Machine learning detects underwater gas leaks.
problem Early detection of gas leaks in underwater reservoirs.
method Machine learning and Passive Acoustic Monitoring (PAM).
result Classification algorithms achieve good performance in detecting leaks.
First-passage percolation affects graph properties like curvature and geodesics.
problem Effect of first-passage percolation on graph curvature and geodesics.
method Randomly perturbs the metric of a graph by assigning random edge lengths.
result Non-positive curvature and geodesic properties are not preserved by first-passage percolation.
Study on dropout in neural networks using percolation theory.
problem Understanding dropout's effect on neural network training.
method Investigates percolation models mimicking dropout in neural networks.
result Dropout can cause a breakdown in neural networks.
Percolation study in non-hyperbolic groups proves non-uniqueness phase.
problem Percolation in acylindrically hyperbolic groups.
method Analyzing Bernoulli bond percolation on Cayley graphs of groups.
result Non-uniqueness phase in percolation on Cayley graphs of acylindrically hyperbolic groups.
Study reveals how dengue spread patterns vary across different years in Recife, Brazil.
problem Understanding spatial organization of dengue transmission in urban areas.
method Spatial analysis of dengue cases using topological data analysis and Vietoris-Rips filtrations.
result Critical percolation thresholds define distinct geometric regimes of dengue spread.
New dimension concept for groups based on percolation probability.
problem Defining a new dimension for groups using percolation probability.
method Introducing percolation dimension pdim(G) for groups G using symmetric probability measures. result The percolation dimension pdim(G) has natural properties like monotonicity and coincides with growth rate exponents for various groups. There have been several spectral bounds for the percolation transition in networks, using spectrum of matrices associated with the network such as the adjacency matrix and the non-backtracking matrix. However they are far from being tight when the network is sparse and displays clustering or transitivity, which is repr…
FPP preserves sublinear Morse boundaries in geodesic graphs.
problem Preserving sublinear Morse boundaries in FPP.
method First passage percolation on geodesic graphs with i.i.d. passage times.
result Sublinear Morse boundaries are invariant under FPP.
Proposes using continuum percolation to analyze data manifolds and improve generative models.
problem Disentangling geometric support from probability distributions in high-dimensional data.
method Establishes a correspondence between topological phase transitions of random geometric graphs and data manifolds, using Percolation Shift metric.
result Demonstrates that Percolation Shift metric captures structural pathologies like mode collapse and guides training to prevent manifold shrinkage and improve fidelity.
We present a plausible micro-founded model for the previously postulated power law finite time singular form of the crash hazard rate in the Johansen-Ledoit-Sornette model of rational expectation bubbles. The model is based on a percolation picture of the network of traders and the concept that clusters of connected tr…
Percolation on complex networks has been used to study computer viruses, epidemics, and other casual processes. Here, we present conditions for the existence of a network specific, observation dependent, phase transition in the updated posterior of node states resulting from actively monitoring the network. Since tradi…
Machine learning predicts critical points for directed percolation models.
problem Determining critical points for directed percolation models.
method Supervised and unsupervised machine learning algorithms (CNN and DBSCAN) were used.
result Machine learning accurately predicts critical points for both models.
Study of first passage percolation on hyperbolic groups, showing velocity and coalescence.
problem Understanding the geometry and dynamics of first passage percolation on hyperbolic groups.
method Investigation of first passage times on Cayley graphs of Gromov-hyperbolic groups with i.i.d. random passage times.
result Existence and almost sure constancy of velocity in almost every direction on the boundary of the group.
Riemannian first-passage percolation (FPP) is a continuum model, with a distance function arising from a random Riemannian metric in Rd. Our main result is a shape theorem for this model, which says that large balls under this metric converge to a deterministic shape under rescaling. As a consequence, we show that …
Neural networks predict shapes of first passage percolation sets.
problem Predicting the shape of first passage percolation sets.
method Used a neural network to predict the shape of the set of discovered sites from the distribution of passage times.
result Neural networks can quickly predict the shape of the set of discovered sites from the distribution of passage times.
We propose a novel probabilistic method for detection of objects in noisy images. The method uses results from percolation and random graph theories. We present an algorithm that allows to detect objects of unknown shapes in the presence of random noise. The algorithm has linear complexity and exponential accuracy and …
We present a set of models of the main stylized facts of market price fluctuations. These models comprise dynamical evolution with threshold dynamics and Langevin price equation with multiplicative noise, percolation models to describe the interaction between traders and hierarchical cascade models to unravel the possi…
Random trees emerge from geodesics in hyperbolic groups.
problem Understanding geodesics in hyperbolic groups.
method Surveying known properties and constructing random trees.
result Rich random geometry of emerging trees.
