From 33bc7e620276f4269ee5f1820e5477135e020b3f Mon Sep 17 00:00:00 2001
From: Douglas Rumbaugh <dbr4@psu.edu>
Date: Sun, 8 Jun 2025 15:04:00 -0400
Subject: Julia updates v2

---
 chapters/sigmod23/background.tex | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

(limited to 'chapters/sigmod23/background.tex')

diff --git a/chapters/sigmod23/background.tex b/chapters/sigmod23/background.tex
index 88f2585..42a52de 100644
--- a/chapters/sigmod23/background.tex
+++ b/chapters/sigmod23/background.tex
@@ -104,7 +104,7 @@ sampling} (WIRS),
     positive weights $w: D\to \mathbb{R}^+$. Given a query
     interval $q = [x, y]$ and an integer $k$, an independent range sampling
     query returns $k$ independent samples from $D \cap q$ with each 
-    point having a probability of $\nicefrac{w(d)}{\sum_{p \in D \cap q}w(p)}$
+    point having a probability of $\frac{w(d)}{\sum_{p \in D \cap q}w(p)}$
     of being sampled.
 \end{definition}
 
@@ -118,7 +118,7 @@ SQL's \texttt{TABLESAMPLE} operator~\cite{postgres-doc}. However, the
 algorithms used to implement this operator have significant limitations
 and do not allow users to maintain statistical independence of the results
 without also running the query to be sampled from in full. Thus, users must
-choose between independece and performance.
+choose between independence and performance.
 
 To maintain statistical independence, Bernoulli sampling is used. This
 technique requires iterating over every record in the result set of the
@@ -198,7 +198,7 @@ call static sampling indices (SSIs) in this chapter,\footnote{
   am retaining the term SSI in this chapter for consistency with the
   original paper, but understand that in the terminology established in
   Chapter~\ref{chap:background}, SSIs are data structures, not indices.
-},
+}
 that are capable of answering sampling queries more efficiently than
 Olken's method relative to the overall data size.  An example of such
 a structure is used in Walker's alias method \cite{walker74,vose91}.
-- 
cgit v1.2.3

