Novel algorithm PSO improves density estimation for multimodal data.
problem Data log-density estimation for multimodal distributions.
method Probabilistic Surface Optimization (PSO) using virtual stochastic forces.
result PSO-LDE achieves superior log-density estimation accuracy.
Study uses GPLFM to create Digital Twin for ferry quay health monitoring.
problem Deterioration of ferry quays due to harsh maritime environments and impacts.
method Gaussian Process Latent Force Model (GPLFM) integrating physics-based model and machine learning.
result GPLFM provides accurate acceleration response estimates, even under simplifying assumptions.
Rapid overlay of chemical structures (ROCS) is a standard tool for the calculation of 3D shape and chemical ("color") similarity. ROCS uses unweighted sums to combine many aspects of similarity, yielding parameter-free models for virtual screening. In this report, we decompose the ROCS color force field into "color com…
A new method for stochastic optimization using virtual gradients.
problem Stochastic optimization challenges in computational efficiency and memory usage.
method Inspired by dynamic programming, SVGD uses a computational graph and automatic differentiation for efficient optimization.
result Experimental results show SVGD outperforms other methods on multiple datasets and network models.
Proposes a virtual bidding strategy for electricity markets using stochastic control.
problem Optimizing electricity prices in day-ahead and real-time markets.
method Modeling price differences as Brownian motion with meteorological variables, transforming into portfolio management problem.
result Developed a strategy to manage electricity prices efficiently.
Geometric approach solves Euler equations with random forces.
problem Solving Euler equations with stochastic forcing.
method Infinite-dimensional geometric approach, combining stochastic analysis and Sobolev mappings.
result Local existence and uniqueness of strong solutions.
Stochastic gradient descent outperforms traditional force-directed methods.
problem Improving graph layout quality and efficiency.
method Applying stochastic gradient descent for stress minimization.
result Stochastic gradient descent is simpler and more robust than traditional methods.
The paper explains emergent phenomena in deep learning using entropic forces.
problem Understanding the cause of emergent phenomena in deep learning and large language models.
method Proposes a rigorous entropic-force theory for neural networks trained with SGD and variants.
result Shows that representation learning is governed by emergent entropic forces that break continuous symmetries and preserve discrete ones.
Estimates log-likelihood of interacting particle systems using virtual particles.
problem Inconsistent estimation of finite-particle log-likelihood in large particle systems.
method Stochastic gradient estimate using continuous trajectory and virtual particle systems.
result Convergence to stationary points of limiting mean-field system's log-likelihood.
Let M^7 a manifold with holonomy in G_2, and Y^3 an associative submanifold with boundary in a coassociative submanifold. In [5], the authors proved that M_{X,Y}, the moduli space of its associative deformations with boundary in the fixed X, has finite virtual dimension. Using Bochner's technique, we give a vanishing t…
We introduce the concept of virtual volatility. This simple but new measure shows how to quantify the uncertainty in the forecast of the drift component of a random walk. The virtual volatility also is a useful tool in understanding the stochastic process for a given portfolio. In particular, and as an example, we were…
We generalize the Arbitrage Pricing Theory (APT) to include the contribution of virtual arbitrage opportunities. We model the arbitrage return by a stochastic process. The latter is incorporated in the APT framework to calculate the correction to the APT due to the virtual arbitrage opportunities. The resulting relatio…
This article is concerned with learning and stochastic control in physical systems which contain unknown input signals. These unknown signals are modeled as Gaussian processes (GP) with certain parametrized covariance structures. The resulting latent force models (LFMs) can be seen as hybrid models that contain a first…
Proposes a new model to price options considering market forces beyond Black-Scholes.
problem Tackles the limitations of the Black-Scholes model in capturing unexpected market behaviors.
method Uses the analogy between quantum harmonic oscillator and financial market dynamics to propose a new market force-driven model.
result Shows how various market forces can be incorporated to modify option pricing, providing practical applications.
In this paper we derive an effective equation for derivative pricing which accounts for the presence of virtual arbitrage opportunities and their elimination by the market. We model the arbitrage return by a stochastic process and find an equation for the average derivative price. This is an integro-differential equati…
A novel method uses GPLFMs for joint input-state estimation in linear structural systems.
problem Combined state and input estimation of linear structural systems.
method Gaussian process latent force models (GPLFMs) combined with Kalman filters.
result GPLFMs outperform conventional Kalman filters in state and input estimation.
