Related papers: Comparison of fine structural mice via coarse iter…

We show that (i) the standard fine structural properties for premice follow from normal iterability (whereas the classical proof relies on iterability for stacks of normal trees), and (ii) every mouse which is finitely generated above its…

Let $M$ be a $\lambda$-indexed (that is, Jensen indexed) premouse. We prove that $M$ is iterable with respect to standard $\lambda$-iteration rules iff $M$ is iterable with respect to a natural version of Mitchell-Steel iteration rules.…

Let $R$ be an iterable weak coarse premouse and let $N$ be a premouse with Mitchell-Steel indexing, produced by a fully backgrounded $L[\mathbb{E}]$-construction of $R$. We identify and correct a problem with the process of resurrection…

Let $M$ be a fine structural mouse and let $F\in M$ be such that $M\models$``$F$ is a total extender'' and $(M||\mathrm{lh}(F),F)$ is a premouse. We show that it follows that $F\in\mathbb{E}^M$, where $\mathbb{E}^M$ is the extender sequence…

In tree based adaptive mesh refinement, elements are partitioned between processes using a space filling curve. The curve establishes an ordering between all elements that derive from the same root element, the tree. When representing more…

We develop the fine structure theory of operator-premice. These are a generalization of standard premice, in which an abstract operator $F$ is used to form the successor steps in the internal hierarchy of the premouse, instead of Jensen's…

We develop the theory of meta-iteration trees, that is, iteration trees whose base "model" is itself an ordinary iteration tree. We prove a comparison theorem for meta-iteration strategies parallel to the one for ordinary iteration…

We give a construction of scales (in the descriptive set theoretic sense) directly from mouse existence hypotheses, without using any determinacy arguments. The construction is related to the Martin-Solovay construction for scales on…

This paper presents an efficient method to perform Structured Matrix Approximation by Separation and Hierarchy (SMASH), when the original dense matrix is associated with a kernel function. Given points in a domain, a tree structure is first…

Assume ZF + AD + $V=L(\mathbb{R})$. We prove some "mouse set" theorems, for definability over $J_\alpha(\mathbb{R})$ where $[\alpha,\alpha]$ is a projective-like gap (of $L(\mathbb{R})$) and $\alpha$ is either a successor ordinal or has…

Given a fine-scale physical theory characterized by an evolutionary system of equations and a set of quantities, defined from the variables of the fine theory, that serve as a coarse representation of the fine scale phenomena, a systematic…

Given a coarse space $(X, \mathcal{E})$, we consider linear orders on $X$ compatible with the coarse structure $\mathcal E$ and explore interplays between these orders and macro-uniform selectors of $(X, \mathcal{E})$.

Automated proof generation for formal software verification remains largely unresolved despite advances in large language models (LLMs). While LLMs perform well in NLP, vision, and code generation, formal verification still requires…

Accurate delineation of fine-scale structures is a very important yet challenging problem. Existing methods use topological information as an additional training loss, but are ultimately making pixel-wise predictions. In this paper, we…

This article is Part I in a series of three papers devoted to determining the minimal complexity of scales in the inner model $K(\mathbb{R})$. Here, in Part I, we shall complete our development of a fine structure theory for $K(\mathbb{R})$…

Deep Learning models enjoy considerable success in Natural Language Processing. While deep architectures produce useful representations that lead to improvements in various tasks, they are often difficult to interpret. This makes the…

We consider the lattice of coarse structures on a set $X$ and study metrizable, locally finite and cellular coarse structures on $X$ from the lattice point of view.

We propose a novel structure selection method for high dimensional (d > 100) sparse vine copulas. Current sequential greedy approaches for structure selection require calculating spanning trees in hundreds of dimensions and fitting the pair…

Structure-based coarse graining of molecular systems offers a systematic route to reproduce the many-body potential of mean force. Unfortunately, common strategies are inherently limited by the molecular mechanics force field employed.…

Realistic physical systems are characterised by emergent interactions across multiple length and time scales, posing a significant challenge for predictive machine learning (ML) models. Most scientific ML models focus on a narrow range of…