OCLEP+ detects anomalies and intrusions with short patterns.
problem Detecting anomalies and intrusions in minimal data.
method One-class Classification using Length statistics of Emerging Patterns Plus.
result Effective detection of anomalies and intrusions with minimal data.
We suggest a new definition for discrete minimal surfaces in terms of sphere packings with orthogonally intersecting circles. These discrete minimal surfaces can be constructed from Schramm's circle patterns. We present a variational principle which allows us to construct discrete analogues of some classical minimal su…
Survey on discrete minimal surfaces and their properties.
problem Discretizing minimal surfaces in Euclidean space.
method Polyhedral surfaces with parallel face offsets and circle patterns.
result All simply connected discrete minimal surfaces can be constructed from circle patterns.
Proposes a new method for finding frequent closed patterns in transaction bases.
problem Frequent closed patterns in transaction bases.
method Partitioning the search space into subcontexts and updating frequent closed patterns with their minimal generators.
result Proposed approach called UFCIGs-DAC for efficient search of frequent closed itemsets.
A new associative memory uses Sinkhorn divergence for efficient pattern retrieval.
problem Efficiently retrieving patterns from large datasets of weighted point clouds.
method Derived retrieval dynamics as a SHK gradient flow, discretized for a deterministic algorithm.
result Proved basin invariance, geometric convergence, and robust recovery from perturbations.
Crochet patterns for minimal surfaces created using trigonometry.
problem Creating crochet patterns for minimal surfaces.
method Using trigonometric identities to calculate arc lengths.
result Crochet instructions for Enneper's surface.
The paper introduces false discovery rate control for BMF to avoid noisy patterns.
problem No guarantees exist for BMF patterns being real, not just noise.
method Proposes false discovery rate (FDR) to control BMF patterns, proving bounds on FDR.
result Improved BMF algorithms using theoretical FDR bounds for rank selection.
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].
Minimal DAMs can recognize patterns in high noise, even with minimal data.
problem Pattern recognition in high noise conditions with limited data.
method Interpolating between DAMs and spin glasses, using minimal dense associative networks and extremizing quenched free-energy.
result Minimal DAMs can correctly recognize patterns even when the signal is very weak and noise is high.
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…
A major breakthrough in the theory of topological algorithms occurred in 1992 when Hyam Rubinstein introduced the idea of an almost normal surface. We explain how almost normal surfaces emerged naturally from the study of geodesics and minimal surfaces. Patterns of stable and unstable geodesics can be used to character…
Given a class of objects, a pattern theorem is a powerful result describing their structure. We show that alternating knots exhibit a pattern theorem, and use this result to prove a long-standing conjecture that alternating knots grow rare. This is currently the best possible analogue of a pair of theorems on alternati…
Algorithm reduces cusps and singular components in maps of surfaces with boundary.
problem Minimizing cusps and singular components in maps of surfaces with boundary.
method Explicit algorithm that modifies maps locally by creating or eliminating pairs of cusps.
result Minimal number of cusps is at most one and minimal number of singular components can be computed.
New satellite knots found that can't be represented by positive braids with full twists.
problem Satellite knots that cannot be represented by positive braids with full twists.
method Analyzing positive minimal braids and their closures to find satellite knots.
result Infinitely many satellite knots with Lorenz patterns and companions are not Lorenz knots.
METRO predicts reactions using minimal templates, reducing computational overhead and achieving state-of-the-art results.
problem Predicting possible reaction substrates for complex molecules from simpler precursors.
method METRO (Molecule-Edit Templates for RetrOsynthesis) uses minimal templates to predict reactions efficiently and accurately.
result METRO achieves state-of-the-art results on standard benchmarks, reducing computational overhead.
This work improves dictionary learning speed without sacrificing accuracy.
problem Prohibitive computational cost of standard dictionary learning methods.
method Approximate dictionary learning using unrolling and gradient descent.
result Unrolling outperforms standard methods in support estimation and early iterations.
We consider the empirical risk minimization problem for linear supervised learning, with regularization by structured sparsity-inducing norms. These are defined as sums of Euclidean norms on certain subsets of variables, extending the usual ℓ1-norm and the group ℓ1-norm by allowing the subsets to overlap. T…
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.