RFC enhances humanoid control to imitate complex human motions.
problem Dynamics mismatch between humanoid models and real humans.
method Residual Force Control (RFC) augments control policies with external forces.
result RFC outperforms state-of-the-art methods in convergence speed and motion quality.
Optimal timing for converting savings into annuities considering mortality risk.
problem Determining the best time to annuitize retirement savings under stochastic mortality.
method Formulated as a three-dimensional optimal stopping problem, reduced to nested one-dimensional problems, solved using PDMP structure.
result Rich structure for the optimal annuitization rule, covering various parameter specifications.
Let M7 be a smooth manifold equipped with a G2-structure φ, and Y3 be an closed compact φ-associative submanifold. In \cite{McL}, R. McLean proved that the moduli space $\bm_{Y,φ}$ of the φ-associative deformations of Y has vanishing virtual dimension. In this paper, we perturb φ into a G2-structu…
We propose a unifying view of two different Bayesian inference algorithms, Stochastic Gradient Markov Chain Monte Carlo (SG-MCMC) and Stein Variational Gradient Descent (SVGD), leading to improved and efficient novel sampling schemes. We show that SVGD combined with a noise term can be framed as a multiple chain SG-MCM…
DeepONet accelerates reliability analysis of stochastic nonlinear systems.
problem Time-dependent reliability analysis of systems with stochastic forcing.
method DeepONet, a novel operator network, learns function-to-function mappings.
result DeepONet efficiently and accurately predicts system responses.
Co-Diffusion predicts drug-target affinity by learning latent manifolds and diffusion, improving generalization.
problem Cold-start regimes in drug-target affinity prediction due to label scarcity and domain shifts.
method Two-stage framework: latent manifold alignment and latent diffusion regularization.
result Significantly outperforms state-of-the-art baselines, especially in zero-shot generalization.
We extend the lifecycle model (LCM) of consumption over a random horizon (a.k.a. the Yaari model) to a world in which (i.) the force of mortality obeys a diffusion process as opposed to being deterministic, and (ii.) a consumer can adapt their consumption strategy to new information about their mortality rate (a.k.a. h…
Gaussian processes (GPs) are a good choice for function approximation as they are flexible, robust to over-fitting, and provide well-calibrated predictive uncertainty. Deep Gaussian processes (DGPs) are multi-layer generalisations of GPs, but inference in these models has proved challenging. Existing approaches to infe…
Simulates financial market orders using anomalous diffusion models.
problem Anomalous diffusion in financial market order dynamics.
method Discrete Time Random Walk with Sibuya waiting times, non-uniform sampling, and cubic spline interpolation.
result Demonstrates price impact for different forcing functions and model parameters.
We study the stochastic multi-armed bandits problem in the presence of adversarial corruption. We present a new algorithm for this problem whose regret is nearly optimal, substantially improving upon previous work. Our algorithm is agnostic to the level of adversarial contamination and can tolerate a significant amount…
We propose a stochastic modified equations (SME) for modeling the asynchronous stochastic gradient descent (ASGD) algorithms. The resulting SME of Langevin type extracts more information about the ASGD dynamics and elucidates the relationship between different types of stochastic gradient algorithms. We show the conver…
GANs improve stochastic parameterization of the Lorenz '96 model.
problem Improving stochastic parameterizations for sub-grid processes.
method Developed a GAN-based stochastic parameterization for the Lorenz '96 model.
result GAN configurations outperform a bespoke parameterization in skillful forecasts and climate simulations.
For certain manifolds, nonnegative Ricci curvature limits dimension and forces almost abelian fundamental group.
problem Bounding the dimension of manifolds with nonnegative Ricci curvature and specific fundamental group properties.
method Dimensional estimates for RCD(0,N) spaces with large Hausdorff dimension. result If dimension is less than 12, the fundamental group is almost abelian.
Generative model calibrates 3D battery cathode morphologies from 2D images.
problem Calibrate 3D morphologies of all-solid-state battery cathodes from 2D microscopy images.
method Combining GANs with excursion sets of Gaussian random fields.
result Calibrated digital twins enable systematic exploration of morphological scenarios.
The paper analyzes optimal retirement timing considering age-dependent mortality risk.
problem Optimal retirement timing under age-dependent mortality risk.
method Formulated as a stochastic control and optimal stopping problem, transformed into a finite time horizon, three-dimensional degenerate optimal stopping problem.
result Existence of an optimal retirement boundary, characterized as a unique solution to a nonlinear integral equation.
