Four distinct curved foldings with a given crease and crease pattern are discovered.
problem Identifying all possible curved foldings with a given crease and crease pattern.
method Analyzing the singular set of curved foldings and the initially given plane curve.
result Four distinct non-congruent curved foldings are found.
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.
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.
Study detects if a circuit bounds a disc using curve intersections.
problem Determining if a circuit bounds an embedded disc.
method Analyzing the group generated by Dehn twists about curves in a circuit.
result Cycle relation between Dehn twists detects disc-boundability.
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.
Paper explores folding patterns of curved creases preserving their geometric properties.
problem Investigating rigid-ruling folding motions of curved crease-rule patterns.
method Deriving conditions for rigid-ruling foldability and analyzing combinations of creases.
result Constant fold-angle creases are only compatible with other constant fold-angle creases.
Paper tackles curve pattern identification from fragmented cultural heritage objects.
problem Identify full design of curve patterns from fragmented cultural heritage objects.
method Two-stage matching algorithm combining template matching and CNN re-ranking.
result Proposed algorithm outperforms traditional methods in identifying curve patterns from fragmented objects.
We give new examples of closed smooth 4-manifolds which support singular metrics of nonpositive curvature, but no smooth ones, thereby answering affirmatively a question of Gromov. The obstruction comes from patterns of incompressible 2-tori sufficiently complicated to force branching of geodesics for nonpositively cur…
Simple heuristics can outperform sophisticated methods in high-dimensional pattern recognition.
problem Quantifying the difficulty of high-dimensional pattern recognition problems.
method Classification benchmarks based on simple random projection heuristics.
result Optimal classification curves asymptotes indicate no structural advantage over simple heuristics.
New knots not slice in rational 4-balls found.
problem Identifying knots not slice in rational homology 4-balls.
method Using generalized Mazur patterns and immersed Heegaard Floer homology.
result Infinitely many examples of pattern knots P not slice in any rational homology 4-ball.
Study on real algebraic curves' moduli spaces using a new complex.
problem Understanding the topology of moduli spaces of real algebraic curves.
method Defined a new complex, the ABC-complex, to encode intersection patterns. result Showed that mapping class groups are virtual duality groups and deduced orbifold homotopy group results.
In this paper is studied the behavior of principal curvature lines near a curve of umbilic points of a smooth surface.
Approach detects outliers in large datasets for credit card fraud.
problem Lack of patterns and changing fraudulent patterns make fraud detection difficult.
method Ensemble of clustering methods to assign consistency scores to data points.
result Area under precision-recall curve is a better evaluation metric for outlier detection.
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.
Study ranks of elliptic curves via prime averages.
problem Classifying elliptic curves by rank.
method Average Frobenius trace over primes, data science experiments.
result Oscillating pattern in average trace values, correlates with rank.
Random geodesics on curved surfaces form a pattern similar to random lines.
problem Understanding the geometry of random paths on curved surfaces.
method Scaling and analysis of tessellations induced by long geodesics.
result The global statistics of tessellations approach those of a Poisson line process.
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.
We describe a general family of curved-crease folding tessellations consisting of a repeating "lens" motif formed by two convex curved arcs. The third author invented the first such design in 1992, when he made both a sketch of the crease pattern and a vinyl model (pictured below). Curve fitting suggests that this init…
Slipknots found in random diagrams almost always.
problem The presence of slipknots in random diagrams.
method Developed knotoid diagrams to study slipknots in knot diagrams.
result Almost all knot diagrams are slipknotted.
Consumer Demand Response (DR) is an important research and industry problem, which seeks to categorize, predict and modify consumer's energy consumption. Unfortunately, traditional clustering methods have resulted in many hundreds of clusters, with a given consumer often associated with several clusters, making it diff…
The paper clusters PK curves using ML, finding it useful for identifying similar patterns.
problem Improving drug development and patient outcomes through ML in pharmacogenomics.
method Unsupervised clustering of PK curves using various dissimilarity measures.
result Euclidean distance is most suitable for clustering PK curves, and clustering can validate pharmacogenomic results.
