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.
Computes homology of an obstruction chain complex in grid homology.
Researchers find a Steenrod square for link Floer homology.
The least squares Monte Carlo algorithm has become popular for solving portfolio optimization problems. A simple approach is to approximate the value functions on a discrete grid of portfolio weights, then use control regression to generalize the discrete estimates. However, the classical global control regression can …
For low-dimensional data sets with a large amount of data points, standard kernel methods are usually not feasible for regression anymore. Besides simple linear models or involved heuristic deep learning models, grid-based discretizations of larger (kernel) model classes lead to algorithms, which naturally scale linear…
Researchers found algorithms to construct toric mosaics and set upper bounds for their numbers.
Inspired by the paper on quantum knots and knot mosaics [23] and grid diagrams (or arc presentations), used extensively in the computations of Heegaard-Floer knot homology [2,3,7,24], we construct the more concise representation of knot mosaics and grid diagrams via mirror-curves. Tame knot theory is equivalent to knot…
A multiple classifiers fusion localization technique using received signal strengths (RSSs) of visible light is proposed, in which the proposed system transmits different intensity modulated sinusoidal signals by LEDs and the signals received by a Photo Diode (PD) placed at various grid points. First, we obtain some {\…
Direction of arrival (DOA) estimation is a classical problem in signal processing with many practical applications. Its research has recently been advanced owing to the development of methods based on sparse signal reconstruction. While these methods have shown advantages over conventional ones, there are still difficu…
Study on typical knots and links using grid diagrams, focusing on size, components, and writhe.
New high-order approximations for CIR process using random grids.
We consider congruences of straight lines in a plane with the combinatorics of the square grid, with all elementary quadrilaterals possessing an incircle. It is shown that all the vertices of such nets (we call them incircular or IC-nets) lie on confocal conics. Our main new results are on checkerboard IC-nets in the p…
Given a grid presentation of a knot (or link) K in the three-sphere, we describe a Heegaard diagram for the knot complement in which the Heegaard surface is a torus and all elementary domains are squares. Using this diagram, we obtain a purely combinatorial description of the knot Floer homology of K.
The study of tiling homology on flat surfaces, proving impossibility of certain tilings.
Tensor completion estimates missing components by exploiting the low-rank structure of multi-way data. The recently proposed methods based on tensor train (TT) and tensor ring (TR) show better performance in image recovery than classical ones. Compared with TT and TR, the projected entangled pair state (PEPS), which is…
The accuracy of least squares calibration using option premiums and particle filtering of price data to find model parameters is determined. Derivative models using exponential Lévy processes are calibrated using regularized weighted least squares with respect to the minimal entropy martingale measure. Sequential impor…
Learning rate annealing improves robustness in stochastic optimization.
Optimal sampling reduces power grid data analysis costs.
Many attempts have been made in recent decades to integrate machine learning (ML) and topological data analysis. A prominent problem in applying persistent homology to ML tasks is finding a vector representation of a persistence diagram (PD), which is a summary diagram for representing topological features. From the pe…
SVM predicts regional rainfall with varying accuracy, best in central US.
We propose a Standing Wave Decomposition (SWD) approximation to Gaussian Process regression (GP). GP involves a costly matrix inversion operation, which limits applicability to large data analysis. For an input space that can be approximated by a grid and when correlations among data are short-ranged, the kernel matrix…
The non-stationarity characteristic of the solar power renders traditional point forecasting methods to be less useful due to large prediction errors. This results in increased uncertainties in the grid operation, thereby negatively affecting the reliability and increased cost of operation. This research paper proposes…
We present a grid diagram analogue of Carter, Rieger and Saito's smooth movie theorem. Specifically, we give definitions for grid movies, grid movie isotopies and present a definition of grid planar isotopy as a particular subset of the grid diagram moves: stabilization, destabilization and commutation. We show that gr…
New learning scheme solves high-dimensional semi-linear PDEs using sparse grids and Picard approximations.
The paper introduces triple grid diagrams to construct Lagrangian surfaces in complex projective space.
Popular machine learning estimators involve regularization parameters that can be challenging to tune, and standard strategies rely on grid search for this task. In this paper, we revisit the techniques of approximating the regularization path up to predefined tolerance in a unified framework and show that its comp…
We consider a univariate semimartingale model for (the logarithm of) an asset price, containing jumps having possibly infinite activity (IA). The nonparametric threshold estimator of the integrated variance IV proposed in Mancini 2009 is constructed using observations on a discrete time grid, and precisely it sums up t…
Half grid diagrams prove every link can be represented by a special type of grid diagram.
Grid homology confirms the Upsilon invariant in knot theory.
GridPyM handles grid diagrams for knot theory.
Grid homology theory for spatial graphs extends skein sequence.
Extends knot invariant to filtered grid complexes.
New method finds grid diagrams for many fibered knots.
The paper connects Legendrian links to cluster algebras via microlocal methods.
This paper introduces a fast, general method for dictionary-free parameter estimation in quantitative magnetic resonance imaging (QMRI) via regression with kernels (PERK). PERK first uses prior distributions and the nonlinear MR signal model to simulate many parameter-measurement pairs. Inspired by machine learning, PE…
Grid homology properties for MOY graphs studied.
Grid homology invariant proved for lens space links.
New trading strategy beats traditional grid in crypto markets.
New method constructs moduli spaces of Lagrangian surfaces in CP^2 from grid diagrams.
Develops equivariant grid homology for strongly invertible knots.
Grid homology shows knot unknotting lower bound.
SKI accelerates GP inference with sparse grids to handle higher dimensions.
Convolutional neural networks handle rotated image symmetries without dimensionality issues.
We propose a Bayesian evidence framework to facilitate transfer learning from pre-trained deep convolutional neural networks (CNNs). Our framework is formulated on top of a least squares SVM (LS-SVM) classifier, which is simple and fast in both training and testing, and achieves competitive performance in practice. The…
The paper studies grid homology for spatial graphs and proves a Künneth formula for connected sums.
In this paper we propose the first non-parametric Bayesian model using Gaussian Processes to make inference on Poisson Point Processes without resorting to gridding the domain or to introducing latent thinning points. Unlike competing models that scale cubically and have a squared memory requirement in the number of da…
Hexagon grid patterns emerge from conformal isometry in grid cell neural networks.
Minimal grid diagrams for 12-crossing prime knots identified.
It will be shown that according to theorems of K. Menger, every neuron grid if identified with a curve is able to preserve the adopted qualitative structure of a data space. Furthermore, if this identification is made, the neuron grid structure can always be mapped to a subset of a universal neuron grid which is constr…