Related papers: The ideas behind the Self Consistent Expansion
The resonant state expansion (RSE), a rigorous perturbative method in electrodynamics, is developed for three-dimensional open optical systems. Results are presented using the analytically solvable homogeneous dielectric sphere as…
Counterfactual explanations (CEs) are advocated as being ideally suited to providing algorithmic recourse for subjects affected by the predictions of machine learning models. While CEs can be beneficial to affected individuals, recent work…
The notion of Self-organized criticality (SOC) had been conceived to interpret the spontaneous emergence of long range correlations in nature. Since then many different models had been introduced to study SOC. All of them have few common…
Discovering the underlying relationships among variables from temporal observations has been a longstanding challenge in numerous scientific disciplines, including biology, finance, and climate science. The dynamics of such systems are…
Training energy-based models (EBMs) with noise-contrastive estimation (NCE) is theoretically feasible but practically challenging. Effective learning requires the noise distribution to be approximately similar to the target distribution,…
The parameter convergence relies on a stringent persistent excitation (PE) condition in adaptive control. Several works have proposed a memory term in the last decade to translate the PE condition to a feasible finite excitation (FE)…
Causal inference methods are widely applied in various decision-making domains such as precision medicine, optimal policy and economics. Central to causal inference is the treatment effect estimation of intervention strategies, such as…
In complex systems, the interplay between nonlinear and stochastic dynamics, e.g., J. Monod's necessity and chance, gives rise to an evolutionary process in Darwinian sense, in terms of discrete jumps among attractors, with punctuated…
Dynamical systems theory provides powerful methods to extract effective macroscopic dynamics from complex systems with slow modes and fast modes. Here we derive and theoretically support a macroscopic, spatially discrete, model for a class…
Emergence and maintenance of excitability is often phrased in terms of arriving at and remaining about a manifold of 'solutions' embedded in a high dimensional parameter space. Alongside studies that extend traditional focus on…
The asymptotic expansion method is generalized from the periodic setting to stationary ergodic stochastic geometries. This will demonstrate that results from periodic asymptotic expansion also apply to non-periodic structures of a certain…
Nonlinear regression problem is one of the most popular and important statistical tasks. The first methods like least squares estimation go back to Gauss and Legendre. Recent models and developments in statistics and machine learning like…
This is an expository article that describes the spectral-theoretic aspects in the study of the stability of self-similar blowup for nonlinear wave equations. The linearization near a self-similar solution leads to a genuinely…
In statistical and nonlinear systems, two qualitatively distinct parameter regions are typically identified: the regular region, characterized by smooth behavior of key quantities, and the critical region, where these quantities exhibit…
Polynomial chaos expansions (PCE) are widely used in the framework of uncertainty quantification. However, when dealing with high dimensional complex problems, challenging issues need to be faced. For instance, high-order polynomials may be…
Growing uncertainty from renewable energy integration and distributed energy resources motivate the need for advanced tools to quantify the effect of uncertainty and assess the risks it poses to secure system operation. Polynomial chaos…
This thesis aims to explore the structure of CFTs with global internal symmetries and beyond via the Large-Charge Expansion (LCE), a semi-classical expansion applicable for states with large global quantum numbers. In the first part of this…
The Transformer architecture, despite its widespread success, struggles with long-context scenarios due to quadratic computation and linear memory growth. While various linear attention variants mitigate these efficiency constraints by…
Large-scale association analysis between multivariate responses and predictors is of great practical importance, as exemplified by modern business applications including social media marketing and crisis management. Despite the rapid…
The symmetric simple exclusion process (SEP), where diffusive particles cannot overtake each other, is a paradigmatic model of transport in the single-file geometry. In this model, the study of currents has attracted a lot of attention, but…