New analysis reveals multi-branched multifractality in time series.
problem Analyzing non-monotonic behavior in mean inter-event times.
method Modified Multifractal Detrended Fluctuation Analysis with Legendre-Fenchel transform.
result Discovery of multi-branched multifractality leading to phase transitions.
New models directly model inter-event times without intensity functions.
problem Learning temporal point processes with intensity-based approaches.
method Normalizing flows and mixture models for flexible and efficient modeling.
result Achieves state-of-the-art performance in prediction tasks.
Reconstructing network connectivity from the collective dynamics of a system typically requires access to its complete continuous-time evolution although these are often experimentally inaccessible. Here we propose a theory for revealing physical connectivity of networked systems only from the event time series their i…
Long-range correlation in financial time series reflects the complex dynamics of the stock markets driven by algorithms and human decisions. Our analysis exploits ultra-high frequency order book data from NASDAQ Nordic over a period of three years to numerically estimate the power-law scaling exponents using detrended …
The fractional Poisson process (FPP) is a counting process with independent and identically distributed inter-event times following the Mittag-Leffler distribution. This process is very useful in several fields of applied and theoretical physics including models for anomalous diffusion. Contrary to the well-known Poiss…
FraudTransformer detects payment fraud by preserving event order and time gaps.
problem Detecting payment fraud in real-world banking streams with irregular time gaps.
method Augments a GPT-style architecture with a dedicated time encoder and a learned positional encoder.
result FraudTransformer outperforms classical and transformer baselines, achieving highest AUROC and PRAUC on held-out test set.
Proposes a neural network solution for queuing dynamics.
problem Modeling service system dynamics with limited parametric assumptions.
method Combines recurrent neural networks and generative adversarial networks.
result Evaluates solution on various datasets, demonstrating effectiveness.
A new model predicts bid-ask spread dynamics in financial markets.
problem Capturing the self-exciting nature of bid-ask spread changes.
method State-dependent Spread Hawkes model (SDSH) incorporating various spread jump sizes and current state impact.
result The SDSH model accurately forecasts spread values at short-term horizons.
Given a stationary point process, an intensity burst is defined as a short time period during which the number of counts is larger than the typical count rate. It might signal a local non-stationarity or the presence of an external perturbation to the system. In this paper we propose a novel procedure for the detection…
A plethora of natural, artificial and social systems exist which do not belong to the Boltzmann-Gibbs (BG) statistical-mechanical world, based on the standard additive entropy SBG and its associated exponential BG factor. Frequent behaviors in such complex systems have been shown to be closely related to q-stati…
New CTRW model explains volatility clustering in stock markets.
problem Missing models for long-term memory in time intervals between observations.
method Introduced a new family of CTRWs with correlated waiting times.
result Successfully describes the decay of nonlinear autocorrelation function in stock market returns.
Variational autoencoder models dynamic latent graphs for neural point processes.
problem Modeling event dynamics with changing trends over time.
method Sequential latent variable model with dynamic latent graphs.
result Higher accuracy in predicting inter-event times and event types.
Proposes a deep neural network for event intensity estimation.
problem Modeling irregular event sequences with historical dependencies.
method Non-parametric deep neural network with multi-channel RNN and fake event epochs.
result Outperforms state-of-the-art baselines on model fitting tasks.
A new method uses Transformers for efficient prediction of marked point processes.
problem Efficiently predicting the next event in a sequence given its history.
method Modeling conditional inter-event times with a mixture of log-normals and marks with a Transformer architecture.
result The method achieves state-of-the-art performance and is faster during inference.
A novel Hawkes Process model captures order sizes in LOBs, improving fit quality and market impact studies.
problem Capturing the variability in order sizes in Limit Order Books (LOBs).
method Compound Hawkes Process with time-varying parameters and non-parametric calibration.
result Improved fit quality and empirical market impact function replication.
Proposes a new framework to disentangle event influences in MTPP.
problem Underexplored how individual events influence overall dynamics over time.
method Decoupled MTPP framework using Neural Ordinary Differential Equations (Neural ODEs).
result Significantly improves performance on real-life datasets compared to state-of-the-art methods.
New method models MTPP without predefined intensity functions.
problem Parameterizing conditional joint PDF for MTPP.
method IFIB framework, modeling p∗(m,t) directly. result Superior experimental results on real and synthetic data.
