arXiv research

The paper compares inserting and stretching points for grid refinement near critical points.

This work refines grid size selection for non-interactive private $K$-means clustering.

For knots in S^3, the bi-graded hat version of knot Floer homology is defined over Z; however, for a link L in S^3 with #|L|=l>1, there are 2^{l-1} bi-graded hat versions of link Floer homology defined over Z, the multi-graded hat version of link Floer homology is only defined over F_2 from holomorphic considerations, …

We present a combinatorial proof for the existence of the sign refined grid homology in lens spaces, and a self contained proof that $\partial_{\mathbb{Z}}^2 = 0$. We also present a Sage program that computes $\widehat{\mathrm{GH}} (L(p,q),K;\mathbb{Z})$, and provide empirical evidence supporting the absence of torsion…

We re-derive Manolescu's unoriented skein exact triangle for knot Floer homology over F_2 combinatorially using grid diagrams, and extend it to the case with Z coefficients by sign refinements. Iteration of the triangle gives a cube of resolutions that converges to the knot Floer homology of an oriented link. Finally, …

Link Floer homology is an invariant for links which has recently been described entirely in a combinatorial way. Originally constructed with mod 2 coefficients, it was generalized to integer coefficients thanks to a sign refinement. In this paper, thanks to the spin extension of the permutation group we give an alterna…

Existing techniques to compress point cloud attributes leverage either geometric or video-based compression tools. We explore a radically different approach inspired by recent advances in point cloud representation learning. Point clouds can be interpreted as 2D manifolds in 3D space. Specifically, we fold a 2D grid on…

Continuous-time optimal stopping solved with deep reinforcement learning

Enhances CEV model pricing with high-order scheme and adaptive time stepping.

Kernelized Support Vector Machines (SVMs) are among the best performing supervised learning methods. But for optimal predictive performance, time-consuming parameter tuning is crucial, which impedes application. To tackle this problem, the classic model selection procedure based on grid-search and cross-validation was …

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 $ε$ in a unified framework and show that its comp…

Study non-monotonic loss functions in CRC, achieving valid risk control with large calibration samples.

The method approximates stationary distributions of Markov models by truncating irrelevant states.

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…

Unified framework for understanding TVO and improving model learning.

We develop a multilevel approach to compute approximate solutions to backward differential equations (BSDEs). The fully implementable algorithm of our multilevel scheme constructs sequential martingale control variates along a sequence of refining time-grids to reduce statistical approximation errors in an adaptive and…

The paper introduces triple grid diagrams to construct Lagrangian surfaces in complex projective space.

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.

Grid homology properties for MOY graphs studied.

3D dust map of the Milky Way improves resolution and accuracy.

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.

Computes homology of an obstruction chain complex in grid homology.

SKI accelerates GP inference with sparse grids to handle higher dimensions.

We describe a high performance parallel implementation of a derivative pricing model, within which we introduce a new parallel method for the calibration of the industry standard SABR (stochastic-αβρ) stochastic volatility model using three strike inputs. SABR calibration involves a non-linear three dimensional minimis…

The study examines numerical aspects of Karhunen-Loève expansions for stochastic processes.

The paper studies grid homology for spatial graphs and proves a Künneth formula for connected sums.

Protocol diagnoses neural HJB-PIDE solvers for Lévy jumps, revealing a missing factor in their importance-proposal density.

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…

The paper analyzes how grid cells perform path integration and learns hexagon grid patterns.

Power grids are one of the most important components of infrastructure in today's world. Every nation is dependent on the security and stability of its own power grid to provide electricity to the households and industries. A malfunction of even a small part of a power grid can cause loss of productivity, revenue and i…

The increasing penetration of distributed energy resources poses numerous reliability issues to the urban distribution grid. The topology estimation is a critical step to ensure the robustness of distribution grid operation. However, the bus connectivity and grid topology estimation are usually hard in distribution gri…

The paper studies how grid cell patterns emerge in neural networks.

This paper proposes a multi-grid method for learning energy-based generative ConvNet models of images. For each grid, we learn an energy-based probabilistic model where the energy function is defined by a bottom-up convolutional neural network (ConvNet or CNN). Learning such a model requires generating synthesized exam…

Combinatorial proof of grid homology properties.

The topology of a power grid affects its dynamic operation and settlement in the electricity market. Real-time topology identification can enable faster control action following an emergency scenario like failure of a line. This article discusses a graphical model framework for topology estimation in bulk power grids (…

Study finds cherry-picking load shaping strategies outperforms others in reducing grid CO2 emissions.

We propose a new approach to solve optimal stopping problems via simulation. Working within the backward dynamic programming/Snell envelope framework, we augment the methodology of Longstaff-Schwartz that focuses on approximating the stopping strategy. Namely, we introduce adaptive generation of the stochastic grids an…