A new method detects hidden driving forces in systems with multiple observables.
problem Hidden driving forces in systems with multiple observables cannot be detected by scalar statistics.
method Cross-spectral witness for hidden nonequilibrium.
result Two simultaneously observed channels retain an off-diagonal cross-spectral sector inaccessible to scalar reductions.
Noise in linear networks minimizes sharpness and leads to shrinkage-thresholding.
problem Minimizing sharpness in diagonal linear networks.
method Stochastic sharpness-aware minimization (SAM) with isotropic noise.
result Noise forces shrinkage-thresholding of true parameters.
New algorithm Momentum-QNG improves optimization of quantum circuits.
problem Optimizing variational quantum circuits to avoid local minima.
method Applied Langevin dynamics to QNG, introducing momentum term.
result Momentum-QNG outperforms basic QNG and other optimizers.
Efficiently allocate budgets for LLM-assisted virtual screening to reduce costs.
problem Reducing the cost of evaluating alternatives in large-scale screening tasks.
method Propose a top-m greedy evaluation mechanism and the EFG-m algorithm for efficient budget allocation. result Prove that EFG-m is both sample-optimal and consistent in large-scale virtual screening. Statistical dynamics of financial systems is investigated, based on a model of a randomly coupled equation system driven by a stochastic Langevin force. Anticorrelations of price returns, and subdiffusion of prices is found from the model, and and compared with those calculated from historical $/EURO exchange rates.
Study efficient pricing for barrier options in stochastic-volatility models with leverage correction.
problem Barrier options are sensitive to volatility dynamics, especially leverage, making accurate pricing difficult.
method Developed a class of continuous-path stochastic-clock volatility models and a systematic small-ρ expansion to incorporate leverage.
result Transform-only pricing formulas for barrier derivatives are fast and numerically stable, even for negative leverage.
Optimizes Bayesian priors for matrix factorization without posterior inference.
problem Selecting optimal priors for Bayesian models in machine learning.
method Prior predictive distribution and virtual statistics matching user-provided or observed data statistics.
result Analytically determines hyperparameters for Poisson factorization models.
Study on Kyle's model with stochastic liquidity impacts asset volatility.
problem Impact of stochastic volatility of noise trading on asset volatility.
method Construct equilibrium for continuous-time Kyle's model with stochastic liquidity.
result In equilibrium, Kyle's Lambda and its inverse are submartingales.
SVD-based methods reduce computational cost for stochastic systems.
problem High dimensionality and Monte Carlo runs in stochastic systems.
method Extending SVD-based model reduction to stochastic differential equations.
result Preserving symplectic structures improves accuracy and energy conservation.
The paper values variable annuities using complex stochastic models and deep learning.
problem Valuation of variable annuities with early surrender options under non-Markovian models.
method Developed a deep signature Least Squares Monte Carlo approach to handle path-dependent continuation values.
result Fair fees increase with Hurst parameters of stock volatility and mortality force.
Many efforts have been devoted to training generative latent variable models with autoregressive decoders, such as recurrent neural networks (RNN). Stochastic recurrent models have been successful in capturing the variability observed in natural sequential data such as speech. We unify successful ideas from recently pr…
Statistic dynamics of financial systems is investigated, basing on a model of randomly coupled equation system driven by stochastic Langevin force. It is found that in stable regime the noise power spectrum of the system is of 1/f^alpha form, with the exponent alpha=3/2 in case of Hermitian coupling matrices, or slight…
New virtualized Δ-move simplifies virtual knots and links.
problem Simplifying virtual knots and links.
method Introducing a new local deformation called the virtualized Δ-move.
result Virtualized Δ-move is an unknotting operation for virtual knots.
Generative models for complex stochastic dynamics using adversarial learning.
problem Data-driven modeling of multistep stochastic dynamics.
method Adversarial learning with GANs and MMD for stable model classes.
result Stable generative models for long-time prediction and stochastic systems.
Virtual index cocycles reformulate virtual link invariants.
problem No specific problem stated; focuses on reformulation.
method Using virtual index cocycles to reformulate invariants.
result Unified reformulation of virtual link invariants.
The paper studies strict equivalence in multi-virtual linkoids with new invariants.
problem Understanding strict equivalence in multi-virtual linkoids.
method Utilizing multi-virtual knot theory, defining strict virtual linkoids, and studying invariants.
result New invariants for strict virtual linkoids are defined.
AI models solved the Kaczmarz algorithm's worst-case complexity.
problem Finding the worst-case complexity of the Kaczmarz algorithm.
method Combining AI models to analyze the Kaczmarz algorithm's performance.
result Discovered the worst-case complexity of the Kaczmarz algorithm.