The present paper introduces a majority orienting model in which the dealers' behavior changes based on the influence of the price to show the oscillation of stock price in the stock market. We show the oscillation of the price for the model by applying the van der Pol equation which is a deterministic approximation of…
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48 results for “Van der Pol Oscillator”
Automatically learns summary features from time series data for likelihood-free inference.
problem Necessity of hand-tailored summary features for time series data in likelihood-free inference.
method Data-driven approach to automatically learn summary features.
result Learning summary features from data can outperform hand-crafted values in likelihood-free inference.
We have carried out simulations of a financial model of the firm to analyse the validity of the concept of Trade on Equity in dynamics. The results exhibit the ability of the borrowing policy connected to a cautious dividend distribution to inject chaos into the profit motion. The 3D system built with the van der Pol's…
We present a deep learning model, DE-LSTM, for the simulation of a stochastic process with an underlying nonlinear dynamics. The deep learning model aims to approximate the probability density function of a stochastic process via numerical discretization and the underlying nonlinear dynamics is modeled by the Long Shor…
Many real-world data sets, especially in biology, are produced by complex nonlinear dynamical systems. In this paper, we focus on brain calcium imaging (CaI) of different organisms (zebrafish and rat), aiming to build a model of joint activation dynamics in large neuronal populations, including the whole brain of zebra…
The paper finds Koopman invariant subspaces using personalized PageRank.
problem Selecting a finite dictionary of observables for Koopman-invariant span.
method Exploiting zero-block structure in EDMD matrices and applying PageRank.
result Personalized PageRank can detect Koopman invariant subspaces.
Soft-constrained PINN solves ODEs with minimal data, improving efficiency and robustness.
problem Sparse and noisy data in experiments and simulations.
method Soft-constrained Physics-informed Neural Network (PINN) with minimal labeled data.
result Soft-constrained PINN reduces need for labeled data and achieves strong generalization.
Graphs from van der Corput sequence embed into Chamanara surface.
problem Embedding graphs from van der Corput sequence into surfaces.
method Constructed -regular graphs from van der Corput sequence and Kronecker sequence, embedded into torus and Chamanara surface.
result Graphs from van der Corput sequence embed into Chamanara surface with one edge removal.
Enhances Koopman operator estimation with intrinsic observables in RKHS.
problem Accurate estimation of Koopman operator and its spectrum.
method Jet Extended Dynamic Mode Decomposition (JetEDMD) leveraging RKHS jets.
result Proves JetEDMD's superiority with error bounds and convergence rate.
Study finds multiple solutions for Van der Waals-Cahn-Hilliard equation on manifolds.
problem Finding multiple solutions for a specific equation on manifolds.
method Combines Lusternik-Schnirelman and Morse theory with a photography method.
result Establishes multiplicity of solutions using topological invariants.
A cubic identity for the Infeld-van der Waerden field is found and its application to verifying an explicit formula for the spinor components of the metric connection is demonstrated.
We study the maximum mean discrepancy (MMD) in the context of critical transitions modelled by fast-slow stochastic dynamical systems. We establish a new link between the dynamical theory of critical transitions with the statistical aspects of the MMD. In particular, we show that a formal approximation of the MMD near …
We give multiplicity results for the solutions of a nonlinear elliptic equation, with an asymmetric double well potential of Van der Waals-Allen--Cahn--Hilliard type, satisfying a linear volume constraint, on a bounded Lipschitz domain $Ω\subset\mathds R^N$. The number of solutions is estimated in terms of topological …
Unified framework detects change-points and estimates parameters in nonlinear systems with regime switching.
problem Detecting change-points and estimating parameters in nonlinear dynamical systems with regime transitions.
method Residual-loss anomaly analysis of physics-informed neural networks, two-stage strategy.
result The method outperforms traditional approaches in change-point localization and parameter estimation accuracy.
Reservoir Computing with Error Correction: Long-term Behaviors of Stochastic Dynamical Systemsmath.DS
Proposes a new method combining Reservoir Computing and Normalizing Flow for predicting stochastic dynamical systems.
problem Predicting and capturing long-term behaviors of stochastic dynamical systems.
method Data-driven framework combining Reservoir Computing and Normalizing Flow, integrating error modeling and both approaches virtues.
result Successfully predicts the long-term evolution of stochastic dynamical systems and replicates dynamical behaviors.
