Global calculus for manifolds with boundary, solving evolution problems.
problem Global solvability of evolution problems on manifolds with boundary.
method Established global functional calculus and Gårding inequality for pseudo-differential operators without local coordinates.
result Global solvability for a class of evolution problems.
New method predicts state evolution for non-first-order algorithms on nonconvex problems.
problem Analyzing nonconvex optimization problems with random data.
method Developed a state evolution for a broader class of algorithms including first-order and saddle point updates.
result Established rigorous state evolution predictions and finite-sample guarantees for non-first-order methods.
Paper tackles unpredictable feature evolution in learning.
problem Learning with unpredictable feature evolution.
method Proposes PUFE method to fill incomplete overlapping period and formulate as matrix completion problem. Uses ensemble method to incorporate old and new feature spaces.
result Theoretical and experimental validation shows PUFE method can always follow the best base models.
ccc-Autoevolutes are closed curves congruent to their evolutes, constructed via symmetry.
problem Constructing closed curves congruent to their evolutes.
method Modified Frenet equation, numerical solutions, symmetry.
result Found the smallest autoevolute as a trefoil knot.
Algorithm improves vanilla option pricing accuracy during and before COVID-19.
problem Improving vanilla option pricing accuracy during and before the pandemic.
method Combinational Mutation Strategy of Differential Evolution (CmDE) algorithm for bi-objective optimization.
result Algorithm approximates real market vanilla option prices more accurately than Black-Scholes.
Optical interpretation of Euler's angle problem for caustics of light rays.
problem Euler's angle problem for caustics of light rays.
method Optical interpretation of intrinsic equations and study of caustics.
result Characterization of curves under specific conditions and novel pantograph equations.
The paper proves differentiability of evolution maps in Lie groups.
problem Differentiability of evolution maps in infinite-dimensional Lie groups.
method Showed sequential continuity (Mackey k-continuity) leading to differentiability.
result Differentiability of evolution maps in Ck-semiregular Lie groups. The evolute of a smooth curve in an m-dimensional Euclidean space is the locus of centers of its osculating spheres, and the evolute of a spatial polygon is the polygon whose consecutive vertices are the centers of the spheres through the consecutive (m+1)-tuples of vertices of the original polygon. We study the iterat…
We propose a methodology for clustering financial time series of stocks' returns, and a graphical set-up to quantify and visualise the evolution of these clusters through time. The proposed graphical representation allows for the application of well known algorithms for solving classical combinatorial graph problems, w…
We study the evolution equations for a regularized version of Dirac-harmonic maps from closed Riemannian surfaces. We establish the existence of a global weak solution for the regularized problem, which is smooth away from finitely many singularities. Moreover, we discuss the convergence of the evolution equations and …
ES and FD gradients converge as optimization dimension grows.
problem Understanding the relationship between Evolution Strategies and Finite Differences gradients.
method Analyzing the convergence of gradients as the optimization dimension increases.
result ES and FD gradients converge as the dimension of the vector under optimization increases.
We describe some relations between the long-time asymptotic behavior of the vacuum Einstein evolution equations and the geometrization of 3-manifolds. These relations are expressed in terms of evolution of CMC hypersurfaces in the vacuum space-time.Some results are also obtained on the singularity avoidance of CMC foli…
New method estimates Schrödinger bridges using ML techniques.
problem Finding most likely stochastic evolution between two distributions.
method Equivalence with maximum likelihood estimation, numerical Gaussian process approach.
result Direct application of ML techniques for SBP estimation.
CR-FM-NES improves NES for high-dimensional optimization.
problem High-dimensional black-box optimization problems.
method CR-FM-NES extends FM-NES with a restricted covariance matrix representation.
result CR-FM-NES achieves significant speedup in high-dimensional problems.
The paper prices European options in a model with changing regimes and jumps.
problem Pricing European options in a model with changing regimes and jumps.
method A regime-switching jump diffusion model with semi-Markov process.
result The locally risk minimizing price of European options is found.
Study on wealth and trading in PoS blockchain.
problem Decentralization and trading incentives in PoS.
method Analytic and stochastic tools, optimal control theory, mean field model.
result Miners balance PoS mining and trading for optimal strategy.
A new method uses surrogate models to speed up landscape evolution model inference.
problem Complex and computationally expensive landscape evolution models.
method Surrogate-assisted parallel tempering for Bayesian inversion.
result Significant reduction in computational cost with preserved solution quality.
