Searcharxiv⌕ Search

arXiv subjects

Jesse Johnson

Publications and source records attributed to Jesse Johnson.

At least 19 recordsLinked to original sources
arXiv2025

Improved Wildfire Spread Prediction with Time-Series Data and the WSTS+ Benchmark

Recent research has demonstrated the potential of deep neural networks (DNNs) to accurately predict wildfire spread on a given day based upon high-dimensional explanatory data from a single preceding day, or from a time series of T preceding days. For the first time, we investigate a large number of existing data-driven wildfire modeling strategies under controlled conditions, revealing the best modeling strategies and resulting in models that achieve state-of-the-art (SOTA) accuracy for both single-day and multi-day input scenarios, as evaluated on a large public benchmark for next-day wildfire spread, termed the WildfireSpreadTS (WSTS) benchmark. Consistent with prior work, we found that models using time-series input obtained the best overall accuracy, suggesting this is an important future area of research. Furthermore, we create a new benchmark, WSTS+, by incorporating four additional years of historical wildfire data into the WSTS benchmark. Our benchmark doubles the number of unique years of historical data, expands its geographic scope, and, to our knowledge, represents the largest public benchmark for time-series-based wildfire spread prediction.

cs.CV↗
arXiv2018

ClinicalVis: Supporting Clinical Task-Focused Design Evaluation

Making decisions about what clinical tasks to prepare for is multi-factored, and especially challenging in intensive care environments where resources must be balanced with patient needs. Electronic health records (EHRs) are a rich data source, but are task-agnostic and can be difficult to use as summarizations of patient needs for a specific task, such as "could this patient need a ventilator tomorrow?" In this paper, we introduce ClinicalVis, an open-source EHR visualization-based prototype system for task-focused design evaluation of interactions between healthcare providers (HCPs) and EHRs. We situate ClinicalVis in a task-focused proof-of-concept design study targeting these interactions with real patient data. We conduct an empirical study of 14 HCPs, and discuss our findings on usability, accuracy, preference, and confidence in treatment decisions. We also present design implications that our findings suggest for future EHR interfaces, the presentation of clinical data for task-based planning, and evaluating task-focused HCP/EHR interactions in practice.

cs.HC↗
arXiv2018

Deep, Skinny Neural Networks are not Universal Approximators

In order to choose a neural network architecture that will be effective for a particular modeling problem, one must understand the limitations imposed by each of the potential options. These limitations are typically described in terms of information theoretic bounds, or by comparing the relative complexity needed to approximate example functions between different architectures. In this paper, we examine the topological constraints that the architecture of a neural network imposes on the level sets of all the functions that it is able to approximate. This approach is novel for both the nature of the limitations and the fact that they are independent of network depth for a broad family of activation functions.

cs.LG↗
arXiv2015

Bridge numbers of knots in the page of an open book

Given any closed, connected, orientable $3$--manifold and integers $g\geq g(M), D > 0$, we show the existence of knots in $M$ whose genus $g$ bridge number is greater than $D$. These knots lie in a page of an open book decomposition of $M$, and the proof proceeds by examining the action of the map induced by the monodromy on the arc and curve complex of a page. A corollary is that there are Berge knots of arbitrarily large genus one bridge number.

math.GT↗
arXiv2014

Bounds for the genus of a normal surface

This paper gives sharp linear bounds on the genus of a normal surface in a triangulated compact, orientable 3--manifold in terms of the quadrilaterals in its cell decomposition---different bounds arise from varying hypotheses on the surface or triangulation. Two applications of these bounds are given. First, the minimal triangulations of the product of a closed surface and the closed interval are determined. Second, an alternative approach to the realisation problem using normal surface theory is shown to be less powerful than its dual method using subcomplexes of polytopes.

math.GT↗
arXiv2014

Thin Tree Position

We introduce a method for creating a special type of tree, called a tree position, from a weighted graph. Leaves of the tree correspond to vertices of the original graph, and the tree edges contain information which can be used to partition these vertices. By repeatedly applying reducing operations to the tree position we arrive at a special type of tree position we call thin, and we show that partitions arising from thin tree positions have especially nice properties. The algorithm is based the topological notion of thin position for knots and 3-manifolds and builds on the previously defined idea of a Topological Intrinsic Lexicographic Order (TILO).

math.CO↗
arXiv2013

Bridge distance and plat projections

We calculate the bridge distance for $m$-bridge knots/links in the $3$-sphere with sufficiently complicated $2m$-plat projections. In particular we show that if the underlying braid of the plat has $n - 1$ rows of twists and all its exponents have absolute value greater than or equal to three then the distance of the bridge sphere is exactly $\lceil n/(2(m - 2)) \rceil$, where $\lceil x \rceil$ is the smallest integer greater than or equal to $x$. As a corollary, we conclude that if such a diagram has more than $4m(m-2)$ rows then the bridge sphere defining the plat projection is the unique minimal bridge sphere for the knot.

