相关论文: 2D growth processes: SLE and Loewner chains
SLAM has matured significantly over the past few years, and is beginning to appear in serious commercial products. While new SLAM systems are being proposed at every conference, evaluation is often restricted to qualitative visualizations…
In this work, we present concepts for the analysis of the evolution of two-dimensional skeletons. By introducing novel persistence concepts, we are able to reduce typical temporal incoherence, and provide insight in skeleton dynamics. We…
Appreciation of Stochastic Loewner evolution (SLE$_\kappa$), as a powerful tool to check for conformal invariant properties of geometrical features of critical systems has been rising. In this paper we use this method to check conformal…
Emerging applications of machine learning in numerous areas involve continuous gathering of and learning from streams of data. Real-time incorporation of streaming data into the learned models is essential for improved inference in these…
We study numerically a two-component A-B spreading model (SMK model) for concave and convex radial growth of 2d-geometries. The seed is chosen to be an occupied circle line, and growth spreads inside the circle (concave geometry) or outside…
Large-eddy simulation developments and validations are presented for an improved simulation of turbulent internal flows. Numerical methods are proposed according to two competing criteria: numerical qualities (precision and spectral…
This paper introduces the annulus SLE$_\kappa$ processes in doubly connected domains. Annulus SLE$_6$ has the same law as stopped radial SLE$_6$, up to a time-change. For $\kappa\not=6$, some weak equivalence relation exists between annulus…
We study the scaling limits of stochastic gradient descent (SGD) with constant step-size in the high-dimensional regime. We prove limit theorems for the trajectories of summary statistics (i.e., finite-dimensional functions) of SGD as the…
On the basis of dynamical principles we derive the Logistic Equation (LE), widely employed (among multiple applications) in the simulation of population growth, and demonstrate that scale-invariance and a mean-value constraint are…
To learn about basic aspects of nano-scale spherical molecular shells during their formation, spherically curved two-dimensional N-particle Lennard-Jones systems are simulated, studying curvature evolution paths at zero-temperature. For…
This report examines numerical aspects of constructing Karhunen-Lo\`{e}ve expansions (KLEs) for second-order stochastic processes. The KLE relies on the spectral decomposition of the covariance operator via the Fredholm integral equation of…
Simulating the time evolution of physical systems is pivotal in many scientific and engineering problems. An open challenge in simulating such systems is their multi-resolution dynamics: a small fraction of the system is extremely dynamic,…
The advancements in additive manufacturing (AM) technology have allowed for the production of geometrically complex parts with customizable designs. This versatility benefits large-scale space-frame structures, as the individual design of…
We prove one-to-one correspondences between certain decreasing Loewner chains in the upper half-plane, a special class of real-valued Markov processes, and quantum stochastic processes with monotonically independent additive increments.…
Diffusion Limited Aggregation (DLA) is a model of fractal growth that was introduced in 1981 and had since attained a paradigmatic status due to its simplicity and its underlying role for a variety of pattern forming processes. Despite…
Starting from a master equation, we derive the evolution equation for the size distribution of elements in an evolving system, where each element can grow, divide into two, and produce new elements. We then probe general solutions of the…
Recent advances in Large Language Models (LLMs) have demonstrated the emergence of capabilities (learned skills) when the number of system parameters and the size of training data surpass certain thresholds. The exact mechanisms behind such…
These Lecture Notes are devoted to an introductory description of some of the most widely applied statistical methods for the analysis of the Large-Scale Structure (LSS) of the Universe. Rather than providing technical details about the…
We analyze the geometry of scaling limits of near-critical 2D percolation, i.e., for $p=p_c+\lambda\delta^{1/\nu}$, with $\nu=4/3$, as the lattice spacing $\delta \to 0$. Our proposed framework extends previous analyses for $p=p_c$, based…
We analyze the full statistics of a stochastic squeeze process. The model's two parameters are the bare stretching rate~$w$, and the angular diffusion coefficient~$D$. We carry out an exact analysis to determine the drift and the diffusion…