The paper tackles learning energies from time-evolving critical points.
problem Learnability of energies from data of critical points.
method Formulates a variational problem and uses Gamma-convergence arguments.
result Minimal solutions from finite observations converge to the exact energy.
Deep learning approximates PDE evolution operators from solution data.
problem Recovering unknown time-dependent PDEs from solution data.
method Approximate evolution operator in modal space, train deep neural network.
result Deep learning method accurately approximates PDE solutions.
A novel approach to analyzing time series generated by complex systems, such as markets, is presented. The basic idea of the approach is the {\it Law of Self-Similar Evolution}, according to which any complex system develops self-similarly. There always exist some internal laws governing the evolution of a system, say …
Gradient descent solves rank-one matrix estimation problem with detailed time evolution analysis.
problem Estimating a rank-one symmetric matrix corrupted by noise.
method Gradient descent on a sphere, using local versions of the semi-circle law.
result Explicit formulas for the time evolution of the estimator and cost function, revealing phase transitions.
The calculus correspondence has been known to exist between generic pedal evolutions and generic wave front evolutions. In this paper, we first extend the known results on the calculus correspondence to evolutions with multi-parameters, and then give applications of calculus correspondence. Moreover, we discuss the pos…
Corrects a mistake in a proof about large portfolios of stochastic volatility models.
problem Problems with a proof in a paper about large portfolios of stochastic volatility models.
method Reestablishes a weaker version of Theorem 3.1 and redevelops regularity theory.
result Most regularity results are replaced by slightly weaker ones.
Approximate message passing (AMP) refers to a class of efficient algorithms for statistical estimation in high-dimensional problems such as compressed sensing and low-rank matrix estimation. This paper analyzes the performance of AMP in the regime where the problem dimension is large but finite. For concreteness, we co…
AI helps forecasters understand TC convective evolution before intensification.
problem Challenges in extracting scientific insights from complex TC data.
method Combining AI prediction algorithms and classical statistical inference.
result Identifies patterns in TC convective structure leading to intensification.
Backlund transformations are used to search for solutions, particularly soliton solutions, of non-linear differential equations. In this paper we present an invariant geometrical theory of Backlund transformations for second order evolution equations with one space variable. The main concept is that of connection defin…
This paper explores the problem of unknotting closed braids and classical knots in mathematical knot theory. We apply evolutionary computation methods to learn sequences of moves that simplify knot diagrams, and show that this can be effective both when the evolution is carried out for individual knots and when a gener…
Word evolution refers to the changing meanings and associations of words throughout time, as a byproduct of human language evolution. By studying word evolution, we can infer social trends and language constructs over different periods of human history. However, traditional techniques such as word representation learni…
Smoothness of graphs evolving by fractional mean curvature is proven.
problem Evolution of graphs by fractional mean curvature.
method Analytic semigroup approach to nonlocal quasilinear evolution equation.
result Short time existence, uniqueness, and optimal Hölder regularity of classical solutions.
ES-MAML uses Evolution Strategies for MAML, avoiding second derivative estimation.
problem Solving the MAML problem with efficient second derivative estimation.
method Applies Evolution Strategies to MAML, avoiding second derivative estimation.
result ES-MAML performs competitively and often better with fewer queries.
Study material evolution using groupoids to track intrinsic properties.
problem Tracking material evolution without considering the whole body.
method Construct a groupoid encoding intrinsic properties and characteristic foliations.
result Define the evolution equation for material points.
Paper confirms Thom's conjecture for nonlinear evolutions on manifolds.
problem Thom's gradient conjecture for nonlinear evolution equations.
method Extending and settling the conjecture in infinite dimensional problems using Łojasiewicz, L. Simon, and Kurdyka-Mostowski-Parusinski's foundational works.
result Uniqueness of the limiting direction and characterization of convergence rates for both classical and infinite dimensional settings.
Framework learns dynamic graph attributes and links co-evolution.
problem Forecasting change of node attributes and link formation in dynamic graphs.
method CoEvoGNN framework with temporal self-attention and joint optimization.
result Framework outperforms baselines on predicting unseen graph snapshots.