math.GT↗
arXiv2013

Distance Two Links

In this paper, we characterize all links in the 3-sphere with bridge number at least three that have a bridge sphere of distance two. We show that a link L has a bridge sphere of distance at most two then it falls into at least one of three categories: (1) The exterior of L contains an essential meridional sphere. (2) L can be decomposed as a tangle product of a Montesinos tangle with an essential tangle in a way that respects the bridge surface and either the Montesinos tangle is rational or the essential tangle contains an incompressible, boundary-incompressible annulus. (3) L is obtained by banding from another link L' that has a bridge sphere of the same Euler characteristic as the bridge sphere for L but of distance 0 or 1.

math.GT↗
arXiv2013

Development of a finite element firn densification model for converting volume changes to mass changes

In regions where ice sheets are increasing in mass, there is a 50-200 m layer of old snow called firn which does not melt in the summer months. The density of firn tracks the transformation of snow into glacial ice at approximately 917 kg m^-3. The process of firn densification is important in at least two ways: 1) it can be a dominant component in the observed rate of change of the surface elevation, and 2) storage of liquid water in the lower density firn layer is now considered a critical component in the mass balance of ice sheets. If the rate of change of surface elevation can be equated with the rate of change in the mass of the ice sheet, we would have an excellent means of monitoring ice sheet mass balance. However, knowledge of firn densification rates is needed to make the inference of mass rate of change from volume rate of change. Several firn models have been created for areas without melt. We have reformulated these models with the finite-element software package FEniCS and integrated them with an enthalpy-formulation. This integration allows us to account for the melting and subsequent re-freezing of firn layers into ice lenses.

physics.geo-ph↗
arXiv2013

Non-uniqueness of high distance Heegaard splittings

Kevin Hartshorn showed that if a three-dimensional manifold $M$ admits a Heegaard surface $Σ$ with Hempel distance $d$ then every incompressible surface in $M$ has genus at least $\frac{d}{2}$. Scharlemann-Tomova generalized this, proving that in such a manifold, every other Heegaard surface for $M$ of genus $g' < \frac{d}{2}$ is a stabilization of $Σ$. In the present paper, we show that Hartshorn's bound is sharp and Scharlemann-Tomova's bound is very close to sharp. In particular, for every pair of integers $g \geq 2, d \geq 2$, we construct a three-manifold $M$ with a genus $g$, distance $d$ Heegaard splitting and an incompressible surface of genus $\frac{d}{2}$. We also construct, for every $d \geq 4$, a three-manifold with a genus $g$, distance $d$ Heegaard surface $Σ$ and a second Heegaard surface with genus $g' = \frac{1}{2} d + g - 1$ that is not a stabilization of $Σ$.

math.GT↗
arXiv2013

The coarse geometry of the Kakimizu complex

We show that the Kakimizu complex of minimal genus Seifert surfaces for a knot in the 3-sphere is quasi-isometric to a Euclidean integer lattice $\mathbb Z^n$ for some $n \geq 0$.

math.GT↗
arXiv2012

Genus bounds bridge number for high distance knots

If a knot K in a closed, orientable 3-manifold M has a bridge surface T with distance at least 3 in the curve complex of T - K, then the genus of any essential surface in its exterior with non-empty, non-meridional boundary gives rise to an upper bound for the bridge number of K with respect to T. In particular, a nontrivial, aspherical, and atoroidal knot K with such a bridge surface has its bridge number bounded by 5 if K has a non-trivial reducing surgery; 6 if K has a non-trivial toroidal surgery; and 4g + 2 if K is null-homologous and has Seifert genus g.

math.GT↗
arXiv2012

Exceptional and cosmetic surgeries on knots

We show that the distance of a link $K$ with respect to a bridge surface of any genus determines a lower bound on the genus of essential surfaces and Heegaard surfaces in the manifolds that result from non-trivial Dehn surgeries on the knot. In particular, knots with high bridge distance do not admit non-trivial non-hyperbolic surgeries or non-trivial cosmetic surgeries. We further show that if a knot has bridge distance at least 3 then its bridge number is bounded above by a function of Seifert genus, or indeed by the genus of (almost) any essential surface or Heegaard surface in the surgered manifold.

math.GT↗
arXiv2012

Topological graph clustering with thin position

A clustering algorithm partitions a set of data points into smaller sets (clusters) such that each subset is more tightly packed than the whole. Many approaches to clustering translate the vector data into a graph with edges reflecting a distance or similarity metric on the points, then look for highly connected subgraphs. We introduce such an algorithm based on ideas borrowed from the topological notion of thin position for knots and 3-dimensional manifolds.

math.GT↗