Two Hawkes models integrate queue sizes to model order flow and improve accuracy.
problem Modeling the stochastic time evolution of a limit order book.
method Queue-reactive Hawkes models with explicit queue size dependencies.
result Hawkes term significantly improves order flow description and queue distributions.
Diffusion means converge to extrinsic means for long times on spheres.
problem Understanding the long-time behavior of diffusion means on manifolds.
method Introduced diffusion means as a parameterized family of location statistics on manifolds, and analyzed their convergence to extrinsic means for long times.
result For real projective spaces and connected compact symmetric spaces, the long-time limit of diffusion means is conjectured to be the extrinsic mean in the isometric embedding.
Improved K-Means++ and K-Means∥ with faster run-time.
problem Efficiently selecting initial seeds for K-means clustering.
method Triangle inequality pruning and dynamic priority queue.
result Up to 17x speedup for K-Means++ and 551x for K-Means$\$.
A new model minimizes investment risk at multiple time points.
problem Minimizing risk in investment portfolios with multiple stopping points.
method Developed a multi-time state mean-variance model using Riccati equations.
result Optimal investment strategies can be derived from a sequence of Riccati equations.
TS-K-means improves financial data clustering with dynamic time warping.
problem Inadequate handling of temporal dependencies in financial time series data.
method Integrates Dynamic Time Warping into Time Series K-means for financial data.
result TS-K-means outperforms traditional K-means in financial data analysis.
Proposes a new model to optimize investment plans with varying terminal times.
problem Improving the classical mean-variance model for continuous time investments.
method Uses stochastic optimal control and varying terminal time to determine optimal strategies.
result Optimal strategies and terminal times can be determined to minimize portfolio variance.
Study proves smooth solutions for fractional mean curvature flow within short time.
problem Short-time existence of smooth solutions for fractional mean curvature flow.
method Established using short-time existence theorem for bounded, C^{1,1}-regular initial sets.
result Smooth solutions exist for both fractional mean curvature flow and volume preserving flow.
We apply the theory of continuous time random walks to study some aspects of the extreme value problem applied to financial time series. We focus our attention on extreme times, specifically the mean exit time and the mean first-passage time. We set the general equations for these extremes and evaluate the mean exit ti…
New study confirms some mean curvature flow solutions have bounded mean curvature.
problem Existence of mean curvature flow singularities with bounded mean curvature.
method Construction of specific solutions in RN for N≥8. result A nontrivial subset of solutions has uniformly bounded mean curvature.
New method solves continuous time mean-variance model for consistent investment strategy.
problem Time-consistent optimal strategy for continuous time mean-variance model.
method Developed a new Bellman principle method.
result Obtained a time-consistent dynamic optimal strategy.
sWk-means clusters multidimensional financial time series into distinct market regimes.
problem Classifying distinct market regimes in multidimensional financial time series.
method Approximated multidimensional Wasserstein distance as sliced Wasserstein distance for clustering.
result sWk-means successfully identifies distinct market regimes in real financial data.
The study classifies constant mean curvature surfaces in curved spaces.
problem Classifying constant mean curvature surfaces in curved spaces.
method Analyzes constant mean curvature isometric immersions into S2imesR and H2imesR. result Provides new classifications of constant mean curvature surfaces in various curved spaces.
The paper studies how certain surfaces evolve over time.
problem Evolution of specific types of surfaces in high dimensions.
method Approximation by simpler problems to prove long-term existence.
result Long-time existence of the Hα-flow for specified surfaces. In this note, we first prove that the solution of mean curvature flow on a finite time interval [0,T) can be extended over time T if the space-time integration of the norm of the second fundamental form is finite. Secondly, we prove that the solution of certain mean curvature flow on a finite time interval [0,T) …
Classifies hypersurfaces with positive constant mean curvature in hyperbolic space.
problem Classifying hypersurfaces with positive constant mean curvature in hyperbolic space.
method Classifies hypersurfaces with rotational symmetry and positive constant r-th mean curvature in HnimesR. result Compact connected hypersurfaces of constant r-th mean curvature embedded in Hnimes[0,∞) with boundary in the slice Hnimes{0} are topological disks under suitable assumptions. Study of prescribed mean curvature flow on noncompact hypersurfaces in Lorentz manifolds.
problem Short time existence and long time existence of prescribed mean curvature flow on noncompact spacelike hypersurfaces.
method Finding sufficient conditions for short time existence and discussing long time existence and convergence.
result Sufficient conditions for short time existence of prescribed mean curvature flow on noncompact spacelike hypersurfaces.