A novel framework infers causal direction from symbolic sequences using pattern entropy.
problem Challenges in discovering causal direction from temporal symbolic data.
method Dictionary Based Pattern Entropy (DPE) framework integrating AIT and Shannon Information Theory. result Minimizing pattern level uncertainty yields a robust framework for causal discovery.
We obtain a unified theory of discrete minimal surfaces based on discrete holomorphic quadratic differentials via a Weierstrass representation. Our discrete holomorphic quadratic differential are invariant under Möbius transformations. They can be obtained from discrete harmonic functions in the sense of the cotangent …
New guarantees for matrix completion from any deterministic sampling patterns.
problem Proving guarantees for low-rank matrix completion from non-random sampling schemes.
method Introduced a graph with observed entries as edges to analyze the performance of constrained nuclear norm minimization algorithm.
result The algorithm can successfully complete the matrix if the observation graph is well-connected and has similar node degrees.
New discrete cmc surfaces defined from sphere packings and combinatorics.
problem Creating constant mean curvature surfaces from discrete data.
method Discrete cmc surfaces defined via sphere packings and combinatorial patterns.
result Construction of discrete cmc surfaces from orthogonal ring patterns.
We derive optimal statistical and computational complexity bounds for exp-concave stochastic minimization in terms of the effective dimension. For common eigendecay patterns of the population covariance matrix, this quantity is significantly smaller than the ambient dimension. Our results reveal interesting connections…
RTM extends TM for continuous output problems using conjunctive clauses.
problem Continuous output problems in machine learning.
method Modified inner inference mechanism to produce a single continuous output.
result RTM achieves better regression accuracy with fewer clauses.
Study on bounds of knot untangling for specific types of knots.
problem Determining upper limits for knot untangling.
method Defined warping degree, examined diagrams combinatorially.
result Upper bounds for unknotting and region unknotting numbers.
The paper explores discrete isothermic nets using checkerboard patterns in quadrilateral nets.
problem Defining and understanding discrete isothermic nets in quadrilateral nets.
method Using checkerboard patterns and discrete differential geometry to define and analyze isothermic nets.
result The class of isothermic nets is invariant under dualization and Moebius transformations.
CLSVAE repairs systematic errors in images with minimal labeled data.
problem Repairing systematic errors in data, especially in images.
method CLSVAE models inliers as a smaller latent space representation, separating inlier and outlier patterns.
result CLSVAE achieves superior repairs with less than 2% labeled data, outperforming other methods.
New neural network can learn multiple patterns at once.
problem Learning multiple patterns simultaneously in neural networks.
method Multitasking Hebbian Network (MHN) for parallel learning of sparse data-sets.
result MHN can handle multiple patterns hierarchically or in parallel, depending on dilution.
In this work we establish the tightest lower bound up-to-date for the minimal crossing number of a satellite knot based on the minimal crossing number of the companion used to build the satellite. If M is the wrapping number of the pattern knot, we essentially show that c(Sat(P,C))>2M2c(C). The existence …
New method detects money laundering in Bitcoin using minimal labels.
problem Detecting money laundering in Bitcoin transactions with scarce labels.
method Active learning approach to anomaly detection.
result 5% of labels are sufficient to match supervised baseline performance.
This paper proposes grid cells encode position via a conformal isometric embedding of 2D physical space.
problem Hexagonal grid firing patterns in grid cells.
method Learning a distance-preserving position embedding in neural space using a recurrent neural network.
result The conformal isometric embedding of 2D physical space into neural space explains hexagonal grid firing patterns.
The standard approach to compressive sampling considers recovering an unknown deterministic signal with certain known structure, and designing the sub-sampling pattern and recovery algorithm based on the known structure. This approach requires looking for a good representation that reveals the signal structure, and sol…
Paper proposes a new tensor imputation method for spatiotemporal traffic data with missing patterns.
problem Imputation of corrupted or incomplete traffic data.
method Truncated tensor Schatten p-norm (TSpN) for spatiotemporal traffic data imputation.
result The proposed method outperforms other state-of-the-art tensor-based imputation models in various missing cases.
