arXiv subjects

Evan Scott

Publications and source records attributed to Evan Scott.

6 recordsLinked to original sources

arXiv2025

Single-View Tomographic Reconstruction Using Learned Primal Dual

The Learned Primal Dual (LPD) method has shown promising results in various tomographic reconstruction modalities, particularly under challenging acquisition restrictions such as limited viewing angles or a limited number of views. We investigate the performance of LPD in a more extreme case: single-view tomographic reconstructions of axially-symmetric targets. This study considers two modalities: the first assumes low-divergence or parallel X-rays. The second models a cone-beam X-ray imaging testbed. For both modalities, training data is generated using closed-form integral transforms, or physics-based ray-tracing software, then corrupted with blur and noise. Our results are then compared against common numerical inversion methodologies.

eess.IV↗

arXiv2025

Equivariant trisections for group actions on four-manifolds

Let $G$ be a finite group, and let $X$ be a smooth, orientable, connected, closed 4-dimensional $G$-manifold. Let $\mathcal{S}$ be a smooth, embedded, $G$-invariant surface in $X$. We introduce the concept of a $G$-equivariant trisection of $X$ and the notion of $G$-equivariant bridge trisected position for $\mathcal{S}$ and establish that any such $X$ admits a $G$-equivariant trisection such that $\mathcal{S}$ is in equivariant bridge trisected position. Our definitions are designed so that $G$-equivariant (bridge) trisections are determined by their spines; hence, the 4-dimensional equivariant topology of a $G$-manifold pair $(X,\mathcal{S})$ can be reduced to the 2-dimensional data of a $G$-equivariant shadow diagram. As an application, we discuss how equivariant trisections can be used to study quotients of $G$-manifolds. We also describe many examples of equivariant trisections, paying special attention to branched covering actions, hyperelliptic involutions, and linear actions on familiar manifolds such as $S^4$, $S^2\times S^2$, and $\mathbb{CP}^2$. We show that equivariant trisections of genus at most one are geometric, and we give a partial classification for genus-two.

math.GT↗

arXiv2025

An equivariant Laudenbach-Po\'enaru theorem

A foundational theorem of Laudenbach and Po\'enaru states that any diffeomorphism of $\#^n(S^1\times S^2)$ extends to a diffeomorphism of $\natural^n(S^1\times B^3)$. We prove a generalization of this theorem that accounts for the presence of a finite group action on $\#^n(S^1\times S^2)$. Our proof is independent of the classical theorem, so by considering the trivial group action, we give a new proof of the classical theorem. Specifically, we show that any finite group action on $\#^n(S^1\times S^2)$ extends to a $\textit{linearly parted}$ action on $\natural^n(S^1\times B^3)$ and that any two such extensions are equivariantly diffeomorphic. Roughly, a linearly parted action respects a decomposition into equivariant $0$-handles and $1$-handles, where, for each handle in the decomposition, its stabilizer acts linearly on that handle. The restriction to linearly parted actions is important, because there are infinitely many distinct nonlinear actions on $B^4$ with identical actions on $\partial B^4$; these nonlinear actions give extensions of the same action on $\partial B^4$ which are $\textit{not}$ equivariantly diffeomorphic. We also prove a more general theorem: Every finite group action on $\left(\#^n(S^1\times S^2),L\right)$, with $L$ an invariant unlink, extends across a pair $\left(\natural^n(S^1\times B^3),\mathcal{D}\right)$, with $\mathcal{D}$ an equivariantly boundary-parallel disk-tangle, and any two such extensions are equivariantly diffeomorphic.

math.GT↗

arXiv2024

Ribbon numbers of 12-crossing knots

The ribbon number of a knot is the minimum number of ribbon singularities among all ribbon disks bounded by that knot. In this paper, we build on the systematic treatment of this knot invariant initiated in recent work of Friedl, Misev, and Zupan. We show that the set of Alexander polynomials of knots with ribbon number at most four contains 56 polynomials, and we use this set to compute the ribbon numbers for many 12-crossing knots. We also study higher-genus ribbon numbers of knots, presenting some examples that exhibit interesting behavior and establishing that the success of the Alexander polynomial at controlling genus-0 ribbon numbers does not extend to higher genera.

math.GT↗

arXiv2022

Two Sufficient Conditions for a Polyhedron to be (Locally) Rupert

Given two cubes of equal size, it is possible - against all odds - to bore a hole through one which is large enough to pass the other straight through. This preposterous property of the cube was first noted by Prince Rupert of the Rhine in the 17th century. Surprisingly, the cube is not alone: many other polyhedra have this property, which we call being Rupert. A concise way to express that a polyhedron is Rupert is to find two orientations $Q$ and $Q'$ of that polyhedron so that $\pi(Q)$ fits inside $\pi(Q')$, with $\pi$ representing the orthogonal projection onto the $xy$-plane. Given this scheme, to bore the hole in $Q'$ we can remove $\pi^{-1}(\pi(Q))$. There is an open conjecture that every convex polyhedron is Rupert. Aiming at this conjecture, we give two sufficient conditions for a polyhedron to be Rupert. Both conditions require the polyhedron to have a particularly simple orientation $Q$, which we alter by a very small amount to get $Q'$ as required above. When a passage is given by a very small alteration like this, we call it a local passage. Restricting to the local case turns out to offer many valuable simplifications. In the process of proving our main theorems, we develop a theory of these local passages, involving an analysis of how small rotations act on simple polyhedra.

math.MG↗

arXiv2019

First Results from an Event Synchronized -- High Repetition Thomson Scattering System at Wendelstein 7-X

The Wendelstein 7-X (W7-X) Thomson scattering (TS) diagnostic was upgraded to transiently achieve kilohertz sampling rates combined with adjustable measuring times. The existing Nd:YAG lasers are employed to repetitively emit "bursts", i.e. multiple laser pulses in a short time interval. Appropriately timing burst in the three available lasers, up to twelve evenly spaced consecutive measurements per burst are possible. The pulse-to-pulse increment within a burst can be tuned from 2 ms to 33.3 ms (500 kHz - 30 Hz). Additionally, an event trigger system was developed to synchronize the burst Thomson scattering measurements to plasma events. Exemplary, a case of fast electron density and temperature evolution after cryogenic H2 pellet injection is presented in order to demonstrate the capabilities of the method.

physics.plasm-ph↗