information.
As machine learning is increasingly used to make real-world decisions, recent research efforts aim to define and ensure fairness in algorithmic decision making. Existing methods often assume a fixed set of observable features to define individuals, but lack a discussion of certain features not being observed at test ti…
FinCast is a foundation model for financial time-series forecasting that outperforms existing methods.
problem Challenges in financial time-series forecasting due to temporal non-stationarity, multi-domain diversity, and varying temporal resolutions.
method FinCast is a foundation model specifically designed for financial time-series forecasting, trained on large-scale financial datasets.
result FinCast exhibits robust zero-shot performance, effectively capturing diverse patterns without domain-specific fine-tuning.
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.
Necessary and sufficient conditions are given for a satellite knot to be fibered. Any knot k~ embeds in an unknotted solid torus V~ with arbitrary winding number in such a way that no satellite knot with pattern (V~,k~) is fibered. In particular, there exist nonfibered satellite knots wit…
MCRapper efficiently computes patterns in data using Monte-Carlo Rademacher Averages.
problem Finding statistically significant patterns in data with limited samples.
method Monte-Carlo Empirical Rademacher Averages (MCERA) for poset families.
result MCRapper provides upper bounds to the discrepancy of functions, enabling efficient pattern mining.
In personalised decision making, evidence is required to determine whether an action (treatment) is suitable for an individual. Such evidence can be obtained by modelling treatment effect heterogeneity in subgroups. The existing interpretable modelling methods take a top-down approach to search for subgroups with heter…
A new kernel measures brain network similarities, improving disease classification.
problem Lack of edge weight information in existing graph kernels for brain connectivity networks.
method Ordinal pattern kernel for weighted brain connectivity networks.
result The ordinal pattern kernel achieves better classification performance than state-of-the-art graph kernels.
New PCA method handles multiple datasets and detects sparse patterns robustly.
problem Handling multi-source data with sparse and outlier-robust PCA.
method Developed a regularization problem with a penalty for structured sparsity and outlier resistance.
result The method detects global and local patterns across multiple data sources robustly.
This paper aims at the problem of link pattern prediction in collections of objects connected by multiple relation types, where each type may play a distinct role. While common link analysis models are limited to single-type link prediction, we attempt here to capture the correlations among different relation types and…