We found a class of triangulated surfaces in Euclidean space which have similar properties as isothermic surfaces in Differential Geometry. We call a surface isothermic if it admits an infinitesimal isometric deformation preserving the mean curvature integrand locally. We show that this class is Möbius invariant. Isoth…
Develops methods to improve demand counterfactuals from imperfect proxies.
problem Imperfect proxies in demand models lead to biased counterfactuals and invalid inference.
method Practical toolkit for market-level and individual data, requiring minimal computation.
result Improves substitution prediction and counterfactual performance.
The paper improves tensor completion bounds using spectral gap.
problem Theoretical limitations in tensor completion, especially for deterministic sampling.
method Bounding the generalization error of tensor completion methods using spectral gap.
result Improved bounds on tensor completion error, reducing rank dependence.
Binary feedback outperforms ordinal comparisons in ranking recovery.
problem Challenges the conventional wisdom that ordinal comparisons offer richer information.
method Proposes a parametric framework for modeling ordinal paired comparisons, binarizing ordinal data, and proving faster convergence rates for binary comparisons.
result Binarizing ordinal data significantly improves ranking recovery accuracy and exhibits a substantial performance gap.
Researchers quantify the relationship between feature depth and performance in deep neural networks.
problem Understanding how depth affects feature extraction and generalization in deep neural networks.
method Adaptive analysis of feature-depth trade-offs in deep nets, proving optimal generalization performance.
result Optimal generalization performance achieved through empirical risk minimization on deep nets.
New method for tensor completion from specific mode observations.
problem Recovering multiway data tensors from partial observations.
method Tensor train decomposition for fiber-wise observations.
result Deterministic recovery guarantees for specific observation patterns.
Meta-learning approach for fast and compressive energy-based memory models.
problem Learning associative memory with fast and compressive models for complex data.
method Meta-learning approach to energy-based memory models (EBMM) using arbitrary neural architectures.
result Demonstrated associative retrieval outperforming existing systems in reconstruction error and compression rate.
This paper is a contribution to interweaving two lines of research that have progressed in separate ways: network analyses of international trade and the literature on African trade and development. Gathering empirical data on African countries has important limitations and so does the space occupied by African countri…
Faster Tsetlin Machines use clause indexing to speed inference and learning.
problem Overfitting and slow inference in Tsetlin Machines.
method Introduced a look-up table that indexes clauses based on feature falsification, enabling faster evaluation of clauses.
result Up to 15 times faster classification and three times faster learning on MNIST and Fashion-MNIST.
Framework synthesizes geological images minimizing patch distribution discrepancy.
problem Synthesizing realistic geological images from a single exemplar.
method Uses kernel discrepancies and generative neural networks for efficient synthesis.
result Synthesized images match visual patterns and spatial statistics of the exemplar.
Using geodesic currents, we provide a theoretical justification for some of the experimental results regarding the behavior of Whitehead's algorithm on non-minimal inputs, that were obtained by Haralick, Miasnikov and Myasnikov via pattern recognition methods. In particular we prove that the images of "random" elements…
Extremely preterm infants commonly require intubation and invasive mechanical ventilation after birth. While the duration of mechanical ventilation should be minimized in order to avoid complications, extubation failure is associated with increases in morbidities and mortality. As part of a prospective observational st…
A new framework detects changepoints in complex data.
problem Detecting structural changes in data with various patterns and trends.
method Iteratively Reweighted Fused Lasso (IRFL) for L0 model selection.
result IRFL achieves accurate changepoint detection across various challenging scenarios.
Identifying context-specific entity networks from aggregated data is an important task, arising often in bioinformatics and neuroimaging. Computationally, this task can be formulated as jointly estimating multiple different, but related, sparse Undirected Graphical Models (UGM) from aggregated samples across several co…
Frequency-specific patterns of neural activity are traditionally interpreted as sustained rhythmic oscillations, and related to cognitive mechanisms such as attention, high level visual processing or motor control. While alpha waves (8-12 Hz) are known to closely resemble short sinusoids, and thus are revealed by Fouri…