Related papers: Reconstructing resurrection
We study a recursively defined sequence which is constructed using the least common multiple. It has been conjectured that every term of that sequence is $1$ or a prime. In this paper we show that this claim is connected to a strong version…
A study of magnetic avalanches in Perminvar, an Fe-Ni-Co alloy, shows that some avalanches are almost exactly reproducible from one magnetic field cycle to the next, while others show significant variability. Averaging over many cycles…
Let $T$ be an o-minimal theory expanding $\mathrm{RCF}$ and $T_\mathrm{convex}$ be the common theory of its models expanded by predicate for a non-trivial $T$-convex valuation ring. We call an elementary extension $(\mathbb{E}, \mathcal{O})…
In the \emph{trace reconstruction problem}, an unknown source string $x \in \{0,1\}^n$ is sent through a probabilistic \emph{deletion channel} which independently deletes each bit with probability $\delta$ and concatenates the surviving…
Optimal reconstruction of a source sequence from multiple noisy traces corrupted by random insertions, deletions, and substitutions typically requires joint processing of all traces, leading to computational complexity that grows…
We prove an iteration theorem which guarantees for a wide class of nice iterations of $\omega_1$-preserving forcings that $\omega_1$ is not collapse, at the price of needing large cardinals to burn as fuel. More precisely, we show that a…
Spatial imaging of magnetic stray fields from magnetic materials is a useful tool for identifying the underlying magnetic configurations of the material. However, transforming the magnetic image into a magnetization image is an ill-poised…
After a short review of the Method of Recursive Counting we introduce a general algebraic description of recursive lattice building. This provides a rigorous framework for discussion of method's limitations.
Nonlinear optical features of a plane structure consisted of silicon disks placed periodically on a silver substrate have been studied in the Littrow reflection scenario. The structure manifests a bistable resonant reflective ability.…
We present a novel, perspicuous framework for building iterated ultrapowers. Furthermore, our framework naturally lends itself to the construction of a certain type of order indiscernibles, here dubbed tight indiscernibles, which are shown…
In this article we show that the reconstructions of semiconductor surfaces can be determined using a genetic procedure. Coupled with highly optimized interatomic potentials, the present approach represents an efficient tool for finding and…
We define combinatorially a partial order on the set partitions and show that it is equivalent to the Bruhat-Chevalley-Renner order on the upper triangular matrices. By considering subposets consisting of set partitions with a fixed number…
Proper EMA-balance (E: kinetic energy; M: momentum; A: angular momentum), pressure-robustness and $Re$-semi-robustness ($Re$: Reynolds number) are three important properties of Navier-Stokes simulations with exactly divergence-free…
We propose a general modeling and algorithmic framework for discrete structure recovery that can be applied to a wide range of problems. Under this framework, we are able to study the recovery of clustering labels, ranks of players, signs…
We define a new lattice structure on the elements of a finite Coxeter group W. This lattice, called the shard intersection order, is weaker than the weak order and has the noncrossing partition lattice NC(W) as a sublattice. The new…
In this paper, we propose a novel algorithm for analysis-based sparsity reconstruction. It can solve the generalized problem by structured sparsity regularization with an orthogonal basis and total variation regularization. The proposed…
This work is concerned with the recovery of piecewise constant images from noisy linear measurements. We study the noise robustness of a variational reconstruction method, which is based on total (gradient) variation regularization. We show…
A high-order quadrature scheme is constructed for the evaluation of Laplace single and double layer potentials and their normal derivatives on smooth surfaces in three dimensions. The construction begins with a harmonic approximation of the…
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 consider a network where an infection cascade has taken place and a subset of infected nodes has been partially observed. Our goal is to reconstruct the underlying cascade that is likely to have generated these observations. We reduce…