A universal rule-based self-learning approach using deep reinforcement learning (DRL) is proposed for the first time to solve nonlinear ordinary differential equations and partial differential equations. The solver consists of a deep neural network-structured actor that outputs candidate solutions, and a critic derived…
t-distributed Stochastic Neighborhood Embedding (t-SNE), a clustering and visualization method proposed by van der Maaten & Hinton in 2008, has rapidly become a standard tool in a number of natural sciences. Despite its overwhelming success, there is a distinct lack of mathematical foundations and the inner workings of…
Proves generic nondegeneracy for solutions under volume constraint in closed manifolds.
problem Proving nondegeneracy for solutions of the Van der Waals-Allen-Cahn-Hilliard equation.
method Adapting techniques from previous research to prove nondegeneracy.
result Generic nondegeneracy for solutions of the Van der Waals-Allen-Cahn-Hilliard equation under a volume constraint in closed manifolds.
Unified framework identifies nonlinear systems using characteristic curves and neural networks.
problem Balancing interpretability and flexibility in nonlinear system identification.
method Combines differential equation structure with neural networks, using characteristic curves as modular components.
result NN-CC approach outperforms other methods in complex nonlinear systems.
Novel knot polynomials from Gaussian calculus show half vanish and determine Jones polynomials.
problem Understanding and characterizing knot polynomials from Gaussian calculus.
method Gaussian calculus of generating series for noncommutative algebras, connected sum of knots.
result Half of the polynomials vanish and three polynomials are explicitly given.
We give a brief review of the definition of the Wang-Yau quasilocal mass and discuss the evaluation of which on surfaces of unit size at null infinity of an axi-symmetric spacetime in Bondi-van der Burg-Metzner coordinates.
The dynamic emulation of non-linear deterministic computer codes where the output is a time series, possibly multivariate, is examined. Such computer models simulate the evolution of some real-world phenomenon over time, for example models of the climate or the functioning of the human brain. The models we are interest…
We prove that any limit-interface corresponding to a locally uniformly bounded, locally energy-bounded sequence of stable critical points of the van der Waals--Cahn--Hilliard energy functionals with perturbation parameter tending to 0 is supported by an embedded smooth stable minimal hypersurface in low dimensions and …
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.
Responding to discussions on missing data models.
problem Clarifying causal and counterfactual views in missing data models.
method Summarizing and responding to comments from discussants.
result Summarized main contributions and addressed each discussion.
A new method ODR-BINDy improves model discovery from noisy data.
problem Discovering models from noisy datasets with error-in-variable problem.
method ODR-BINDy uses orthogonal distance regression with Bayesian model selection.
result ODR-BINDy consistently outperforms existing methods in recovering correct models.
We consider the concept of Stokes-Dirac structures in boundary control theory proposed by van der Schaft and Maschke. We introduce Poisson reduction in this context and show how Stokes-Dirac structures can be derived through symmetry reduction from a canonical Dirac structure on the unreduced phase space. In this way, …
A comprehensive survey on parallel submanifolds in Riemannian and pseudo-Riemannian manifoldsmath.DG
A submanifold of a Riemannian manifold is called a parallel submanifold if its second fundamental form is parallel with respect to the van der Waerden-Bortolotti connection. From submanifold point of view, parallel submanifolds are the simplest Riemannian submanifolds next to totally geodesic ones. Parallel submanifold…
We study non-degenerate, totally umbilical surfaces of a special class of pseudo-Riemannian manifolds, namely Walker three-manifolds. We show that such surfaces are either one of a totally geodesic family described by Calvaruso and Van der Veken or the ambient manifold must be locally conformally flat (here the surface…
First I will explain my motivation to introduce the -invariants for Riemannian manifolds. I will also recall the notions of ideal immersions and best ways of living. Then I will present a few of the many applications of -invariants to several areas in mathematics. Finally, I will present two optimal inequalities …
New spoofing strategies show PoL verification is more vulnerable than previously thought.
problem Vulnerability of Proof-of-Learning verification mechanisms.
method Developed new spoofing strategies that can be reproduced across different configurations and are more cost-effective.
result Current PoL verification is not robust to adversaries and requires further understanding of optimization in deep learning.
Paper proposes robust methods to detect and treat outliers in multivariate loss reserving.
problem Distortion of traditional reserving techniques by outliers in past claims data.
method Two robust bivariate chain-ladder techniques: Adjusted Outlyingness and Bagdistance.
result Improved accuracy in estimating outstanding claim liabilities through robust methods.
