New model predicts energy prices volatility by smoothing time variation and persistence.
problem Separate study of volatility's time variation and persistence.
method Dynamic persistence model that allows shocks with heterogeneous persistence to vary smoothly over time.
result Significantly improves volatility forecasts over state-of-the-art models.
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 θp was defined for non-equilibrium critical phenomena \cite{Janssen,Majumdar}, and describing dynamic behavior in an economic index \c…
The paper examines how long-memory dynamics, rough-volatility, and persistence affect equity volatility forecasting.
problem The study investigates how long-memory dynamics, rough-volatility, and persistence impact equity volatility forecasting.
method The paper combines semiparametric long-memory estimation, rough-volatility diagnostics, and structured forecasting regressions.
result Persistence measures improve out-of-sample volatility forecasts, particularly during periods of elevated market volatility and in volatility-managed portfolio applications.
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.
New framework detects time-varying economic persistence.
problem Time-varying persistence in economic shocks.
method Localized regression techniques to identify evolving heterogeneity.
result Substantial persistence variations align with macroeconomic events.
This paper investigates dynamics that persist under isotopy in classes of orientation-preserving homeomorphisms of orientable surfaces. The persistence of periodic points with respect to periodic and strong Nielsen equivalence is studied. The existence of a dynamically minimal representative with respect to these relat…
Study shows similarities and differences in crypto and equity dynamics during pandemic.
problem Comparing cryptocurrency and equity market dynamics during the pandemic.
method New methodologies applied to study cryptocurrency and equity market dynamics, including recently introduced methods for trajectory and anomaly analysis.
result Cryptocurrencies exhibit stronger collective dynamics and correlation, while equities show greater persistence in anomalies over time.
This study uses persistent homology to analyze complex transitional networks from time series data.
problem Lack of effective tools to summarize complex topology in transitional networks.
method Persistent homology from topological data analysis applied to coarse-grained state-space networks (CGSSN).
result CGSSN improves dynamic state detection and noise robustness compared to other methods.
Topological data analysis quantifies structural dynamics using persistent homology.
problem Analyzing the shape and topology of structural dynamics data.
method Topological Data Analysis (TDA) with persistent homology to quantify shape over scales.
result Persistent homology reveals significant changes in manifold shape due to damage, not temperature.
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…
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…
The evolution with time of the correlation structure of equity returns is studied by means of a filtered network approach investigating persistences and recurrences and their implications for risk diversification strategies. We build dynamically Planar Maximally Filtered Graphs from the correlation structure over a rol…
Study non-Weinstein Liouville geometry via hyperbolic dynamics, proving rigidity results.
problem Characterize non-Weinstein Liouville geometry with persistent transverse skeleton.
method Anosov 3-flows, Liouville Interpolation Systems, non-singular partially hyperbolic flows, hyperbolic dynamics.
result Mitsumatsu's examples characterize 4D non-Weinstein Liouville geometry with 3D persistent transverse skeleton.
Paper shows equivalence between MM and PH for n-D Morse functions.
problem Relationship between Mathematical Morphology and Persistent Homology.
method Examined pairing of extrema in Morse functions using dynamics and persistence.
result Equivalence proven between dynamics and persistence on n-D Morse functions.
Study cosmic structures using Topological Data Analysis and Persistence Energy.
problem Investigate cosmic web evolution in ΛCDM 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.
Framework for analyzing dynamic topological changes in point clouds using persistent homology and dynamic optimal transport.
problem Analyzing transient structural reorganizations during dynamic phase transitions in time-evolutionary point clouds.
method Hierarchical dynamic evaluation framework driven by topological and hypergraph reconstruction strategy.
result Combining transport-based alignment with multi-scale entropy diagnostics for dynamic topological analysis.
PMP extends GNNs to handle past states efficiently.
problem Efficient querying of data structures dependent on previous states.
method Persistent Message Passing (PMP) which persists past states through new nodes.
result Significantly outperforms GNNs in handling out-of-distribution data.
We study the inference of a model of dynamic networks in which both communities and links keep memory of previous network states. By considering maximum likelihood inference from single snapshot observations of the network, we show that link persistence makes the inference of communities harder, decreasing the detectab…
Topological method detects Hopf bifurcations from time series.
problem Detecting Hopf bifurcations in nonlinear systems from time series data.
method Persistent homology applied to Takens embedding for phase space reconstructions.
result A simple scalar topological functional identifies critical bifurcation points.
News sentiment in U.S. economic newspapers has become more persistent over 45 years.
problem Understanding the temporal dynamics of U.S. economic news sentiment over time.
method Daily economic news sentiment index from 1980-2025, analyzed using sentiment indexes.
result News sentiment states have become more persistent, with longer residence times in optimistic or pessimistic regimes.
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 t. The nearest neighbour quenched interactions are drawn from a bin…
Persistent homology provides a new, efficient molecular descriptor for protein dynamics.
problem Designing effective molecular descriptors for high-dimensional MD trajectories.
method Introduced masked Flood complex, a protein-tailored modification of simplicial complexes, for persistent homology.
result Persistent homology-based descriptors are competitive across protein dynamics tasks, including frame-level observable regression and MSM estimation.
Simplicial persistence measures financial market dynamics, revealing long-term structure evolution.
problem Understanding the long-term structure evolution of financial markets.
method Simplicial persistence, null models, TMFG filtering, thresholding, generative process analysis.
result More liquid markets exhibit slower persistence decay, suggesting higher fragility to systemic shocks.