This paper proposes a percolation-based model of new-product diffusion in the spirit of Solomon et al. (2000) and Goldenberg et al. (2000). A consumer buys the new product if she has formed her individual valuation of the product (reservation price) and if this valuation is greater or equal than the price of the produc…
Study on connectivity and geometry of random Coxeter groups.
problem Connectivity threshold for square percolation on random graphs.
method Probabilistic combinatorics and techniques from geometric group theory.
result Determines connectivity threshold and cubical coarse median structure for random Coxeter groups.
This paper presents the R package GAS for the analysis of time series under the Generalized Autoregressive Score (GAS) framework of Creal et al. (2013) and Harvey (2013). The distinctive feature of the GAS approach is the use of the score function as the driver of time-variation in the parameters of nonlinear models. T…
The study extends stochastic block models to geometric settings, focusing on community detection and information flow.
problem Generalizing community detection and information flow models to geometric settings.
method Considered a geometric random graph over a homogeneous metric space, defined a geometric counterpart of flow of information on trees.
result Sufficient conditions for recovering locations and for percolation of information in geometric settings.
Study geodesics on graphs with random lengths, proving bi-infinite paths exist.
problem Existence of bi-infinite geodesic paths on graphs with random edge lengths.
method Sublinear Morse geodesics and first passage percolation analysis.
result Proves the existence of bi-infinite geodesic paths in graphs with specific properties.
Square percolation determines threshold for group divergence in random graphs.
problem Threshold for quadratic divergence in random right-angled Coxeter groups.
method Square-graph analysis of random graphs to determine connectivity and divergence.
result Threshold probability for quadratic divergence is \( p_c(n) = \sqrt{\sqrt{6}-2}/\sqrt{n} \).
GAS models have been recently proposed in time-series econometrics as valuable tools for signal extraction and prediction. This paper details how financial risk managers can use GAS models for Value-at-Risk (VaR) prediction using the novel GAS package for R. Details and code snippets for prediction, comparison and back…
We develop an unsupervised, nonparametric, and scalable statistical learning method for detection of unknown objects in noisy images. The method uses results from percolation theory and random graph theory. We present an algorithm that allows to detect objects of unknown shapes and sizes in the presence of nonparametri…
For a given real generic curve $\ga: S^1\to \Bbb {RP}^n$ let $D_\ga$ denote the ruled hypersurface in RPn consisting of all osculating subspaces to $\ga$ of codimension 2. A curve $\ga: S^1\to \Bbb {RP}^n$ is called convex if the total number of its intersection points (counted with multiplicities) with any h…
The question we address here is of whether phenomena of collective bankruptcies are related to self-organized criticality. In order to answer it we propose a simple model of banking networks based on the random directed percolation. We study effects of one bank failure on the nucleation of contagion phase in a financia…
This paper analyzes Ethereum's gas fees and their derivatives, providing a comprehensive model.
problem Understanding and predicting gas fees on the Ethereum blockchain.
method Analyzed Ethereum's gas fee structure and used a fractional Ornstein-Uhlenbeck process to model gas prices.
result A model for pricing and trading gas fee derivatives to hedge against volatility.
Modeling Bitcoin Lightning Network emergence as percolation process.
problem Feasibility of the Lightning Network's emergence.
method Fitness-dependent network model based on percolation theory.
result Phase transition delineating sustainable vs. unsustainable Lightning Network states.
Geodesic X-ray transform proves injective for smooth one-forms on gas giant manifolds.
problem Injectivity of geodesic X-ray transform for one-forms on specific manifolds.
method Pestov identity and asymptotic analysis of short geodesics.
result Geodesic X-ray transform is solenoidally injective for smooth one-forms on gas giant manifolds.
New framework captures non-autonomous IFS limit set topology.
problem Understanding topological properties of non-autonomous IFS limit sets.
method Homological framework applied to fractal square.
result Provides insights into fractal topology, answering Mandelbrot's percolation problem.
Deep learning improves combustor anomaly detection in gas turbines.
problem Improving anomaly detection performance in gas turbine combustors.
method Hierarchically learned features from exhaust gas temperature sensor measurements using deep learning.
result Deep learning-based anomaly detection significantly improved combustor anomaly detection performance.