Develops a Gaussian model to compute the Alexander polynomial of knots.
problem Computing the Alexander polynomial of knots.
method Uses perturbed Gaussian functions, Heisenberg algebra, and tensor-contraction formalism.
result Associates a Gaussian function to a knot whose partition function recovers the Alexander polynomial.
We prove an upper bound for the evaluation of all classical SU(2) spin networks conjectured by Garoufalidis and van der Veen. This implies one half of the analogue of the volume conjecture which they proposed for classical spin networks. We are also able to obtain the other half, namely, an exact determination of the s…
New derivation of knot invariants from universal invariant.
problem Deriving knot invariants from universal invariant.
method Using Hopf algebra and a Mathematica implementation to compute .
result Derivation of large-color expansion from universal invariant.
We use Bonahon-Wong's trace map to study character varieties of the once-punctured torus and of the 4-punctured sphere. We clarify a relationship with cluster algebra associated with ideal triangulations of surfaces, and we show that the Goldman Poisson algebra of loops on surfaces is recovered from the Poisson structu…
Elastic stripsmath.DG
Motivated by the problem of finding an explicit description of a developable narrow Moebius strip of minimal bending energy, which was first formulated by M. Sadowsky in 1930, we will develop the theory of elastic strips. Recently E.L. Starostin and G.H.M. van der Heijden found a numerical description for an elastic Mo…
The aim of this paper is to state and prove polynomial analogues of the classical Manning inequality relating the topological entropy of a geodesic flow with the growth rate of the volume of balls in the universal covering. To this aim we use two numerical conjugacy invariants, the {\em strong polynomial entropy $h_{po…
This paper classifies flat submanifolds with a special type of curvature form.
problem Classifying flat submanifolds with a specific curvature property.
method Using Moebius geometry and curvature operators to classify submanifolds.
result Classification of umbilic-free isometric immersions with flat normal bundle and semi-parallel Moebius second fundamental form.
We use the formalism of Geometrothermodynamics to describe chemical reactions in the context of equilibrium thermodynamics. Any chemical reaction in a closed system is shown to be described by a geodesic in a dimensional manifold that can be interpreted as the equilibrium space of the reaction. We first show this i…
It was proven in [B.-Y. Chen, F. Dillen, J. Van der Veken and L. Vrancken, Curvature inequalities for Lagrangian submanifolds: the final solution, Differ. Geom. Appl. 31 (2013), 808-819] that every Lagrangian submanifold of a complex space form of constant holomorphic sectional curvature sat…
Satellite Operations and math.GT
Study satellite operations on knot invariant θ, proving additivity and distinguishing knots.
problem Behavior of knot invariant θ under satellite operations.
method Proved additivity, introduced computational tool, verified conjecture for 2977 knots.
result Distinguished knots using invariant θ and verified conjecture for 2977 primes.
New knot invariants derived using quantum cluster algebras.
problem Deriving new knot invariants from quantum cluster algebras.
method Interpreting -matrix of as cluster transformation, introducing auxiliary parameter .
result Derives perturbed-Alexander invariants with higher-order terms in .
The CAP slope is Bayes' theorem in cumulative coordinates, unlocking the weight of evidence, Somers' D, and Gini coefficient.
problem Calibration and weight of evidence
method Identifying the CAP slope as Bayes' theorem
result Revealing the CAP slope as Bayes' theorem
Four-dimensional scanning transmission electron microscopy (4D-STEM) of local atomic diffraction patterns is emerging as a powerful technique for probing intricate details of atomic structure and atomic electric fields. However, efficient processing and interpretation of large volumes of data remain challenging, especi…
Paper proposes a new method for predicting DER adoption with hierarchical guarantees.
problem Accurately predicting DER adoption in electric grids with uncertainty and spatial disparity.
method Multivariate Hawkes process for modeling DER adoption dynamics and split conformal prediction algorithm for hierarchical validity.
result Empirical evaluation shows superior predictive accuracy and uncertainty calibration compared to existing methods.
Study embeddability of 2-complexes in 4-space, proving Heawood family's excluded minors.
problem Whether a 2-dimensional CW complex embeds in .
method Operations preserving embeddability, constructions of non-preserving transformations, study of 4-flat graphs.
result Prove 78 graphs of Heawood family are excluded minors for 4-flat graphs.
Study of knot invariant growth for twisted knots.
problem Understanding the behavior of a knot invariant for families of knots.
method Analyzing the perturbed Alexander invariant for twisted knots.
result Coefficients of the invariant grow linearly as the number of twists increases.