Study efficient geodesics in curve complex using dot graphs.
problem Characterize efficient geodesics in curve complexes.
method Introduced dot graphs to record intersection patterns and used them to prove existence and properties of efficient geodesics.
result The shape of dot graphs for efficient geodesics is contained within a spindle shape region, controlling curve coordinates.
We consider smooth 1-parameter families of plane curves tangent to a semicubic parabola, when the curvature radius of their curves at the tangency point vanishes at the cusp point. We find the $\A$-normal form of these families, their envelopes and local patterns near the cusp. We obtain a new codimension 2 singularity…
The study computes invariants of satellite knots using bordered Floer homology.
problem Computing invariants of satellite knots with specific patterns.
method Using bordered Floer homology and the immersed curve interpretation of the bordered pairing theorem.
result Satellites with thin fibered companions or specific patterns have thin knot Floer homology.
Data science reveals patterns in elliptic curve ranks and coefficients.
problem Understanding rational points on elliptic curves via BSD conjecture.
method Data science, machine learning, topological data analysis.
result Patterns and distributions in rank versus Weierstrass coefficients.
Machine learning classifies complex geometric patterns with high accuracy.
problem Classifying extension degree of dessins d'enfants over the rationals.
method Deep feed-forward neural network trained on machine learning.
result 0.92 accuracy in classification with 0.03 standard error.
Automorphisms of curve graphs and systolic complexes are isomorphic to mapping class groups for small k.
problem Understanding the automorphism groups of curve graphs and systolic complexes.
method Proving isomorphisms between automorphism groups and mapping class groups for small k.
result Automorphism groups of curve graphs and systolic complexes are isomorphic to mapping class groups for small k.
Estimation of facial expressions, as spatio-temporal processes, can take advantage of kernel methods if one considers facial landmark positions and their motion in 3D space. We applied support vector classification with kernels derived from dynamic time-warping similarity measures. We achieved over 99% accuracy - measu…
Classifies 3-braids from choreographic motions on Lissajous curves, linking them to mapping classes and geodesics.
problem Classifying 3-braids from choreographic motions on Lissajous curves.
method Parametrization in terms of levels and slopes, using dilatation and geodesic cutting sequences.
result Dilatation of pseudo-Anosov mapping classes increases with level or slope.
This paper identifies and analyzes the Epochal Sawtooth Phenomenon in training loss curves.
problem Training loss oscillations in adaptive gradient-based optimizers.
method Empirical analysis of Adam and other optimizers, focusing on β parameters, batch size, data shuffling, and sample replacement. result The Epochal Sawtooth Phenomenon (ESP) is a recurring pattern in training loss curves, arising from adaptive learning rate adjustments and data shuffling.
Minimal area of Teichmüller curves in genus two is found to be 3π/5.
problem Finding the minimum hyperbolic area of Teichmüller curves in genus two.
method Combining small-area classification of orbifolds and affine descent construction for quadratic differentials, excluding patterns by arithmetic, marked-point, and covering obstructions.
result The minimum hyperbolic area of Teichmüller curves in genus two is 3π/5.
Deep neural networks show some layers better align with data than others.
problem Understanding why some layers in deep neural networks better align with data.
method Introducing the Equilibrium Hypothesis to connect alignment pattern to signal propagation.
result The Equilibrium Hypothesis explains the ascent-descent pattern of alignment in deep neural networks.
EvoRate metric assesses learnability of sequential data by measuring predictive information.
problem Model misspecification due to misinterpreting patterns in sequential data.
method Predictive information framework based on mutual information between past and future.
result Temporal patterns fundamentally constrain learnability; optimal predictors cannot outperform intrinsic information limit.
