We present a relatively detailed analysis of the persistence probability distributions in financial dynamics. Compared with the auto-correlation function, the persistence probability distributions describe dynamic correlations non-local in time. Universal and non-universal behaviors of the German DAX and Shanghai Index…
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48 results for “Persistence probability”
Geometry of the Ising persistence problem and the universal Bonnet-Manin Painlevé VI distributionmath-ph
New geometric insights reveal the persistence distribution in spin systems.
problem Determining the full persistence probability distribution in non-Markovian stochastic processes.
method Exact Fredholm Pfaffian structure and Painlevé VI system analysis.
result Recovery of the universal persistence exponent and its geometric interpretation.
Modeling poverty transitions in India over 54 years, showing rising but persistent poverty.
problem Understanding and addressing poverty dynamics in India over long periods.
method Stochastic model of Geometric Brownian Motion with reallocation (RGBM).
result Annual poverty transitions are common, but poverty persists, especially among the poorest.
We investigated the critical dynamics on the daily Taiwan stock exchange index (TSE) from 1971 to 2005, and the 5-min intraday data from 1996 to 2005. A global persistence exponent was defined for non-equilibrium critical phenomena \cite{Janssen,Majumdar}, and describing dynamic behavior in an economic index \c…
In topological data analysis, persistent homology is used to study the "shape of data". Persistent homology computations are completely characterized by a set of intervals called a bar code. It is often said that the long intervals represent the "topological signal" and the short intervals represent "noise". We give ev…
Despite the obvious similarities between the metrics used in topological data analysis and those of optimal transport, an optimal-transport based formalism to study persistence diagrams and similar topological descriptors has yet to come. In this article, by considering the space of persistence diagrams as a space of d…
We study the temporal fluctuations in time-dependent stock prices (both individual and composite) as a stochastic phenomenon using general techniques and methods of nonequilibrium statistical mechanics. In particular, we analyze stock price fluctuations as a non-Markovian stochastic process using the first-passage stat…
Persistent entropy detects phase transitions in complex systems.
problem Detecting phase transitions in complex systems.
method Established a general theorem for persistent entropy to reliably detect phase transitions, introduced operational framework for finite-time computations.
result Persistent entropy exhibits an asymptotically non-vanishing gap across phases, robust numerical signatures across experiments.
Introduces TSI, a variance-based measure for persistence barcodes.
problem Capturing structural variability in persistence barcodes.
method Variance-based scalar measure, TSI, and complementary TSigI.
result TSI captures structural variability complementary to entropy.
We study the persistence phenomenon in a socio-econo dynamics model using computer simulations at a finite temperature on hypercubic lattices in dimensions up to 5. The model includes a ` social\rq local field which contains the magnetization at time . The nearest neighbour quenched interactions are drawn from a bin…
Market makers face a trade-off between fill probability and post-fill returns, requiring contrarian strategies.
problem Navigating the trade-off between fill probability and post-fill returns in market making.
method Analysis of live trading data from Binance Bitcoin perpetual.
result A negative correlation between maker fill likelihood and post-fill returns, necessitating contrarian strategies.
Develops a more flexible HDP-HMM for temporal data segmentation.
problem Limited expressiveness of sticky HDP-HMM due to stationary self-persistence probability.
method Introduces recurrent sticky HDP-HMM with a novel Gibbs sampling strategy.
result RS-HDP-HMM outperforms other models in segmentation tasks.
New approach uses distributed persistence for stable, parallelizable topological analysis of large point clouds.
problem Estimating the full persistence diagram of large point clouds is expensive, unstable, and not a sufficient statistic.
method Proposes distributed persistence as a new invariant, which is perfectly parallelizable, more stable, and has a rich inverse theory.
result The map from point clouds to distributed persistence invariants is a global quasi-isometry, interpolating between purely geometric and topological invariants.
A new model separates persistence and transition priors in HDP-HMM.
problem Limitation of sticky HDP-HMM in expressing different persistence strengths.
method Developed a disentangled sticky HDP-HMM (DS-HDP-HMM) with novel Gibbs sampling algorithms.
result DS-HDP-HMM outperforms sticky HDP-HMM and HDP-HMM on synthetic and real data.
The study reveals a persistent bias in the distribution of holonomy on compact hyperbolic 3-manifolds.
problem The distribution of holonomy on compact hyperbolic 3-manifolds is not uniformly distributed.
method An asymptotic count of closed geodesics by their length and holonomy, and analysis of spectral parameters.
result A normalized, smoothed bias count of holonomy is distributed according to a probability distribution, controlled by the number of zero spectral parameters.
