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arXiv research

A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.

169,051 papers · 148 categories

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48 results for 1D vectors

In this paper, we introduce an inclined curves according to parallel transport frame. Also, we define a vector field called Darboux vector field of an inclined curve in and we give a new characterization such as: "α: I \subset R \rightarrow E^4 is an inclined curve \Leftrightarrow k_1 \int k_1ds + k_2 \int \k_2 +k_3ds …

2013-03-29abs ↗pdf ↗

The note answers a question about Betti numbers for 1D Euclidean space.

problem Understanding Betti numbers for vector fields and differential forms in 1D Euclidean space.
method Using Euler vector field and Lie superalgebra structure.
result The Betti numbers are 1 for the case where primary and secondary weights are equal.

Improved robustness of 1D CNNs for heart arrhythmia classification.

problem Improving the robustness of 1D CNNs for classification tasks.
method Parameterization using Cayley transform and controllability Gramian for Lipschitz-bounded CNNs.
result Improved robustness of trained Lipschitz-bounded 1D CNNs for heart arrhythmia classification.

Split learning preserves privacy in 1D CNN models for detecting heart abnormalities.

problem Privacy leakage in 1D CNN models under split learning.
method Implemented and validated an 1D CNN model under split learning, applied privacy leakage mitigation techniques.
result Split learning alone is insufficient to maintain raw data privacy in 1D CNN models.

Gradient descent trains shallow neural networks to approximate functions in 1D.

problem Approximating functions in 1D with shallow neural networks trained by gradient descent.
method Gradient descent optimization of non-convex weight space for finite width networks in 1D.
result Gradient descent can approximate functions in 1D with a minimal number of weights, balancing practical performance and theoretical capabilities.

Study improves mortality prediction in ICU patients using feature engineering and 1D CNN.

problem Improving mortality prediction in ICU patients with high-dimensional, imbalanced, and missing data.
method Feature engineering, 1D Convolutional Neural Network (1D CNN), traditional machine learning algorithms.
result Best AUC of 0.848 achieved with 1D CNN model.

Develops a framework for 1D geometric field theories and proves they are equivalent to vector bundles.

problem Classifying 1D geometric field theories.
method Formalizes geometric functorial field theories with geometric structures and smooth variations.
result 1D field theories are equivalent to vector bundles with connection and bilinear pairing.

Study on the complexity of 1D ReLU neural networks, proving growth in linear regions.

problem Understanding the complexity and expressivity of 1D ReLU neural networks.
method Analyzing the number of linear regions in randomly initialized, fully connected 1D ReLU networks in the infinite-width limit.
result The expected number of linear regions grows as a function of the number of neurons in each layer.

Study shows how 3+1D cosmologies can evolve to de Sitter space under certain conditions.

problem Understanding the evolution of 3+1D cosmologies with specific symmetry constraints.
method Mean Curvature Flow methods applied to cosmologies with positive cosmological constant and specific symmetry groups.
result Asymptotically, 3+1D cosmologies evolve to de Sitter space under certain conditions.

Supervised dimensionality reduction has emerged as an important theme in the last decade. Despite the plethora of models and formulations, there is a lack of a simple model which aims to project the set of patterns into a space defined by the classes (or categories). To this end, we set up a model in which each class i…

2016-10-27abs ↗pdf ↗

Estimates reliability of nuclear fuel using advanced modeling techniques.

problem Determining the reliability of TRISO-coated particle fuel, which has small failure probabilities and expensive computational models.
method Coupled active learning, multifidelity modeling, and subset simulation.
result Multifidelity modeling strategies consistently reduce the number of high-fidelity model calls.

Study shows inflation in 3+1D cosmologies with bounded scalar potential and specific symmetry.

problem Understanding inflation in 3+1D cosmologies with specific constraints.
method Mean curvature flow and asymptotic analysis of metric variations, stress-energy tensor, and inflaton field dynamics.
result Inflation occurs in 3+1D cosmologies with specific constraints, demonstrating it is possible with inhomogeneous initial conditions.

Simulating fluid flow in geological formations requires mesh generation, lithology mapping to the cells, and computing geometric properties such as normal vectors and volume of cells. The purpose of this research work is to compute and process the geometrical information required for performing numerical simulations in…

2006-07-17abs ↗pdf ↗

Estimates latent positions in 1D torus from noisy pairwise affinities.

problem Estimating latent positions in a 1D torus from noisy pairwise affinities.
method Introduced an estimation procedure with provable localization error of O(log(n)/n)O(\sqrt{\log(n)/n}).
result The estimation procedure provably localizes latent positions with a maximum error of O(log(n)/n)O(\sqrt{\log(n)/n}).

