arXiv subjects

Lindsay Erickson

Publications and source records attributed to Lindsay Erickson.

5 recordsLinked to original sources

arXiv2026

Sensitivity Analysis White Paper

Sensitivity analysis is an important component of simulation-based decision support because it helps analysts determine which inputs most strongly influence model outcomes under uncertainty. This paper organizes the broad sensitivity analysis literature into a coherent framework for use in complex simulation settings, with particular attention to military applications. We review major classes of methods, including local and global approaches, variance-based techniques, screening methods, derivative-based methods, and uncertainty quantification tools, and relate them to common analytical objectives such as factor prioritization, factor fixing, variance reduction, and factor mapping. The paper also discusses sensitivity auditing as a complementary perspective that emphasizes transparency, assumption tracking, and responsible use of models in decision-relevant settings.

cs.SE↗

arXiv2014

Deformation invariance of rational pairs

Rational pairs, recently introduced by Kollár and Kovács, generalize rational singularities to pairs $(X,D)$. Here $X$ is a normal variety and $D$ is a reduced divisor on $X$. Integral to the definition of a rational pair is the notion of a thrifty resolution, also defined by Kollár and Kovács, and in order to work with rational pairs it is often necessary to know whether a given resolution is thrifty. In this paper we present several foundational results that are helpful for identifying thrifty resolutions and analyzing their behavior. We also show that general hyperplane sections of rational pairs are again rational. In 1978, Elkik proved that rational singularities are deformation invariant. Our main result is an analogue of this theorem for rational pairs: given a flat family $X\to S$ and a Cartier divisor $D$ on $X$, if the fibers over a smooth point $s\in S$ form a rational pair, then $(X,D)$ is also rational near the fiber $X_s$.

math.AG↗

arXiv2012

2-Colored Matchings in a 3-Colored K^{3}_{12}

Let $K_{n}^{r}$ denote the complete $r$-uniform hypergraph on $n$ vertices. A matching $M$ in a hypergraph is a set of pairwise vertex disjoint edges. Recent Ramsey-type results rely on lemmas about the size of monochromatic matchings. A starting point for this study comes from a well-known result of Alon, Frankl, and Lovász (1986). Our motivation is to find the smallest $n$ such that every $t$-coloring of $K_{n}^{r}$ contains an $s$-colored matching of size $k$. It has been conjectured that in every coloring of the edges of $K_n^r$ with 3 colors there is a 2-colored matching of size at least $k$ provided that $n \geq kr + \lfloor \frac{k-1}{r+1} \rfloor$. The smallest test case is when $r=3$ and $k=4$. We prove that in every 3-coloring of the edges of $K_{12}^3$ there is a 2-colored matching of size 4.

math.CO↗

arXiv2012

Nim on hypercubes

The ordinary game of Nim has a long history and is well-known in the area of combinatorial game theory. The solution to the ordinary game of Nim has been known for many years and lends itself to numerous other solutions to combinatorial games. Nim was extended to graphs by taking a fixed graph with a playing piece on a given vertex and assigning positive integer weight to the edges that correspond to a pile of stones in the ordinary game of Nim. Players move alternately from the playing piece across incident edges, removing weight from edges as they move. This paper solves Nim on hypercubes in the unit weight case completely. We briefly discuss the arbitrary weight case and its ties to known results.

math.CO↗

arXiv2010

Nim on the Complete Graph

The game of Nim as played on graphs was introduced in Nim on Graphs I and extended in Nim on Graphs II by Masahiko Fukuyama. His papers detail the calculation of Grundy numbers for graphs under specific circumstances. We extend these results and introduce the strategy for even cycles. This paper examines a more general class of graphs by restricting the edge weight to one. We provide structural conditions for which there exist a winning strategy. This yields the solution for the complete graph.

math.CO↗