Related papers: Microlocal analysis and evolution equations
Observations are an essential component of the simulation based studies on artificial-evolutionary systems (AES) by which entities are identified and their behavior is observed to uncover higher-level "emergent" phenomena. Because of the…
We consider evolutionary equations of the form $u_t=F(u, w)$ where $w=D_x^{-1}D_yu$ is the nonlocality, and the right hand side $F$ is polynomial in the derivatives of $u$ and $w$. The recent paper \cite{FMN} provides a complete list of…
This review is an introduction to theoretical models and mathematical calculations for biological evolution, aimed at physicists. The methods in the field are naturally very similar to those used in statistical physics, although the…
Local polynomial regression struggles with several challenges when dealing with sparse data. The difficulty in capturing local features of the underlying function can lead to a potential misrepresentation of the true relationship.…
S.Block and H.Esnault constructed the local Fourier transform for D-modules. We present a different approach to the local Fourier transform, which makes its properties almost tautological. We apply the local Fourier transform to compute the…
We provide a quantum method for simulating Hamiltonian evolution with complexity polynomial in the logarithm of the inverse error. This is an exponential improvement over existing methods for Hamiltonian simulation. In addition, its scaling…
We study semi-linear evolutionary problems where the linear part is the generator of a positive $C_0$-semigroup. The non-linear part is assumed to be quasi-increasing. Given an initial value in between a sub- and a super-solution of the…
These short notes collect some thoughts about the way Butcher-Oemler-like and evolutionary studies are performed. We emphasize the shortcomings of several overlooked technical ingredients in the above type of studies, with the hope of…
These notes are the write-up of my 2008 PCMI lectures on multiplier ideals. They aim to give an introduction to the algebro-geometric side of the theory, with an emphasis on its global aspects. The focus is on concrete examples and…
Context: Evolutionary algorithms typically require a large number of evaluations (of solutions) to converge - which can be very slow and expensive to evaluate.Objective: To solve search-based software engineering (SE) problems, using fewer…
AfterLearnER (After Learning Evolutionary Retrofitting) consists in applying evolutionary optimization to refine fully trained machine learning models by optimizing a set of carefully chosen parameters or hyperparameters of the model, with…
We study the local and global existence of solutions to a semilinear evolution equation driven by a mixed local-nonlocal operator of the form \( L = -\Delta + (-\Delta)^{\alpha/2} \), where \( 0 < \alpha < 2 \). The Cauchy problem under…
The paper addresses the study and applications of a broad class of extended-real-valued functions, known as optimal value or marginal functions, which are frequently appeared in variational analysis, parametric optimization, and a variety…
Differential equations may possess coefficients that vary on a spectrum of scales. Because coefficients are typically multiplicative in real space, they turn into convolution operators in spectral space, mixing all wavenumbers. However, in…
We deal with the existence of solutions having L2 regularity for a class of non autonomous evolution equations. Associated with the equation, a general non local condition is studied. The technique we used combines a finite dimensional…
We study the well-posedness of nonautonomous nonlinear delay equations in $\mathbb{R}^{n}$ as evolutionary equations in a proper Hilbert space. We present a construction of solving operators (nonautonomous case) or nonlinear semigroups…
Evolutionary computation offers a variety of tools to solve complex real-world optimization problems. However, research often focuses on smaller, simplified problems and optimization algorithms that sometimes miss expectations in real-world…
In this note, we analyze an abstract evolution equation with time-dependent time delay and time-dependent delay feedback coefficient. We assume that the operator corresponding to the nondelayed part of the model generates an exponentially…
The nonlinear Fourier transform discussed in these notes is the map from the potential of a one dimensional discrete Dirac operator to the transmission and reflection coefficients thereof. Emphasis is on this being a nonlinear variant of…
The existence of weak solutions to the obstacle problem for a nonlocal semilinear fourth-order parabolic equation is shown, using its underlying gradient flow structure. The model governs the dynamics of a microelectromechanical system with…