Many datasets can be viewed as a noisy sampling of an underlying space, and tools from topological data analysis can characterize this structure for the purpose of knowledge discovery. One such tool is persistent homology, which provides a multiscale description of the homological features within a dataset. A useful re…
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.
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.
The persistence diagram is an increasingly useful tool from Topological Data Analysis, but its use alongside typical machine learning techniques requires mathematical finesse. The most success to date has come from methods that map persistence diagrams into vector spaces, in a way which maximizes the structure preserve…
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…
Quantum circuits predict volatility dynamics preserving asymmetry.
problem Modeling volatility time series with asymmetry.
method Single-qubit quantum circuit learning (QCL) applied to synthetic data generated by Rational GARCH model.
result QCL-based predictions preserve negative return-volatility correlation and anti-persistent behavior.
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…
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.
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 t. The nearest neighbour quenched interactions are drawn from a bin…
New method uses DTW to evaluate neural network forecasts of geomagnetic indices.
problem Evaluation metrics fail to capture persistence behavior in neural network forecasts.
method Dynamic Time Warping (DTW) to measure time series similarity, training neural networks to remove persistence.
result DTW reveals persistence behavior in neural network forecasts, confirming visual inspection.
Study uses topological signatures to quantify financial market complexity.
problem Capturing temporal organization beyond volatility measures.
method Null validated topological approach using L1 norm of persistence landscapes. result Persistence landscape norms reveal dynamical structure during market stress.
We study soft persistence (existence in subsequent temporal layers of motifs from the initial layer) of motif structures in Triangulated Maximally Filtered Graphs (TMFG) generated from time-varying Kendall correlation matrices computed from stock prices log-returns over rolling windows with exponential smoothing. We ob…
Extends Morse-Forman theory to vector-valued functions for multiparameter persistence.
problem Computing multiparameter persistence with new tools and methods.
method Adapting Forman's theory to vectorial setting and using combinatorial topological dynamics.
result Established more general result for sublevel sets and found a way to induce Morse decomposition.
Study reveals investor heterogeneity in Korean equity market cash flows.
problem Investor heterogeneity and its impact on market dynamics.
method Detrended fluctuation analysis (DFA) on aggregated cash flows.
result Persistence in cash flows varies by investor type, with retail flows showing strong persistence.
Paper uses TDA to assess cryptocurrency risk by measuring phase space instability.
problem Traditional risk measures fail to capture market dynamics' geometric structure.
method Applied Takens' Delay Embedding Theorem to generate point cloud, computed persistent homology groups, defined Topological Persistence Norm.
result Proposed leverage calibration heuristic based on persistence of 1-dimensional cycles.
When an online learning algorithm is used to estimate the unknown parameters of a model, the signals interacting with the parameter estimates should not decay too quickly for the optimal values to be discovered correctly. This requirement is referred to as persistency of excitation, and it arises in various contexts, s…
This letter investigates the dynamic relationship between market efficiency, liquidity, and multifractality of Bitcoin. We find that before 2013 liquidity is low and the Hurst exponent is less than 0.5, indicating that the Bitcoin time series is anti-persistent. After 2013, as liquidity increased, the Hurst exponent ro…
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.
Reducing volatility proxy improves apparent market correlation dynamics.
problem Attributing apparent slow collective market dynamics to intrinsic or driver inheritance.
method Coupled Ornstein-Uhlenbeck model with VIX proxy, decomposing and controlling for autocorrelation.
result VIX-coupled model reduces effective relaxation time from 298 to 61 trading days, improving fit over bare mean reversion.
Unreduced PDs can perform similarly to reduced PDs in machine learning tasks.
problem Ignoring much of the information in persistence diagrams in machine learning pipelines.
method Developed methods to generate topological feature vectors from unreduced boundary matrices.
result Unreduced PDs can perform on par with, and sometimes outperform, fully-reduced PDs in machine learning tasks.
New method decomposes Markov chain rewards into persistent and transient components.
problem Ambiguity in classical evaluation methods for Markov chains with reducible and periodic states.
method Minimal exact quotient by the real peripheral invariant subspace, decomposing rewards into persistent and transient components.
result Exact comparison with classical methods shows that the new decomposition reallocates the same information, making persistent modes explicit.
DYMAG uses dynamic waveforms to improve graph neural networks.
problem Improving graph neural networks for better graph understanding.
method DYMAG employs dynamical system-based waveforms for message aggregation in graph neural networks.
result DYMAG outperforms baseline models in graph recovery, property prediction, and random graph generation.
This paper explains how predictable order flow can lead to Brownian motion in financial prices.
problem Why financial prices exhibit Brownian motion despite predictable order flow.
method Generalized Lillo-Mike-Farmer model to nonlinear price-impact dynamics, mapping to Lévy-walk model.
result Price dynamics remain diffusive under the square-root law, even with persistent order flow.
The last decades have not only been characterized by an explosive growth of data, but also an increasing appreciation of data as a valuable resource. Their value comes with the ability to extract meaningful patterns that are of economic, societal or scientific relevance. A particular challenge is the identification of …
Improved forecasting of investment dynamics across heterogeneous panels using a two-stage model.
problem Forecasting investment dynamics in heterogeneous panels with varying dynamics.
method Two-stage architecture: global pooled AR(1) for shared persistence, local models for residual dynamics.
result Significant improvement in out-of-sample R2 from 0.630 to 0.677, with a gain of 0.047.