We study the persistence phenomenon in a socio-econo dynamics model using computer simulations at a finite temperature on hypercubic lattices in dimensions up to 5. The model includes a ` social\rq local field which contains the magnetization at time . The nearest neighbour quenched interactions are drawn from a bin…
The conventional formal tool to detect effects of the financial persistence is in terms of the Hurst exponent. A typical corresponding result is that its value comes out close to 0.5, as characteristic for geometric Brownian motion, with at most small departures from this value in either direction depending on the mark…
In financial markets, the order flow, defined as the process assuming value one for buy market orders and minus one for sell market orders, displays a very slowly decaying autocorrelation function. Since orders impact prices, reconciling the persistence of the order flow with market efficiency is a subtle issue. A poss…
Wavelet analysis reveals non-linear dynamics in cryptocurrency prices.
problem Understanding non-linear dynamics in high-frequency cryptocurrency prices.
method Wavelet analysis of frequency and time variables.
result Cyclical persistence at different frequencies in cryptocurrency prices.
Detection of Small Holes by the Scale-Invariant Robust Density-Aware Distance (RDAD) Filtrationmath.ST
A new method detects small holes in noisy data.
problem Detecting small holes in high-density regions from noise.
method Robust Density-Aware Distance (RDAD) filtration, incorporating distance-to-measure concept.
result The RDAD filtration prolongs the persistences of small holes, making them distinguishable from noise.
TabPFN's internal geometry topology correlates with dataset reliability.
problem Understanding TabPFN's behavior on structurally difficult tabular geometries.
method Using zigzag persistent homology, studying TabPFN's internal representations on synthetic tabular tasks with known topology.
result Topology of TabPFN's internal representation geometry is strongly associated with dataset-level reliability.
Hidden semi-Markov models (HSMMs) are latent variable models which allow latent state persistence and can be viewed as a generalization of the popular hidden Markov models (HMMs). In this paper, we introduce a novel spectral algorithm to perform inference in HSMMs. Unlike expectation maximization (EM), our approach cor…
Approaches for approximating persistent homology for large datasets.
problem Inability to compute persistent homology for large datasets.
method Multiple subsampling framework for statistical approximation of persistent homology.
result Derivation of finite sample convergence rates for empirical means of persistent homology.
Persistence landscapes map persistence diagrams into a function space, which may often be taken to be a Banach space or even a Hilbert space. In the latter case, it is a feature map and there is an associated kernel. The main advantage of this summary is that it allows one to apply tools from statistics and machine lea…
RCLA reduces noise in topological data analysis, preserving essential structure.
problem Noise in large datasets obscures topological features in persistent homology.
method Grid-based RCLA integrates data reduction and denoising with a threshold parameter.
result RCLA provides a theoretical guarantee and automatic parameter selection.
Proposes deep graph persistence to address neural persistence issues in deep learning.
problem Variance of weights and lack of spatial structure in deep neural networks impact neural persistence.
method Extends neural persistence to the whole network, considering interactions between layers.
result Deep graph persistence alleviates variance-related issues and captures persistent paths through the network.
In this manuscript we analyse the leading statistical properties of fluctuations of (log) 3-month US Treasury bill quotation in the secondary market, namely: probability density function, autocorrelation, absolute values autocorrelation, and absolute values persistency. We verify that this financial instrument, in spit…
Paper proves -means clustering works on persistence diagrams.
problem Complex geometry of persistence diagram space.
method Proves convergence of -means on persistence diagram space.
result Performance of -means on persistence diagrams and measures is superior.
Formula for interleaving distance of rectangle persistence modules.
problem Calculating distances between rectangle persistence modules.
method Formulas based on rectangle geometry, extended to decomposable modules.
result Closed formulas for interleaving and bottleneck distances.
This paper demonstrates the flaws of co-persistence theory proposed by Bollerslev and Engle (1993) which cause the theory can hardly be applied. With the introduction of the half-life of decay coefficient as the measure of the persistence, and both the weak definition of persistence and co-persistence in variance, this…
Optimizes wavelets for graph classification using spectral wavelet signatures and persistence diagrams.
problem Graph classification with geometric properties encoded in persistence diagrams.
method Optimizes spectral wavelets for graph datasets to capture best-suited features for classification.
result Competitive performance in graph classification problems compared to other persistence-based architectures.
New method for analyzing multiparameter persistence modules from smooth functions.
problem Analyzing multiparameter persistence modules from smooth functions.
method Generalized Morse theory applied to cobordism and Cerf theory.
result Complete description of persistence modules as direct sums of indecomposables.