Quantum computer method for pricing lookback options with jumps.
problem Pricing lookback options with discrete monitoring and jump conditions.
method Variational Quantum Imaginary Time Evolution (VarQITE) method to solve non-Hermitian Schrodinger equation.
result Quantum algorithm can handle jump conditions in lookback options pricing.
Study magnetic field evolution in inhomogeneous axion stars.
problem Magnetic field evolution in axion stars with spatial inhomogeneity.
method Derived new induction equation for magnetic field, analyzed CS waves interactions, and considered compact domain effects.
result Spatial inhomogeneity of pseudoscalar field significantly affects magnetic field evolution.
Continuous curve evolution depends on initial shape on sphere.
problem Evolution of a curve on a sphere by curvature flow.
method Study of curve evolution using curvature flow and level-set flow.
result Evolution depends continuously on initial curve in Fréchet distance.
Study on slow convergence in geometric variational problems.
problem Slow convergence of solutions in geometric variational problems.
method Identifying necessary conditions for slowly converging solutions and characterizing their convergence rate and direction.
result Characterization of the rate and direction of convergence for slowly converging solutions.
CausalEvolve improves efficiency and discovery in open-ended scientific tasks.
problem Lack of targeted guidance and knowledge organization in evolve-based agents.
method Causal scratchpad that identifies and reasons about guiding factors for evolution.
result Effective improvement in evolutionary efficiency and better solutions.
The paper studies circular evolutes and involutes of framed curves in Euclidean space.
problem Investigating properties of framed curves and their evolutes and involutes.
method Definition and analysis of circular evolutes and involutes of framed curves, properties of normal surfaces, and their relations.
result Circular evolutes and involutes of framed curves are opposite operations under suitable assumptions, similar to fronts in the Euclidean plane.
The paper studies curve evolution using the PLR equation and its solutions.
problem Investigating the evolution of space curves governed by the PLR equation.
method Examined the Lund-Regge evolution and derived its representation in the Frenet frame, aligning with the Lax system of the PLR equation. Developed a construction method for curve families via the Sym formula.
result Described the Lund-Regge evolution corresponding to Date multi-soliton solutions to the PLR equation.
In this paper we introduce a new geometric flow --- the hyperbolic gradient flow for graphs in the (n+1)-dimensional Euclidean space Rn+1. This kind of flow is new and very natural to understand the geometry of manifolds. We particularly investigate the global existence of the evolution of convex hypers…
The paper defines evolutes and involutes for framed curves and their properties.
problem Defining evolutes and involutes for framed curves with singular points.
method Using the theory of framed curves and Bertrand type curves.
result Conditions for evolutes and involutes being inverse operations of framed curves.
Deep learning improves evolutionary algorithms' adaptability.
problem Improving evolutionary algorithms' adaptability to various circumstances.
method Using deep reinforcement learning to dynamically adjust evolutionary algorithms' strategies.
result Deep learning enhances evolutionary algorithms' fitness increase and attainable fitness.
Study predicts evolution patterns for pretzel knots, revealing abrupt transitions and hidden non-linearity.
problem Predicting evolution of Khovanov polynomials for pretzel knots.
method Conjectured explicit evolution formulas, revealed abrupt transitions, and identified additional Lyapunov exponents.
result Abrupt transitions and hidden non-linearity in evolution of Khovanov polynomials for thick knots.
Study the geometry and dynamics of skew evolutes and involutes, related to bicycle kinematics.
problem Understanding the geometry and dynamics of skew evolutes and involutes.
method Investigate the skew evolute and involute maps, comparing them to bicycle kinematics.
result The skew evolute and involute maps have properties analogous to bicycle kinematics.
This paper introduces SS-MAMP to address convergence issues in AMP algorithms.
problem Convergence issues in AMP algorithms for signal reconstruction.
method Proposes SS-MAMP algorithm framework for right-unitarily invariant sensing matrices and Lipschitz-continuous local processors.
result Covariance matrices of SS-MAMP are L-banded and convergent, ensuring optimal convergence.
Study evolutes of curves with varying smoothness.
problem Understanding evolutes of curves with low smoothness.
method Analyzing the relationship between curve smoothness and evolute regularity.
result Evolutes have one less order of smoothness than the parent curve in generic cases.
We present several models to describe the stochastic evolution of stocks that show some strong resistance at some level and generalize to this situation the evolution based upon geometric Brownian motion. If volatility and drift are related in a certain way we show that our model can be integrated in an exact way. The …