Based on Markvorsen and Palmer's work on mean time exit and isoperimetric inequalities we establish slightly better isoperimetric inequalities and mean time exit estimates for minimal submanifolds of N×R. We also prove isoperimetric inequalities for submanifolds of Hadamard spaces with tamed second fund…
Estimates for VPMCF show ancient MCF solutions and finite-time behavior.
problem Volume Preserving Mean Curvature Flow (VPMCF) behavior and singularities.
method Nonlocal estimates and blowup analysis.
result Ancient solutions to MCF and finite-time behavior of VPMCF.
Proves Arnold-Thom conjecture for surfaces' arrival times.
problem Existence of limit tangents for gradient flow lines of surfaces.
method Gradient flow lines of mean curvature flows with neck or cylindrical singularities.
result Proves Arnold's conjecture for all mean convex mean curvature flows of surfaces.
We study the provenance of singularity formation under mean curvature flow and volume preserving mean curvature flow in an axially symmetric setting. We prove that if the mean curvature is uniformly bounded on any finite time interval, then no singularities can develop during that time under both mean curvature flow an…
Study of discrete-time mean-variance model using reinforcement learning.
problem Discrete-time model with more general return distribution assumptions.
method Entropy-based exploration cost, reinforcement learning algorithm design.
result Optimal investment strategy with Gaussian density function.
Flow of spacelike hypersurfaces converges to flat slice in asymptotically flat spacetimes.
problem Long-time behavior of mean curvature flow in asymptotically flat spacetimes.
method Analysis of mean curvature flow in Lorentzian product manifolds.
result Mean curvature flow converges uniformly to a flat slice as time goes to infinity.
Study shows submanifolds can't be immersed in certain spaces.
problem Non-immersibility of submanifolds with infinite mean exit time.
method Not based on the weak maximum principle at infinity, generalizes previous results.
result Estimates for complete tower of moments for submanifolds with small mean curvature.
New method controls mean exit time in stochastic systems using machine learning and quasipotential.
problem Controlling mean exit time in stochastic dynamical systems with white noise.
method Developed a neural network to compute the quasipotential function and designed an algorithm to calculate the controller.
result Effective and accurate control strategy demonstrated through numerical experiments.
The study finds new constant mean curvature surfaces in curved spaces.
problem Finding surfaces with constant mean curvature in curved spaces.
method Analyzing families of surfaces in S2imesR and H2imesR. result New families of surfaces with constant mean curvature, including non-equivariant examples.
Study shows uniform-time chaos propagation in mean field Langevin dynamics.
problem Understanding the convergence of marginal distributions in mean field dynamics.
method Assumed functional convexity of energy, used Lp-convergence and Wasserstein metrics. result Uniform-in-time propagation of chaos proved in both L2-Wasserstein and relative entropy. Compact mean curvature flow solutions with bounded curvature in high dimensions are constructed.
problem Constructing compact mean curvature flow solutions with bounded mean curvature.
method Following Velázquez, Guo, Sesum, and Stolarski's arguments, constructing solutions in \(\mathbb{R}^n\) with \(n \geq 8\).
result Compact mean curvature flow solutions with bounded mean curvature in \(\mathbb{R}^n\) are constructed.
Unified estimates for mean curvature in Lorentz-Minkowski space.
problem Estimating mean curvature for space-like and time-like graphs.
method Using gradient bounds to derive Heinz-type estimates.
result Unified vanishing theorem for mean curvature of constant mean curvature graphs.
The paper finds new constant mean curvature hypersurfaces in spheres.
problem Finding new constant mean curvature hypersurfaces in spheres.
method Analyzing hypersurfaces of specific types in spheres with given symmetries.
result Existence of new compact embedded CMC-hypersurfaces in spheres.
This paper gives a new proof that maximal, globally hyperbolic, flat spacetimes of dimension n≥3 with compact Cauchy hypersurfaces are globally foliated by Cauchy hypersurfaces of constant mean curvature, and that such spacetimes admit a globally defined constant mean curvature time function precisely when they a…
Mean curvature flow with uniform bounds on curvature and its gradient
problem Mean curvature flow
method Uniform bounds on curvature and its gradient
result Smooth extension past singular time