The percolation model of stock market speculation allows an asymmetry (in the return distribution) leading to fast downward crashes and slow upward recovery. We see more small upturns and more intermediate downturns.
We develop a novel method for detection of signals and reconstruction of images in the presence of random noise. The method uses results from percolation theory. We specifically address the problem of detection of multiple objects of unknown shapes in the case of nonparametric noise. The noise density is unknown and ca…
Study the Hessian geometry of an ideal gas in a centrifuge.
problem Understanding the Hessian geometry of an ideal gas in a centrifuge.
method Investigate the Hessian geometry associated with an ideal gas in a spherical centrifuge, using the action of the Euclidean rotation group.
result The Hessian geometry of a spherical rigid body is isometric to a hyperbolic space in the high angular velocity limit.
The prediction of the gas production from mature gas wells, due to their complex end-of-life behavior, is challenging and crucial for operational decision making. In this paper, we apply a modified deep LSTM model for prediction of the gas flow rates in mature gas wells, including the uncertainties in input parameters.…
Introduces GA-P/E, a growth-adjusted stock valuation measure.
problem Evaluating stock value and predicting future returns.
method Computes a payback period adjusted for earnings growth, using a sorted portfolio methodology.
result Low GA-P/E stocks outperform high GA-P/E stocks in absolute and risk-adjusted returns.
Improved GAS models using trees and forests for better forecasts.
problem Improving forecasts from GAS models to avoid curse of dimensionality.
method Localized parameters using decision trees and random forests.
result Significantly outperform baseline GAS model in empirical analyses.
Improved gas demand forecasting using ensemble methods.
problem Short-term prediction of gas demand components.
method Nine base forecasters (Ridge Regression, GP, NN, ANN, Torus, LASSO, Elastic Net, RF, SVR) and four ensemble predictors (simple, weighted, subset, SVR aggregation) were evaluated.
result Ensemble predictors outperformed individual base forecasters and TSO predictions.
Paper improves gas species identification in complex mixtures using neural networks.
problem Identifying gas species in multi-gas mixtures with high accuracy.
method Multi-label neural networks with optimal thresholding for IR spectroscopy.
result Optimal thresholding improves classification performance over conventional methods.
This study compares GNNs and GA-MLPs, finding GA-MLPs can distinguish graphs but not count walks.
problem Comparing expressive power and graph isomorphism testing capabilities of GNNs and GA-MLPs.
method GA-MLPs augment node features with multi-hop operators and apply MLPs node-wise; GNNs are compared as a baseline.
result GA-MLPs can distinguish almost all non-isomorphic graphs but cannot count attributed walks, unlike GNNs.
Paper proposes GAS-ALD model for financial risk prediction.
problem Skewed distribution of financial return data.
method Generalized autoregressive score (GAS) framework with asymmetric Laplace distribution (ALD).
result GAS-ALD model predicts VaR and ES more accurately than traditional models.
Optimizes routing in decentralized exchanges with gas fees.
problem Routing in decentralized exchanges with fixed gas fees.
method General optimization framework with mixed-integer model, incorporating gas fees.
result Explicit Karush-Kuhn-Tucker system linking prices, fees, and activation.
We calculate the free energy of Coulomb gas systems on Riemann surfaces.
problem Analyzing the free energy of Coulomb gas systems on Riemann surfaces.
method Using bosonization formula and analytic torsion, we derive the asymptotic expansion of the partition function.
result We prove the geometric version of the Zabrodin-Wiegmann conjecture in the determinantal case.
Study the geometry of gas giant planets to infer their internal structure.
problem Determine the interior structure of gas giant planets using boundary data.
method Geometric analysis of Riemannian manifolds with conformal blow-up at the boundary.
result The interior structure of a gas giant is uniquely determined by different types of boundary data.
GAS-Norm improves deep learning time series forecasting in non-stationary settings.
problem Deep learning models struggle with non-stationary time series data.
method Combines GAS model for adaptive normalization with deep neural networks.
result Improves deep learning performance in 21 out of 25 settings.
Modeling gas fee competition in decentralized exchanges to optimize arbitrage profits.
problem Gas fees and transaction ordering in decentralized exchanges create arbitrage opportunities.
method Developed a first equilibrium model of gas fee competition between two arbitrageurs under three transaction reversion settings.
result Mixed equilibria exist, and their characteristics depend on inventory risk and transaction settings.