This paper tests yield curve generators for property-casualty insurers.
problem Quantifying interest-rate risk for property-casualty insurers with high bond holdings.
method Develops and tests yield curve generators to quantify bond-value changes.
result Tests yield curve generators against known distributional properties of yield curves.
DeepCausalMMM models marketing impacts using deep learning and causal inference.
problem Traditional MMM approaches struggle with non-linear dynamics and temporal patterns.
method Combines deep learning, causal inference, and marketing science. Uses GRUs for temporal patterns and DAG structure for channel dependencies.
result Captures non-linear dynamics and temporal patterns in marketing impacts.
Unified theory explains and mitigates double descent in data reconstruction.
problem Understanding and mitigating double descent in reduced order modeling.
method Data-Noise Averaging theory, sufficient criteria, detailed risk curve prediction, regularization mechanisms.
result Detailed risk curves predicted at reduced computational cost, instability traced to individual sensors.
The paper calculates Veech groups and Galois invariants for general origamis.
problem Understanding the structure and symmetries of origamis and their Galois invariants.
method Developed an algorithm to calculate Veech groups and orbits of Galois invariants for general origamis.
result Calculated Veech groups and Galois invariants for all origamis of degree d≤7. Lower bounds on unknotting number for cabled knots.
problem Difficulty in computing unknotting number and understanding its behavior under cabling.
method Combining knot Floer homology bounds with computations of cable knot Floer homology.
result Established a lower bound on the unknotting number of cable knots in terms of winding number.
This paper restricts efficient geodesics to non-separating curves.
problem Finding efficient geodesics in the complex of curves.
method Analysis of the dot graph and surgeries.
result Efficient geodesics can be restricted to the non-separating curve complex.
A rapid pattern-recognition approach to characterize driver's curve-negotiating behavior is proposed. To shorten the recognition time and improve the recognition of driving styles, a k-means clustering-based support vector machine ( kMC-SVM) method is developed and used for classifying drivers into two types: aggressiv…
Associated to oriented surfaces immersed in R^3 here are studied pairs of transversal foliations with singularities, defined on the Elliptic region, where the Gaussian curvature K, given by the product of the principal curvatures k_1, k_2 of the immersion, is positive. The leaves of the foliations are the lines of M- m…
A new method for pricing options with flexible volatility shapes.
problem Parameterizing risk-neutral distributions for accurate option pricing.
method Parsimonious and interpretable parameters for direct control over implied volatility curves.
result Accurate calibration across a large dataset of option curves.
Here are studied pairs of transversal foliations with singularities, defined on the Elliptic region (where the Gaussian curvature K is positive) of an oriented surface immersed in R3. The leaves of the foliations are the lines of geometric mean curvature, along which the normal curvature is given …
New multi-spiral approach improves packaging of thick membranes.
problem Deploying thick membranes on curved surfaces efficiently.
method Multi-spiral folding approach with prismatic folding lines.
result Improved deployment performance of thick membranes on curved surfaces.
GLMM trees identify subgroups with different growth patterns in longitudinal data.
problem Identifying subgroups with distinct growth trajectories in longitudinal studies.
method Extended GLMM trees for longitudinal data.
result Extended GLMM trees outperform other methods in accuracy and speed.
New methods predict drug interactions using drug co-medication patterns and graph matching.
problem Predicting adverse drug reactions from drug combinations.
method Developed novel kernels over drug combinations using support vector machines and graph matching to measure similarities.
result Achieved an AUC of 0.912 on a real-world dataset.
We give a detailed account of correlations between credit sector/quality and treasury curve factors, using the robust framework of the Barclays POINT Global Risk Model. Consistent with earlier studies, we find a strong negative correlation between sector spreads and rate shifts. However, we also observe that the correl…
The highly detailed international trade data among all countries in the world during 1971-2000 shows that the kinds of export goods and the logarithmic GDP (gross domestic production) of a country has an S-shaped relationship. This indicates all countries can be divided into three stages accordingly. First, the poor co…