Develops robust persistence diagrams using kernel methods.
problem Persistence diagrams are sensitive to data perturbations.
method Constructs robust persistence diagrams from superlevel filtrations of robust density estimators using reproducing kernels.
result Robust persistence diagrams are consistent estimators in bottleneck distance.
This paper interprets critical scales in persistent homology for compact metric spaces.
problem Understanding critical scales in persistent homology for general compact metric spaces.
method Analyzing local minima of the distance function and their impact on persistence.
result Each decrease in zero-dimensional persistence and increase in one-dimensional persistence is induced by local minima of the distance function.
MuRiT efficiently computes multi-parameter persistence barcodes.
problem Efficient computation of multi-parameter persistent homology.
method Vietoris-Rips transformation to reduce multi-parameter to single-parameter computation.
result MuRiT computes pathwise persistence barcodes for multi-filtered flag complexes.
How social reinforcement learning can lead to metastable polarisation and the voter modelphysics.soc-ph
Study shows social reinforcement learning can lead to persistent but metastable polarization.
problem Understanding the persistence and dynamics of opinion polarization.
method Simulation and mathematical analysis of a reinforcement learning model of opinion dynamics.
result Polarization observed in the model is metastable and will eventually lead to consensus.
Stable topological summary captures evolving dependency structure in dynamic Bayesian networks.
problem Missing larger-scale patterns in evolving dependency structures in dynamic Bayesian networks.
method Topological approach using Dynamic Bayesian Graphs and persistent homology.
result Stable topological summary (barcodes) captures evolving dependency structure in DBNs.
Persistent homology can recognize knotting in curves.
problem Recognizing knotting in curves
method Compute one-dimensional persistent homology, extract cycle representatives, and assign a hypergraph curvature-based score.
result Systematic differences between knotted and unknotted structures are revealed.
This article analyzes the relationship between co-persistence and hedging which indicates co-persistence ratio is just the long-term hedging ratio. The new method of exhaustive search algorithm for deriving co-persistence ratio is derived in the article. And we also develop a new hedging strategy of combining co-persis…
Persistence diagrams are important descriptors in Topological Data Analysis. Due to the nonlinearity of the space of persistence diagrams equipped with their {\em diagram distances}, most of the recent attempts at using persistence diagrams in machine learning have been done through kernel methods, i.e., embeddings of …
Computational topology has recently known an important development toward data analysis, giving birth to the field of topological data analysis. Topological persistence, or persistent homology, appears as a fundamental tool in this field. In this paper, we study topological persistence in general metric spaces, with a …
A new approach to reinforcement learning improves policy performance by adjusting control frequency.
problem Improving reinforcement learning performance by optimizing control frequency.
method Introducing action persistence and a novel algorithm, PFQI, to learn optimal value function at a given persistence.
result PFQI effectively learns optimal value function with action persistence, improving reinforcement learning performance.
Given a compact geodesic space we apply the fundamental group and alternatively the first homology group functor to the corresponding Rips or Čech filtration of to obtain what we call a persistence. This paper contains the theory describing such persistence: properties of the set of critical points, their preci…
A new method compares persistent cycles in topological data.
problem Comparing persistent homology representations of two spaces.
method Direct comparison of individual persistent cycles based on persistence intervals and spatial placement.
result Demonstrated the effectiveness of the method in topological inference.
Persistence Spheres: a Bi-continuous Linear Representation of Measures for Partial Optimal Transportstat.ML
Improved persistence spheres map measures to functions, stable under partial transport.
problem Representing and comparing measures in topological machine learning.
method Persistence spheres map measures to continuous functions on the sphere, stable under 1-Wasserstein partial transport.
result Persistence spheres provide a stable, parameter-free representation of measures, improving upon existing methods.
We introduce several geometric notions, including the width of a homology class, to the theory of persistent homology. These ideas provide geometric interpretations of persistence diagrams. Indeed, we give quantitative and geometric descriptions of the "life span" or "persistence" of a homology class. As a case study, …
This article addresses persistent tangles. These are tangles whose presence in a knot diagram forces that diagram to be knotted. We provide new methods for constructing persistent tangles. Our techniques rely mainly on the existence of non-trivial colorings for the tangles in question. Our main result in this article i…
Study cosmic structures using Topological Data Analysis and Persistence Energy.
problem Investigate cosmic web evolution in CDM cosmologies.
method Apply LITE method to embed persistence diagrams into vector spaces and analyze cosmic structures.
result Discover a correlation between Persistence Energy and redshift values.