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.
Square percolation determines threshold for group divergence in random graphs.
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 …
Study on connectivity and geometry of random Coxeter groups.
New framework captures non-autonomous IFS limit set topology.
First-passage percolation affects graph properties like curvature and geodesics.
Study on dropout in neural networks using percolation theory.
Percolation study in non-hyperbolic groups proves non-uniqueness phase.
Study reveals how dengue spread patterns vary across different years in Recife, Brazil.
New dimension concept for groups based on percolation probability.
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.
Proposes using continuum percolation to analyze data manifolds and improve generative models.
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.
Riemannian first-passage percolation (FPP) is a continuum model, with a distance function arising from a random Riemannian metric in . 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.
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…
This paper initiates the study of topological arbiters, a concept rooted in Poincare-Lefschetz duality. Given an n-dimensional manifold W, a topological arbiter associates a value 0 or 1 to codimension zero submanifolds of W, subject to natural topological and duality axioms. For example, there is a unique arbiter on $…
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…
The study extends stochastic block models to geometric settings, focusing on community detection and information flow.
Study geodesics on graphs with random lengths, proving bi-infinite paths exist.
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…
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…
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…
The ungrammatical sentence "The key to the cabinets are on the table" is known to lead to an illusion of grammaticality. As discussed in the meta-analysis by Jaeger et al., 2017, faster reading times are observed at the verb are in the agreement-attraction sentence above compared to the equally ungrammatical sentence "…
We study first passage percolation (FPP) on a Gromov-hyperbolic group with boundary equipped with the Patterson-Sullivan measure . We associate an i.i.d.\ collection of random passage times to each edge of a Cayley graph of , and investigate classical questions about the asymptotics of first pass…
New method combines gradient optimization with constraint-based techniques for causal discovery.
Modelling of contagion in interbank networks is discussed. A model taking into account bow-tie structure and dissasortativity of interbank networks is developed. The model is shown to provide a good quantitative description of the Russian interbank market. Detailed arguments favoring the non-percolative nature of conta…
New geometric analysis of PWSPDs balances density and geometry in high-dimensional data.
A number of papers claim that a Log Periodic Power Law (LPPL) fitted to financial market bubbles that precede large market falls or 'crashes', contain parameters that are confined within certain ranges. The mechanism that has been claimed as underlying the LPPL, is based on influence percolation and a martingale condit…
Proposes a probabilistic framework for smart contract risk quantification.
We study analytically and numerically Minsky instability as a combination of top-down, bottom-up and peer-to-peer positive feedback loops. The peer-to-peer interactions are represented by the links of a network formed by the connections between firms, contagion leading to avalanches and percolation phase transitions pr…
A self-organized model with social percolation process is proposed to describe the propagations of information for different trading ways across a social system and the automatic formation of various groups within market traders. Based on the market structure of this model, some stylized observations of real market can…
We describe, at the microscopic level, the dynamics of N interacting components where the probability is very small when N is large that a given component interact more than once, directly or indirectly, up to time t, with any other component. Due to this fact, we can consider, at the macroscopic level, the quadratic s…
Develops a method for random manifolds and submanifolds, focusing on 3-ball knots.
We propose improved methods to identify stock groups using the correlation matrix of stock price changes. By filtering out the marketwide effect and the random noise, we construct the correlation matrix of stock groups in which nontrivial high correlations between stocks are found. Using the filtered correlation matrix…
We introduce the concept of community trees that summarizes topological structures within a network. A community tree is a tree structure representing clique communities from the clique percolation method (CPM). The community tree also generates a persistent diagram. Community trees and persistent diagrams reveal topol…
A new algorithm of the analysis of correlation among economy time series is proposed. The algorithm is based on the power law classification scheme (PLCS) followed by the analysis of the network on the percolation threshold (NPT). The algorithm was applied to the analysis of correlations among GDP per capita time serie…
In the present work we introduce a stochastic cellular automata model in order to simulate the dynamics of the stock market. A direct percolation method is used to create a hierarchy of clusters of active traders on a two dimensional grid. Active traders are characterised by the decision to buy, (+1), or sell, (-1), a …
We present a homogenization theorem for isotropically-distributed point defects, by considering a sequence of manifolds with increasingly dense point defects. The loci of the defects are chosen randomly according to a weighted Poisson point process, making it a continuous version of the first passage percolation model.…
The Tobin tax is an often discussed method to tame speculation and get a source of income. The discussion is especially heated when the financial markets are in crisis. In this article we refer to foreign exchange markets. The Tobin tax should be a small international tax affecting all currency transactions and thus co…
The Lightning Network is a so-called second-layer technology built on top of the Bitcoin blockchain to provide "off-chain" fast payment channels between users, which means that not all transactions are settled and stored on the main blockchain. In this paper, we model the emergence of the Lightning Network as a (bond) …
Study geodesic trees and exceptional directions in FPP on hyperbolic groups.
In the series of our earlier papers on the subject, we proposed a novel statistical hypothesis testing method for detection of objects in noisy images. The method uses results from percolation theory and random graph theory. We developed algorithms that allowed to detect objects of unknown shapes in the presence of non…
We introduce the notion of connection thickness of spheres in a Cayley graph, related to dead-ends and their retreat depth. It was well-known that connection thickness is bounded for finitely presented one-ended groups. We compute that for natural generating sets of lamplighter groups on a line or on a tree, connection…
We study statistical detection of grayscale objects in noisy images. The object of interest is of unknown shape and has an unknown intensity, that can be varying over the object and can be negative. No boundary shape constraints are imposed on the object, only a weak bulk condition for the object's interior is required…