This study analyzes a non-orientable spacetime model in 1+1D quantum gravity.

problem Analyzing a non-orientable spacetime model in 1+1D quantum gravity.
method Formulated a Jackiw-Teitelboim gravity toy model on the Möbius band, computed Stiefel-Whitney classes, and analyzed the Dirac operator.
result Half-integer momentum quantization, spectral symmetry, vanishing mod-2 index, and η_D(0) = 0 follow.

Study no-arbitrage conditions in 1D diffusion markets with interest rates.

problem Determining no-arbitrage conditions in 1D diffusion markets with interest rates.
method Established deterministic criteria for no-arbitrage notions in terms of scale function and speed measure.
result Revealed various effects, e.g., NIP not excluded by reflecting boundaries.

New method trains generative models without discriminators, improving stability and accuracy.

problem Training implicit generative models with adversarial discriminators leads to instability and mode-dropping.
method Invariant statistical loss function, avoiding discriminators.
result Successfully trains generative models for various complex distributions without mode-dropping.

A simple block configures optimal kernel sizes for time series classification.

problem Choosing the right kernel size for time series classification.
method Proposes Omni-Scale block (OS-block) with kernel sizes determined by prime numbers.
result Models with OS-block achieve state-of-the-art performance on time series benchmarks.

Capsule networks improve temporal data understanding, achieving 96.21% ECG accuracy.

problem Improving temporal data understanding with capsule networks.
method Generated capsules along temporal and channel dimensions, learning contrasting relationships.
result Achieved 96.21% accuracy on ECG signal beat categories, surpassing state-of-the-art.

The paper proposes an ensemble of convolution-based methods for fault detection in gearboxes.

problem Fault detection in planetary gearboxes using vibration signals.
method Ensemble of three convolution kernel-based methods (ROCKET, 1D CNN with ResNet, FCN).
result Outperforms other approaches with over 98.8% accuracy.

The author studies regions foliated by 1D families of functions and their applications.

problem Understanding regions represented as foliated forms and natural smooth maps onto them.
method Investigates natural smooth maps respecting canonical projections and moment maps, focusing on foliated regions.
result Discusses the 1st derivative of functions and critical sets in foliated regions.

Ridgeless ReLU networks interpolate datasets and extrapolate based on curvature signs.

problem Interpolating and extrapolating 1D datasets with ReLU networks.
method Minimizes 2\ell_2-norm of weights, extrapolates based on curvature signs.
result Ridgeless ReLU interpolants extrapolate as nearest neighbor curvature extrapolation.

Deep neural networks continue to show improved performance with increasing depth, an encouraging trend that implies an explosion in the possible permutations of network architectures and hyperparameters for which there is little intuitive guidance. To address this increasing complexity, we propose Evolutionary DEep Net…

2017-09-26abs ↗pdf ↗

Paper proposes a method to reduce hallucinations in diffusion models using Laplacian score sharpening.

problem Hallucinations in diffusion models create incoherent or unrealistic samples.
method Post-hoc adjustment to the score function during inference using Laplacian approximation.
result Significantly reduces the rate of hallucinated samples across various data types.

State-of-the-art speaker diarization systems utilize knowledge from external data, in the form of a pre-trained distance metric, to effectively determine relative speaker identities to unseen data. However, much of recent focus has been on choosing the appropriate feature extractor, ranging from pre-trained ii-vectors…

2018-11-01abs ↗pdf ↗

A new tensor network method for image classification reduces computation cost.

problem Efficiently classifying images in high-dimensional spaces.
method Proposes a multi-layered tensor network (MLTN) that performs one MPS operation per layer, reducing computation cost.
result Reduces computation cost without degrading performance.

DPI quantifies phase differences in 1D and multidimensional signals using Riesz transform.

problem Quantifying phase differences in signals of varying dimensions.
method Riesz transform framework for harmonic analysis.
result DPI detects hypersynchronization and subtle changes in images and artworks.

CNN improves OSA diagnosis accuracy from PSG data.

problem Manual PSG analysis by specialists is tedious, time-consuming, and prone to errors.
method 1D CNN architecture with convolutional and FCN layers for OSA severity classification.
result Proposed CNN model achieves excellent classification results without manual preprocessing.